Encyclopaedia Britannica, 11th Edition, "Dyer, Sir Edward" to "Echidna" (part 2)

EADS, JAMES BUCHANAN (1820-1887), American engineer, was born at Lawrenceburg, Indiana, on the 23rd of May 1820. His first engineering work of any importance was in raising sunken steamers. In 1845 he established glass works in St Louis. During the Civil War he constructed ironclad steamers and mortar boats for the Federal government. His next important engineering achievement was the construction of the great steel arch bridge across the Mississippi at St Louis (see Bridge, fig. 29), upon which he was engaged from 1867 till 1874. The work, however, upon which his reputation principally rests was his deepening and fixing the channel at the mouths of the Mississippi by means of jetties, whereby the narrowed stream was made to scour out its own channel and carry the sediment out to sea. Shortly before his death he projected a scheme for a ship railway across the Isthmus of Tehuantepec, in lieu of an isthmian canal. He died at Nassau, in the Bahamas, on the 8th of March 1887.

EAGLE (Fr. aigle, from the Lat. aquila), the name generally given to the larger diurnal birds of prey which are not vultures; but the limits of the subfamily Aquilinae have been very variously assigned by different writers on systematic ornithology, and there are eagles smaller than certain buzzards. By some authorities the Laemmergeier of the Alps, and other high mountains of Europe, North Africa and Asia, is accounted an eagle, but by others the genus Gypaetus is placed with the Vulturidae as its common English name (bearded vulture) shows. There are also other forms, such as the South American Harpyia and its allies, which though generally called eagles have been ranked as buzzards. In the absence of any truly scientific definition of the family Aquilinae it is best to leave these and many other more or less questionable members of the group—such as the genera Spizaetus, Circaetus, Spilornis, Helotarsus, and so forth—and to treat here of those whose position cannot be gainsaid.

True eagles inhabit all the regions of the world, and some seven or eight species at least are found in Europe, of which two are resident in the British Islands. In England and in the Lowlands of Scotland eagles only exist as stragglers; but in the Hebrides and some parts of the Highlands a good many may yet be found, and their numbers appear to have rather increased of late years than diminished; for the foresters and shepherds, finding that a high price can be got for their eggs, take care to protect the owners of the eyries, which are nearly all well known, and to keep up the stock by allowing them at times to rear their young. There are also now not a few occupiers of Scottish forests who interfere so far as they can to protect the king of birds. In Ireland the extirpation of eagles seems to have been carried on almost unaffected by the prudent considerations which in the northern kingdom have operated so favourably for the race, and except in the wildest parts of Donegal, Mayo and Kerry, eagles in the sister island are almost birds of the past.

Of the two British species the erne (Icel. Œrn) or sea-eagle (by some called also the white-tailed and cinereous eagle)—Haliaetus albicilla—affects chiefly the coast and neighbourhood of inland waters, living in great part on the fish and refuse that is thrown up on the shore, though it not unfrequently takes living prey, such as lambs, hares and rabbits. On these last, indeed, young examples mostly feed when they wander southward in autumn, as they yearly do, and appear in England. The adults (fig. 1) are distinguished by their prevalent greyish-brown colour, their pale head, yellow beak and white tail—characters, however, wanting in the immature, which do not assume the perfect plumage for some three or four years. The eyry is commonly placed in a high cliff or on an island in a lake—sometimes on the ground, at others in a tree—and consists of a vast mass of sticks in the midst of which is formed a hollow lined with Luzula sylvatica (as first observed by John Wolley) or some similar grass, and here are laid the two or three white eggs. In former days the sea-eagle seems to have bred in several parts of England—as the Lake district, and possibly even in the Isle of Wight and on Dartmoor. This species inhabits all the northern part of the Old World from Iceland to Kamchatka, and breeds in Europe so far to the southward as Albania. In the New World, however, it is only found in Greenland, being elsewhere replaced by the white-headed or bald eagle, H. leucocephalus, a bird of similar habits, and the chosen emblem of the United States of America. In the far east of Asia occurs a still larger and finer sea-eagle, H. pelagicus, remarkable for its white thighs and upper wing-coverts. South-eastern Europe and India furnish a much smaller species, H. leucoryphus, which has its representative, H. leucogaster, in the Malay Archipelago and Australia, and, as allies in South Africa and Madagascar, H. vocifer and H. vociferoides respectively. All these eagles may be distinguished by their scaly tarsi, while the group next to be treated of have the tarsi feathered to the toes.

The golden or mountain eagle, Aquila chrysaetus, is the second British species. This also formerly inhabited England, and a nest, found in 1668 in the Peak of Derbyshire, is well described by Willughby, in whose time it was said to breed also in the Snowdon range. It seldom if ever frequents the coast, and is more active on the wing than the sea-eagle, being able to take some birds as they fly, but a large part of its sustenance is the flesh of animals that die a natural death. Its eyry is generally placed and built like that of the other British species, but the neighbourhood of water is not requisite. The eggs, from two to four in number, vary from a pure white to a mottled, and often highly coloured, surface, on which appear different shades of red and purple. The adult bird (fig. 2) is of a rich dark brown, with the elongated feathers of the neck, especially on the nape, light tawny, in which imagination sees a “golden” hue, and the tail marbled with brown and ashy-grey. In the young the tail is white at the base, and the neck has scarcely any tawny tint. The golden eagle does not occur in Iceland, but occupies suitable situations over the rest of the Palaearctic Region and a considerable portion of the Nearctic—though the American bird has been, by some, considered a distinct species. Domesticated, it has many times been trained to take prey for its master in Europe, and to this species is thought to belong an eagle habitually used by the Kirghiz Tatars, who call it Bergut or Bearcoot, for the capture of antelopes, foxes and wolves. It is carried hooded on horseback or on a perch between two men, and released when the quarry is in sight. Such a bird, when well trained, is valued, says P.S. Pallas, at the price of two camels. It is quite possible, however, that more than one kind of eagle is thus used, and the services of A. heliaca (which is the imperial eagle of some writers) and of A. mogilnik—both of which are found in central Asia, as well as in south-eastern Europe—may also be employed.

A smaller form of eagle, which has usually gone under the name of A. naevia, is now thought by the best authorities to include three local races, or, in the eyes of some, species. They inhabit Europe, North Africa and western Asia to India, and two examples of one of them—A. clanga, the form which is somewhat plentiful in north-eastern Germany—have occurred in Cornwall. The smallest true eagle is A. pennata, which inhabits southern Europe, Africa and India. Differing from other eagles of their genus by its wedge-shaped tail, though otherwise greatly resembling them, is the A. audax of Australia. Lastly may be noticed here a small group of eagles, characterized by their long legs, forming the genus Nisaetus, of which one species, N. fasciatus, is found in Europe.

(A. N.)

Lord Breadalbane (d. 1871) was perhaps the first large landowner who set the example that has been since followed by others. On his unrivalled forest of Black Mount, eagles—elsewhere persecuted to the death—were by him ordered to be unmolested so long as they were not numerous enough to cause considerable depredations on the farmers’ flocks. He thought that the spectacle of a soaring eagle was a fitting adjunct to the grandeur of his Argyllshire mountain scenery, and a good equivalent for the occasional loss of a lamb, or the slight deduction from the rent paid by his tenantry in consequence.

As already stated, the site chosen varies greatly. Occasionally placed in a niche in what passes for a perpendicular cliff to which access could only be gained by a skilful cragsman with a rope, the writer has known a nest to within 10 or 15 yds. of which he rode on a pony. Two beautiful views of as many golden eagles’ nests, drawn on the spot by Joseph Wolf, are given in the Ootheca Wolleyana, and a fine series of eggs is also figured in the same work.

Which species may have been the traditional emblem of Roman power, and the Ales Jovis, is very uncertain.

EAGLEHAWK, a borough of Bendigo county, Victoria, Australia, 105 m. by rail N.N.W. of Melbourne and 4 m. from Bendigo, with which it is connected by steam tramway. Pop. (1901) 8130. It stands on the Bendigo gold-bearing reef, and its mines are important.

EAGRE (a word of obscure origin; the earliest form seems to be higre, Latinized as higra, which William of Malmesbury gives as the name of the bore in the Severn; the New English Dictionary rejects the usual derivations from the O. Eng. eagor or egor, which is seen in compounds meaning “flood,” and also the connexion with the Norse sea-god Aegir), a tide wave of great height rushing up an estuary (see Bore), used locally of the Humber and Trent.

EAKINS, THOMAS (1844- ), American portrait and figure painter, was born at Philadelphia, on the 25th of July 1844. A pupil of J.L. Gérôme, in the École des Beaux-Arts, Paris, and Also of Léon Bonnat, besides working in the studio of the sculptor Dumont, he became a prolific portrait painter. He also painted genre pictures, sending to the Centennial Exhibition at Philadelphia, in 1876, the “Chess Players,” now in the Metropolitan Museum of Art, New York. A large canvas, “The Surgical Clinic of Professor Gross,” owned by Jefferson Medical College, Philadelphia, contains many life-sized figures. Eakins, with his pupil Samuel Murray (b. 1870), modelled the heroic “Prophets” for the Witherspoon Building, Philadelphia, and his work in painting has a decided sculptural quality. He was for some years professor of anatomy at the schools of the Pennsylvania Academy of Fine Arts in Philadelphia. A man of great inventiveness, he experimented in many directions, depicting on canvas modern athletic sports, the negro, and early American life, but he is best known by his portraits. He received awards at the Columbian (1893), Paris (1900), Pan-American (1900), and the St Louis (1904), Expositions; and won the Temple medal in the Pennsylvania Academy of Fine Arts, and the Proctor prize of the National Academy of Design.

EALING, a municipal borough in the Ealing parliamentary division of Middlesex, England, suburban to London, 9 m. W. of St Paul’s cathedral. Pop. (1891) 23,979; (1901) 33,031. The nucleus of the town, the ancient village, lies south of the highroad to Uxbridge, west of the open Ealing Common. The place is wholly residential. At St Mary’s church, almost wholly rebuilt c. 1870, are buried John Oldmixon, the historian (d. 1742), and Horne Tooke (d. 1812). The church of All Saints (1905) commemorates Spencer Perceval, prime minister, who was assassinated in the House of Commons in 1812. It was erected under the will of his daughter Frederica, a resident of Ealing. Gunnersbury Park, south of Ealing Common, is a handsome Italian mansion. Among former owners of the property was Princess Amelia, daughter of George II., who lived here from 1761 till her death in 1786. The name of Gunnersbury is said to be traceable to the residence here of Gunilda, niece of King Canute. The manor of Ealing early belonged to the see of London, but it is not mentioned in Domesday and its history is obscure.

EAR (common Teut.; O.E. éare, Ger. Ohr, Du. oor, akin to Lat. auris, Gr. οὖς), in anatomy, the organ of hearing. The human ear is divided into three parts—external, middle and internal. The external ear consists of the pinna and the external auditory meatus. The pinna is composed of a yellow fibro-cartilaginous framework covered by skin, and has an external and an internal or cranial surface. Round the margin of the external surface in its upper three quarters is a rim called the helix (fig. 1, a), in which is often seen a little prominence known as Darwin’s tubercle, representing the folded-over apex of a prick-eared ancestor. Concentric with the helix and nearer the meatus is the antihelix (c), which, above, divides into two limbs to enclose the triangular fossa of the antihelix. Between the helix and the antihelix is the fossa of the helix. In front of the antihelix is the deep fossa known as the concha (fig. 1, d), and from the anterior part of this the meatus passes inward into the skull. Overlapping the meatus from in front is a flap called the tragus, and below and behind this is another smaller flap, the antitragus. The lower part of the pinna is the lobule (e), which contains no cartilage. On the cranial surface of the pinna elevations correspond to the concha and to the fossae of the helix and antihelix. The pinna can be slightly moved by the anterior, superior and posterior auricular muscles, and in addition to these there are four small intrinsic muscles on the external surface, known as the helicis major and minor, the tragicus and the antitragicus, and two on the internal surface called the obliquus and transversus. The external auditory meatus (fig. 1, n) is a tube running at first forward and upward, then a little backward and then forward and slightly downward; of course all the time it is also running inward until the tympanic membrane is reached. The tube is about an inch long, its outer third being cartilaginous and its inner two-thirds bony. It is lined by skin in its whole length, the sweat glands of which are modified to secrete the wax or cerumen.

a, Helix.

b, Antitragus.

c, Antihelix.

d, Concha.

e, Lobule.

f, Mastoid process.

g, Portio dura.

h, Styloid process.

k, Internal carotid artery.

l, Eustachian tube.

m, Tip of petrous process.

n, External auditory meatus.

o, Membrana tympani.

p, Tympanum.

1, points to malleus.

2, to incus.

3, to stapes.

4, to cochlea.

5, 6, 7, the three semicircular canals.

8 and 9, facial and auditory nerves.

The middle ear or tympanum (fig. 1, p) is a small cavity in the temporal bone, the shape of which may perhaps be realized by imagining a hock bottle subjected to lateral pressure in such a way that its circular section becomes triangular, the base of the triangle being above. The neck of the bottle, also laterally compressed, will represent the Eustachian tube (fig. 1, l), which runs forward, inward and downward, to open into the naso-pharynx, and so admits air into the tympanum. The bottom of the bottle will represent the posterior wall of the tympanum, from the upper part of which an opening leads backward into the mastoid antrum and so into the air-cells of the mastoid process. Lower down is a little pyramid which transmits the stapedius muscle, and at the base of this is a small opening known as the iter chordae posterius, for the chorda tympani to come through from the facial nerve. The roof is formed by a very thin plate of bone, called the tegmen tympani, which separates the cavity from the middle fossa of the skull. Below the roof the upper part of the tympanum is somewhat constricted off from the rest, and to this part the term “attic” is often applied. The floor is a mere groove formed by the meeting of the external and internal walls. The outer wall is largely occupied by the tympanic membrane (fig. 1, o), which entirely separates the middle ear from the external auditory meatus; it is circular, and so placed that it slopes from above, downward and inward, and from behind, forward and inward. Externally it is lined by skin, internally by mucous membrane, while between the two is a firm fibrous membrane, convex inward about its centre to form the umbo. Just in front of the membrane on the outer wall is the Glaserian fissure leading to the glenoid cavity, and close to this is the canal of Huguier for the chorda tympani nerve. The inner wall shows a promontory caused by the cochlea and grooved by the tympanic plexus of nerves; above and behind it is the fenestra ovalis, while below and behind the fenestra rotunda is seen, closed by a membrane. Curving round, above and behind the promontory and fenestrae, is a ridge caused by the aqueductus Fallopii or canal for the facial nerve. The whole tympanum is about half an inch from before backward, and half an inch high, and is spanned from side to side by three small bones, of which the malleus (fig. 1, 1) is the most external. This is attached by its handle to the umbo of the tympanic membrane, while its head lies in the attic and articulates posteriorly with the upper part of the next bone or incus (fig. 1, 2). The long process of the incus runs downward and ends in a little knob called the os orbiculare, which is jointed on to the stapes or stirrup bone (fig. 1, 3). The two branches of the stapes are anterior and posterior, while the footplate fits into the fenestra ovalis and is bound to it by a membrane. It will thus be seen that the stapes lies nearly at right angles to the long process of the incus. From the front of the malleus a slender process projects forward into the Glaserian fissure, while from the back of the incus the posterior process is directed backward and is attached to the posterior wall of the tympanum. These two processes form a fulcrum by which the lever action of the malleus and incus is brought about, so that when the handle of the malleus is pushed in by the membrane the head moves out; the top of the incus, attached to it, also moves out, and the os orbiculare moves in, and so the stapes is pressed into the fenestra ovalis. The stapedius and tensor tympanic muscles, the latter of which enters the tympanum in a canal just above the Eustachian tube to be attached to the malleus, modify the movements of the ossicles.

The mucous membrane lining the tympanum is continuous through the Eustachian tube with that of the naso-pharynx, and is reflected on to the ossicles, muscles and chorda tympani nerve. It is ciliated except where it covers the membrana tympani, ossicles and promontory; here it is stratified.

Fig. 2.—Diagram of the Membranous Labyrinth.

DC, Ductus cochlearis.

dr, Ductus reuniens.

S, Sacculus.

U, Utriculus.

dv, Ductus endolymphaticus.

SC, Semicircular canals.

(After Waldeyer.)

The internal ear or labyrinth consists of a bony and a membranous part, the latter of which is contained in the former. The bony labyrinth is composed of the vestibule, the semicircular canals and the cochlea. The vestibule lies just internal to the posterior part of the tympanum, and there would be a communication between the two, through the fenestra ovalis, were it not that the footplate of the stapes blocks the way. The inner wall of the vestibule is separated from the bottom of the internal auditory meatus by a plate of bone pierced by many foramina for branches of the auditory nerve (fig. 1, 9), while at the lower part is the opening of the aqueductus vestibuli, by means of which a communication is established with the posterior cranial fossa. Posteriorly the three semicircular canals open into the vestibule; of these the external (fig. 1, 7) has two independent openings, but the superior and posterior (fig. 1, 5 and 6) join together at one end and so have a common opening, while at their other ends they open separately. The three canals have therefore five openings into the vestibule instead of six. One end of each canal is dilated to form its ampulla. The superior semicircular canal is vertical, and the two pillars of its arch are nearly external and internal; the external canal is horizontal, its two pillars being anterior and posterior, while the convexity of the arch of the posterior canal is backward and its two pillars are superior and inferior. Anteriorly the vestibule leads into the cochlea (fig. 1, 4), which is twisted two and a half times round a central pillar called the modiolus, the whole cochlea forming a rounded cone something like the shell of a snail though it is only about 5 mm. from base to apex. Projecting from the modiolus is a horizontal plate which runs round it from base to apex like a spiral staircase; this is known as the lamina spiralis, and it stretches nearly half-way across the canal of the cochlea. At the summit it ends in a little hook named the hamulus. The modiolus is pierced by canals which transmit branches of the auditory nerve to the lamina spiralis.

Fig. 3.—cl, Columnar cells covering the crista acustica; p, peripheral, and c, central processes of auditory cells; n, nerve fibres. (After Rüdinger.)

The membranous labyrinth lies in the bony labyrinth, but does not fill it; between the two is the fluid called perilymph, while inside the membranous labyrinth is the endolymph. In the bony vestibule lie two membranous bags, the saccule (fig. 2, S) in front, and the utricle (fig. 2, U) behind; each of these has a special patch or macula to which twigs of the auditory nerve are supplied, and in the mucous membrane of which specialized hair cells are found (fig. 3, p).

Attached to the maculae are crystals of carbonate of lime called otoconia. The membranous semicircular canals are very much smaller in section than the bony; in the ampulla of each is a ridge, the crista acustica, which is covered by a mucous membrane containing sensory hair cells like those in the maculae. All the canals open into the utricle. From the lower part of the saccule a small canal called the ductus endolymphaticus (fig. 2, dv) runs into the aqueductus vestibuli; it is soon joined by a small duct from the utricle, and ends, close to the dura mater of the posterior fossa of the cranium, as the saccus endolymphaticus, which may have minute perforations through which the endolymph can pass. Anteriorly the saccule communicates with the membranous cochlea or scala media by a short ductus reuniens (fig. 2, dr). A section through each turn of the cochlea shows the bony lamina spiralis, already noticed, which is continued right across the canal by the basilar membrane (fig. 4, bm), thus cutting the canal into an upper and lower half and connected with the outer wall by the strong spiral ligament (fig. 4, sl). Near the free end of the lamina spiralis another membrane called the membrane of Reissner (fig. 4, mR) is attached, and runs outward and upward to the outer wall, taking a triangular slice out of the upper half of the section. There are now three canals seen in section, the upper of which is the scala vestibuli (fig. 4, SV), the middle and outer the scala media, ductus cochlearis or true membranous cochlea (fig. 4, DC), while the lower is the scala tympani (fig. 4, ST). The scala vestibuli and scala tympani communicate at the apex of the cochlea by an opening known as the helicotrema, so that the perilymph can here pass from one canal to the other. At the base of the cochlea the perilymph in the scala vestibuli is continuous with that in the vestibule, but that in the scala tympani bathes the inner surface of the membrane stretched across the fenestra rotunda, and also communicates with the subarachnoid space through the aqueductus cochleae, which opens into the posterior cranial fossa. The scala media containing endolymph communicates, as has been shown, with the saccule through the canalis reuniens, while, at the apex of the cochlea, it ends in a blind extremity of considerable morphological interest called the lagena.

m, Modiolus.

0, Outer wall of cochlea.

SV, Scala vestibuli.

ST, Scala tympani.

DC, Ductus cochlearis.

mR, Membrane of Reissner.

bm, Basilar membrane.

cs, Crista spiralis.

sl, Spiral ligament.

sg, Spiral ganglion of auditory nerve.

oc, Organ of Corti.

The scala media contains the essential organ of hearing or organ of Corti (fig. 4, oc), which lies upon the inner part of the basilar membrane; it consists of a tunnel bounded on each side of the inner and outer rods of Corti; on each side of these are the inner and outer hair cells, between the latter of which are found the supporting cells of Deiters. Most externally are the large cells of Hensen. A delicate membrane called the lamina reticularis covers the top of all these, and is pierced by the hairs of the hair cells, while above this is the loose membrana tectoria attached to the periosteum of the lamina spiralis, near its tip, internally, and possibly to some of Deiter’s cells externally. The cochlear branch of the auditory nerve enters the lamina spiralis, where a spiral ganglion (fig. 4, sg) is developed on it; after this it is distributed to the inner and outer hair cells.

(From R. Howden—Cunningham’s Text-Book of Anatomy.)

For further details see Text-Book of Anatomy, edited by D.J. Cunningham (Edinburgh, 1906); Quain’s Elements of Anatomy (London, 1893); Gray’s Anatomy (London, 1905); A Treatise on Anatomy, edited by H. Morris (London, 1902); A Text-Book of Human Anatomy, by A. Macalister (London, 1889).

Embryology.—The pinna is formed from six tubercles which appear round the dorsal end of the hyomandibular cleft or, more strictly speaking, pouch. Those for the tragus and anterior part of the helix belong to the first or mandibular arch, while those for the antitragus, antihelix and lobule come from the second or hyoid arch. The tubercle for the helix is dorsal to the end of the cleft where the two arches join. The external auditory meatus, tympanum and Eustachian tube are remains of the hyomandibular cleft, the membrana tympani being a remnant of the cleft membrane and therefore lined by ectoderm outside and entoderm inside. The origin of the ossicles is very doubtful. H. Gadow’s view, which is one of the latest, is that all three are derived from the hyomandibular plate which connects the dorsal ends of the hyoid and mandibular bars (Anatomischer Anzeiger, Bd. xix., 1901, p. 396). Other papers which should be consulted are those of E. Gaupp, Anatom. Hefte, Ergebnisse, Bd. 8, 1898, p. 991, and J.A. Hammar, Archiv f. mikr. Anat. lix., 1902. These papers will give a clue to the immense literature of the subject. The internal ear first appears as a pit from the cephalic ectoderm, the mouth of which in Man and other mammals closes up, so that a pear-shaped cavity is left. The stalk of the pear which is nearest the point of invagination is called the recessus labyrinthi, and this, after losing its connexion with the surface of the embryo, grows backward toward the posterior cranial fossa and becomes the ductus endolymphaticus. The lower part of the vesicle grows forward and becomes the cochlea, while from the upper part three hollow circular plates grow out, the central parts of which disappear, leaving the margin as the semicircular canals. Subsequently constrictions appear in the vesicle marking off the saccule and utricle. From the surrounding mesoderm the petrous bone is formed by a process of chondrification and ossification.

See W. His, Junr., Archiv f. Anat. und Phys., 1889, supplement, p. 1; also Streeter, Am. Journ. of Anat. vi., 1907.

Comparative Anatomy.—The ectodermal inpushing of the internal ear has probably a common origin with the organs of the lateral line of fish. In the lower forms the ductus endolymphaticus retains its communication with the exterior on the dorsum of the head, and in some Elasmobranchs the opening is wide enough to allow the passage of particles of sand into the saccule. It is probable that this duct is the same which, taking a different direction and losing its communication with the skin, abuts on the posterior cranial fossa of higher forms (see Rudolf Krause, “Die Entwickelung des Aq. vestibuli seu d. Endelymphaticus,” Anat. Anzeiger, Bd. xix., 1901, p. 49). In certain Teleostean fishes the swim bladder forms a secondary communication with the internal ear by means of special ossicles (see G. Ridewood, Journ. Anat. & Phys. vol. xxvi.). Among the Cyclostomata the external semicircular canals are wanting; Petromyzon has the superior and posterior only, while in Myxine these two appear to be fused so that only one is seen. In higher types the three canals are constant. Concretions of carbonate of lime are present in the internal ears of almost all vertebrates; when these are very small they are called otoconia, but when, as in most of the teleostean fishes, they form huge concretions, they are spoken of as otoliths. One shark, Squatina, has sand instead of otoconia (C. Stewart, Journ. Linn. Society, xxix. 409). The utricle, saccule, semicircular canals, ductus endolymphaticus and a short lagena are the only parts of the ear present in fish.

The Amphibia have an important sensory area at the base of the lagena known as the macula acustica basilaris, which is probably the first rudiment of a true cochlea. The ductus endolymphaticus has lost its communication with the skin, but it is frequently prolonged into the skull and along the spinal canal, from which it protrudes, through the intervertebral foramina, bulging into the coelom. This is the case in the common frog (A. Coggi, Anat. Anz. 5. Jahrg., 1890, p. 177). In this class the tympanum and Eustachian tube are first developed; the membrana tympani lies flush with the skin of the side of the head, and the sound-waves are transmitted from it to the internal ear by a single bony rod—the columella.

In the Reptilia the internal ear passes through a great range of development. In the Chelonia and Ophidia the cochlea is as rudimentary as in the Amphibia, but in the higher forms (Crocodilia) there is a lengthened and slightly twisted cochlea, at the end of which the lagena forms a minute terminal appendage. At the same time indications of the scalae tympani and vestibuli appear. As in the Amphibia the ductus endolymphaticus sometimes extends into the cranial cavity and on into other parts of the body. Snakes have no tympanic membrane. In the birds the cochlea resembles that of the crocodiles, but the posterior semicircular canal is above the superior where they join one another. In certain lizards and birds (owls) a small fold of skin represents the first appearance of an external ear. In the monotremes the internal ear is reptilian in its arrangement, but above them the mammals always have a spirally twisted cochlea, the number of turns varying from one and a half in the Cetacea to nearly five in the rodent Coelogenys. The lagena is reduced to a mere vestige. The organ of Corti is peculiar to mammals, and the single columella of the middle ear is replaced by the three ossicles already described in Man (see Alban Doran, “Morphology of the Mammalian Ossicula auditus,” Proc. Linn. Soc., 1876-1877, xiii. 185; also Trans. Linn. Soc. 2nd Ser. Zool. i. 371). In some mammals, especially Carnivora, the middle ear is enlarged to form the tympanic bulla, but the mastoid cells are peculiar to Man.

For further details see G. Retzius, Das Gehörorgan der Wirbelthiere (Stockholm, 1881-1884); Catalogue of the Museum of the R. College of Surgeons—Physiological Series, vol. iii. (London, 1906); R. Wiedersheim’s Vergleichende Anatomie der Wirbeltiere (Jena, 1902).

(F. G. P.)

Diseases of the Ear

Modern scientific aural surgery and medicine (commonly known as Otology) dates from the time of Sir William Wilde of Dublin (1843), whose work marked a great advance in the application of anatomical, physiological and therapeutical knowledge to the study of this organ. Less noticeable contributions to the subject had not long before been made by Saunders (1827), Kramer (1833), Pilcher (1841) and Yearsley (1841). The next important event in the history of otology was the publication of J. Toynbee’s book in 1860 containing his valuable anatomical and pathological observations. Von Tröltsch of Würzburg, following on the lines of Wilde and Toynbee, produced two well-known works in 1861 and 1862, laying the foundation of the study in Germany. In that country and in Austria he was followed by Hermann Schwartze, Politzer, Gruber, Weber-Liel, Rüdinger, Moos and numerous others. France produced Itard, de la Charrière, Menière, Loewenberg and Bonnafont; and Belgium, Charles Delstanche, father and son. In Great Britain the work was carried on by James Hinton (1874), Peter Allen (1871), Patterson Cassells and Sir William Dalby. In America we may count among the early otologists Edward H. Clarke (1858), D.B. St John Roosa, H. Knapp, Clarence J. Blake, Albert H. Buck and Charles Burnett. Other workers all over the world are too numerous to mention.

Various Diseases and Injuries.—Diseases of the ear may affect any of the three divisions, the external, middle or internal ear. The commoner affections of the auricle are eczema, various tumours (simple and malignant), and serous and sebaceous cysts. Haematoma auris (othaematoma), or effusion of blood into the auricle, is often due to injury, but may occur spontaneously, especially in insane persons. The chief diseases of the external auditory canal are as follows:—impacted cerumen (or wax), circumscribed (or furuncular) inflammation, diffuse inflammation, strictures due to inflammatory affections, bony growths, fungi (otomycosis), malignant disease, caries and necrosis, and foreign bodies.

Diseases of the middle ear fall into two categories, suppurative and non-suppurative (i.e. with and without the formation of pus). Suppurative inflammation of the middle ear is either acute or chronic, and is in either case accompanied by perforation of the drum head and discharge from the ear. The chief importance of these affections, in addition to the symptoms of pain, deafness, discharge, &c., is the serious complications which may ensue from their neglect, viz. aural polypi, caries and necrosis of the bone, affections of the mastoid process, including the mastoid antrum, paralysis of the facial nerve, and the still more serious intracranial and vascular infective diseases, such as abscess in the brain (cerebrum or cerebellum), meningitis, with subdural and extradural abscesses, septic thrombosis of the sigmoid and other venous sinuses, and pyaemia. It is owing to the possibility of these complications that life insurance companies usually, and rightly, inquire as to the presence of ear discharge before accepting a life. Patterson Cassells of Glasgow urged this special point as long ago as 1877. Acute suppurative disease of the middle ear is often due to the exanthemata, scarlatina, measles and smallpox, and to bathing and diving. It may also be caused by influenza, diphtheria and pulmonary phthisis.

Non-suppurative disease of the middle ear may be acute or chronic. In the acute form the inflammation is less violent than in the acute suppurative inflammation, and is rarely accompanied by perforation. Chronic non-suppurative inflammation may be divided into the moist form, in which the symptoms are improved by inflation of the tympanum through the Eustachian tube, and the dry form (including sclerosis), which is more intractable and in which this procedure has little or no beneficial effect. Diseases of the internal ear may be primary or secondary to an affection of the tympanum or to intracranial disease.

Injuries to any part of the ear may occur, among the commoner being injuries to the auricle, rupture of the drum head (from explosions, blows on the ear or the introduction of sharp bodies into the ear canal), and injuries from fractured skull. Congenital malformations of the ear are most frequently met with in the auricle and external canal.

Methods of Examination.—The methods of examining the ear are roughly threefold:—(1) Testing the hearing with watch, voice and tuning-fork. The latter is especially used to distinguish between disease of the middle ear (conducting apparatus) and that of the internal ear (perceptive apparatus). Our knowledge of the subject has been brought to its present state by the labours of many observers, notably Weber, Rinne, Schwabach, Lucae and Gellé. (2) Examination of the canal and drum-head with speculum and reflector, introduced by Kramer, Wilde and von Tröltsch. (3) Examination of the drum-cavity through the Eustachian tube by the various methods of inflation.

Symptoms.—The chief symptoms of ear diseases are deafness, noises in the ear (tinnitus aurium), giddiness, pain and discharge. Deafness (or other disturbance of hearing) and noises may occur from disease in almost any part of the ear. Purulent discharge usually comes from the middle ear. Giddiness is more commonly associated with affections of the internal ear.

Treatment.—Ear diseases are treated on ordinary surgical and medical lines, due regard being had to the anatomical and physiological peculiarities of this organ of sense, and especially to its close relationship, on the one hand to the nose and naso-pharynx, and on the other hand to the cranium and its contents. The chief advance in aural surgery in recent years has been in the surgery of the mastoid process and antrum. The pioneers of this work were H. Schwartze of Halle, and Stacke of Erfurt, who have been followed by a host of workers in all parts of the world. This development led to increased attention being paid to the intracranial complications of suppurative ear disease, in the treatment of which great strides have been made in the last few years.

Effects of Diseases of the Nose on the Ear.—The influence of diseases of the nose and naso-pharynx on ear diseases was brought out by Loewenberg of Paris, Voltolini of Breslau, and especially by Wilhelm Meyer of Copenhagen, the discoverer of adenoid vegetations of the naso-pharynx (“adenoids”), who recognized the great importance of this disease and gave an inimitable account of it in the Trans. of the Royal Medical and Chirurgical Society of London, 1870, and the Archiv für Ohrenheilkunde, 1873. Adenoid vegetations, which consist of an abnormal enlargement of Luschka’s tonsil in the vault of the pharynx, frequently give rise to ear disease in children, and, if not attended to, lay the foundation of nasal and ear troubles in after life. They are often associated with enlargement of the faucial tonsils.

Journals.—In 1864 the Archiv für Ohrenheilkunde was started by Politzer and Schwartze, and, in 1867, the Monatsschrift für Ohrenheilkunde (a monthly publication) was founded by Voltolini, Gruber, Weber-Liel and Rüdinger. Appearing first as the Archives of Ophthalmology and Otology, simultaneously in English and German, in 1869, the Archives of Otology became a separate publication under the editorship of Knapp, Moos and Roosa in 1879. Amongst other journals now existing are Annales des maladies de l’oreille et du larynx (Paris), Journal of Laryngology (London), Centralblatt für Ohrenheilkunde (Leipzig), &c.

Societies.—The earliest society formed was the American Otological Society (1868), which held annual meetings and published yearly transactions. Flourishing societies for the study of otology (sometimes combined with laryngology) exist in almost all civilized countries, and they usually publish transactions consisting of original papers and cases. The Otological Society of the United Kingdom was founded in 1900.

International Congresses.—International Otological congresses have been held at intervals of about four years at New York, Milan, Basel, Brussels, Florence, London and Bordeaux (1904). The proceedings of the congresses appear as substantial volumes.

Hospitals.—The earliest record of a public institution for the treatment of ear diseases is a Dispensary for Diseases of the Eye and Ear in London, started by Saunders and Cooper, which existed in 1804; the aural part, however, was soon closed, so that the actual oldest institution appears to be the Royal Ear Hospital, London, which was founded by Curtis in 1816. Four years later there was started the New York Eye and Ear Infirmary. At the present time in every large town of Europe and America ear diseases are treated either in separate departments of general hospitals or in institutions especially devoted to the purpose.

For a history of otology from the earliest times refer to A Practical Treatise on the Diseases of the Ear, by D.B. St John Roosa, M.D., LL.D. (6th edition, New York, 1885), and for a general account of the present state of otological science to A Text-Book of the Diseases of the Ear for Students and Practitioners, by Professor Dr Adam Politzer, transl. by Milton J. Ballin, Ph.B., M.D., and Clarence J. Heller, M.D. (4th edition, London, 1902).

(E. C. B.*)

EARL, a title and rank of nobility (corresponding to Lat. comes; Fr. comte), now the third in order of the British peerage, and accordingly intervening between marquess and viscount. Earl, however, is the oldest title and rank of English nobles, and was the highest until the year 1337, when the Black Prince was created duke of Cornwall by Edward III.

The nature of a modern earldom is readily understood, since it is a rank and dignity of nobility which, while it confers no official power or authority, is inalienable, indivisible, and descends in regular succession to all the heirs under the limitation in the grant until, on their failure, it becomes extinct.

The title is of Scandinavian origin, and first appears in England under Canute as jarl, which was englished as eorl. Like the ealdorman, whose place he took, the eorl was a great royal officer, who might be set over several counties, but who presided separately in the county court of each with the bishop of the diocese. Although there were counts in Normandy before the Norman Conquest, they differed in character from the English earls, and the earl’s position appears to have been but slightly modified by the Conquest. He was still generally entitled to the “third penny” of the county, but his office tended, under Norman influence, to become an hereditary dignity and his sphere was restricted by the Conqueror to a single county. The right to the “third penny” is a question of some obscurity, but its possession seems to have been deemed the distinctive mark of an earl, while the girding with “the sword of the county” formed the essential feature in his creation or investiture, as it continued to do for centuries later. The fact that every earl was the earl of a particular county has been much obscured by the loose usage of early times, when the style adopted was sometimes that of the noble’s surname (e.g. the Earls Ferrers), sometimes that of his chief seat (e.g. the Earls of Arundel), and sometimes that of the county. Palatine earldoms, or palatinates, were those which possessed regalia, i.e. special privileges delegated by the crown. The two great examples, which dated from Norman times, were Chester and Durham, where the earl and the bishop respectively had their own courts and jurisdiction, and were almost petty sovereigns.

The earliest known charter creating an earl is that by which Stephen bestowed on Geoffrey de Mandeville, in or about 1140, the earldom of Essex as an hereditary dignity. Several other creations by Stephen and the empress Maud followed in quick succession. From at least the time of the Conquest the earl had a double character; he was one of the “barons,” or tenants in chief, in virtue of the fief he held of the crown, as well as an earl in virtue of his “belting” (with the sword) and his “third penny” of the county. His fief would descend to the heirs of his body; and the earliest charters creating earldoms were granted with the same “limitation.” The dignity might thus descend to a woman, and, in that case, like the territorial fief, it would be held by her husband, who might be summoned to parliament in right of it. The earldom of Warwick thus passed through several families till it was finally obtained, in 1449, by the Kingmaker, who had married the heiress of the former earls. But in the case of “co-heiresses” (more daughters than one), the king determined which, if any, should inherit the dignity.

The 14th century saw some changes introduced. The earldom of March, created in 1328, was the first that was not named from a county or its capital town. Under Edward III. also an idea appears to have arisen that earldoms were connected with the tenure of lands, and in 1337 several fresh ones were created and large grants of lands made for their support. The first earldom granted with limitation to the heirs male of the grantee’s body was that of Nottingham in 1383. Another innovation was the grant of the first earldom for life only in 1377. The girding with the sword was the only observance at a creation till the first year of Edward VI., when the imposition of the cap of dignity and a circlet of gold was added. Under James I. the patent of creation was declared to be sufficient without any ceremony. An earl’s robe of estate has three bars of ermine, but possibly it had originally four.

Something should be said of anomalous earldoms with Norman or Scottish styles. The Norman styles originated either under the Norman kings or at the time of the conquest of Normandy by the house of Lancaster. To the former period belonged that of Aumale, which successive fresh creations, under the Latinized form “Albemarle” have perpetuated to the present day (see Albemarle, Earls and Dukes of). The so-called earls of Eu and of Mortain, in that period, were really holders of Norman comtés. Henry V. and his son created five or six, it is said, but really seven at least, Norman countships or earldoms, of which Harcourt (1418), Perche (1419), Dreux (1427) and Mortain (? 1430) were bestowed on English nobles, Eu (1419), and Tankerville (1419) on English commoners, and Longueville (1419) on a foreigner, Gaston de Foix. Of these the earldom of “Eu” was assumed by the earls of Essex till the death of Robert, the parliament’s general (1646), while the title of Tankerville still survives under a modern creation (1714). An anomalous royal licence of 1661 permitted the earl of Bath to use the title of earl of Corbeil by alleged hereditary right. Of Scottish earldoms recognized in the English parliament the most remarkable case is that of the Lords Umfraville, who were summoned for three generations (1297-1380), as earls of Angus; Henry, Lord Beaumont, also was summoned as earl of Buchan from 1334 to 1339.

The earldom of Chester is granted to the princes of Wales on their creation, and the Scottish earldom of Carrick is held by the eldest son of the sovereign under act of parliament.

The premier earldom is that of Arundel (q.v.), but as this is at present united with the dukedom of Norfolk, the oldest earldom not merged in a higher title is that of Shrewsbury (1442), the next in seniority being Derby (1485), and Huntingdon (1529). These three have been known as “the catskin earls,” a term of uncertain origin. The ancient earldom of Wiltshire (1397) was unsuccessfully claimed in 1869 by Mr Scrope of Danby, and that of Norfolk (1312), in 1906, by Lord Mowbray and Stourton.

The premier earldom of Scotland as recognized by the Union Roll (1707), is that of Crawford, held by the Lindsays since its creation in 1398; but it is not one of the ancient “seven earldoms.” The Decreet of Ranking (1606) appears to have recognized the earldom of Sutherland as the most ancient in virtue of a charter of 1347, but the House of Lords’ decision of 1771 recognized it as having descended from at least the year 1275, and it may be as old as 1228. It is at present united with the dukedom of Sutherland. The original “seven earldoms” (of which it was one) represented seven provinces, each of which was under a “mormaer.” This Celtic title was rendered “jarl” by the Norsemen, and under Alexander I. (c. 1115) began to be replaced by earl (comes), owing to Anglo-Norman influence, which also tended to make these earldoms less official and more feudal.

In Ireland the duke of Leinster is, as earl of Kildare, premier earl as well as premier duke.

An earl is “Right Honourable,” and is styled “My Lord.” His eldest son bears his father’s “second title,” and therefore, that second title being in most cases a viscounty, he generally is styled “Viscount”; where, as with Devon and Huntingdon, there is no second title, one may be assumed for convenience; under all circumstances, however, the eldest son of an earl takes precedence immediately after the viscounts. The younger sons of earls are “Honourable,” but all their daughters are “Ladies.” In formal documents and instruments, the sovereign, when addressing or making mention of any peer of the degree of an earl, usually designates him “trusty and well-beloved cousin,”—a form of appellation first adopted by Henry IV., who either by descent or alliance was actually related to every earl and duke in the realm. The wife of an earl is a countess; she is “Right Honourable,” and is styled “My Lady.” For the earl’s coronet see Crown and Coronet.

See Lord’s Reports on the Dignity of a Peer; Pike’s Constitutional History of the House of Lords; Selden’s Titles of Honour; G.E. C(okayne)’s Complete Peerage; Round’s Geoffrey de Mandeville.

(J. H. R.)

EARLE, JOHN (c. 1601-1665), English divine, was born at York about 1601. He matriculated at Christ Church, Oxford, but migrated to Merton, where he obtained a fellowship. In 1631 he was proctor and also chaplain to Philip, earl of Pembroke, then chancellor of the university, who presented him to the rectory of Bishopston in Wiltshire. His fame spread, and in 1641 he was appointed chaplain and tutor to Prince Charles. In 1643 he was elected one of the Assembly of Divines at Westminster, but his sympathies with the king and with the Anglican Church were so strong that he declined to sit. Early in 1643 he was chosen chancellor of the cathedral of Salisbury, but of this preferment he was soon deprived as a “malignant.” After Cromwell’s great victory at Worcester, Earle went abroad, and was named clerk of the closet and chaplain to Charles II. He spent a year at Antwerp in the house of Isaac Walton’s friend, George Morley, who afterwards became bishop of Winchester. He next joined the duke of York (James II.) at Paris, returning to England at the Restoration. He was at once appointed dean of Westminster, and in 1661 was one of the commissioners for revising the liturgy. He was on friendly terms with Richard Baxter. In November 1662 he was consecrated bishop of Worcester, and was translated, ten months later, to the see of Salisbury, where he conciliated the nonconformists. He was strongly opposed to the Conventicle and Five Mile Acts. During the great plague Earle attended the king and queen at Oxford, and there he died on the 17th of November 1665.

Earle’s chief title to remembrance is his witty and humorous work entitled Microcosmographie, or a Peece of the World discovered, in Essayes and Characters, which throws light on the manners of the time. First published anonymously in 1628, it became very popular, and ran through ten editions in the lifetime of the author. The style is quaint and epigrammatic; and the reader is frequently reminded of Thomas Fuller by such passages as this: “A university dunner is a gentlemen follower cheaply purchased, for his own money has hyr’d him.” Several reprints of the book have been issued since the author’s death; and in 1671 a French translation by J. Dymock appeared with the title of Le Vice ridiculé. Earle was employed by Charles II. to make the Latin translation of the Eikon Basilike, published in 1649. A similar translation of R. Hooker’s Ecclesiastical Polity was accidentally destroyed.

“Dr Earle,” says Lord Clarendon in his Life, “was a man of great piety and devotion, a most eloquent and powerful preacher, and of a conversation so pleasant and delightful, so very innocent, and so very facetious, that no man’s company was more desired and loved. No man was more negligent in his dress and habit and mien, no man more wary and cultivated in his behaviour and discourse. He was very dear to the Lord Falkland, with whom he spent as much time as he could make his own.”

See especially Philip Bliss’s edition of the Microcosmographie (London, 1811), and E. Arber’s Reprint (London, 1868).

EARLE, RALPH (1751-1801), American historical and portrait painter, was born at Leicester, Massachusetts, on the 11th of May 1751. Like so many of the colonial craftsmen, Earle was self-taught, and for many years was an itinerant painter. He went with the Governor’s Guard to Lexington and made battle sketches, from which in 1775 he painted four scenes, engraved by Amos Doolittle, which are probably the first historical paintings by an American. After the War of Independence, Earle went to London, entered the studio of Benjamin West, and painted the king and many notables. After his return to America in 1786 he made portraits of Timothy Dwight, Governor Caleb Strong, Roger Sherman, and other prominent men. He also painted a large picture of Niagara Falls. He died at Bolton, Connecticut, on the 16th of August 1801.

EARL MARSHAL, in England, a functionary who ranks as the eighth of the great officers of state. He is the head of the college of arms, and has the appointment of the kings-of-arms, heralds and pursuivants at his discretion. He attends the sovereign in opening and closing the session of parliament, walking opposite to the lord great chamberlain on his or her right hand. It is his duty to make arrangements for the order of all state processions and ceremonials, especially for coronations and royal marriages and funerals. Like the lord high constable he rode into Westminster Hall with the champion after a coronation, till the coronation banquet was abandoned, taking his place on the left hand, and with the lord great chamberlain he assists at the introduction of all newly-created peers into the House of Lords.

The marshal appears in the feudal armies to have been in command of the cavalry under the constable, and to have in some measure superseded him as master of the horse in the royal palace. He exercised joint and co-ordinate jurisdiction with the constable in the court of chivalry, and afterwards became the sole judge of that tribunal till its obsolescence. The marshalship of England was formerly believed to have been inherited from the Clares by the Marshal family, who had only been marshals of the household. It was held, however, by the latter family, as the office of chief (magister) marshal, as early as the days of Henry I. Through them, under Henry III., it passed to the Bigods, as their eldest co-heirs. In 1306 it fell to the crown on the death of the last Bigod, earl of Norfolk, who had made Edward I. his heir, and in 1316 it was granted by Edward II. to his own younger brother, Thomas “of Brotherton,” earl of Norfolk. As yet the style of the office was only “marshal” although the last Bigod holder, being an earl, was sometimes loosely spoken of as the earl marshal. The office, having reverted to the crown, was granted out anew by Richard II., in 1385, to Thomas Mowbray, earl of Nottingham, the representative of Thomas “of Brotherton.” In 1386 the style of “earl marshal” was formally granted to him in addition. After several attainders and partial restorations in the reigns of the Tudors and the Stuarts, the earl marshalship was granted anew to the Howards by Charles II. in 1672 and entailed on their male line, with many specific remainders and limitations, under which settlement it has regularly descended to the present duke of Norfolk. Its holders, however, could not execute the office until the Roman Catholic emancipation, and had to appoint deputies. The duke is styled earl marshal “and hereditary marshal of England,” but the double style would seem to be an error, though the Mowbrays, with their double creation (1385, 1386) might have claimed it. His Grace appends the letters “E.M.” to his signature, and bears behind his shield two batons crossed in saltire, the marshal’s rod (virga) having been the badge of the office from Norman times. There appear to have been hereditary marshals of Ireland, but their history is not well ascertained. The Keiths were Great Marischals of Scotland from at least the days of Robert Bruce, and were created earls marischal in or about 1458, but lost both earldom and office by the attainder of George, the 10th earl, in 1716. (See also Marshal; State, Great Officers of.)

See “The Marshalship of England,” in J.H. Round, Commune of London and Other Studies (London, 1899); G.E. C(okayne)’s Complete Peerage.

(J. H. R.)

EARLOM, RICHARD (1742-1822), English mezzotint engraver, was born and died in London. His natural faculty for art appears to have been first called into exercise by admiration for the lord mayor’s state coach, just decorated by Cipriani. He tried to copy the paintings, and was sent to study under Cipriani. He displayed great skill as a draughtsman, and at the same time acquired without assistance the art of engraving in mezzotint. In 1765 he was employed by Alderman Boydell, then one of the most liberal promoters of the fine arts, to make a series of drawings from the pictures at Houghton Hall; and these he afterwards engraved in mezzotint. His most perfect works as engraver are perhaps the fruit and flower pieces after the Dutch artists Van Os and Van Huysum. Amongst his historical and figure subjects are—“Agrippina,” after West; “Love in Bondage,” after Guido Reni; the “Royal Academy,” the “Embassy of Hyderbeck to meet Lord Cornwallis,” and a “Tiger Hunt,” the last three after Zoffany; and “Lord Heathfield,” after Sir Joshua Reynolds. Earlom also executed a series of 200 facsimiles of the drawings and sketches of Claude Lorraine, which was published in 3 vols. folio, under the title of Liber veritatis (1777-1819).

EARLSTON (formerly Ercildoune, of which it is a corruption), a parish and market town of Berwickshire, Scotland. Pop. (1901) 1049. It is situated on Leader Water in Lauderdale, 72½ m. S.E. of Edinburgh by the North British railway branch line from Reston Junction to St Boswells, and about 4 m. N.E. of Melrose. When the place was a hamlet of rude huts it was called Arcioldun or “Prospect Fort,” with reference to Black Hill (1003 ft.), on the top of which may yet be traced the concentric rings of the British fort by which it was crowned. It is said to be possible to make out the remains of the cave-dwellings of the Ottadeni, the aborigines of the district. In the 12th and 13th centuries the Lindsays and the earls of March and Dunbar were the chief baronial families. The particular link with the remote past, however, is the ivy-clad ruin of the ancient tower, “The Rhymer’s Castle,” the traditional residence of Thomas Learmont, commonly called Thomas of Ercildoune, or Thomas the Rhymer, poet and prophet, and friend of the Fairies, who was born here about 1225. Rhymer’s Tower was crumbling to pieces, and its stones were being used in the erection of dykes, cottages and houses, when the Edinburgh Border Counties Association acquired the relic and surrounding lands in 1895, and took steps to prevent further spoliation and decay. The leading manufactures are ginghams, tweeds and shirtings, and the town is also an important agricultural centre, stock sales taking place at regular intervals and cattle and horse fairs being held every year. Some 3 m. away is the estate of Bemersyde, said to have been in the possession of the Haigs for nearly 1000 years. The prospect from Bemersyde Hill was Sir Walter Scott’s favourite view. The castle at Bemersyde was erected in 1535 to secure the peace of the Border.

EARLY, JUBAL ANDERSON (1816-1894), American soldier and lawyer, was born in Franklin county, Virginia, on the 3rd of November 1816, and graduated at the U.S. Military Academy in 1837. He served in the Seminole War of 1837-38, after which he resigned in order to practise law in Franklin county, Va. He also engaged in state politics, and served in the Mexican War as a major of Virginia volunteers. He was strongly opposed to secession, but thought it his duty to conform to the action of his state. As a colonel in the Confederate army, he rendered conspicuous service at the first battle of Bull Run (q.v.). Promoted brigadier-general, and subsequently major-general, Early served throughout the Virginian campaigns of 1862-63, and defended the lines of Fredericksburg during the battle of Chancellorsville. At Gettysburg he commanded his division of Ewell’s corps. In the campaign of 1864 Early, who had now reached the rank of lieutenant-general, commanded the Confederate forces in the Shenandoah Valley. The action of Lynchburg left him free to move northwards, his opponent being compelled to march away from the Valley. Early promptly utilized his advantage, crossed the Potomac, and defeated, on the Monocacy, all the troops which could be gathered to meet him. He appeared before the lines of Washington, put part of Maryland and Pennsylvania under contribution, and only retired to the Valley when threatened by heavy forces hurriedly sent up to Washington. He then fought a successful action at Winchester, reappeared on the Potomac, and sent his cavalry on a raid into Pennsylvania. A greatly superior army was now formed under General Sheridan to oppose Early. In spite of his skill and energy the Confederate leader was defeated in the battles of Winchester and Fisher’s Hill. Finally, on the 19th of October, after inflicting at first a severe blow upon the Federal army in its camps on Cedar Creek, he was decisively beaten by Sheridan. (See Shenandoah Valley Campaigns.) Waynesboro (March 1865) was his last fight, after which he was relieved from his command. General Early was regarded by many as the ablest soldier, after Lee and Jackson, in the Army of Northern Virginia, and one of the ablest in the whole Confederate army. That he failed to make headway against an army far superior in numbers, and led by a general of the calibre of Sheridan, cannot be held to prove the falsity of this judgment. After the peace he went to Canada, but in 1867 returned to resume the practice of law. For a time he managed in conjunction with General Beauregard the Louisiana lottery. He died at Lynchburg, Va., on the 2nd of March 1894. General Early was for a time president of the Southern Historical Society, and wrote, besides various essays and historical papers, A Memoir of the Last Year of the War, &c. (1867).

EARLY ENGLISH PERIOD, in architecture, the term given by Rickman to the first pointed or Gothic style in England, nominally 1189-1307, which succeeded the Romanesque or Norman period towards the end of the 12th century, and developed into the Decorated period in the commencement of the 14th century. It is chiefly characterized by the almost universal employment of the pointed arch, not only in arches of wide span such as those of the nave arcade, but for doorways and windows. The actual introduction of the pointed arch took place at a much earlier date, as in the nave arcade of the Cistercian Abbey of Buildwas (1140), though the clerestory window above has semicircular arches. It is customary, therefore, to make allowance for a transitional epoch from the middle of the 12th century. Although the pointed arches used are sometimes equilateral and sometimes drop-arches, the lancet-arch is the most characteristic. The period is best recognized in England by the great depth given to the hollows of the mouldings, alternating with fillets and rolls, by the decoration of the hollows with the dog-tooth ornament, by the circular abacus of the capitals, and the employment of slender detached shafts of Purbeck marble which are attached to piers by circular moulded shaft-rings (Fr. anneau).

The arches are sometimes cusped; circles with trefoils, quatrefoils, &c., are introduced into the tracery, and large rose windows in the transept or nave, as at Lincoln (1220). The conventional foliage decorating the capitals is of great beauty and variety, and extends to spandrils, bosses, &c. In the spandrils of the arches of the nave, transept or choir arcades, diaper work is occasionally found, as in the transept of Westminster Abbey. The latter is one of the chief examples of the period, to which must be added the cathedral of Salisbury (except the tower); the Galilee at Ely; nave and transept of Wells (1225-1240); nave of Lincoln; west front of Peterborough; and the minster at Beverley.

(R. P. S.)

EARN, the name of a loch and river in Perthshire, Scotland. The loch, lying almost due east and west, is 6½ m. long and 4⁄5 m. in maximum breadth, 287 ft. deep, with a mean depth of 138 ft., covers an area of nearly 4 sq. m., has a drainage basin of over 54½ sq. m., and stands 317 ft. above the sea. Its waters are said never to freeze. It discharges by the river Earn. The points of interest on its shores are Lochearnhead (at the southern extremity of Glen Ogle), which has a station on the Callander-Oban railway, and the ruins of St Blane’s chapel; Edinample Castle, an old turreted mansion belonging to the marquess of Breadalbane, situated in well-wooded grounds near the pretty falls of the Ample; Ardvorlich House, the original of Darlinvarach in Scott’s Legend of Montrose, and the village of St Fillans at the foot of the loch, once the terminus of the branch of the Caledonian railway from Perth. The river flows out of Loch Earn, pursues an eastward course with a gentle inclination towards the south, and reaches the Firth of Tay, 6½ m. below Perth, after a total run of 49 m. Its chief tributaries on the right are the Ruchil, Machany, Ruthven, May and Farg, and on the left, the Lednock and Turret. It is navigable by vessels of 50 tons as far up as Bridge of Earn, and is a notable fishing stream, abounding with salmon and trout, perch and pike being also plentiful. On the Lednock are the falls of the Devil’s Cauldron and on the Turret and its feeders several graceful cascades. The principal places of interest on the banks of the Earn are Dunira, the favourite seat of Henry Dundas, 1st Viscount Melville, who took the title of his barony from the estate and to whose memory an obelisk was raised on the adjoining hill of Dunmore; the village of Comrie; the town of Crieff; the ruined castle of Innerpeffray, founded in 1610 by the 1st Lord Maderty, close to which is the library founded in 1691 by the 3rd Lord Maderty, containing some rare black-letter books and the Bible that belonged to the marquess of Montrose; Gascon Hall, now in ruins, but with traditions reaching back to the days of Wallace; Dupplin Castle, a fine Tudor mansion, seat of the earl of Kinnoull, who derives from it the title of his viscounty; Aberdalgie, Forgandenny and Bridge of Earn, a health resort situated amidst picturesque surroundings. Strathearn, as the valley of the Earn is called, extending from the loch to the Firth of Tay, is a beautiful and, on the whole, fertile tract, though liable at times to heavy floods. The earl of Perth is hereditary steward of Strathearn.

EARNEST (probably a corruption of the obsolete arles or erles, adapted from Lat. equivalent arrha, due to a confusion with the adjective “earnest,” serious, O. Eng. eornust, cognate with Ger. ernst), the payment of a sum of money by the buyer of goods to the seller on the conclusion of a bargain as a pledge for its due performance. It is almost similar to the arrha of the Roman law, which may be traced back in the history of legal institutions to a period when the validity of a contract depended not so much upon the real intention of the parties, as upon the due observance of a prescribed ceremony. But earnest was never part payment, which arrha might have been. Apart from its survival as a custom, its chief importance in English law is its recognition by the Statute of Frauds as giving validity to contracts for the sale of goods of a value exceeding £10 (see Sale of Goods). It is in that statute clearly distinguished from part payment, consequently any sum, however small, would be sufficient as earnest, being given as a token that the contract is binding and should be expressly stated so by the giver. The giving of earnest, or hand-money, as it is sometimes called, has now fallen into very general disuse.

EAR-RING, an ornament worn pendent from the ear, and generally suspended (especially among the more civilized races) by means of a ring or hook passing through the pendulous lobe of the ear. Among savage races the impulse to decorate, or at any rate to modify the appearance of the ear, is almost universal. With such peoples the ear appendage is chiefly remarkable for its extravagant dimensions. Many examples may be seen in the ethnographic galleries of the British Museum. The Berawan people of Borneo use plugs through the lobe of the ear 3¾ in. in diameter. More extraordinary still is an example of a stone ear-plug worn by a Masai, 4½ in. in diameter and weighing 2 ℔ 14 oz. (Man, 1905, p. 22). It is stated that according to the Masai standard of fashion, the lobes of the ears should be enlarged so as to be capable of meeting above the head. Among the superior races, though ear ornaments of extravagant size and elaboration are not unknown, moderation in size is commonly observed, and greater attention is paid to workmanship and fineness of material.

From La Grande Encyclopédie.

Fig. 1.—Ear-ring from an Assyrian bas relief.

From La Grande Encyclopédie.

Fig. 2.—Thetis crossing the sea, with the armour of Achilles. Ear-ring from the Crimea, Hermitage museum.

The general usage appears to have been to have ear-rings worn in pairs, the two ornaments in all respects resembling each other; in ancient times, or more recently among Oriental races, a single ear-ring has sometimes been worn. The use of this kind of ornament, which constantly was of great value, dates from the remotest historical antiquity, the earliest mention of ear-rings occurring in the book of Genesis. It appears probable that the ear-rings of Jacob’s family, which he buried with his strange idols at Bethel, were regarded as amulets or talismans, such unquestionably being the estimation in which some ornaments of this class have been held from a very early period, as they still are held in the East. Thus in New Zealand ear-rings are decorated with the teeth of enemies, and with talismanic sharks’ teeth. Among all the Oriental races of whom we have any accurate knowledge, the Hebrews and Egyptians excepted, ear-rings always have been in general use by both sexes; while in the West, as well as by the Hebrews and Egyptians, as a general rule they have been considered exclusively female ornaments. By the Greeks and Romans also ear-rings were worn only by women, and the wearing of them by a man is often spoken of as distinctively oriental.

In archaic art, ear-rings are frequently represented or their traces are left in the perforated ear lobes of early statues. After the 4th century such perforations occur seldom. In one instance, a Greek inscription records the weight of the detachable gold ornaments on a statue, among which a pair of ear-rings is included. Ear-rings of characteristic form are frequently discovered by excavation. In Egypt, a system of pendent chains is found hanging from a disk. In Assyria the decoration consists of pendants or knobs attached to a rigid ring. In the early civilization represented by Dr Schliemann’s Trojan investigations, pieces of gold plate are suspended by parallel chains. In the Mycenaean period, ear-rings are infrequent in Greece, but have been found in abundance in the Mycenaean finds of Enkomi (Cyprus) in the form of pendent bulls’-heads, or of decorative forms based on the bull’s head. In the tombs of the Greek settlers in the Crimea (4th century B.C.), ear-rings are found of marvellous complexity and beauty. The lexicographer Pollux, speaking of the names given to ear-rings, derived from their forms, mentions caryatids, hippocamps and centauresses. Jewels of the same class, of exquisite beauty and of workmanship that is truly wonderful, have been rescued from the sepulchres of ancient Etruria. Ear-rings of comparatively simple forms, but set with pearls and other stones, were the mode in Rome. In some instances, the stones were of fabulous value. During the Byzantine period they once more attained an extravagant size. Researches among the burial places of Anglo-Saxon Britain have led to the discovery of jewels in considerable numbers, which among their varieties include ear-rings executed in a style that proves the Anglo-Saxons to have made no inconsiderable advances in the arts of civilization.

These same ornaments, which never have fallen into disuse, enjoy at the present day a considerable degree of favour, and the tide of fashion has set towards their increased use. Like all other modern jewels, however, the ear-rings of our own times as works of art can claim no historical attributes, because they consist as well of reproductions from all past ages and of every race as of fanciful productions that certainly can be assigned to no style of art whatever. As one of the curiosities of the subject it may be mentioned that Antonia, wife of Drusus, is said by Pliny to have attached a pair of ear-rings to her pet lamprey.

EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. ἔραζε, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in the Lat. arare, obsolete Eng. “ear,” and Gr. ἀροῦν, but this is now considered very doubtful; see G. Curtius, Greek Etymology, Eng. trans., i. 426; Max Müller, Lectures, 8th ed. i. 294). From early times the word “earth” has been used in several connexions—from that of soil or ground to that of the planet which we inhabit, but it is difficult to trace the exact historic sequence of the diverse usages. In the cosmogony of the Pythagoreans, Platonists and other philosophers, the term or its equivalent denoted an element or fundamental quality which conferred upon matter the character of earthiness; and in the subsequent development of theories as to the ultimate composition of matter by the alchemists, iatrochemists, and early phlogistonists an element of the same name was retained (see Element). In modern chemistry, the common term “earth” is applied to certain oxides:—the ”alkaline earths” (q.v.) are the oxides of calcium (lime), barium (baryta) and strontium (strontia); the ”rare earths” (q.v.) are the oxides of a certain class of rare metals.

The Earth

The terrestrial globe is a member of the Solar system, the third in distance from the Sun, and the largest within the orbit of Jupiter. In the wider sense it may be regarded as composed of a gaseous atmosphere (see Meteorology), which encircles the crust or lithosphere (see Geography), and surface waters or hydrosphere (see Ocean and Oceanography). The description of the surface features is a branch of Geography, and the discussions as to their origin and permanence belongs to Physiography (in the narrower sense), physiographical geology, or physical geography. The investigation of the crust belongs to geology and of rocks in particular to petrology.

In the present article we shall treat the subject matter of the Earth as a planet under the following headings:—(1) Figure and Size, (2) Mass and Density, (3) Astronomical Relations, (4) Evolution and Age. These subjects will be treated summarily, readers being referred to the article Astronomy and to the cross-references for details.

1. Figure and Size.—To primitive man the Earth was a flat disk with its surface diversified by mountains, rivers and seas. In many cosmogonies this disk was encircled by waters, unmeasurable by man and extending to a junction with the sky; and the disk stood as an island rising up through the waters from the floor of the universe, or was borne as an immovable ship on the surface. Of such a nature was the cosmogony of the Babylonians and Hebrews; Homer states the same idea, naming the encircling waters Ὠκεανός; and Hesiod regarded it as a disk midway between the sky and the infernal regions. The theory that the Earth extended downwards to the limit of the universe was subjected to modification when it was seen that the same sun and stars reappeared in the east after their setting in the west. But man slowly realized that the earth was isolated in space, floating freely as a balloon, and much speculation was associated about that which supported the Earth. Tunnels in the foundations to permit the passage of the sun and stars were suggested; the Greeks considered twelve columns to support the heavens, and in their mythology the god Atlas appears condemned to support the columns; while the Egyptians had the Earth supported by four elephants, which themselves stood on a tortoise swimming on a sea. Earthquakes were regarded as due to a movement of these foundations; in Japan this was considered to be due to the motion of a great spider, an animal subsequently replaced by a cat-fish; in Mongolia it is a hog; in India, a mole; in some parts of South America, a whale; and among some of the North American Indians, a giant tortoise.

The doctrine of the spherical form has been erroneously assigned to Thales; but he accepted the Semitic conception of the disk, and regarded the production of springs after earthquakes as due to the inrushing of the waters under the Earth into fissures in the surface. His pupil, Anaximander (610-547), according to Diogenes Laërtius, believed it to be spherical (see The Observatory, 1894, P. 208); and Anaximenes probably held a similar view. The spherical form is undoubtedly a discovery of Pythagoras, and was taught by the Pythagoreans and by the Eleatic Parmenides. The expositor of greatest moment was Aristotle; his arguments are those which we employ to-day:—the ship gradually disappearing from hull to mast as it recedes from the harbour to the horizon; the circular shadow cast by the Earth on the Moon during an eclipse, and the alteration in the appearance of the heavens as one passes from point to point on the Earth’s surface. He records attempts made to determine the circumference; but the first scientific investigation in this direction was made 150 years later by Eratosthenes. The spherical form, however, only became generally accepted after the Earth’s circumnavigation (see Geography).

The historical development of the methods for determining the figure of the Earth (by which we mean a theoretical surface in part indicated by the ocean at rest, and in other parts by the level to which water freely communicating with the oceans by canals traversing the land masses would rise) and the mathematical investigation of this problem are treated in the articles Earth, Figure of the, and Geodesy; here the results are summarized. Sir Isaac Newton deduced from the mechanical consideration of the figure of equilibrium of a mass of rotating fluid, the form of an oblate spheroid, the ellipticity of a meridian section being 1/231, and the axes in the ratio 230 : 231. Geodetic measurements by the Cassinis and other French astronomers pointed to a prolate form, but the Newtonian figure was proved to be correct by the measurement of meridional arcs in Peru and Lapland by the expeditions organized by the French Academy of Sciences. More recent work points to an elliptical equatorial section, thus making the earth pear-shaped. The position of the longer axis is somewhat uncertain; it is certainly in Africa, Clarke placing it in longitude 8° 15′ W., and Schubert in longitude 41° 4′ E.; W.J. Sollas, arguing from terrestrial symmetry, has chosen the position lat. 6° N., long. 28° E., i.e. between Clarke’s and Schubert’s positions. For the lengths of the axes and the ellipticity of the Earth, see Earth, Figure of the.

2. Mass and Density.—The earliest scientific investigation on the density and mass of the Earth (the problem is really single if the volume of the Earth be known) was made by Newton, who, mainly from astronomical considerations, suggested the limiting densities 5 and 6; it is remarkable that this prophetic guess should be realized, the mean value from subsequent researches being about 5½, which gives for the mass the value 6 × 1021 tons. The density of the Earth has been determined by several experimenters within recent years by methods described in the article Gravitation; the most probable value is there stated to be 5.527.

3. Astronomical Relations.—The grandest achievements of astronomical science are undoubtedly to be associated with the elucidation of the complex motion of our planet. The notion that the Earth was fixed and immovable at the centre of an immeasurable universe long possessed the minds of men; and we find the illustrious Ptolemy accepting this view in the 2nd century A.D., and rejecting the notion of a rotating Earth—a theory which had been proposed as early as the 5th century B.C. by Philolaus on philosophical grounds, and in the 3rd century B.C. by the astronomer Aristarchus of Samos. He argued that if the Earth rotated then points at the equator had the enormous velocity of about 1000 m. per hour, and as a consequence there should be terrific gales from the east; the fact that there were no such gales invalidated, in his opinion, the theory. The Ptolemaic theory was unchallenged until 1543, in which year the De Revolutionibus orbium Celestium of Copernicus was published. In this work it was shown that the common astronomical phenomena could be more simply explained by regarding the Earth as annually revolving about a fixed Sun, and daily rotating about itself. A clean sweep was made of the geocentric epicyclic motions of the planets which Ptolemy’s theory demanded, and in place there was substituted a procession of planets about the Sun at different distances. The development of the Copernican theory—the corner-stone of modern astronomy—by Johann Kepler and Sir Isaac Newton is treated in the article Astronomy: History; here we shall summarily discuss the motions of our planet and its relation to the solar system.

The Earth has two principal motions—revolution about the Sun, rotation about its axis; there are in addition a number of secular motions.

Revolution.—The Earth revolves about the Sun in an elliptical orbit having the Sun at one focus. The plane of the orbit is termed the ecliptic; it is inclined to the Earth’s equator at an angle termed the obliquity, and the points of intersection of the equator and ecliptic are termed the equinoctial points. The major axis of the ellipse is the line of apsides; when the Earth is nearest the Sun it is said to be in perihelion, when farthest it is in aphelion. The mean distance of the Earth from the Sun is a most important astronomical constant, since it is the unit of linear measurement; its value is about 93,000,000 m., and the difference between the perihelion and aphelion distances is about 3,000,000 m. The eccentricity of the orbit is 0.016751. A tabular comparison of the orbital constants of the Earth and the other planets is given in the article Planet. The period of revolution with regard to the Sun, or, in other words, the time taken by the Sun apparently to pass from one equinox to the same equinox, is the tropical or equinoctial year; its length is 365 d. 5 hrs. 48 m. 46 secs. It is about 20 minutes shorter than the true or sidereal year, which is the time taken for the Sun apparently to travel from one star to it again. The difference in these two years is due to the secular variation termed precession (see below). A third year is named the anomalistic year, which is the time occupied in the passage from perihelion to perihelion; it is a little longer than the sidereal.

Rotation.—The Earth rotates about an axis terminating at the north and south geographical poles, and perpendicular to the equator; the period of rotation is termed the day (q.v.), of which several kinds are distinguished according to the body or point of reference. The rotation is performed from west to east; this daily rotation occasions the diurnal motion of the celestial sphere, the rising of the Sun and stars in the east and their setting in the west, and also the phenomena of day and night. The inclination of the axis to the ecliptic brings about the presentation of places in different latitudes to the more direct rays of the sun; this is revealed in the variation in the length of daylight with the time of the year, and the phenomena of seasons.

Although the rotation of the Earth was an accepted fact soon after its suggestion by Copernicus, an experimental proof was wanting until 1851, when Foucault performed his celebrated pendulum experiment at the Pantheon, Paris. A pendulum about 200 ft. long, composed of a flexible wire carrying a heavy iron bob, was suspended so as to be free to oscillate in any direction. The bob was provided with a style which passed over a table strewn with fine sand, so that the style traced the direction in which the bob was swinging. It was found that the oscillating pendulum never retraced its path, but at each swing it was apparently deviated to the right, and moreover the deviations in equal times were themselves equal. This means that the floor of the Pantheon was moving, and therefore the Earth was rotating. If the pendulum were swung in the southern hemisphere, the deviation would be to the left; if at the equator it would not deviate, while at the poles the plane of oscillation would traverse a complete circle in 24 hours.

The rotation of the Earth appears to be perfectly uniform, comparisons of the times of transits, eclipses, &c., point to a variation of less than 1⁄100th of a second since the time of Ptolemy. Theoretical investigations on the phenomena of tidal friction point, however, to a retardation, which may to some extent be diminished by the accelerations occasioned by the shrinkage of the globe, and some other factors difficult to evaluate (see Tide).

We now proceed to the secular variations.

Precession.—The axis of the earth does not preserve an invariable direction in space, but in a certain time it describes a cone, in much the same manner as the axis of a top spinning out of the vertical. The equator, which preserves approximately the same inclination to the ecliptic (there is a slight variation in the obliquity which we shall mention later), must move so that its intersections with the ecliptic, or equinoctial points, pass in a retrograde direction, i.e. opposite to that of the Earth. This motion is termed the precession of the equinoxes, and was observed by Hipparchus in the 2nd century B.C.; Ptolemy corrected the catalogue of Hipparchus for precession by adding 2° 40′ to the longitudes, the latitudes being unaltered by this motion, which at the present time is 50.26″ annually, the complete circuit being made in about 26,000 years. Owing to precession the signs of the zodiac are traversing paths through the constellations, or, in other words, the constellations are continually shifting with regard to the equinoctial points; at one time the vernal equinox Aries was in the constellations of that name; it is now in Pisces, and will then pass into Aquarius. The pole star, i.e. the star towards which the Earth’s axis points, is also shifting owing to precession; in about 2700 B.C. the Chinese observed α Draconis as the pole star (at present α Ursae minoris occupies this position and will do so until 3500); in 13600 Vega (α Lyrae) the brightest star in the Northern hemisphere, will be nearest.

Precession is the result of the Sun and the Moon’s attraction on the Earth not being a single force through its centre of gravity. If the Earth were a homogeneous sphere the attractions would act through the centre, and such forces would have no effect upon the rotation about the centre of gravity, but the Earth being spheroidal the equatorial band which stands up as it were beyond the surface of a sphere is more strongly attracted, with the result that the axis undergoes a tilting. The precession due to the Sun is termed the solar precession and that due to the Moon the lunar precession; the joint effect (two-thirds of which is due to the Moon) is the luni-solar precession. Solar precession is greatest at the solstices and zero at the equinoxes; the part of luni-solar precession due to the Moon varies with the position of the Moon in its orbit. The obliquity is unchanged by precession (see Precession of the Equinoxes).

Nutation.—In treating precession we have stated that the axis of the Earth traces a cone, and it follows that the pole describes a circle (approximately) on the celestial sphere, about the pole of the ecliptic. This is not quite true. Irregularities in the attracting forces which occasion precession also cause a slight oscillation backwards and forwards over the mean precessional path of the pole, the pole tracing a wavy line or nodding. Both the Sun and Moon contribute to this effect. Solar nutation depends upon the position of the Sun on the ecliptic; its period is therefore 1 year, and in extent it is only 1.2″; lunar nutation depends upon the position of the Moon’s nodes; its period is therefore about 18.6 years, the time of revolution of the nodes, and its extent is 9.2″. There is also given to the obliquity a small oscillation to and fro. Nutation is one of the great discoveries of James Bradley (1747).

Planetary Precession.—So far we have regarded the ecliptic as absolutely fixed, and treated precession as a real motion of the equator. The ecliptic (q.v.), however, is itself subject to a motion, due to the attractions of the planets on the Earth. This effect also displaces the equinoctial points. Its annual value is 0.13″. The term General Precession in longitude is given to the displacement of the intersection of the equator with the apparent ecliptic on the latter. The standard value is 50.2453″, which prevailed in 1850, and the value at 1850 + t, i.e. the constant of precession, is 50.2453″ + 0.0002225″ t. This value is also liable to a very small change. The nutation of the obliquity at time 1850 + t is given by the formula 23° 27′ 32.0″ − 0.47″ t. Complete expressions for these functions are given in Newcomb’s Spherical Astronomy (1908), and in the Nautical Almanac.

The variation of the line of apsides is the name given to the motion of the major axis of the Earth’s orbit along the ecliptic. It is due to the general influence of the planets, and the revolution is effected in 21,000 years.

The variation of the eccentricity denotes an oscillation of the form of the Earth’s orbit between a circle and ellipse. This followed the mathematical researches of Lagrange and Leverrier. It was suggested by Sir John Herschel in 1830 that this variation might occasion great climatic changes, and James Croll developed the theory as affording a solution of the glacial periods in geology (q.v.).

Variation of Latitude.—Another secular motion of the Earth is due to the fact that the axis of rotation is not rigidly fixed within it, but its polar extremities wander in a circle of about 50 ft. diameter. This oscillation brings about a variability in terrestrial latitudes, hence the name. Euler showed mathematically that such an oscillation existed, and, making certain assumptions as to the rigidity of the Earth, deduced that its period was 305 days; S.C. Chandler, from 1890 onwards, deduced from observations of the stars a period of 428 days; and Simon Newcomb explained the deviation of these periods by pointing out that Euler’s assumption of a perfectly rigid Earth is not in accordance with fact. For details of this intricate subject see the articles Latitude and Earth, Figure of the.

4. Evolution and Age.—In its earliest history the mass now consolidated as the Earth and Moon was part of a vast nebulous aggregate, which in the course of time formed a central nucleus—our Sun—which shed its outer layers in such a manner as to form the solar system (see Nebular Theory). The moon may have been formed from the Earth in a similar manner, but the theory of tidal friction suggests the elongation of the Earth along an equatorial axis to form a pear-shaped figure, and that in the course of time the protuberance shot off to form the Moon (see Tide). The age of the Earth has been investigated from several directions, as have also associated questions related to climatic changes, internal temperature, orientation of the land and water (permanence of oceans and continents), &c. These problems are treated in the articles Geology and Geography.

Aristotle regarded the Earth as having an upper inhabited half and a lower uninhabited one, and the air on the lower half as tending to flow upwards through the Earth. The obstruction of this passage brought about an accumulation of air within the Earth, and the increased pressure may occasion oscillations of the surface, which may be so intense as to cause earthquakes.

EARTH, FIGURE OF THE. The determination of the figure of the earth is a problem of the highest importance in astronomy, inasmuch as the diameter of the earth is the unit to which all celestial distances must be referred.

Historical.

Reasoning from the uniform level appearance of the horizon, the variations in altitude of the circumpolar stars as one travels towards the north or south, the disappearance of a ship standing out to sea, and perhaps other phenomena, the earliest astronomers regarded the earth as a sphere, and they endeavoured to ascertain its dimensions. Aristotle relates that the mathematicians had found the circumference to be 400,000 stadia (about 46,000 miles). But Eratosthenes (c. 250 B.C.) appears to have been the first who entertained an accurate idea of the principles on which the determination of the figure of the earth really depends, and attempted to reduce them to practice. His results were very inaccurate, but his method is the same as that which is followed at the present day—depending, in fact, on the comparison of a line measured on the earth’s surface with the corresponding arc of the heavens. He observed that at Syene in Upper Egypt, on the day of the summer solstice, the sun was exactly vertical, whilst at Alexandria at the same season of the year its zenith distance was 7° 12′, or one-fiftieth of the circumference of a circle. He assumed that these places were on the same meridian; and, reckoning their distance apart as 5000 stadia, he inferred that the circumference of the earth was 250,000 stadia (about 29,000 miles). A similar attempt was made by Posidonius, who adopted a method which differed from that of Eratosthenes only in using a star instead of the sun. He obtained 240,000 stadia (about 27,600 miles) for the circumference. Ptolemy in his Geography assigns the length of the degree as 500 stadia.

The Arabs also investigated the question of the earth’s magnitude. The caliph Abdallah al Mamun (A.D. 814), having fixed on a spot in the plains of Mesopotamia, despatched one company of astronomers northwards and another southwards, measuring the journey by rods, until each found the altitude of the pole to have changed one degree. But the result of this measurement does not appear to have been very satisfactory. From this time the subject seems to have attracted no attention until about 1500, when Jean Fernel (1497-1558), a Frenchman, measured a distance in the direction of the meridian near Paris by counting the number of revolutions of the wheel of a carriage. His astronomical observations were made with a triangle used as a quadrant, and his resulting length of a degree was very near the truth.

Willebrord Snell substituted a chain of triangles for actual linear measurement. He measured his base line on the frozen surface of the meadows near Leiden, and measured the angles of his triangles, which lay between Alkmaar and Bergen-op-Zoom, with a quadrant and semicircles. He took the precaution of comparing his standard with that of the French, so that his result was expressed in toises (the length of the toise is about 6.39 English ft.). The work was recomputed and reobserved by P. von Musschenbroek in 1729. In 1637 an Englishman, Richard Norwood, published a determination of the figure of the earth in a volume entitled The Seaman’s Practice, contayning a Fundamentall Probleme in Navigation experimentally verified, namely, touching the Compasse of the Earth and Sea and the quantity of a Degree in our English Measures. He observed on the 11th of June 1633 the sun’s meridian altitude in London as 62° 1′, and on the 6th of June 1635, his meridian altitude in York as 59° 33′. He measured the distance between these places partly with a chain and partly by pacing. By this means, through compensation of errors, he arrived at 367,176 ft. for the degree—a very fair result.

The application of the telescope to angular instruments was the next important step. Jean Picard was the first who in 1669, with the telescope, using such precautions as the nature of the operation requires, measured an arc of meridian. He measured with wooden rods a base line of 5663 toises, and a second or base of verification of 3902 toises; his triangulation extended from Malvoisine, near Paris, to Sourdon, near Amiens. The angles of the triangles were measured with a quadrant furnished with a telescope having cross-wires. The difference of latitude of the terminal stations was determined by observations made with a sector on a star in Cassiopeia, giving 1° 22′ 55″ for the amplitude. The terrestrial measurement gave 78,850 toises, whence he inferred for the length of the degree 57,060 toises.

Hitherto geodetic observations had been confined to the determination of the magnitude of the earth considered as a sphere, but a discovery made by Jean Richer (d. 1696) turned the attention of mathematicians to its deviation from a spherical form. This astronomer, having been sent by the Academy of Sciences of Paris to the island of Cayenne, in South America, for the purpose of investigating the amount of astronomical refraction and other astronomical objects, observed that his clock, which had been regulated at Paris to beat seconds, lost about two minutes and a half daily at Cayenne, and that in order to bring it to measure mean solar time it was necessary to shorten the pendulum by more than a line (about 1⁄12th of an in.). This fact, which was scarcely credited till it had been confirmed by the subsequent observations of Varin and Deshayes on the coasts of Africa and America, was first explained in the third book of Newton’s Principia, who showed that it could only be referred to a diminution of gravity arising either from a protuberance of the equatorial parts of the earth and consequent increase of the distance from the centre, or from the counteracting effect of the centrifugal force. About the same time (1673) appeared Christian Huygens’ De Horologio Oscillatorio, in which for the first time were found correct notions on the subject of centrifugal force. It does not, however, appear that they were applied to the theoretical investigation of the figure of the earth before the publication of Newton’s Principia. In 1690 Huygens published his De Causa Gravitatis, which contains an investigation of the figure of the earth on the supposition that the attraction of every particle is towards the centre.

Between 1684 and 1718 J. and D. Cassini, starting from Picard’s base, carried a triangulation northwards from Paris to Dunkirk and southwards from Paris to Collioure. They measured a base of 7246 toises near Perpignan, and a somewhat shorter base near Dunkirk; and from the northern portion of the arc, which had an amplitude of 2° 12′ 9″, obtained for the length of a degree 56,960 toises; while from the southern portion, of which the amplitude was 6° 18′ 57″, they obtained 57,097 toises. The immediate inference from this was that, the degree diminishing with increasing latitude, the earth must be a prolate spheroid. This conclusion was totally opposed to the theoretical investigations of Newton and Huygens, and accordingly the Academy of Sciences of Paris determined to apply a decisive test by the measurement of arcs at a great distance from each other—one in the neighbourhood of the equator, the other in a high latitude. Thus arose the celebrated expeditions of the French academicians. In May 1735 Louis Godin, Pierre Bouguer and Charles Marie de la Condamine, under the auspices of Louis XV., proceeded to Peru, where, assisted by two Spanish officers, after ten years of laborious exertion, they measured an arc of 3° 7′, the northern end near the equator. The second party consisted of Pierre Louis Moreau de Maupertuis, Alexis Claude Clairault, Charles Étienne Louis Camus, Pierre Charles Lemonnier, and Reginaud Outhier, who reached the Gulf of Bothnia in July 1736; they were in some respects more fortunate than the first party, inasmuch as they completed the measurement of an arc near the polar circle of 57′ amplitude and returned within sixteen months from the date of their departure.

The measurement of Bouguer and De la Condamine was executed with great care, and on account of the locality, as well as the manner in which all the details were conducted, it has always been regarded as a most valuable determination. The southern limit was at Tarqui, the northern at Cotchesqui. A base of 6272 toises was measured in the vicinity of Quito, near the northern extremity of the arc, and a second base of 5260 toises near the southern extremity. The mountainous nature of the country made the work very laborious, in some cases the difference of heights of two neighbouring stations exceeding 1 mile; and they had much trouble with their instruments, those with which they were to determine the latitudes proving untrustworthy. But they succeeded by simultaneous observations of the same star at the two extremities of the arc in obtaining very fair results. The whole length of the arc amounted to 176,945 toises, while the difference of latitudes was 3° 7′ 3″. In consequence of a misunderstanding that arose between De la Condamine and Bouguer, their operations were conducted separately, and each wrote a full account of the expedition. Bouguer’s book was published in 1749; that of De la Condamine in 1751. The toise used in this measure was afterwards regarded as the standard toise, and is always referred to as the Toise of Peru.

The party of Maupertuis, though their work was quickly despatched, had also to contend with great difficulties. Not being able to make use of the small islands in the Gulf of Bothnia for the trigonometrical stations, they were forced to penetrate into the forests of Lapland, commencing operations at Torneå, a city situated on the mainland near the extremity of the gulf. From this, the southern extremity of their arc, they carried a chain of triangles northward to the mountain Kittis, which they selected as the northern terminus. The latitudes were determined by observations with a sector (made by George Graham) of the zenith distance of α and δ Draconis. The base line was measured on the frozen surface of the river Torneå about the middle of the arc; two parties measured it separately, and they differed by about 4 in. The result of the whole was that the difference of latitudes of the terminal stations was 57′ 29″ .6, and the length of the arc 55,023 toises. In this expedition, as well as in that to Peru, observations were made with a pendulum to determine the force of gravity; and these observations coincided with the geodetic results in proving that the earth was an oblate and not prolate spheroid.

In 1740 was published in the Paris Mémoires an account, by Cassini de Thury, of a remeasurement by himself and Nicolas Louis de Lacaille of the meridian of Paris. With a view to determine more accurately the variation of the degree along the meridian, they divided the distance from Dunkirk to Collioure into four partial arcs of about two degrees each, by observing the latitude at five stations. The results previously obtained by J. and D. Cassini were not confirmed, but, on the contrary, the length of the degree derived from these partial arcs showed on the whole an increase with an increasing latitude. Cassini and Lacaille also measured an arc of parallel across the mouth of the Rhone. The difference of time of the extremities was determined by the observers at either end noting the instant of a signal given by flashing gunpowder at a point near the middle of the arc.

While at the Cape of Good Hope in 1752, engaged in various astronomical observations, Lacaille measured an arc of meridian of 1° 13′ 17″, which gave him for the length of the degree 57,037 toises—an unexpected result, which has led to the remeasurement of the arc by Sir Thomas Maclear (see Geodesy).

Passing over the measurements made between Rome and Rimini and on the plains of Piedmont by the Jesuits Ruggiero Giuseppe Boscovich and Giovanni Battista Beccaria, and also the arc measured with deal rods in North America by Charles Mason and Jeremiah Dixon, we come to the commencement of the English triangulation. In 1783, in consequence of a representation from Cassini de Thury on the advantages that would accrue from the geodetic connexion of Paris and Greenwich, General William Roy was, with the king’s approval, appointed by the Royal Society to conduct the operations on the part of England, Count Cassini, Méchain and Delambre being appointed on the French side. A precision previously unknown was attained by the use of Ramsden’s theodolite, which was the first to make the spherical excess of triangles measurable. The wooden rods with which the first base was measured were replaced by glass rods, which were afterwards rejected for the steel chain of Ramsden. (For further details see Account of the Trigonometrical Survey of England and Wales.)

Shortly after this, the National Convention of France, having agreed to remodel their system of weights and measures, chose for their unit of length the ten-millionth part of the meridian quadrant. In order to obtain this length precisely, the remeasurement of the French meridian was resolved on, and deputed to J.B.J. Delambre and Pierre François André Méchain. The details of this operation will be found in the Base du système métrique décimale. The arc was subsequently extended by Jean Baptiste Biot and Dominique François Jean Arago to the island of Iviza. Operations for the connexion of England with the continent of Europe were resumed in 1821 to 1823 by Henry Kater and Thomas Frederick Colby on the English side, and F.J.D. Arago and Claude Louis Mathieu on the French.

The publication in 1838 of Friedrich Wilhelm Bessel’s Gradmessung in Ostpreussen marks an era in the science of geodesy. Here we find the method of least squares applied to the calculation of a network of triangles and the reduction of the observations generally. The systematic manner in which all the observations were taken with the view of securing final results of extreme accuracy is admirable. The triangulation, which was a small one, extended about a degree and a half along the shores of the Baltic in a N.N.E. direction. The angles were observed with theodolites of 12 and 15 in. diameter, and the latitudes determined by means of the transit instrument in the prime vertical—a method much used in Germany. (The base apparatus is described in the article Geodesy.)

The principal triangulation of Great Britain and Ireland, which was commenced in 1783 under General Roy, for the more immediate purpose of connecting the observatories of Greenwich and Paris, had been gradually extended, under the successive direction of Colonel E. Williams, General W. Mudge, General T.F. Colby, Colonel L.A. Hall, and Colonel Sir Henry James; it was finished in 1851. The number of stations is about 250. At 32 of these the latitudes were determined with Ramsden’s and Airy’s zenith sectors. The theodolites used for this work were, in addition to the two great theodolites of Ramsden which were used by General Roy and Captain Kater, a smaller theodolite of 18 in. diameter by the same mechanician, and another of 24 in. diameter by Messrs Troughton and Simms. Observations for determination of absolute azimuth were made with those instruments at a large number of stations; the stars α, δ, and λ Ursae Minoris and 51 Cephei being those observed always at the greatest azimuths. At six of these stations the probable error of the result is under 0.4″, at twelve under 0.5″, at thirty-four under 0.7″: so that the absolute azimuth of the whole network is determined with extreme accuracy. Of the seven base lines which have been measured, five were by means of steel chains and two with Colby’s compensation bars (see Geodesy). The triangulation was computed by least squares. The total number of equations of condition for the triangulation is 920; if therefore the whole had been reduced in one mass, as it should have been, the solution of an equation of 920 unknown quantities would have occurred as a part of the work. To avoid this an approximation was resorted to; the triangulation was divided into twenty-one parts or figures; four of these, not adjacent, were first adjusted by the method explained, and the corrections thus determined in these figures carried into the equations of condition of the adjacent figures. The average number of equations in a figure is 44; the largest equation is one of 77 unknown quantities. The vertical limb of Airy’s zenith sector is read by four microscopes, and in the complete observation of a star there are 10 micrometer readings and 12 level readings. The instrument is portable; and a complete determination of latitude, affected with the mean of the declination errors of two stars, is effected by two micrometer readings and four level readings. The observation consists in measuring with the telescope micrometer the difference of zenith distances of two stars which cross the meridian, one to the north and the other to the south of the observer at zenith distances which differ by not much more than 10′ or 15′, the interval of the times of transit being not less than one nor more than twenty minutes. The advantages are that, with simplicity in the construction of the instrument and facility in the manipulation, refraction is eliminated (or nearly so, as the stars are generally selected within 25° of the zenith), and there is no large divided circle. The telescope, which is counterpoised on one side of the vertical axis, has a small circle for finding, and there is also a small horizontal circle. This instrument is universally used in American geodesy.

The principal work containing the methods and results of these operations was published in 1858 with the title “Ordnance Trigonometrical Survey of Great Britain and Ireland. Account of the observations and calculations of the principal triangulation and of the figure, dimensions and mean specific gravity of the earth as derived therefrom. Drawn up by Captain Alexander Ross Clarke, R.E., F.R.A.S., under the direction of Lieut.-Colonel H. James, R.E., F.R.S., M.R.I.A., &c.” A supplement appeared in 1862: “Extension of the Triangulation of the Ordnance Survey into France and Belgium, with the measurement of an arc of parallel in 52° N. from Valentia in Ireland to Mount Kemmel in Belgium. Published by ... Col. Sir Henry James.”

Extensive operations for surveying India and determining the figure of the earth were commenced in 1800. Colonel W. Lambton started the great meridian arc at Punnae in latitude 8° 9′, and, following generally the methods of the English survey, he carried his triangulation as far north as 20° 30′. The work was continued by Sir George (then Captain) Everest, who carried it to the latitude of 29° 30′. Two admirable volumes by Sir George Everest, published in 1830 and in 1847, give the details of this undertaking. The survey was afterwards prosecuted by Colonel T.T. Walker, R.E., who made valuable contributions to geodesy. The working out of the Indian chains of triangle by the method of least squares presents peculiar difficulties, but, enormous in extent as the work was, it has been thoroughly carried out. The ten base lines on which the survey depends were measured with Colby’s compensation bars.

The survey is detailed in eighteen volumes, published at Dehra Dun, and entitled Account of the Operations of the Great Trigonometrical Survey of India. Of these the first nine were published under the direction of Colonel Walker; and the remainder by Colonels Strahan and St G.C. Gore, Major S.G. Burrard and others. Vol. i., 1870, treats of the base lines; vol. ii., 1879, history and general descriptions of the principal triangulation and of its reduction; vol. v., 1879, pendulum operations (Captains T.P. Basevi and W.T. Heaviside); vols. xi., 1890, and xviii., 1906, latitudes; vols. ix., 1883, x., 1887, xv., 1893, longitudes; vol. xvii., 1901, the Indo-European longitude-arcs from Karachi to Greenwich. The other volumes contain the triangulations.

In 1860 Friedrich Georg Wilhelm Struve published his Arc du méridien de 25° 20′ entre le Danube et la Mer Glaciale mesuré depuis 1816 jusqu’en 1855. The latitudes of the thirteen astronomical stations of this arc were determined partly with vertical circles and partly by means of the transit instrument in the prime vertical. The triangulation, a great part of which, however, is a simple chain of triangles, is reduced by the method of least squares, and the probable errors of the resulting distances of parallels is given; the probable error of the whole arc in length is ± 6.2 toises. Ten base lines were measured. The sum of the lengths of the ten measured bases is 29,863 toises, so that the average length of a base line is 19,100 ft. The azimuths were observed at fourteen stations. In high latitudes the determination of the meridian is a matter of great difficulty; nevertheless the azimuths at all the northern stations were successfully determined,—the probable error of the result at Fuglenaes being ± 0″.53.

Before proceeding with the modern developments of geodetic measurements and their application to the figure of the earth, we must discuss the “mechanical theory,” which is indispensable for a full understanding of the subject.

Mechanical Theory.

Newton, by applying his theory of gravitation, combined with the so-called centrifugal force, to the earth, and assuming that an oblate ellipsoid of rotation is a form of equilibrium for a homogeneous fluid rotating with uniform angular velocity, obtained the ratio of the axes 229:230, and the law of variation of gravity on the surface. A few years later Huygens published an investigation of the figure of the earth, supposing the attraction of every particle to be towards the centre of the earth, obtaining as a result that the proportion of the axes should be 578 : 579. In 1740 Colin Maclaurin, in his De causa physica fluxus et refluxus maris, demonstrated that the oblate ellipsoid of revolution is a figure which satisfies the conditions of equilibrium in the case of a revolving homogeneous fluid mass, whose particles attract one another according to the law of the inverse square of the distance; he gave the equation connecting the ellipticity with the proportion of the centrifugal force at the equator to gravity, and determined the attraction on a particle situated anywhere on the surface of such a body. In 1743 Clairault published his Théorie de la figure de la terre, which contains a remarkable theorem (“Clairault’s Theorem”), establishing a relation between the ellipticity of the earth and the variation of gravity from the equator to the poles. Assuming that the earth is composed of concentric ellipsoidal strata having a common axis of rotation, each stratum homogeneous in itself, but the ellipticities and densities of the successive strata varying according to any law, and that the superficial stratum has the same form as if it were fluid, he proved that

g′ − g + e = 5 m,

g 2

where g, g′ are the amounts of gravity at the equator and at the pole respectively, e the ellipticity of the meridian (or “flattening”), and m the ratio of the centrifugal force at the equator to g. He also proved that the increase of gravity in proceeding from the equator to the poles is as the square of the sine of the latitude. This, taken with the former theorem, gives the means of determining the earth’s ellipticity from observation of the relative force of gravity at any two places. P.S. Laplace, who devoted much attention to the subject, remarks on Clairault’s work that “the importance of all his results and the elegance with which they are presented place this work amongst the most beautiful of mathematical productions” (Isaac Todhunter’s History of the Mathematical Theories of Attraction and the Figure of the Earth, vol. i. p. 229).

The problem of the figure of the earth treated as a question of mechanics or hydrostatics is one of great difficulty, and it would be quite impracticable but for the circumstance that the surface differs but little from a sphere. In order to express the forces at any point of the body arising from the attraction of its particles, the form of the surface is required, but this form is the very one which it is the object of the investigation to discover; hence the complexity of the subject, and even with all the present resources of mathematicians only a partial and imperfect solution can be obtained.

We may here briefly indicate the line of reasoning by which some of the most important results may be obtained. If X, Y, Z be the components parallel to three rectangular axes of the forces acting on a particle of a fluid mass at the point x, y, z, then, p being the pressure there, and ρ the density,

dp = ρ(Xdx + Ydy + Zdz);

and for equilibrium the necessary conditions are, that ρ(Xdx + Ydy + Zdz) be a complete differential, and at the free surface Xdx + Ydy + Zdz = 0. This equation implies that the resultant of the forces is normal to the surface at every point, and in a homogeneous fluid it is obviously the differential equation of all surfaces of equal pressure. If the fluid be heterogeneous then it is to be remarked that for forces of attraction according to the ordinary law of gravitation, if X, Y, Z be the components of the attraction of a mass whose potential is V, then

Xdx + Ydy + Zdz = dV dx + dV dy + dV dz,

dx dy dz

which is a complete differential. And in the case of a fluid rotating with uniform velocity, in which the so-called centrifugal force enters as a force acting on each particle proportional to its distance from the axis of rotation, the corresponding part of Xdx + Ydy + Zdz is obviously a complete differential. Therefore for the forces with which we are now concerned Xdx + Ydy + Zdz = dU, where U is some function of x, y, z, and it is necessary for equilibrium that dp = ρdU be a complete differential; that is, ρ must be a function of U or a function of p, and so also p a function of U. So that dU = 0 is the differential equation of surfaces of equal pressure and density.

We may now show that a homogeneous fluid mass in the form of an oblate ellipsoid of revolution having a uniform velocity of rotation can be in equilibrium. It may be proved that the attraction of the ellipsoid x² + y² + z²(1 + ε²) = c²(1 + ε²); upon a particle P of its mass at x, y, z has for components

X = − Ax, Y = − Ay, Z = − Cz,

where

A = 2πk²ρ( 1 + ε² tan−1ε − 1 ),

ε³ ε²

C = 4πk²ρ( 1 + ε² − 1 + ε² tan−1ε),

ε² ε³

and k² the constant of attraction. Besides the attraction of the mass of the ellipsoid, the centrifugal force at P has for components + xω², + yω², 0; then the condition of fluid equilibrium is

(A − ω²)xdx + (A − ω²)ydy + Czdz = 0,

which by integration gives

(A − ω²)(x² + y²) + Cz² = constant.

This is the equation of an ellipsoid of rotation, and therefore the equilibrium is possible. The equation coincides with that of the surface of the fluid mass if we make

A − ω² = C / (1 + ε²),

which gives

ω² = 3 + ε² tan−1ε − 3 .

2πk²ρ ε³ ε²

In the case of the earth, which is nearly spherical, we obtain by expanding the expression for ω² in powers of ε², rejecting the higher powers, and remarking that the ellipticity e = ½ε²,

ω² / 2πk²ρ = 4ε² / 15 = 8e / 15.

Now if m be the ratio of the centrifugal force to the intensity of gravity at the equator, and a = c(1 + e), then

m = aω² / 4⁄3πk²ρa, ∴ ω² / 2πk²ρ = 2⁄3m.

In the case of the earth it is a matter of observation that m = 1/289, hence the ellipticity

e = 5m / 4 = 1/231,

so that the ratio of the axes on the supposition of a homogeneous fluid earth is 230 : 231, as stated by Newton.

Now, to come to the case of a heterogeneous fluid, we shall assume that its surfaces of equal density are spheroids, concentric and having a common axis of rotation, and that the ellipticity of these surfaces varies from the centre to the outer surface, the density also varying. In other words, the body is composed of homogeneous spheroidal shells of variable density and ellipticity. On this supposition we shall express the attraction of the mass upon a particle in its interior, and then, taking into account the centrifugal force, form the equation expressing the condition of fluid equilibrium. The attraction of the homogeneous spheroid x² + y² + z²(1 + 2e) = c²(1 + 2e), where e is the ellipticity (of which the square is neglected), on an internal particle, whose co-ordinates are x = f, y = 0, z = h, has for its x and z components

X′ = −4⁄3πk²ρf(1 − 2⁄5e), Z′ = −4⁄3πk²ρh(1 + 4⁄5e),

the Y component being of course zero. Hence we infer that the attraction of a shell whose inner surface has an ellipticity e, and its outer surface an ellipticity e + de, the density being ρ, is expressed by

dX′ = 4⁄3 · 2⁄5πk²ρf de, dZ′ = −4⁄3 · 4⁄5πk²ρh de.

To apply this to our heterogeneous spheroid; if we put c1 for the semiaxis of that surface of equal density on which is situated the attracted point P, and c0 for the semiaxis of the outer surface, the attraction of that portion of the body which is exterior to P, namely, of all the shells which enclose P, has for components

X0 = 8⁄15πk²f ∫c0c1 ρ de dc, Z0 = 16⁄15πk²h ∫c0c1 ρ de dc,

dc dc

both e and ρ being functions of c. Again the attraction of a homogeneous spheroid of density ρ on an external point f, h has the components

X″ = −4⁄3πk²ρfr−3 {c³(1 + 2e) − λec5},

Z″ = −4⁄3πk²ρhr−3 {c³(1 + 2e) − λ′ec5},

where λ = 3⁄5(4h² − f²) / r4, λ′ = 3⁄5(2h² − 3f²) / r4, and r² = f² + h².

Now e being considered a function of c, we can at once express the attraction of a shell (density ρ) contained between the surface defined by c + dc, e + de and that defined by c, e upon an external point; the differentials with respect to c, viz. dX″ dZ″, must then be integrated with ρ under the integral sign as being a function of c. The integration will extend from c = 0 to c = c1. Thus the components of the attraction of the heterogeneous spheroid upon a particle within its mass, whose co-ordinates are f, 0, h, are

X = −4⁄3πk²f [ 1 ∫c10 ρ d{c³(1 + 2e)} − λ ∫c10 ρ d(ec5) + 2⁄5 ∫c0c1 ρ de],

r3 r3

Z = −4⁄3πk²h [ 1 ∫c10 ρ d{c³(1 + 2e)} − λ′ ∫c10 ρ d(ec5) + 4⁄5 ∫c0c1 ρ de].

r3 r3

We take into account the rotation of the earth by adding the centrifugal force fω² = F to X. Now, the surface of constant density upon which the point f, 0, h is situated gives (1 − 2e) fdf + hdh = 0; and the condition of equilibrium is that (X + F)df + Zdh = 0. Therefore,

(X + F) h = Zf (1 − 2e),

which, neglecting small quantities of the order e² and putting ω²t² = 4π²k², gives

2e ∫c10 ρd{c³(1 + 2e)} − 6 ∫c10 ρd(ec5) − 6 ∫c10 ρde = 3π .

r³ 5r5 5 t²

Here we must now put c for c1, c for r; and 1 + 2e under the first integral sign may be replaced by unity, since small quantities of the second order are neglected. Two differentiations lead us to the following very important differential equation (Clairault):

d²e + 2ρc² · de + ( 2ρc − 6 ) e = 0.

dc² ∫ρc² dc dc ∫ρc² dc c²

When ρ is expressed in terms of c, this equation can be integrated. We infer then that a rotating spheroid of very small ellipticity, composed of fluid homogeneous strata such as we have specified, will be in equilibrium; and when the law of the density is expressed, the law of the corresponding ellipticities will follow.

If we put M for the mass of the spheroid, then

M = 4π ∫c0 ρd{c³(1 + 2e)}; and m = c³ · 4π² ,

3 M t²

and putting c = c0 in the equation expressing the condition of equilibrium, we find

M(2e − m) = 4 π · 6 ∫c0 ρ d(ec5).

3 5c²

Making these substitutions in the expressions for the forces at the surface, and putting r/c = 1 + e − e(h/c)², we get

G cos φ = Mk² {1 − e − 3 m + ( 5 m − 2e) h² } f

ac 2 2 c² c

G sin φ = Mk² {1 + e − 3 m + ( 5 m − 2e) h² } h .

ac 2 2 c² c

Here G is gravity in the latitude φ, and a the radius of the equator. Since

sec φ = (c/f){1 + e + (eh²/c²)},

G = Mk² {1 − 3 m +( 5 m − e) sin² φ},

ac 2 2

an expression which contains the theorems we have referred to as discovered by Clairault.

The theory of the figure of the earth as a rotating ellipsoid has been especially investigated by Laplace in his Mécanique celeste. The principal English works are:—Sir George Airy, Mathematical Tracts, a lucid treatment without the use of Laplace’s coefficients; Archdeacon Pratt’s Attractions and Figure of the Earth; and O’Brien’s Mathematical Tracts; in the last two Laplace’s coefficients are used.

In 1845 Sir G.G. Stokes (Camb. Trans. viii.; see also Camb. Dub. Math. Journ., 1849, iv.) proved that if the external form of the sea—imagined to percolate the land by canals—be a spheroid with small ellipticity, then the law of gravity is that which we have shown above; his proof required no assumption as to the ellipticity of the internal strata, or as to the past or present fluidity of the earth. This investigation admits of being regarded conversely, viz. as determining the elliptical form of the earth from measurements of gravity; if G, the observed value of gravity in latitude φ, be expressed in the form G = g(1 + β sin² φ), where g is the value at the equator and β a coefficient. In this investigation, the square and higher powers of the ellipticity are neglected; the solution was completed by F.R. Helmert with regard to the square of the ellipticity, who showed that a term with sin² 2φ appeared (see Helmert, Geodäsie, ii. 83). For the coefficient of this term, the gravity measurements give a small but not sufficiently certain value; we therefore assume a value which agrees best with the hypothesis of the fluid state of the entire earth; this assumption is well supported, since even at a depth of only 50 km. the pressure of the superincumbent crust is so great that rocks become plastic, and behave approximately as fluids, and consequently the crust of the earth floats, to some extent, on the interior (even though this may not be fluid in the usual sense of the word). This is the geological theory of “Isostasis” (cf. Geology); it agrees with the results of measurements of gravity (vide infra), and was brought forward in the middle of the 19th century by J.H. Pratt, who deduced it from observations made in India.

The sin² 2φ term in the expression for G, and the corresponding deviation of the meridian from an ellipse, have been analytically established by Sir G.H. Darwin and E. Wiechert; earlier and less complete investigations were made by Sir G.B. Airy and O. Callandreau. In consequence of the sin² 2φ term, two parameters of the level surfaces in the interior of the earth are to be determined; for this purpose, Darwin develops two differential equations in the place of the one by Clairault. By assuming Roche’s law for the variation of the density in the interior of the Earth, viz. ρ = ρ1 − k(c/c1)², k being a coefficient, it is shown that in latitude 45°, the meridian is depressed about 3¼ metres from the ellipse, and the coefficient of the term sin²φ cos²φ (= ¼ sin²2φ) is −0.0000295. According to Wiechert the earth is composed of a kernel and a shell, the kernel being composed of material, chiefly metallic iron, of density near 8.2, and the shell, about 900 miles thick, of silicates, &c., of density about 3.2. On this assumption the depression in latitude 45° is 2¾ metres, and the coefficient of sin²φ cos²φ is, in round numbers, −0.0000280. To this additional term in the formula for G, there corresponds an extension of Clairault’s formula for the calculation of the flattening from β with terms of the higher orders; this was first accomplished by Helmert.

For a long time the assumption of an ellipsoid with three unequal axes has been held possible for the figure of the earth, in consequence of an important theorem due to K.G. Jacobi, who proved that for a homogeneous fluid in rotation a spheroid is not the only form of equilibrium; an ellipsoid rotating round its least axis may with certain proportions of the axes and a certain time of revolution be a form of equilibrium. It has been objected to the figure of three unequal axes that it does not satisfy, in the proportions of the axes, the conditions brought out in Jacobi’s theorem (c : a < 1/√2). Admitting this, it has to be noted, on the other hand, that Jacobi’s theorem contemplates a homogeneous fluid, and this is certainly far from the actual condition of our globe; indeed the irregular distribution of continents and oceans suggests the possibility of a sensible divergence from a perfect surface of revolution. We may, however, assume the ellipsoid with three unequal axes to be an interpolation form. More plausible forms are little adapted for computation. Consequently we now generally take the ellipsoid of rotation as a basis, especially so because measurements of gravity have shown that the deviation from it is but trifling.

Local Attraction.

In speaking of the figure of the earth, we mean the surface of the sea imagined to percolate the continents by canals. That this surface should turn out, after precise measurements, to be exactly an ellipsoid of revolution is a priori improbable. Although it may be highly probable that originally the earth was a fluid mass, yet in the cooling whereby the present crust has resulted, the actual solid surface has been left most irregular in form. It is clear that these irregularities of the visible surface must be accompanied by irregularities in the mathematical figure of the earth, and when we consider the general surface of our globe, its irregular distribution of mountain masses, continents, with oceans and islands, we are prepared to admit that the earth may not be precisely any surface of revolution. Nevertheless, there must exist some spheroid which agrees very closely with the mathematical figure of the earth, and has the same axis of rotation. We must conceive this figure as exhibiting slight departures from the spheroid, the two surfaces cutting one another in various lines; thus a point of the surface is defined by its latitude, longitude, and its height above the “spheroid of reference.” Calling this height N, then of the actual magnitude of this quantity we can generally have no information, it only obtrudes itself on our notice by its variations. In the vicinity of mountains it may change sign in the space of a few miles; N being regarded as a function of the latitude and longitude, if its differential coefficient with respect to the former be zero at a certain point, the normals to the two surfaces then will lie in the prime vertical; if the differential coefficient of N with respect to the longitude be zero, the two normals will lie in the meridian; if both coefficients are zero, the normals will coincide. The comparisons of terrestrial measurements with the corresponding astronomical observations have always been accompanied with discrepancies. Suppose A and B to be two trigonometrical stations, and that at A there is a disturbing force drawing the vertical through an angle δ, then it is evident that the apparent zenith of A will be really that of some other place A′, whose distance from A is rδ, when r is the earth’s radius; and similarly if there be a disturbance at B of the amount δ′, the apparent zenith of B will be really that of some other place B′, whose distance from B is rδ′. Hence we have the discrepancy that, while the geodetic measurements deal with the points A and B, the astronomical observations belong to the points A′, B′. Should δ, δ′ be equal and parallel, the displacements AA′, BB′ will be equal and parallel, and no discrepancy will appear. The non-recognition of this circumstance often led to much perplexity in the early history of geodesy. Suppose that, through the unknown variations of N, the probable error of an observed latitude (that is, the angle between the normal to the mathematical surface of the earth at the given point and that of the corresponding point on the spheroid of reference) be ε, then if we compare two arcs of a degree each in mean latitudes, and near each other, say about five degrees of latitude apart, the probable error of the resulting value of the ellipticity will be approximately ±1⁄500ε, ε being expressed in seconds, so that if ε be so great as 2″ the probable error of the resulting ellipticity will be greater than the ellipticity itself.

It is necessary at times to calculate the attraction of a mountain, and the consequent disturbance of the astronomical zenith, at any point within its influence. The deflection of the plumb-line, caused by a local attraction whose amount is k²Aδ, is measured by the ratio of k²Aδ to the force of gravity at the station. Expressed in seconds, the deflection Λ is

Λ = 12″.447Aδ / ρ,

where ρ is the mean density of the earth, δ that of the attracting mass, and A = ƒs−3xdv, in which dv is a volume element of the attracting mass within the distance s from the point of deflection, and x the projection of s on the horizontal plane through this point, the linear unit in expressing A being a mile. Suppose, for instance, a table-land whose form is a rectangle of 12 miles by 8 miles, having a height of 500 ft. and density half that of the earth; let the observer be 2 miles distant from the middle point of the longer side. The deflection then is 1″.472; but at 1 mile it increases to 2″.20.

At sixteen astronomical stations in the English survey the disturbance of latitude due to the form of the ground has been computed, and the following will give an idea of the results. At six stations the deflection is under 2″, at six others it is between 2″ and 4″, and at four stations it exceeds 4″. There is one very exceptional station on the north coast of Banffshire, near the village of Portsoy, at which the deflection amounts to 10″, so that if that village were placed on a map in a position to correspond with its astronomical latitude, it would be 1000 ft. out of position! There is the sea to the north and an undulating country to the south, which, however, to a spectator at the station does not suggest any great disturbance of gravity. A somewhat rough estimate of the local attraction from external causes gives a maximum limit of 5″, therefore we have 5″ which must arise from unequal density in the underlying strata in the surrounding country. In order to throw light on this remarkable phenomenon, the latitudes of a number of stations between Nairn on the west, Fraserburgh on the east, and the Grampians on the south, were observed, and the local deflections determined. It is somewhat singular that the deflections diminish in all directions, not very regularly certainly, and most slowly in a south-west direction, finally disappearing, and leaving the maximum at the original station at Portsoy.

The method employed by Dr C. Hutton for computing the attraction of masses of ground is so simple and effectual that it can hardly be improved on. Let a horizontal plane pass through the given station; let r, θ be the polar co-ordinates of any point in this plane, and r, θ, z, the co-ordinates of a particle of the attracting mass; and let it be required to find the attraction of a portion of the mass contained between the horizontal planes z = 0, z = h, the cylindrical surfaces r = r1, r = r2, and the vertical planes θ = θ1, θ = θ2. The component of the attraction at the station or origin along the line θ = 0 is

k²δ ∫r2r1 ∫θ2θ1 ∫h0 r²cosθ dr dθ dz = k²δh (sinθ2 − sinθ1) log{r2 + (r2² + h²)1/2 / r1 + (r1² + h²)1/2}.

(r² + z²)3/2

By taking r2 − r1, sufficiently small, and supposing h also small compared with r1 + r2 (as it usually is), the attraction is

k²δ (r2 − r1) (sinθ2 − sinθ1) h/r,

where r = ½ (r1 + r2). This form suggests the following procedure. Draw on the contoured map a series of equidistant circles, concentric with the station, intersected by radial lines so disposed that the sines of their azimuths are in arithmetical progression. Then, having estimated from the map the mean heights of the various compartments, the calculation is obvious.

In mountainous countries, as near the Alps and in the Caucasus, deflections have been observed to the amount of as much as 30″, while in the Himalayas deflections amounting to 60″ were observed. On the other hand, deflections have been observed in flat countries, such as that noted by Professor K.G. Schweizer, who has shown that, at certain stations in the vicinity of Moscow, within a distance of 16 miles the plumb-line varies 16″ in such a manner as to indicate a vast deficiency of matter in the underlying strata; deflections of 10″ were observed in the level regions of north Germany.

Since the attraction of a mountain mass is expressed as a numerical multiple of δ : ρ the ratio of the density of the mountain to that of the earth, if we have any independent means of ascertaining the amount of the deflection, we have at once the ratio ρ : δ, and thus we obtain the mean density of the earth, as, for instance, at Schiehallion, and afterwards at Arthur’s Seat. Experiments of this kind for determining the mean density of the earth have been made in greater numbers; but they are not free from objection (see Gravitation).

Let us now consider the perturbation attending a spherical subterranean mass. A compact mass of great density at a small distance under the surface of the earth will produce an elevation of the mathematical surface which is expressed by the formula

y = aμ {(1 − 2u cosθ + u²)−1/2 − 1},

where a is the radius of the (spherical) earth, a (1 − u) the distance of the disturbing mass below the surface, μ the ratio of the disturbing mass to the mass of the earth, and aθ the distance of any point on the surface from that point, say Q, which is vertically over the disturbing mass. The maximum value of y is at Q, where it is y = aμu (1 − u). The deflection at the distance aθ is Λ = μu sinθ (1 − 2u cosθ + u²)−3/2, or since θ is small, putting h + u = 1, we have Λ = μθ (h² + θ²)−3/2. The maximum deflection takes place at a point whose distance from Q is to the depth of the mass as 1 : √2, and its amount is 2μ/3 √3h². If, for instance, the disturbing mass were a sphere a mile in diameter, the excess of its density above that of the surrounding country being equal to half the density of the earth, and the depth of its centre half a mile, the greatest deflection would be 5″, and the greatest value of y only two inches. Thus a large disturbance of gravity may arise from an irregularity in the mathematical surface whose actual magnitude, as regards height at least, is extremely small.

The effect of the disturbing mass μ on the vibrations of a pendulum would be a maximum at Q; if v be the number of seconds of time gained per diem by the pendulum at Q, and σ the number of seconds of angle in the maximum deflection, then it may be shown that v/σ = π√3/10.

The great Indian survey, and the attendant measurements of the degree of latitude, gave occasion to elaborate investigations of the deflection of the plumb-line in the neighbourhood of the high plateaus and mountain chains of Central Asia. Archdeacon Pratt (Phil. Trans., 1855 and 1857), in instituting these investigations, took into consideration the influence of the apparent diminution of the mass of the earth’s crust occasioned by the neighbouring ocean-basins; he concluded that the accumulated masses of mountain chains, &c., corresponded to subterranean mass diminutions, so that over any level surface in a fixed depth (perhaps 100 miles or more) the masses of prisms of equal section are equal. This is supported by the gravity measurements at Moré in the Himalayas at a height of 4696 metres, which showed no deflection due to the mountain chain (Phil. Trans., 1871); more recently, H.A. Faye (Compt. rend., 1880) arrived at the same conclusion for the entire continent.

This compensation, however, must only be regarded as a general principle; in certain cases, the compensating masses show marked horizontal displacements. Further investigations, especially of gravity measurements, will undoubtedly establish other important facts. Colonel S.G. Burrard has recently recalculated, with the aid of more exact data, certain Indian deviations of the plumb-line, and has established that in the region south of the Himalayas (lat. 24°) there is a subterranean perturbing mass. The extent of the compensation of the high mountain chains is difficult to recognize from the latitude observations, since the same effect may result from different causes; on the other hand, observations of geographical longitude have established a strong compensation.

Meridian Arcs.

The astronomical stations for the measurement of the degree of latitude will generally lie not exactly on the same meridian; and it is therefore necessary to calculate the arcs of meridian M which lie between the latitude of neighbouring stations. If S be the geodetic line calculated from the triangulation with the astronomically determined azimuths α1 and α2, then

M = S cos α {1 + 1⁄12 S² sin²α ...},

cos ½Δα α²

in which 2α = α1 + α2 − 180°, Δα = α2 − α1 − 180°.

The length of the arc of meridian between the latitudes φ1 and φ2 is

M = ∫φ2φ1 ρdφ = α ∫φ2φ1 (1 − e²) dφ

(1 − e² sin²φ)3/2

where a²e² = a² − b²; instead of using the eccentricity e, put the ratio of the axes b : a = 1 − n : 1 + n, then

M = ∫φ2φ1 b (1 + n) (1 − n²) dφ .

(1 + 2n cos2φ + n²)3/2

This, after integration, gives

M/b = (1 + n + 5 n² + 5 n³)α0 − (3n + 3n² + 21 n³)α1 + ( 15 n² + 15 n³)α2 − ( 35 n³)α3,

4 4 8 8 8 24

where

α0 = φ2 − φ1

α1 = sin (φ2 − φ1) cos (φ2 + φ1)

α2 = sin 2(φ2 − φ1) cos 2(φ2 + φ1)

α3 = sin 3(φ2 − φ1) cos 3(φ2 + φ1).

The part of M which depends on n³ is very small; in fact, if we calculate it for one of the longest arcs measured, the Russian arc, it amounts to only an inch and a half, therefore we omit this term, and put for M/b the value

(1 + n + 5 n²)α0 − (3n + 3n²)α1 + ( 15 n²)α2.

4 8

Now, if we suppose the observed latitudes to be affected with errors, and that the true latitudes are φ1 + x1, φ2 + x2; and if further we suppose that n1 + dn is the true value of a − b : a + b, and that n1 itself is merely a very approximate numerical value, we get, on making these substitutions and neglecting the influence of the corrections x on the position of the arc in latitude, i.e. on φ1 + φ2,

M/b = (1 + n1 + 5 n1²)α0 − (3n1 + 3n1²)α1 + ( 15 n1²)α2 + { (1 + 5 n1)α0 − (3 + 6n1)α1 + ( 15 n1)α2 }dn

4 8 2 4

+ {1 + n1 − 3n dα1 }dα0;

dα0

here dα0 = x2 − x1; and as b is only known approximately, put b = b1(1 + u); then we get, after dividing through by the coefficient of dα0, which is = 1 + n1 − 3n1 cos(φ2 − φ1) cos(φ2 + φ1), an equation of the form x2 = x1 + h + fu + gv, where for convenience we put v for dn.

Now in every measured arc there are not only the extreme stations determined in latitude, but also a number of intermediate stations so that if there be i + 1 stations there will be i equations

x2 = x1 + f1u + g1v + h1

x3 = x1 + f2u + g2v + h2

xi = x1 + fiu + giv + hi

In combining a number of different arcs of meridian, with the view of determining the figure of the earth, each arc will supply a number of equations in u and v and the corrections to its observed latitudes. Then, according to the method of least squares, those values of u and v are the most probable which render the sum of the squares of all the errors x a minimum. The corrections x which are here applied arise not from errors of observation only. The mere uncertainty of a latitude, as determined with modern instruments, does not exceed a very small fraction of a second as far as errors of observation go, but no accuracy in observing will remove the error that may arise from local attraction. This, as we have seen, may amount to some seconds, so that the corrections x to the observed latitudes are attributable to local attraction. Archdeacon Pratt objected to this mode of applying least squares first used by Bessel; but Bessel was right, and the objection is groundless. Bessel found, in 1841, from ten meridian arcs with a total amplitude of 50°.6:

a = 3272077 toises = 6377397 metres.

e (ellipticity) = (a − b) / a ≈ 1/299.15 (prob. error ± 3.2).

The probable error in the length of the earth’s quadrant is ± 336 m.

We now give a series of some meridian-arcs measurements, which were utilized in 1866 by A.R. Clarke in the Comparisons of the Standards of Length, pp. 280-287; details of the calculations are given by the same author in his Geodesy (1880), pp. 311 et seq.

The data of the French arc from Formentera to Dunkirk are—

Stations. Astronomical
Latitudes. Distance of
Parallels.

° ′ ″ Ft.

Formentera 38 39 53.17 · ·

Mountjouy 41 21 44.96 982671.04

Barcelona 41 22 47.90 988701.92

Carcassonne 43 12 54.30 1657287.93

Pantheon 48 50 47.98 3710827.13

Dunkirk 51 2 8.41 4509790.84

The distance of the parallels of Dunkirk and Greenwich, deduced from the extension of the triangulation of England into France, in 1862, is 161407.3 ft., which is 3.9 ft. greater than that obtained from Captain Kater’s triangulation, and 3.2 ft. less than the distance calculated by Delambre from General Roy’s triangulation. The following table shows the data of the English arc with the distances in standard feet from Formentera.

° ′ ″ Ft.

Formentera · · · ·

Greenwich 51 28 38.30 4671198.3

Arbury 52 13 26.59 4943837.6

Clifton 53 27 29.50 5394063.4

Kellie Law 56 14 53.60 6413221.7

Stirling 57 27 49.12 6857323.3

Saxavord 60 49 37.21 8086820.7

The latitude assigned in this table to Saxavord is not the directly observed latitude, which is 60° 49′ 38.58″, for there are here a cluster of three points, whose latitudes are astronomically determined; and if we transfer, by means of the geodesic connexion, the latitude of Gerth of Scaw to Saxavord, we get 60° 49′ 36.59″; and if we similarly transfer the latitude of Balta, we get 60° 49′ 36.46″. The mean of these three is that entered in the above table.

For the Indian arc in long. 77° 40′ we have the following data:—

° ′ ″ Ft.

Punnea 8 9 31.132 · ·

Putchapolliam 10 59 42.276 1029174.9

Dodagunta 12 59 52.165 1756562.0

Namthabad 15 5 53.562 2518376.3

Daumergida 18 3 15.292 3591788.4

Takalkhera 21 5 51.532 4697329.5

Kalianpur 24 7 11.262 5794695.7

Kaliana 29 30 48.322 7755835.9

The data of the Russian arc (long. 26° 40′) taken from Struve’s work are as below:—

° ′ ″ Ft.

Staro Nekrasovsk 45 20 2.94 · ·

Vodu-Luy 47 1 24.98 616529.81

Suprunkovzy 48 45 3.04 1246762.17

Kremenets 50 5 49.95 1737551.48

Byelin 52 2 42.16 2448745.17

Nemesh 54 39 4.16 3400312.63

Jacobstadt 56 30 4.97 4076412.28

Dorpat 58 22 47.56 4762421.43

Hogland 60 5 9.84 5386135.39

Kilpi-maki 62 38 5.25 6317905.67

Torneå 65 49 44.57 7486789.97

Stuor-oivi 68 40 58.40 8530517.90

Fuglenaes 70 40 11.23 9257921.06

From the are measured in Cape Colony by Sir Thomas Maclear in long. 18° 30′, we have

° ′ ″ Ft.

North End 29 44 17.66 · ·

Heerenlogement Berg 31 58 9.11 811507.7

Royal Observatory 33 56 3.20 1526386.8

Zwart Kop 34 13 32.13 1632583.3

Cape Point 34 21 6.26 1678375.7

And, finally, for the Peruvian arc, in long. 281° 0′,

° ′ ″ Ft.

Tarqui 3 4 32.068 · ·

Cotchesqui 0 2 31.387 1131036.3

Having now stated the data of the problem, we may seek that oblate ellipsoid (spheroid) which best represents the observations. Whatever the real figure may be, it is certain that if we suppose it an ellipsoid with three unequal axes, the arithmetical process will bring out an ellipsoid, which will agree better with all the observed latitudes than any spheroid would, therefore we do not prove that it is an ellipsoid; to prove this, arcs of longitude would be required. The result for the spheroid may be expressed thus:—

a = 20926062 ft. = 6378206.4 metres.
b = 20855121 ft. = 6356583.8 metres.
b : a = 293.98 : 294.98.

As might be expected, the sum of the squares of the 40 latitude corrections, viz. 153.99, is greater in this figure than in that of three axes, where it amounts to 138.30. For this case, in the Indian arc the largest corrections are at Dodagunta, + 3.87″, and at Kalianpur, − 3.68″. In the Russian arc the largest corrections are + 3.76″, at Torneå, and − 3.31″, at Staro Nekrasovsk. Of the whole 40 corrections, 16 are under 1.0″, 10 between 1.0″ and 2.0″, 10 between 2.0″ and 3.0″, and 4 over 3.0″. The probable error of an observed latitude is ± 1.42″; for the spheroidal it would be very slightly larger. This quantity may be taken therefore as approximately the probable amount of local deflection.

If ρ be the radius of curvature of the meridian in latitude φ, ρ′ that perpendicular to the meridian, D the length of a degree of the meridian, D′ the length of a degree of longitude, r the radius drawn from the centre of the earth, V the angle of the vertical with the radius-vector, then

Ft.

ρ = 20890606.6 − 106411.5 cos 2φ + 225.8 cos 4φ

ρ′ = 20961607.3 − 35590.9 cos 2φ + 45.2 cos 4φ

D = 364609.87 − 1857.14 cos 2φ + 3.94 cos 4φ

D′ = 365538.48 cos φ − 310.17 cos 3φ + 0.39 cos 5φ

Log r/a = 9.9992645 + .0007374 cos 2φ − .0000019 cos 4φ

V = 700.44″ sin 2φ − 1.19″ sin 4φ.

A.R. Clarke has recalculated the elements of the ellipsoid of the earth; his values, derived in 1880, in which he utilized the measurements of parallel arcs in India, are particularly in practice. These values are:—

a = 20926202 ft. = 6378249 metres,
b = 20854895 ft. = 6356515 metres,
b : a = 292.465 : 293.465.

The calculation of the elements of the ellipsoid of rotation from measurements of the curvature of arcs in any given azimuth by means of geographical longitudes, latitudes and azimuths is indicated in the article Geodesy; reference may be made to Principal Triangulation, Helmert’s Geodasie, and the publications of the Kgl. Preuss. Geod. Inst.:—Lotabweichungen (1886), and Die europ. Längengradmessung in 52° Br. (1893). For the calculation of an ellipsoid with three unequal axes see Comparison of Standards, preface; and for non-elliptical meridians, Principal Triangulation, p. 733.

Gravitation-Measurements.

According to Clairault’s theorem (see above) the ellipticity e of the mathematical surface of the earth is equal to the difference 5⁄2m − β, where m is the ratio of the centrifugal force at the equator to gravity at the equator, and β is derived from the formula G = g(1 + β sin²φ). Since the beginning of the 19th century many efforts have been made to determine the constants of this formula, and numerous expeditions undertaken to investigate the intensity of gravity in different latitudes. If m be known, it is only necessary to determine β for the evaluation of e; consequently it is unnecessary to determine G absolutely, for the relative values of G at two known latitudes suffice. Such relative measurements are easier and more exact than absolute ones. In some cases the ordinary thread pendulum, i.e. a spherical bob suspended by a wire, has been employed; but more often a rigid metal rod, bearing a weight and a knife-edge on which it may oscillate, has been adopted. The main point is the constancy of the pendulum. From the formula for the time of oscillation of the mathematically ideal pendulum, t = 2π√l/G, l being the length, it follows that for two points G1 / G2 = t2² / t1².

In 1808 J.B. Biot commenced his pendulum observations at several stations in western Europe; and in 1817-1825 Captain Louis de Freycinet and L.I. Duperrey prosecuted similar observations far into the southern hemisphere. Captain Henry Kater confined himself to British stations (1818-1819); Captain E. Sabine, from 1819 to 1829, observed similarly, with Kater’s pendulum, at seventeen stations ranging from the West Indies to Greenland and Spitsbergen; and in 1824-1831, Captain Henry Foster (who met his death by drowning in Central America) experimented at sixteen stations; his observations were completed by Francis Baily in London. Of other workers in this field mention may be made of F.B. Lütke (1826-1829), a Russian rear-admiral, and Captains J.B. Basevi and W.T. Heaviside, who observed during 1865 to 1873 at Kew and at 29 Indian stations, particularly at Moré in the Himalayas at a height of 4696 metres. Of the earlier absolute determinations we may mention those of Biot, Kater, and Bessel at Paris, London and Königsberg respectively. The measurements were particularly difficult by reason of the length of the pendulums employed, these generally being second-pendulums over 1 metre long. In about 1880, Colonel Robert von Sterneck of Austria introduced the half-second pendulum, which permitted far quicker and more accurate work. The use of these pendulums spread in all countries, and the number of gravity stations consequently increased: in 1880 there were about 120, in 1900 there were about 1600, of which the greater number were in Europe. Sir E. Sabine calculated the ellipticity to be 1/288.5, a value shown to be too high by Helmert, who in 1884, with the aid of 120 stations, gave the value 1/299.26, and in 1901, with about 1400 stations, derived the value 1/298.3. The reason for the excessive estimate of Sabine is that he did not take into account the systematic difference between the values of G for continents and islands; it was found that in consequence of the constitution of the earth’s crust (Pratt) G is greater on small islands of the ocean than on continents by an amount which may approach to 0.3 cm. Moreover, stations in the neighbourhood of coasts shelving to deep seas have a surplus, but a little smaller. Consequently, Helmert conducted his calculations of 1901 for continents and coasts separately, and obtained G for the coasts 0.036 cm. greater than for the continents, while the value of β remained the same. The mean value, reduced to continents, is

G = 978.03 (1 + 0.005302 sin²φ − 0.000007 sin²2φ) cm/sec².

The small term involving sin² 2φ could not be calculated with sufficient exactness from the observations, and is therefore taken from the theoretical views of Sir G.H. Darwin and E. Wiechert. For the constant g = 978.03 cm. another correction has been suggested (1906) by the absolute determinations made by F. Kühnen and Ph. Furtwängler at Potsdam.

A report on the pendulum measurements of the 19th century has been given by Helmert in the Comptes rendus des séances de la 13e conférence générale de l’Association Géod. Internationale à Paris (1900), ii. 139-385.

A difficulty presents itself in the case of the application of measurements of gravity to the determination of the figure of the earth by reason of the extrusion or standing out of the land-masses (continents, &c.) above the sea-level. The potential of gravity has a different mathematical expression outside the masses than inside. The difficulty is removed by assuming (with Sir G.G. Stokes) the vertical condensation of the masses on the sea-level, without its form being considerably altered (scarcely 1 metre radially). Further, the value of gravity (g) measured at the height H is corrected to sea-level by + 2gH/R, where R is the radius of the earth. Another correction, due to P. Bouguer, is − 3⁄2gδH/ρR, where δ is the density of the strata of height H, and ρ the mean density of the earth. These two corrections are represented in “Bouguer’s Rule”: gH = gs (1 − 2H/R + 3δH / 2ρR), where gH is the gravity at height H, and gs the value at sea-level. This is supposed to take into account the attraction of the elevated strata or plateau; but, from the analytical method, this is not correct; it is also disadvantageous since, in general, the land-masses are compensated subterraneously, by reason of the isostasis of the earth’s crust.

In 1849 Stokes showed that the normal elevations N of the geoid towards the ellipsoid are calculable from the deviations Δg of the acceleration of gravity, i.e. the differences between the observed g and the value calculated from the normal G formula. The method assumes that gravity is measured on the earth’s surface at a sufficient number of points, and that it is conformably reduced. In order to secure the convergence of the expansions in spherical harmonics, it is necessary to assume all masses outside a surface parallel to the surface of the sea at a depth of 21 km. (= R × ellipticity) to be condensed on this surface (Helmert, Geod. ii. 172). In addition to the reduction with 2gH/R, there still result small reductions with mountain chains and coasts, and somewhat larger ones for islands. The sea-surface generally varies but very little by this condensation. The elevation (N) of the geoid is then equal to

N = R ∫π FG−1Δgψψ,

where ψ is the spherical distance from the point N, and Δgψ denotes the mean value of Δg for all points in the same distance ψ around; F is a function of ψ, and has the following values:—

Ψ = 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180°

F = 1 1.22 0.94 0.47 −0.06 −0.54 −0.90 −1.08 −1.08 −0.91 −0.62 −0.27 +0.08 0.36 0.53 0.56 0.46 0.26 0

H. Poincaré (Bull. Astr., 1901, p. 5) has exhibited N by means of Lamé’s functions; in this case the condensation is effected on an ellipsoidal surface, which approximates to the geoid. This condensation is, in practice, the same as to the geoid itself.

If we imagine the outer land-masses to be condensed on the sea-level, and the inner masses (which, together with the outer masses, causes the deviation of the geoid from the ellipsoid) to be compensated in the sea-level by a disturbing stratum (which, according to Gauss, is possible), and if these masses of both kinds correspond at the point N to a stratum of thickness D and density δ, then, according to Helmert (Geod. ii. 260) we have approximately

Δg = 3 · g ( δD − N).

2 R ρ

Since N slowly varies empirically, it follows that in restricted regions (of a few 100 km. in diameter) Δg is a measure of the variation of D. By applying the reduction of Bouguer to g, D is diminished by H and only gives the thickness of the ideal disturbing mass which corresponds to the perturbations due to subterranean masses. Δg has positive values on coasts, small islands, and high and medium mountain chains, and occasionally in plains; while in valleys and at the foot of mountain ranges it is negative (up to 0.2 cm.). We conclude from this that the masses of smaller density existing under high mountain chains lie not only vertically underneath but also spread out sideways.

The European Arc of Parallel in 52° Lat.

Many measurements of degrees of longitudes along central parallels in Europe were projected and partly carried out as early as the first half of the 19th century; these, however, only became of importance after the introduction of the electric telegraph, through which calculations of astronomical longitudes obtained a much higher degree of accuracy. Of the greatest moment is the measurement near the parallel of 52° lat., which extended from Valentia in Ireland to Orsk in the southern Ural mountains over 69° long, (about 6750 km.). F.G.W. Struve, who is to be regarded as the father of the Russo-Scandinavian latitude-degree measurements, was the originator of this investigation. Having made the requisite arrangements with the governments in 1857, he transferred them to his son Otto, who, in 1860, secured the co-operation of England. A new connexion of England with the continent, via the English Channel, was accomplished in the next two years; whereas the requisite triangulations in Prussia and Russia extended over several decennaries. The number of longitude stations originally arranged for was 15; and the determinations of the differences in longitude were uniformly commenced by the Russian observers E.I. von Forsch, J.I. Zylinski, B. Tiele and others; Feaghmain (Valentia) being reserved for English observers. With the concluding calculation of these operations, newer determinations of differences of longitudes were also applicable, by which the number of stations was brought up to 29. Since local deflections of the plumb-line were suspected at Feaghmain, the most westerly station, the longitude (with respect to Greenwich) of the trigonometrical station Killorglin at the head of Dingle Bay was shortly afterwards determined.

The results (1891-1894) are given in volumes xlvii. and l. of the memoirs (Zapiski) of the military topographical division of the Russian general staff, volume li. contains a reconnexion of Orsk. The observations made west of Warsaw are detailed in the Die europ. Längengradmessung in 52° Br., i. and ii., 1893, 1896, published by the Kgl. Preuss. Geod. Inst.

The following figures are quoted from Helmert’s report “Die Grösse der Erde” (Sitzb. d. Berl. Akad. d. Wiss., 1906, p. 535):—

Easterly Deviation of the Astronomical Zenith.

Name. Longitude.

Feaghmain −10 21 −3.3

Killorglin −9 47 +2.8

Haverfordwest −4 58 +1.6

Greenwich 0 0 +1.5

Rosendaël-Nieuport +2 35 −1.7

Bonn +7 6 −4.4

Göttingen +9 57 −2.4

Brocken +10 37 +2.3

Leipzig +12 23 +2.7

Rauenberg-Berlin +13 23 +1.7

Grossenhain +13 33 −2.9

Schneekoppe +15 45 +0.1

Springberg +16 37 +0.8

Breslau-Rosenthal +17 2 +3.5

Trockenberg +18 53 −0.5

Schönsee +18 54 −2.9

Mirov +19 18 +2.2

Warsaw +21 2 +1.9

Grodno +23 50 −2.8

Bobruisk +29 14 +0.5

Orel +36 4 +4.4

Lipetsk +39 36 +0.2

Saratov +46 3 +6.4

Samara +50 5 −2.6

Orenburg +55 7 +1.7

Orsk +58 34 −8.0

These deviations of the plumb-line correspond to an ellipsoid having an equatorial radius (a) of nearly 6,378,000 metres (prob. error ± 70 metres) and an ellipticity 1/299.15. The latter was taken for granted; it is nearly equal to the result from the gravity-measurements; the value for a then gives Ση² a minimum (nearly). The astronomical values of the geographical longitudes (with regard to Greenwich) are assumed, according to the compensation of longitude differences carried out by van de Sande Bakhuyzen (Comp. rend, des séances de la commission permanente de l’Association Géod. Internationale à Genève, 1893, annexe A.I.). Recent determinations (Albrecht, Astr. Nach., 3993/4) have introduced only small alterations in the deviations, a being slightly increased.

Of considerable importance in the investigation of the great arc was the representation of the linear lengths found in different countries, in terms of the same unit. The necessity for this had previously occurred in the computation of the figure of the earth from latitude-degree-measurements. A.R. Clarke instituted an extensive series of comparisons at Southampton (see Comparisons of Standards of Length of England, France, Belgium, Prussia, Russia, India and Australia, made at the Ordnance Survey Office, Southampton, 1866, and a paper in the Philosophical Transactions for 1873, by Lieut.-Col. A.R. Clarke, C.B., R.E., on the further comparisons of the standards of Austria, Spain, the United States, Cape of Good Hope and Russia) and found that 1 toise = 6.39453348 ft., 1 metre = 3.28086933 ft.

In 1875 a number of European states concluded the metre convention, and in 1877 an international weights-and-measures bureau was established at Breteuil. Until this time the metre was determined by the end-surfaces of a platinum rod (mètre des archives); subsequently, rods of platinum-iridium, of cross-section , were constructed, having engraved lines at both ends of the bridge, which determine the distance of a metre. There were thirty of the rods which gave as accurately as possible the length of the metre; and these were distributed among the different states (see Weights and Measures). Careful comparisons with several standard toises showed that the metre was not exactly equal to 443,296 lines of the toise, but, in round numbers, 1/75000 of the length smaller. The metre according to the older relation is called the “legal metre,” according to the new relation the “international metre.” The values are (see Europ. Längengradmessung, i. p. 230):—

Legal metre = 3.28086933 ft., International metre = 3.2808257 ft.

The values of a given above are in terms of the international metre; the earlier ones in legal metres, while the gravity formulae are in international metres.

The International Geodetic Association (Internationale Erdmessung).

On the proposition of the Prussian lieutenant-general, Johann Jacob Baeyer, a conference of delegates of several European states met at Berlin in 1862 to discuss the question of a “Central European degree-measurement.” The first general conference took place at Berlin two years later; shortly afterwards other countries joined the movement, which was then named “The European degree-measurement.” From 1866 till 1886 Prussia had borne the expense incident to the central bureau at Berlin; but when in 1886 the operations received further extension and the title was altered to “The International Earth-measurement” or “International Geodetic Association,” the co-operating states made financial contributions to this purpose. The central bureau is affiliated with the Prussian Geodetic Institute, which, since 1892, has been situated on the Telegraphenberg near Potsdam. After Baeyer’s death Prof. Friedrich Robert Helmert was appointed director. The funds are devoted to the advancement of such scientific works as concern all countries and deal with geodetic problems of a general or universal nature. During the period 1897-1906 the following twenty-one countries belonged to the association:—Austria, Belgium, Denmark, England, France, Germany, Greece, Holland, Hungary, Italy, Japan, Mexico, Norway, Portugal, Rumania, Russia, Servia, Spain, Sweden, Switzerland and the United States of America. At the present time general conferences take place every three years.

Baeyer projected the investigation of the curvature of the meridians and the parallels of the mathematical surface of the earth stretching from Christiania to Palermo for 12 degrees of longitude; he sought to co-ordinate and complete the network of triangles in the countries through which these meridians passed, and to represent his results by a common unit of length. This proposition has been carried out, and extended over the greater part of Europe; as a matter of fact, the network has, with trifling gaps, been carried over the whole of western and central Europe, and, by some chains of triangles, over European Russia. Through the co-operation of France, the network has been extended into north Africa as far as the geographical latitude of 32°; in Greece a network, united with those of Italy and Bosnia, has been carried out by the Austrian colonel, Heinrich Hartl; Servia has projected similar triangulations; Rumania has begun to make the triangle measurements, and three base lines have been measured by French officers with Brunner’s apparatus. At present, in Rumania, there is being worked a connexion between the arc of parallel in lat. 47°/48° in Russia (stretching from Astrakan to Kishinev) with Austria-Hungary. In the latter country and in south Bavaria the connecting triangles for this parallel have been recently revised, as well as the French chain on the Paris parallel, which has been connected with the German net by the co-operation of German and French geodesists. This will give a long arc of parallel, really projected in the first half of the 19th century. The calculation of the Russian section gives, with an assumed ellipticity of 1/299.15, the value a = 6377350 metres; this is rather uncertain, since the arc embraces only 19° in longitude.

We may here recall that in France geodetic studies have recovered their former expansion under the vigorous impulse of Colonel (afterwards General) François Perrier. When occupied with the triangulation of Algeria, Colonel Perrier had conceived the possibility of the geodetic junction of Algeria to Spain, over the Mediterranean; therefore the French meridian line, which was already connected with England, and was thus produced to the 60th parallel, could further be linked to the Spanish triangulation, cross thence into Algeria and extend to the Sahara, so as to form an arc of about 30° in length. But it then became urgent to proceed to a new measurement of the French arc, between Dunkirk and Perpignan. In 1869 Perrier was authorized to undertake that revision. He devoted himself to that work till the end of his career, closed by premature death in February 1888, at the very moment when the Dépôt de la guerre had just been transformed into the Geographical Service of the Army, of which General F. Perrier was the first director. His work was continued by his assistant, Colonel (afterwards General) J.A.L. Bassot. The operations concerning the revision of the French arc were completed only in 1896. Meanwhile the French geodesists had accomplished the junction of Algeria to Spain, with the help of the geodesists of the Madrid Institute under General Carlos Ibañez (1879), and measured the meridian line between Algiers and El Aghuat (1881). They have since been busy in prolonging the meridians of El Aghuat and Biskra, so as to converge towards Wargla, through Ghardaïa and Tuggurt. The fundamental co-ordinates of the Panthéon have also been obtained anew, by connecting the Panthéon and the Paris Observatory with the five stations of Bry-sur-Marne, Morlu, Mont Valérien, Chatillon and Montsouris, where the observations of latitude and azimuth have been effected.

According to the calculations made at the central bureau of the international association on the great meridian arc extending from the Shetland Islands, through Great Britain, France and Spain to El Aghuat in Algeria, a = 6377935 metres, the ellipticity being assumed as 1/299.15. The following table gives the difference: astronomical-geodetic latitude. The net does not follow the meridian exactly, but deviates both to the west and to the east; actually, the meridian of Greenwich is nearer the mean than that of Paris (Helmert, Grösse d. Erde).

West Europe-Africa Meridian-arc.

Name. Latitude. A.-G.

Saxavord 60 49.6 −4.0

Balta 60 45.0 −6.1

Ben Hutig 58 33.1 +0.3

Cowhythe 57 41.1 +7.3

Great Stirling 57 27.8 −2.3

Kellie Law 56 14.9 −3.7

Calton Hill 55 57.4 +3.5

Durham 54 46.1 −0.9

Burleigh Moor 54 34.3 +2.1

Clifton Beacon 53 27.5 +1.3

Arbury Hill 52 13.4 −3.0

Greenwich 51 28.6 −2.5

Nieuport 51 7.8 −0.4

Rosendaël 51 2.7 −0.9

Lihons 49 49.9 +0.5

Panthéon 48 50.8 −0.0

Chevry 48 0.5 +2.2

Saligny le Vif 47 2.7 +3.0

Arpheuille 46 13.7 +6.3

Puy de Dôme 45 46.5 +7.0

Rodez 44 21.4 +1.7

Carcassonne 43 13.3 +0.7

Rivesaltes 42 45.2 −0.7

Montolar 41 38.5 +3.6

Lérida 41 37.0 −0.2

Javalon 40 13.8 −0.2

Desierto 40 5.0 −4.5

Chinchilla 38 55.2 +2.2

Mola de Formentera 38 39.9 −1.2

Tetíca 37 15.2 +3.5

Roldan 36 56.6 −6.0

Conjuros 36 44.4 −12.6

Mt. Sabiha 35 39.6 +6.5

Nemours 35 5.8 +7.4

Bouzaréah 36 48.0 +2.9

Algiers (Voirol) 36 45.1 −9.1

Guelt ès Stel 35 7.8 −1.0

El Aghuat 33 48.0 −2.8

While the radius of curvature of this arc is obviously not uniform (being, in the mean, about 600 metres greater in the northern than in the southern part), the Russo-Scandinavian meridian arc (from 45° to 70°), on the other hand, is very uniformly curved, and gives, with an ellipticity of 1/299.15, a = 6378455 metres; this arc gives the plausible value 1/298.6 for the ellipticity. But in the case of this arc the orographical circumstances are more favourable.

The west-European and the Russo-Scandinavian meridians indicate another anomaly of the geoid. They were connected at the Central Bureau by means of east-to-west triangle chains (principally by the arc of parallel measurements in lat. 52°); it was shown that, if one proceeds from the west-European meridian arcs, the differences between the astronomical and geodetic latitudes of the Russo-Scandinavian arc become some 4″ greater.

The central European meridian, which passes through Germany and the countries adjacent on the north and south, is under review at Potsdam (see the publications of the Kgl. Preuss. Geod. Inst., Lotabweichungen, Nos. 1-3). Particular notice must be made of the Vienna meridian, now carried southwards to Malta. The Italian triangulation is now complete, and has been joined with the neighbouring countries on the north, and with Tunis on the south.

The United States Coast and Geodetic Survey has published an account of the transcontinental triangulation and measurement of an arc of the parallel of 39°, which extends from Cape May (New Jersey), on the Atlantic coast, to Point Arena (California), on the Pacific coast, and embraces 48° 46′ of longitude, with a linear development of about 4225 km. (2625 miles). The triangulation depends upon ten base-lines, with an aggregate length of 86 km. the longest exceeding 17 km. in length, which have been measured with the utmost care. In crossing the Rocky Mountains, many of its sides exceed 100 miles in length, and there is one side reaching to a length of 294 km., or 183 miles; the altitude of many of the stations is also considerable, reaching to 4300 metres, or 14,108 ft., in the case of Pike’s Peak, and to 14,421 ft. at Elbert Peak, Colo. All geometrical conditions subsisting in the triangulation are satisfied by adjustment, inclusive of the required accord of the base-lines, so that the same length for any given line is found, no matter from what line one may start.

Over or near the arc were distributed 109 latitude stations, occupied with zenith telescopes; 73 azimuth stations; and 29 telegraphically determined longitudes. It has thus been possible to study in a very complete manner the deviations of the vertical, which in the mountainous regions sometimes amount to 25 seconds, and even to 29 seconds.

With the ellipticity 1/299.15, a = 6377897 ± 65 metres (prob. error); in this calculation, however, some exceedingly perturbed stations are excluded; for the employed stations the mean perturbation in longitude is ± 4.9″ (zenith-deflection east-to-west ± 3.8″).

The computations relative to another arc, the “eastern oblique arc of the United States,” are also finished. It extends from Calais (Maine) in the north-east, to the Gulf of Mexico, and terminates at New Orleans (Louisiana), in the south. Its length is 2612 km. (1623 miles), the difference of latitude 15° 1′, and of longitude 22° 47′. In the main, the triangulation follows the Appalachian chain of mountains, bifurcating once, so as to leave an oval space between the two branches. It includes among its stations Mount Washington (1920 metres) and Mount Mitchell (2038 metres). It depends upon six base-lines, and the adjustment is effected in the same manner as for the arc of the parallel. The astronomical data have been afforded by 71 latitude stations, 17 longitude stations, and 56 azimuth stations, distributed over the whole extent of the arc. The resulting dimensions of an osculating spheroid were found to be

a = 6378157 metres ± 90 (prob. error),
e (ellipticity) = 1/304.5 ± 1.9 (prob. error).

With the ellipticity 1/399.15, a = 6378041 metres ± 80 (prob. er.).

During the years 1903-1906 the United States Coast and Geodetic Survey, under the direction of O.H. Tittmann and the special management of John F. Hayford, executed a calculation of the best ellipsoid of rotation for the United States. There were 507 astronomical determinations employed, all the stations being connected through the net-work of triangles. The observed latitudes, longitude and azimuths were improved by the attractions of the earth’s crust on the hypothesis of isostasis for three depths of the surface of 114, 121 and 162 km., where the isostasis is complete. The land-masses, within the distance of 4126 km., were taken into consideration. In the derivation of an ellipsoid of rotation, the first case proved itself the most favourable, and there resulted:—

a = 6378283 metres ± 74 (prob. er.), ellipticity = 1/297.8 ± 0.9 (prob. er.).

The most favourable value for the depth of the isostatic surface is approximately 114 km.

The measurement of a great meridian arc, in long. 98° W., has been commenced; it has a range of latitude of 23°, and will extend over 50° when produced southwards and northwards by Mexico and Canada. It may afterwards be connected with the arc of Quito. A new measurement of the meridian arc of Quito was executed in the years 1901-1906 by the Service géographique of France under the direction of the Académie des Sciences, the ground having been previously reconnoitred in 1899. The new arc has an amplitude in latitude of 5° 53′ 33″, and stretches from Tulcan (lat. 0° 48′ 25″) on the borders of Columbia and Ecuador, through Columbia to Payta (lat. − 5° 5′ 8″) in Peru. The end-points, at which the chain of triangles has a slight north-easterly trend, show a longitude difference of 3°. Of the 74 triangle points, 64 were latitude stations; 6 azimuths and 8 longitude-differences were measured, three base-lines were laid down, and gravity was determined from six points, in order to maintain indications over the general deformation of the geoid in that region. Computations of the attraction of the mountains on the plumb-line are also being considered. The work has been much delayed by the hardships and difficulties encountered. It was conducted by Lieut.-Colonel Robert Bourgeois, assisted by eleven officers and twenty-four soldiers of the geodetic branch of the Service géographique. Of these officers mention may be made of Commandant E. Maurain, who retired in 1904 after suffering great hardships; Commandant L. Massenet, who died in 1905; and Captains I. Lacombe, A. Lallemand, and Lieut. Georges Perrier (son of General Perrier). It is conceivable that the chain of triangles in longitude 98° in North America may be united with that of Ecuador and Peru: a continuous chain over the whole of America is certainly but a question of time. During the years 1899-1902 the measurement of an arc of meridian was made in the extreme north, in Spitzbergen, between the latitudes 76° 38′ and 80° 50′, according to the project of P.G. Rosén. The southern part was determined by the Russians—O. Bäcklund, Captain D.D. Sergieffsky, F.N. Tschernychev, A. Hansky and others—during 1899-1901, with the aid of 1 base-line, 15 trigonometrical, 11 latitude and 5 gravity stations. The northern part, which has one side in common with the southern part, has been determined by Swedes (Professors Rosén, father and son, E. Jäderin, T. Rubin and others), who utilized 1 base-line, 9 azimuth measurements, 18 trigonometrical, 17 latitude and 5 gravity stations. The party worked under excessive difficulties, which were accentuated by the arctic climate. Consequently, in the first year, little headway was made.

Sir David Gill, when director of the Royal Observatory, Cape Town, instituted the magnificent project of working a latitude-degree measurement along the meridian of 30° long. This meridian passes through Natal, the Transvaal, by Lake Tanganyika, and from thence to Cairo; connexion with the Russo-Scandinavian meridian arc of the same longitude should be made through Asia Minor, Turkey, Bulgaria and Rumania. With the completion of this project a continuous arc of 105° in latitude will have been measured.

Extensive triangle chains, suitable for latitude-degree measurements, have also been effected in Japan and Australia.

Besides, the systematization of gravity measurements is of importance, and for this purpose the association has instituted many reforms. It has ensured that the relative measurements made at the stations in different countries should be reduced conformably with the absolute determinations made at Potsdam; the result was that, in 1906, the intensities of gravitation at some 2000 stations had been co-ordinated. The intensity of gravity on the sea has been determined by the comparison of barometric and hypsometric observations (Mohn’s method). The association, at the proposal of Helmert, provided the necessary funds for two expeditions:—English Channel—Rio de Janeiro, and the Red Sea—Australia—San Francisco—Japan. Dr O. Hecker of the central bureau was in charge; he successfully overcame the difficulties of the work, and established the tenability of the isostatic hypothesis, which necessitates that the intensity of gravity on the deep seas has, in general, the same value as on the continents (without regard to the proximity of coasts).

As the result of the more recent determinations, the ellipticity, compression or flattening of the ellipsoid of the earth may be assumed to be very nearly 1/298.3; a value determined in 1901 by Helmert from the measurements of gravity. The semi-major axis, a, of the meridian ellipse may exceed 6,378,000 inter. metres by about 200 metres. The central bureau have adopted, for practical reasons, the value 1/299.15, after Bessel, for which tables exist; and also the value a = 6377397.155 (1 + 0.0001).

The methods of theoretical astronomy also permit the evaluation of these constants. The semi-axis a is calculable from the parallax of the moon and the acceleration of gravity on the earth; but the results are somewhat uncertain: the ellipticity deduced from lunar perturbations is 1/297.8 ± 2 (Helmert, Geodäsie, ii. pp. 460-473); William Harkness (The Solar Parallax and its related Constants, 1891) from all possible data derived the values: ellipticity = 1/300.2 ± 3, a = 6377972 ± 125 metres. Harkness also considered in this investigation the relation of the ellipticity to precession and nutation; newer investigations of the latter lead to the limiting values 1/296, 1/298 (Wiechert). It was clearly noticed in this method of determination that the influence of the assumption as to the density of the strata in the interior of the earth was but very slight (Radau, Bull. astr. ii. (1885) 157). The deviations of the geoid from the flattened ellipsoid of rotation with regard to the heights (the directions of normals being nearly the same) will scarcely exceed ± 100 metres (Helmert).

The basis of the degree- and gravity-measurements is actually formed by a stationary sea-surface, which is assumed to be level. However, by the influence of winds and ocean currents the mean surface of the sea near the coasts (which one assumes as the fundamental sea-surface) can deviate somewhat from a level surface. According to the more recent levelling it varies at the most by only some decimeters.

It is well known that the masses of the earth are continually undergoing small changes; the earth’s crust and sea-surface reciprocally oscillate, and the axis of rotation vibrates relatively to the body of the earth. The investigation of these problems falls in the programme of the Association. By continued observations of the water-level on sea-coasts, results have already been obtained as to the relative motions of the land and sea (cf. Geology); more exact levelling will, in the course of time, provide observations on countries remote from the sea-coast. Since 1900 an international service has been organized between some astronomical stations distributed over the north parallel of 39° 8′, at which geographical latitudes are observed whenever possible. The association contributes to all these stations, supporting four entirely: two in America, one in Italy, and one in Japan; the others partially (Tschardjui in Russia, and Cincinnati observatory). Some observatories, especially Pulkowa, Leiden and Tokyo, take part voluntarily. Since 1906 another station for South America and one for Australia in latitude − 31° 55′ have been added. According to the existing data, geographical latitudes exhibit variations amounting to ± 0.25″, which, for the greater part, proceed from a twelve- and a fourteen-month period.

(A. R. C; F. R. H.)

Eratosthenes Batavus, seu de terrae ambitus vera quantitate suscitatus, a Willebrordo Snellio, Lugduni-Batavorum (1617).

O. Callandreau, “Mémoire sur la théorie de la figure des planètes,” Ann. obs. de Paris (1889); G.H. Darwin, “The Theory of the Figure of the Earth carried to the Second Order of Small Quantities,” Mon. Not. R.A.S., 1899; E. Wiechert, “Über die Massenverteilung im Innern der Erde,” Nach. d. kön. G. d. W. zu Gött., 1897.

See I. Todhunter, Proc. Roy. Soc., 1870.

J.H. Jeans, “On the Vibrations and Stability of a Gravitating Planet,” Proc. Roy. Soc. vol. 71; G.H. Darwin, “On the Figure and Stability of a liquid Satellite,” Phil. Trans. 206, p. 161; A.E.H. Love, “The Gravitational Stability of the Earth,” Phil. Trans. 207, p. 237; Proc. Roy. Soc. vol. 80.

Survey of India, “The Attraction of the Himalaya Mountains upon the Plumb Line in India” (1901), p. 98.

Account of Experiments to Determine the Figure of the Earth by means of a Pendulum vibrating Seconds in Different Latitudes (1825).

Helmert, Theorien d. höheren Geod. ii., Leipzig, 1884.

Helmert, Sitzber. d. kgl. preuss. Ak. d. Wiss. zu Berlin (1901), p. 336.

“Bestimmung der absoluten Grösse der Schwerkraft zu Potsdam mit Reversionspendeln” (Veröffentlichung des kgl. preuss. Geod. Inst., N.F., No. 27).

Die Königl. Observatorien für Astrophysik, Meteorologie und Geodäsie bei Potsdam (Berlin, 1890); Verhandlungen der I. Allgemeinen Conferenz der Bevollmächtigten zur mitteleurop. Gradmessung, October, 1864, in Berlin (Berlin, 1865); A. Hirsch, Verhandlungen der VIII. Allg. Conf. der Internationalen Erdmessung, October, 1886, in Berlin (Berlin, 1887); and Verhandlungen der XI. Allg. Conf. d. I. E., October, 1895, in Berlin (1896).

Ibañez and Perrier, Jonction géod. et astr. de l’Algérie avec l’Espagne (Paris, 1886); Mémorial du dépôt général de la guerre, t. xii.: Nouvelle méridienne de France (Paris, 1885, 1902, 1904); Comptes rendus des séances de la 12e-19e conférence générale de l’Assoc. Géod. Internat., 1898 at Stuttgart, 1900 at Paris, 1903 at Copenhagen, 1906 at Budapest (Berlin, 1899, 1901, 1904, 1908); A. Ferrero, Rapport sur les triangulations, prés. à la 12e conf. gén. 1898.

R. Schumann, C. r. de Budapest, p. 244.

O. and A. Börsch, “Verbindung d. russ.-skandinav. mit der franz.-engl. Breitengradmessung” (Verhandlungen der 9. Allgem. Conf. d. I. E. in Paris, 1889, Ann. xi.).

U.S. Coast and Geodetic Survey; H.S. Pritchett, superintendent. The Transcontinental Triangulation and the American Arc of the Parallel, by C.A. Schott (Washington, 1900).

U.S. Coast and Geodetic Survey; O.H. Tittmann, superintendent. The Eastern Oblique Arc of the United States, by C.A. Schott (1902).

Missions scientifiques pour la mesure d’un arc de méridien au Spitzberg entreprises en 1899-1902 sous les auspices des gouvernements russe et suédois. Mission russe (St Pétersbourg, 1904); Mission suédoise (Stockholm, 1904).

Sir David Gill, Report on the Geodetic Survey of South Africa, 1833-1892 (Cape Town, 1896), vol. ii. 1901, vol. iii. 1905.

O. Hecker, Bestimmung der Schwerkraft a. d. Atlantischen Ozean (Veröffentl. d. Kgl. Preuss. Geod. Inst. No. 11), Berlin, 1903.

F.R. Helmert. “Neuere Fortschritte in der Erkenntnis der math. Erdgestalt” (Verhandl. des VII. Internationalen Geographen-Kongresses, Berlin, 1899), London, 1901.

C. Lallemand, “Rapport sur les travaux du service du nivellement général de la France, de 1900 à 1906″ (Comp. rend. de la 14e conf. gén. de l’Assoc. Géod-Intern., 1903, p. 178).

T. Albrecht, Resultate des internat. Breitendienstes, i. and ii. (Berlin, 1903 and 1906); F. Klein and A. Sommerfeld, Über die Theorie des Kreisels, iii. p. 672; R. Spitaler, “Die periodischen Luftmassenverschiebungen und ihr Einfluss auf die Lagenänderung der Erdaxe” (Petermanns Mitteilungen, Ergänzungsheft, 137); S. Newcomb, “Statement of the Theoretical Laws of the Polar Motion” (Astronomical Journal, 1898, xix. 158); F.R. Helmert, “Zur Erklärung der beobachteten Breitenänderungen” (Astr. Nachr. No. 3014); J. Weeder, “The 14-monthly period of the motion of the Pole from determinations of the azimuth of the meridian marks of the Leiden observatory” (Kon. Ak. van Wetenschappen to Amsterdam, 1900); A. Sokolof, “Détermination du mouvement du pôle terr. au moyen des mires méridiennes de Poulkovo” (Mél. math. et astr. vii., 1894); J. Bonsdorff, “Beobachtungen von δ Cassiopejae mit dem grossen Zenitteleskop” (Mitteilungen der Nikolai-Hauptsternwarte zu Pulkowo, 1907); J. Larmor and E.H. Hills, “The irregular movement of the Earth’s axis of rotation: a contribution towards the analysis of its causes” (Monthly Notices R.A.S., 1906, lxvii. 22); A.S. Cristie, “The latitude variation Tide” (Phil. Soc. of Wash., 1895, Bull. xiii. 103); H.G. van de Sande Bakhuysen, “Über die Änderung der Polhöhe” (Astr. Nachr. No. 3261); A.V. Bäcklund, “Zur Frage nach der Bewegung des Erdpoles” (Astr. Nachr. No. 3787); R. Schumann, “Über die Polhöhenschwankung” (Astr. Nachr. No. 3873); “Numerische Untersuchung” (Ergänzungshefte zu den Astr. Nachr. No. 11); Weitere Untersuchungen (No. 4142); Bull. astr., 1900, June, report of different theoretical memoirs.

EARTH CURRENTS. After the invention of telegraphy it was soon found that telegraph lines in which the circuit is completed by the earth are traversed by natural electric currents which occasionally interfere seriously with their use, and which are known as “earth currents.”

1. Amongst the pioneers in investigating the subject were several English telegraphists, e.g. W.H. Barlow (1) and C.V. Walker (2), who were in charge respectively of the Midland and South-Eastern telegraph systems. Barlow noticed the existence of a more or less regular diurnal variation, and the result—confirmed by all subsequent investigators—that earth currents proper occur in a line only when both ends are earthed. Walker, as the result of general instructions issued to telegraph clerks, collected numerous statistics as to the phenomena during times of large earth currents. His results and those given by Barlow both indicate that the lines to suffer most from earth currents in England have the general direction N.E. to S.W. As Walker points out, it is the direction of the terminal plates relative to one another that is the essential thing. At the same time he noticed that whilst at any given instant the currents in parallel lines have with rare exceptions the same direction, some lines show normally stronger currents than others, and he suggested that differences in the geological structure of the intervening ground might be of importance. This is a point which seems still somewhat obscure.

Our present knowledge of the subject owes much to practical men, but even in the early days of telegraphy the fact that telegraph systems are commercial undertakings, and cannot allow the public to wait the convenience of science, was a serious obstacle to their employment for research. Thus Walker feelingly says, when regretting his paucity of data during a notable earth current disturbance: “Our clerks were at their wits’ end to clear off the telegrams.... At a time when observations would have been very highly acceptable they were too much occupied with their ordinary duties.” Some valuable observations have, however, been made on long telegraph lines where special facilities have been given.

Amongst these may be mentioned the observations on French lines in 1883 described by E.E. Blavier (3), and those on two German lines Berlin-Thorn and Berlin-Dresden during 1884 to 1888 discussed by B. Weinstein (4).

2. Of the experimental lines specially constructed perhaps the best known are the Greenwich lines instituted by Sir G.B. Airy (5), the lines at Pawlowsk due to H. Wild (6), and those at Parc Saint Maur, near Paris (7).

Experimental Lines.—At Greenwich observations were commenced in 1865, but there have been serious disturbances due to artificial currents from electric railways for many years. There are two lines, one to Dartford distant about 10 m., in a direction somewhat south of east, the other to Croydon distant about 8 m., in a direction west of south.

Information from a single line is incomplete, and unless this is clearly understood erroneous ideas may be derived. The times at which the current is largest and least, or when it vanishes, in an east-west line, tell nothing directly as to the amplitude at the time of the resultant current. The lines laid down at Pawlowsk in 1883 lay nearly in and perpendicular to the geographical meridian, a distinct desideratum, but were only about 1 km. long. The installation at Parc Saint Maur, discussed by T. Moureaux, calls for fuller description. There are three lines, one having terminal earth plates 14.8 km. apart in the geographical meridian, a second having its earth plates due east and west of one another, also 14.8 km. apart, and the third forming a closed circuit wholly insulated from the ground. In each of the three lines is a Deprez d’Arsonval galvanometer. Light reflected from the galvanometer mirrors falls on photographic paper wound round a drum turned by clockwork, and a continuous record is thus obtained.

3. Each galvanometer has a resistance of about 200 ohms, but is shunted by a resistance of only 2 ohms. The total effective resistances in the N.-S. and E.-W. lines are 225 and 348 ohms respectively. If i is the current recorded, L, g and s the resistances of the line, galvanometer and shunt respectively, then E, the difference of potential between the two earth plates, is given by

E = i (1 + g/s) {L + gs / (g + s)}.

To calibrate the record, a Daniell cell is put in a circuit including 1000 ohms and the three galvanometers as shunted. If i′ be the current recorded, e the E.M.F. of the cell, then e = i′ (1 + g/s) {1000 + 3gs / (g + s)}. Under the conditions at Parc Saint Maur we may write 2 for gs / (g + s), and 1.072 for e, and thence we have approximately E = 0.240 (i / i′) for the N.-S. line, and E = −0.371(i / i′) for the E.-W. line.

The method of standardization assumes a potential difference between earth plates which varies slowly enough to produce a practically steady current. There are several causes producing currents in a telegraph wire which do not satisfy this limitation. During thunderstorms surgings may arise, at least in overhead wires, without these being actually struck. Again, if the circuit includes a variable magnetic field, electric currents will be produced independently of any direct source of potential difference. In the third circuit at Parc Saint Maur, where no earth plates exist, the current must be mainly due to changes in the earth’s vertical magnetic field, with superposed disturbances due to atmospheric electricity or aerial waves. Even in the other circuits, magnetic and atmospheric influences play some part, and when their contribution is important, the galvanometer deflection has an uncertain value. What a galvanometer records when traversed by a suddenly varying current depends on other things than its mere resistance.

Even when the current is fairly steady, its exact significance is not easily stated. In the first place there is usually an appreciable E.M.F. between a plate and the earth in contact with it, and this E.M.F. may vary with the temperature and the dryness of the soil. Naturally one employs similar plates buried to the same depth at the two ends, but absolute identity and invariability of conditions can hardly be secured. In some cases, in short lines (8), there is reason to fear that plate E.M.F.’s have been responsible for a good deal that has been ascribed to true earth currents. With deep earth plates, in dry ground, this source of uncertainty can, however, enter but little into the diurnal inequality.

4. Another difficulty is the question of the resistance in the earth itself. A given E.M.F. between plates 10 m. apart may mean very different currents travelling through the earth, according to the chemical constitution and condition of the surface strata.

According to Professor A. Schuster (9), if ρ and ρ’ be the specific resistances of the material of the wire and of the soil, the current i which would pass along an underground cable formed of actual soil, equal in diameter to the wire connecting the plates, is given by i = i′ρ / ρ′, where i′ is the observed current in the wire. As ρ’ will vary with the depth, and be different at different places along the route, while discontinuities may arise from geological faults, water channels and so on, it is clear that even the most careful observations convey but a general idea as to the absolute intensity of the currents in the earth itself. In Schuster’s formula, as in the formulae deduced for Parc Saint Maur, it is regarded as immaterial whether the wire connecting the plates is above or below ground. This view is in accordance with records obtained by Blavier (3) from two lines between Paris and Nancy, the one an air line, the other underground.

5. The earliest quantitative results for the regular diurnal changes in earth currents are probably those deduced by Airy (5) from the records at Greenwich between 1865 and 1867. Airy resolved the observed currents from the two Greenwich lines in and perpendicular to the magnetic meridian (then about 21° to the west of astronomical north). The information given by Airy as to the precise meaning of the quantities he terms “magnetic tendency” to north and to west is somewhat scanty, but we are unlikely to be much wrong in accepting his figures as proportional to the earth currents from magnetic east to west and from magnetic north to south respectively. Airy gives mean hourly values for each month of the year. The corresponding mean diurnal inequality for the whole year appears in Table 1., the unit being arbitrary. In every month the algebraic mean of the 24 hourly values represented a current from north to south in the magnetic meridian, and from east to west in the perpendicular direction; in the same arbitrary units used in Table I. the mean values of these two “constant” currents were respectively 777 and 559.

6. Diurnal Variation.—Probably the most complete records of diurnal variation are those discussed by Weinstein (4), which depend on several years’ records on lines from Berlin to Dresden and to Thorn. Relative to Berlin the geographical co-ordinates of the other two places are:

Thorn 0° 29′ N. lat. 5° 12′ E. long.

Dresden 1° 28′ S. lat. 0° 21′ E. long.

Thus the Berlin-Dresden line was directed about 8½° east of south, and the Berlin-Thorn line somewhat more to the north of east. The latter line had a length about 2.18 times that of the former. The resistances in the two lines were made the same, so if we suppose the difference of potential between earth plates along a given direction to vary as their distance apart, the current observed in the Thorn-Berlin line has to be divided by 2.18 to be comparable with the other. In this way, resolving along and perpendicular to the geographical meridian, Weinstein gives as proportional to the earth currents from east to west and from south to north respectively

J = 0.147i′ + 0.435i, and J′ = 0.989i′ − 0.100i,

where i and i’ are the observed currents in the Thorn-Berlin and Dresden-Berlin lines respectively, both being counted positive when flowing towards Berlin.

It is tacitly assumed that the average earth conductivity is the same between Berlin and Thorn as between Berlin and Dresden. It should also be noticed that local time at Berlin and Thorn differs by fully 20 minutes, while the crests of the diurnal variations in short lines at the two places would probably occur about the same local time. The result is probably a less sharp occurrence of maxima and minima, and a relatively smaller range, than in a short line having the same orientation.

Table I.

Mean Diurnal Inequalities for the year. Numerical Values of resultant
current.

Greenwich. Thorn-Berlin-Dresden. Thorn-Berlin-Dresden.

Hour. North
to
South
(Mag.) East
to
West
(Mag.) Berlin
to
Dresden. Thorn
to
Berlin. North
to
South
(Ast.) East
to
West
(Ast.) Mean hourly values from

Year. Winter. Equinox. Summer.

1 −94 −41 −17 −13 −20 −10 81 94 51 98

2 −68 −24 −6 −13 −9 −11 84 115 39 97

3 −44 −8 −1 −1 −1 −1 84 113 31 108

4 −18 +9 −20 +15 −17 +17 101 94 58 127

5 −30 −1 −79 +21 −74 +32 122 58 78 230

6 −63 −33 −139 +5 −136 +26 148 80 139 225

7 −121 −80 −138 −36 −144 −14 166 155 206 136

8 −175 −123 −7 −98 −28 −92 203 152 185 271

9 −156 −137 +249 −156 +212 −184 305 67 272 575

10 −43 −77 +540 −184 +494 −254 557 232 628 811

11 +82 +1 +722 −165 +678 −-263 728 411 885 887

Noon +207 +66 +673 −107 +642 −200 675 441 848 735

1 +245 +94 +404 −20 +395 −79 400 284 510 406

2 +205 +113 +35 +55 +46 +47 98 68 103 125

3 +153 +97 −261 +99 −237 +132 272 136 355 324

4 +159 +108 −397 +114 −368 +167 404 218 503 492

5 +167 +118 −391 +108 −363 +160 397 206 453 532

6 +125 +95 −311 +96 −287 +137 319 176 333 446

7 +43 +55 −237 +85 −216 +115 247 180 250 312

8 −22 +4 −191 +74 −173 +98 201 207 217 181

9 −115 −49 −168 +59 −153 +81 174 208 194 120

10 −138 −74 −135 +40 −125 +58 138 155 149 111

11 −136 −70 −84 +18 −79 +29 89 64 95 107

Midnight −147 −80 −43 −2 −43 +4 91 42 119 111

It was found that the average current derived from a number of undisturbed days on either line might be regarded as made up of a “constant part” plus a regular diurnal inequality, the constant part representing the algebraic mean value of the 24 hourly readings. In both lines the constant part showed a decided alteration during the third year—changing sign in one line—in consequence, it is believed, of alterations made in the earth plates. The constant part was regarded as a plate effect, and was omitted from further consideration. Table I. shows in terms of an arbitrary unit—whose relation to that employed for Greenwich data is unknown—the diurnal inequality in the currents along the two lines, and the inequalities thence calculated for ideal lines in and perpendicular to the geographical meridian. Currents are regarded as positive when directed from Berlin to Dresden and from north to south, the opposite point of view to that adopted by Weinstein. The table also shows the mean numerical value of the resultant current (the “constant” part being omitted) for each hour of the day, for the year as a whole, and for winter (November to February), equinox (March, April, September, October) and summer (May to August). There is a marked double period in both the N.-S. and E.-W. currents. In both cases the numerically largest currents occur from 10 A.M. to noon, the directions then being from north to south and from west to east. The currents tend to die out and change sign about 2 P.M., the numerical magnitude then rising again rapidly to 4 or 5 P.M. The current in the meridian is notably the larger. The numerical values assigned to the resultant current are arithmetic means from the several months composing the season in question.

7. The mean of the 24 hourly numerical values of the resultant current for each month of the year a deducible from Weinstein’s data—the unit being the same as before—are given in Table II.

Table II.—Mean Numerical Value of Resultant Current.

Jan. Feb. March April May June July Aug. Sep. Oct. Nov. Dec.

152 211 293 328 313 314 337 300 258 235 165 132

There is thus a conspicuous minimum at mid-winter, and but little difference between the monthly means from April to August. This is closely analogous to what is seen in the daily range of the magnetic elements in similar latitudes (see Magnetism, Terrestrial). There is also considerable resemblance between the curve whose ordinates represent the diurnal inequality in the current passing from north to south, and the curve showing the hourly change in the westerly component of the horizontal magnetic force in similar European latitudes.

8. Relations with Sun-spots, Auroras and Magnetic Storms.—Weinstein gives curves representing the mean diurnal inequality for separate years. In both lines the diurnal amplitudes were notably smaller in the later years which were near sun-spot minimum. This raises a presumption that the regular diurnal earth currents, like the ranges of the magnetic elements, follow the 11-year sun-spot period. When we pass to the large and irregular earth currents, which are of practical interest in telegraphy, there is every reason to suppose that the sun-spot period applies. These currents are always accompanied by magnetic disturbances, and when specially striking by brilliant aurora. One most conspicuous example of this occurred in the end of August and beginning of September 1859. The magnetic disturbances recorded were of almost unexampled size and rapidity, the accompanying aurora was extraordinarily brilliant, and E.M.F.’s of 700 and 800 volts are said to have been reached on telegraph lines 500 to 600 km. long. It is doubtful whether the disturbances of 1859 have been equalled since, but earth current voltages of the order of 0.5 volts per mile have been recorded by various authorities, e.g. Sir W.H. Preece (10).

It was the practice for several years to publish in the Ann. du bureau central météorologique synchronous magnetic and earth current curves from Parc Saint Maur corresponding to the chief disturbances of the year. In most cases there is a marked similarity between the curve of magnetic declination and that of the north-south earth current. At times there is also a distinct resemblance between the horizontal force magnetic curve and that of the east-west earth current, but exceptions to this are not infrequent. Similar phenomena appear in synchronous Greenwich records published by Airy in 1868; these show a close accordance between the horizontal force curves and those of the currents from magnetic east to west. Originally it was supposed by Airy that whilst rapid movements in the declination and north-south current curves sometimes occurred simultaneously, there was a distinct tendency for the latter to precede the former. More recent examinations of the Greenwich records by W. Ellis (11), and of the Parc St Maur curves by Moureaux, have not confirmed this result, and it is now believed that the two phenomena are practically simultaneous.

There has also been a conflict of views as to the connexion between magnetic and earth current disturbances. Airy’s observations tended to suggest that the earth current was the primary cause, and the magnetic disturbance in considerable part at least its effect. Others, on the contrary, have supposed earth currents to be a direct effect of changes in the earth’s magnetic field. The prevailing view now is that both the magnetic and the earth current disturbances are due to electric currents in the upper atmosphere, these upper currents becoming visible at times as aurora.

9. There seems some evidence that earth currents can be called into existence by purely local causes, notably difference of level. Thus K.A. Brander (12) has observed a current flowing constantly for a good many days from Airolo (height 1160 metres) to the Hospice St Gotthard (height 2094 metres). In an 8-km. line from Resina to the top of Vesuvius L. Palmieri (13)—observing in 1889 at three-hour intervals from 9 A.M. to 9 P.M.—always found a current running uphill so long as the mountain was quiet. On a long line from Vienna to Graz A. Baumgartner (14) found that the current generally flowed from both ends towards intervening higher ground during the day, but in the opposite directions at night. During a fortnight in September and October 1885 hourly readings were taken of the current in the telegraph cable from Fort-William to Ben Nevis Observatory, and the results were discussed by H.N. Dickson (15), who found a marked preponderance of currents up the line to the summit. The recorded mean data, otherwise regarded, represent a “constant” current, equal to 29 in the arbitrary units employed by Dickson, flowing up the line, together with the following diurnal inequality, + denoting current towards Fort-William (i.e. down the hill, and nearly east to west).

Hour 1 2 3 4 5 6 7 8 9 10 11 12

A.M. −21 −41 +13 +23 +55 −3 +25 −32 −59 −62 −46 +6

P.M. +24 +18 +115 +18 +75 −5 +50 −9 −56 −37 −28 −34

There is thus a diurnal inequality, which is by no means very irregular considering the limited number of days, and it bears at least a general resemblance to that shown by Weinstein’s figures for an east-west line in Germany. This will serve to illustrate the uncertainties affecting these and analogous observations. A constant current in one direction may arise in whole or part from plate E.M.F.’s; a current showing a diurnal inequality will naturally arise between any two places some distance apart whether they be at different levels or not. Finally, when records are taken only for a short time, doubts must arise as to the generality of the results. During the Ben Nevis observations, for instance, we are told that the summit was almost constantly enveloped in fog or mist. By having three earth plates in the same vertical plane, one at the top of a mountain, the others at opposite sides of it, and then observing the currents between the summit and each of the base stations, as well as directly between the base stations—during an adequate number of days representative of different seasons of the year and different climatic conditions—many uncertainties would soon be removed.

10. Artificial Currents.—The great extension in the applications of electricity to lighting, traction and power transmission, characteristic of the end of the 19th century, has led to the existence of large artificial earth currents, which exert a disturbing influence on galvanometers and magnetic instruments, and also tend to destroy metal pipes. In the former case, whilst the disturbance is generally loosely assigned to stray or “vagabond” earth currents, this is only partly correct. The currents used for traction are large, and even if there were a perfectly insulated return there would be a considerable resultant magnetic field at distances from the track which were not largely in excess of the distance apart of the direct and return currents (16). At a distance of half a mile or more from an electric tram line the disturbance is usually largest in magnetographs recording the vertical component of the earth’s field. The magnets are slightly displaced from the position they would occupy if undisturbed, and are kept in continuous oscillation whilst the trams are running (17). The extent of the oscillation depends on the damping of the magnets.

The distance from an electric tram line where the disturbance ceases to be felt varies with the system adopted. It also depends on the length of the line and its subdivision into sections, on the strength of the currents supplied, the amount of leakage, the absence or presence of “boosters,” and finally on the sensitiveness of the magnetic instruments. At the U.S. Coast and Geodetic Survey’s observatory at Cheltenham the effect of the Washington electric trams has been detected by highly sensitive magnetographs, though the nearest point of the line is 12 m. away (18). Amongst the magnetic observatories which have suffered severely from this cause are those at Toronto, Washington (Naval Observatory), Kew, Paris (Parc St Maur), Perpignan, Nice, Lisbon, Vienna, Rome, Bombay (Colaba) and Batavia. In some cases magnetic observations have been wholly suspended, in others new observatories have been built on more remote sites.

As regards damage to underground pipes, mainly gas and water pipes, numerous observations have been made, especially in Germany and the United States. When electric tramways have uninsulated returns, and the potential of the rails is allowed to differ considerably from that of the earth, very considerable currents are found in neighbouring pipes. Under these conditions, if the joints between contiguous pipes forming a main present appreciable resistance, whilst the surrounding earth through moisture or any other cause is a fair conductor, current passes locally from the pipes to the earth causing electrolytic corrosion of the pipes. Owing to the diversity of interests concerned, the extent of the damage thus caused has been very variously estimated. In some instances it has been so considerable as to be the alleged cause of the ultimate failure of water pipes to stand the pressure they are exposed to.

Bibliography.—See Svante August Arrhenius, Lehrbuch der kosmischen Physik (Leipzig, 1903), pp. 984-990. For lists of references see J.E. Burbank, Terrestrial Magnetism, vol. 10 (1905), p. 23, and P. Bachmetjew (8). For papers descriptive of corrosion of pipes, &c., by artificial currents see Science Abstracts (in recent years in the volumes devoted to engineering) under the heading “Traction, Electric; Electrolysis.” The following are the references in the text:—(1) Phil. Trans. R.S. for 1849, pt. i. p. 61; (2) Phil. Trans. R.S. vol. 151 (1861), p. 89, and vol. 152 (1862), p. 203; (3) Étude des courants telluriques (Paris, 1884); (4) Die Erdströme im deutschen Reichstelegraphengebiet (Braunschweig, 1900); (5) Phil. Trans. R.S. vol. 158 (1868), p. 465, and vol. 160 (1870), p. 215; (6) Mém. de l’Académie St-Pétersbourg, t. 31, No. 12 (1883); (7) T. Moureaux, Ann. du Bureau Central Mét. (Année 1893), 1 Mem. p. B 23; (8) P. Bachmetjew, Mém. de l’Académie St-Pétersbourg, vol. 12, No. 3 (1901); (9) Terrestrial Magnetism, vol. 3 (1898), p. 130; (10) Journal Tel. Engineers (1881); (11) Proc. R.S. vol. 52 (1892), p. 191; (12) Akad. Abhandlung (Helsingfors, 1888); (13) Acad. Napoli Rend. (1890), and Atti (1894, 1895); (14) Pogg. Ann. vol. 76, p. 135; (15) Proc. R.S.E. vol. 13, p. 530; (16) A. Rücker, Phil. Mag. 1 (1901), p. 423, and R.T. Glazebrook, ibid. p. 432; (17) J. Edler, Elektrotech. Zeit. vol. 20 (1899); (18) L.A. Bauer, Terrestrial Magnetism, vol. 11 (1906), p. 53.

(C. Ch.)

EARTH-NUT, the English name for a plant known botanically as Conopodium denudatum (or Bunium flexuosum), a member of the natural order Umbelliferae, which has a brown tuber-like root-stock the size of a chestnut. It grows in woods and fields, has a slender flexuous smooth stem 2 to 3 ft. high, much-divided leaves, and small white flowers in many-rayed terminal compound umbels. Boswell Syme, in English Botany, iv. 114, says: “The common names of this plant in England are various. It is known as earth-nut, pig-nut, ar-nut, kipper-nut, hawk-nut, jar-nut, earth-chestnut and ground-nut. Though really excellent in taste and unobjectionable as food, it is disregarded in England by all but pigs and children, both of whom appreciate it and seek eagerly for it.” Dr Withering describes the roots as little inferior to chestnuts. In Holland and elsewhere on the continent of Europe they are more generally eaten.

EARTH PILLAR, a pillar of soft rock, or earth, capped by some harder material that has protected it from denudation. The “bad lands” of western North America furnish numerous examples. Here “the formations are often beds of sandstone or shale alternating with unindurated beds of clay. A semi-arid climate where the precipitation is much concentrated seems to be most favourable to the development of this type of formation.” The country round the Dead Sea, where loose friable sandy clay is capped by harder rock, produces “bad-land” topography. The cap of hard rock gives way at the joints, and the water making its way downwards washes away the softer material directly under the cracks, which become wider, leaving isolated columns of clay capped with hard sandstone or limestone. These become smaller and fewer as denudation proceeds, the pillars standing a great height at times, until finally they all disappear.

EARTHQUAKE. Although the terrible effects which often accompany earthquakes have in all ages forced themselves upon the attention of man, the exact investigation of seismic phenomena dates only from the middle of the 19th century. A new science has been thus established under the name of seismology (Gr. σεισμός, an earthquake).

History.—Accounts of earthquakes are to be found scattered through the writings of many ancient authors, but they are, for the most part, of little value to the seismologist. There is a natural tendency to exaggeration in describing such phenomena, sometimes indeed to the extent of importing a supernatural element into the description. It is true that attempts were made by some ancient writers on natural philosophy to offer a rational explanation of earthquake phenomena, but the hypotheses which their explanations involved are, as a rule, too fanciful to be worth reproducing at the present day. It is therefore unnecessary to dwell upon the references to seismic phenomena which have come down to us in the writings of such historians and philosophers as Thucydides, Aristotle and Strabo, Seneca, Livy and Pliny. Nor is much to be gleaned from the pages of medieval and later writers on earthquakes, of whom the most notable are Fromondi (1527), Maggio (1571) and Travagini (1679). In England, the earliest work worthy of mention is Robert Hooke’s Discourse on Earthquakes, written in 1668, and read at a later date before the Royal Society. This discourse, though containing many passages of considerable merit, tended but little to a correct interpretation of the phenomena in question. Equally unsatisfactory were the attempts of Joseph Priestley and some other scientific writers of the 18th century to connect the cause of earthquakes with electrical phenomena. The great earthquake of Lisbon in 1755 led the Rev. John Michell, professor of mineralogy at Cambridge, to turn his attention to the subject; and in 1760 he published in the Philosophical Transactions a remarkable essay on the Cause and Phenomena of Earthquakes. A suggestion of much scientific interest was made by Thomas Young, when in his Lectures on Natural Philosophy, published in 1807, he remarked that an earthquake “is probably propagated through the earth nearly in the same manner as a noise is conveyed through the air.” The recognition of the fact that the seismologist has to deal with the investigation of wave-motion in solids lies at the very base of his science. In 1846 Robert Mallet communicated to the Royal Irish Academy his first paper “On the Dynamics of Earthquakes”; and in the following year W. Hopkins, of Cambridge, presented to the British Association a valuable report in which earthquake phenomena were discussed in some detail. Mallet’s labours were continued for many years chiefly in the form of Reports to the British Association, and culminated in his great work on the Neapolitan earthquake of 1857. An entirely new impetus, however, was given to the study of earthquakes by an energetic body of observers in Japan, who commenced their investigations about the year 1880, mainly through the influence of Prof. John Milne, then of Tokyo. Their work, carried on by means of new instruments of precision, and since taken up by observers in many parts of the world, has so extended our knowledge of earthquake-motion that seismology has now become practically a new department of physical science.

It is hardly too much to say, however, that the earliest systematic application of scientific principles to the study of the effects of an earthquake was made by Mallet in his investigation of the Neapolitan earthquake mentioned above. It is true, the great Calabrian earthquake of 1783 had been the subject of careful inquiry by the Royal Academy of Naples, as also by Deodat Dolomieu and some other scientific authorities; but in consequence of the misconception which at that time prevailed with regard to the nature of seismic activity, the results of the inquiry, though in many ways interesting, were of very limited scientific value. It was reserved for Mallet to undertake for the first time an extensive series of systematic observations in an area of great seismic disturbance, with the view of explaining the phenomena by the application of the laws of wave-motion.

The “Great Neapolitan Earthquake,” by which more than 12,300 lives were lost, was felt in greater or less degree over all Italy south of the parallel of 42°, and has been regarded as ranking third in order of severity among the recorded earthquakes of Europe. The principal shock occurred at about 10 P.M. on the 16th of December 1857; but, as is usually the case, it had been preceded by minor disturbances and was followed by numerous after-shocks which continued for many months. Early in 1858, aided by a grant from the Royal Society, Mallet visited the devastated districts, and spent more than two months in studying the effects of the catastrophe, especially examining, with the eye of an engineer, the cracks and ruins of the buildings. His voluminous report was published in 1862, and though his methods of research and his deductions have in many cases been superseded by the advance of knowledge, the report still remains a memorable work in the history of seismology.

Much of Mallet’s labour was directed to the determination of the position and magnitude of the subterranean source from which the vibratory impulses originated. This is known variously as the seismic centre, centrum, hypocentre, origin or focus. It is often convenient to regard this centre theoretically as a point, but practically it must be a locus or space of three dimensions, which in different cases varies much in size and shape, and may be of great magnitude. That part of the surface of the earth which is vertically above the centre is called the epicentre; or, if of considerable area, the epicentral or epifocal tract. A vertical line joining the epicentre and the focus was termed by Mallet the seismic vertical. He calculated that in the case of the Neapolitan earthquake the focal cavity was a curved lamelliform fissure, having a length of about 10 m. and a height of about 3½ m., whilst its width was inconsiderable. The central point of this fissure, the theoretical seismic centre, he estimated to have been at a depth of about 6½ m. from the surface. Dr C. Davison, in discussing Mallet’s data, was led to the conclusion that there were two distinct foci, possibly situated on a fault, or plane of dislocation, running in a north-west and south-east direction. Mallet located his epicentre near the village of Caggiano, not far from Polla, while the other seems to have been in the neighbourhood of Montemurro, about 25 m. to the south-east.

The intensity, or violence, of an earthquake is greatest in or near the epicentre, whence it decreases in all directions. A line drawn through points of equal intensity forms a curve round the epicentre known as an isoseist, an isoseismal or an isoseismic line. If the intensity declined equally in all directions the isoseismals would be circles, but as this is rarely if ever the case in nature they usually become ellipses and other closed curves. The tract which is most violently shaken was termed by Mallet the meizoseismic area, whilst the line of maximum destruction is known as the meizoseismic line. That isoseismal along which the decline of energy is most rapid was called by K. von Seebach a pleistoseist.

In order to determine the position of the seismic centre, Mallet made much use of the cracks in damaged buildings, especially in walls of masonry, holding that the direction of such fractures must generally be at right angles to that in which the normal earthquake-wave reached them. In this way he obtained the “angle of emergence” of the wave. He also assumed that free-falling bodies would be overthrown and projected in the direction of propagation of the wave, so that the epicentre might immediately be found from the intersection of such directions. These data are, however, subject to much error, especially through want of homogeneity in the rocks, but Mallet’s work was still of great value.

A different method of ascertaining the depth of the focus was adopted by Major C.E. Dutton in his investigation of the Charleston earthquake of the 31st of August 1886 for the U.S. Geological Survey. This catastrophe was heralded by shocks of greater or less severity a few days previously at Summerville, a village 22 m. north-west of Charleston. The great earthquake occurred at 9.51 P.M., standard time of the 75th meridian, and in about 70 seconds almost every building in Charleston was more or less seriously damaged, while many lives were lost. The epicentral tract was mainly a forest region with but few buildings, and the principal records of seismological value were afforded by the lines of railway which traversed the disturbed area. In many places these rails were flexured and dislocated. Numerous fissures opened in the ground, and many of these discharged water, mixed sometimes with sand and silt, which was thrown up in jets rising in some cases to a height of 20 ft. Two epicentres were recognized—one near Woodstock station on the South Carolina railway, and the other, being the centre of a much smaller tract, about 14 m. south-west of the first and near the station of Rantowles on the Charleston and Savannah line. Around these centres and far away isoseismal lines were drawn, the relative intensity at different places being roughly estimated by the effects of the catastrophe on various structures and natural objects, or, where visible records were wanting, by personal evidence, which is often vague and variable. The Rossi-Forel scale was adopted. This is an arbitrary scale formulated by Professor M.S. de Rossi, of Rome, and Dr F.A. Forel, of Geneva, based mostly on the ordinary phenomena observed during an earthquake, and consisting of ten degrees, of which the lowest is the feeblest, viz. I. Microseismic shock; II. Extremely feeble shock; III. Very feeble shock; IV. Feeble; V. Shock of moderate intensity; VI. Fairly strong shock; VII. Strong shock; VIII. Very strong shock; IX. Extremely strong shock; X. Shock of extreme intensity. Other conventional scales, some being less detailed, have been drawn up by observers in such earthquake-shaken countries as Italy and Japan. A curve, or theoretical isoseismal, drawn through certain points where the decline of intensity on receding from the epicentre seems to be greatest was called by Dutton an “index-circle”; and it can be shown that the radius of such a circle multiplied by the square root of 3 gives the focal depth theoretically. In this way it was computed that in the Charleston earthquake the origin under Woodstock must have had a depth of about 12 m. and that near Rantowles a depth of nearly 8 m. The determination of the index-circle presents much difficulty, and the conclusions must be regarded as only approximate.

It is probable, according to R.D. Oldham, that local earthquakes may originate in the “outer skin” of the earth, whilst a large world-shaking earthquake takes its origin in the deeper part of the “crust,” whence such a disturbance is termed a bathyseism. Large earthquakes may have very extended origins, with no definite centre, or with several foci.

The gigantic disaster known as the “Great Indian Earthquake,” which occurred on the 12th of June 1897, was the subject of careful investigation by the Geological Survey of India and was described in detail by the superintendent, R.D. Oldham. It is sometimes termed the Assam earthquake, since it was in that province that the effects were most severe, but the shocks were felt over a large part of India, and indeed far beyond its boundaries. Much of the area which suffered most disturbance was a wild country, sparsely populated, with but few buildings of brick or stone from which the violence of the shocks could be estimated. The epicentral tract was of great size, having an estimated area of about 6000 sq. m., but the mischief was most severe in the neighbourhood of Shillong, where the stonework of bridges, churches and other buildings was absolutely levelled to the ground. After the main disturbance, shocks of greater or less severity continued at intervals for many weeks. It is supposed that this earthquake was connected with movement of subterranean rock-masses of enormous magnitude along a great thrust-plane, or series of such planes, having a length of about 200 m. and a maximum breadth of not less than 50 m. It is pointed out by Oldham that this may be compared for size with the great Faille du Midi in Belgium, which is known to extend for a distance of 120 m. The depth of the principal focus, though not actually capable of determination, was probably less than 5 m. from the surface. From the focus many secondary faults and fractures proceeded, some reaching the surface of the ground. Enormous landslips accompanied the earthquake, and as an indirect effect of these slides the form of the water-courses became in certain cases modified. Permanent changes of level were also observed.

Eight years after the great Assam earthquake India was visited by another earthquake, which, though less intense, resulted in the loss of about 20,000 lives. This catastrophe is known as the Kangra earthquake, since its centre seems to have been located in the Kangra valley, in the north-west Himalaya. It occurred on the 4th of April 1905, and the first great shocks were felt in the chief epifocal district at about 6.9 a.m., Madras time. Although the tract chiefly affected was around Kangra and Dharmsala, there was a subordinate epifocal tract in Dehra Dun and the neighbourhood of Mussoorie, whilst the effects of the earthquake extended in slight measure to Lahore and other cities of the plain. It is estimated that the earthquake was felt over an area of about 1,625,000 m. Immediately after the calamity a scientific examination of its effects was made by the Geological Survey of India, and a report was drawn up by the superintendent, C.S. Middlemiss.

The great earthquake, which, with the subsequent fire, wrought such terrible destruction in and around San Francisco on the 18th of April 1906, was the most disastrous ever recorded in California. It occurred between 10 and 15 minutes after 5 A.M., standard time of the 120th meridian. The moment at which the disaster began and the duration of the shock varied at different localities in the great area over which the earthquake was felt. At San Francisco the main shock lasted rather more than one minute.

According to the official Report, the earthquake was due to rupture and movement along the plane of the San Andreas fault, one of a series which runs for several hundred miles approximately in a N.W. and S.E. direction near the coast line. Evidence of fresh movement along this plane of dislocation was traced for a distance of 190 m. from San Juan on the south to Point Arena on the north. There the trace of the fault is lost beneath the sea, but either the same fault or another appears 75 m. to the north at Point Delgada. The belt of disturbed country is notoriously unstable, and part of the fault had been known as the “earthquake crack.” The direction is marked by lines of straight cliffs, long ponds and narrow depressions, forming a Rift, or old line of seismic disturbance. According to Dr G.K. Gilbert the earthquake zone has a length of 300 or 400 m. The principal displacement of rock, in 1906, was horizontal, amounting generally to about 10 ft. (maximum 21 ft.), but there was also locally a slight vertical movement, which towards the north end of the fault reached 3 ft. Movement was traced for a distance of about 270 m., and it is estimated that at least 175,000 sq. m. of country must have been disturbed. In estimating the intensity of the earthquake in San Francisco a new scale was introduced by H.O. Wood. The greatest structural damage occurred on soft alluvial soil and “made ground.” Most of the loss of property in San Francisco was due to the terrible fire which followed the earthquake and was beyond control owing to the destruction of the system of water-supply.

Immediately after the catastrophe a California Earthquake Investigation Committee was appointed by the governor of the state; and the American Association for the Advancement of Science afterwards instituted a Seismological Committee. The elaborate Report of the State Investigation Committee, by the chairman, Professor A.C. Lawson, was published in 1908.

On the 17th of August 1906 a disastrous earthquake occurred at Valparaiso, and the year 1906 was marked generally by exceptional seismic activity.

The Jamaica earthquake of the 14th of January 1907 appears to have accompanied movement of rock along an east and west fracture or series of fractures under the sea a few miles from the city of Kingston. The statue of Queen Victoria at Kingston was turned upon its pedestal the eighth of a revolution.

A terrible earthquake occurred in Calabria and Sicily on December 28, 1908, practically destroying Messina and Reggio. According to the official returns the total loss of life was 77,283. Whilst the principal centre seems to have been in the Strait of Messina, whence the disturbance is generally known as the Messina earthquake, there were independent centres in the Calabrian peninsula, a country which had been visited by severe earthquakes not long previously, namely on September 8, 1905, and October 23, 1907. The principal shock of the great Messina earthquake of 1908 occurred at 5.21 A.M. (4.21 Greenwich time), and had a duration of from 30 to 40 seconds. Neither during nor immediately before the catastrophe was there any special volcanic disturbance at Etna or at Stromboli, but it is believed that there must have been movement along a great plane of weakness in the neighbourhood of the Strait of Messina, which has been studied by E. Cortese. The sea-floor in the strait probably suffered great disturbance, resulting in the remarkable movement of water observed on the coast. At first the sea retired, and then a great wave rolled in, followed by others generally of decreasing amplitude, though at Catania the second was said to have been greater than the first. At Messina the height of the great wave was 2.70 metres, whilst at Ali and Giardini it reached 8.40 metres and at San Alessio as much as 11.7 metres. At Malta the tide-gauge recorded a wave of 0.91 metre. The depth of the chief earthquake-centre was estimated by Dr E. Oddone at about 9 kilometres. The earthquake and accompanying phenomena were studied also by Professor A. Riccò, Dr M. Baratta and Professor G. Platania and by Dr F. Omori of Tokyo. After the great disturbance, shocks continued to affect the region intermittently for several months. In certain respects the earthquake of 1908 presented much resemblance to the great Calabrian catastrophe of 1783.

It has been proposed by R.D. Oldham that the disturbance which causes the fracture and permanent displacement of the rocks during an earthquake should be called an “earthshake,” leaving the term earthquake especially for the vibratory motion. The movement of the earthquake is molecular, whilst that of the earthshake is molar. Subsequently he suggested the terms mochleusis and orchesis (μοχλέυω, I heave; ὀρχέομαι, I dance), to denote respectively the molar and the molecular movement, retaining the word earthquake for use in its ordinary sense.

In most earthquakes the proximate cause is generally regarded as the fracture and sudden movement of underground rock-masses. Disturbances of this type are known as “tectonic” earthquakes, since they are connected with the folding and faulting of the rocks of the earth’s crust. They indicate a relief of the strain to which the rock-masses are subjected by mountain-making and other crustal movements, and they are consequently apt to occur along the steep face of a table-land or the margin of a continent with a great slope from land to sea. In many cases the immediate seat of the originating impulse is located beneath the sea, giving rise to submarine disturbances which have been called “seaquakes.” Much attention has been given to these suboceanic disturbances by Professor E. Rudolph.

Professor J.H. Jeans has pointed out that the regions of the earth’s crust most affected by earthquakes lie on a great circle corresponding with the equator of the slightly pear-shaped figure that he assigns to the earth. This would represent a belt of weakness, subject to crushing, from the tendency of the pear to pass into a spherical or spheroidal form under the action of internal stresses. According to the comte de Montessus de Ballore, the regions of maximum seismic instability appear to be arranged on two great circles, inclined to each other at about 67°. These are the Circumpacific and Mediterranean zones.

Maps of the world, showing the origins of large earthquakes each year, accompany the Annual Reports of the Seismological Committee of the British Association, drawn up by Professor Milne. It is important to note that Professor Milne has shown a relationship between earthquake-frequency and the wandering of the earth’s pole from its mean position. Earthquakes seem to have been most frequent when the displacement of the pole has been comparatively great, or when the change in the direction of movement has been marked. Valuable earthquake catalogues have been compiled at various times by Alexis Perrey, R. and J.W. Mallet, John Milne, T. Oldham, C.W.C. Fuchs, F. de Montessus de Ballore and others.

Such earthquakes as are felt from time to time in Great Britain may generally be traced to the formation of faults, or rather to incidents in the growth of old faults. The East Anglian earthquake of the 22nd of April 1884—the most disastrous that had occurred in the British Isles for centuries—was investigated by Prof. R. Meldola and W. White on behalf of the Essex Field Club. The shocks probably proceeded from two foci—one near the villages of Peldon and Abberton, the other near Wivenhoe and Rowhedge, in N.E. Essex. It is believed that the superficial disturbance resulted from rupture of rocks along a deep fault. An attempt has been made by H. Darwin, for the Seismological Committee of the British Association, to detect and measure any gradual movement of the strata along a fault, by observation at the Ridgeway fault, near Upway, in Dorsetshire. Dr C. Davison in studying the earthquakes which have originated in Britain since 1889 finds that several have been “twins.” A twin earthquake has two maxima of intensity proceeding from two foci, whereas a double earthquake has its successive impulses from what is practically a single focus. The Hereford earthquake of December 1896, which resulted in great structural damage, was a twin, having one epicentre near Hereford and the other near Ross. Davison refers it to a slip along a fault-plane between the anticlinal areas of Woolhope and May Hill; and according to the same authority the Inverness earthquake of the 18th of September 1901 was referable to movement along a fault between Loch Ness and Inverness. The South Wales earthquake of June 27, 1906, was probably due to movement connected with the Armorican system of folds, striking in an east and west direction.

It may be noted that when a slip occurs along a fault, the displacement underground may be but slight and may die out before reaching the surface, so that no scarp is formed. In connexion, however, with a seismic disturbance of the first magnitude the superficial features may be markedly affected. Thus, the great Japan earthquake of October 1891—known often as the Mino-Owari earthquake—was connected with the formation or development of a fault which, according to Professor B. Koto, was traced on the surface for a distance of nearly 50 m. and presented in places a scarp with a vertical throw of as much as 20 ft., while probably the maximum displacement underground was very much greater.

Although most earthquakes seem to be of tectonic type, there are some which are evidently connected, directly or indirectly, with volcanic activity (see Volcano). Such, it is commonly believed, were the earthquakes which disturbed the Isle of Ischia in 1881 and 1883, and were studied by Professor J. Johnston-Lavis and G. Mercalli. In addition to the tectonic and volcanic types, there are occasional earthquakes of minor importance which may be referred to the collapse of the roof of caverns, or other falls of rock in underground cavities at no great depth. According to Prof. T.J.J. See most earthquakes are due, directly or indirectly, to the explosive action of steam, formed chiefly by the leakage of sea-water through the ocean floor.

Whatever the nature of the impulse which originates the earthquake, it gives rise to a series of waves which are propagated through the earth’s substance and also superficially. In one kind, known as normal or condensational waves, or waves of elastic compression, the particles vibrate to and from the centre of disturbance, moving in the direction in which the wave travels, and therefore in a way analogous to the movement of air in a sound-wave. Associated with this type are other waves termed transverse waves, or waves of elastic distortion, in which the particles vibrate across or around the direction in which the wave is propagated. The normal waves result from a temporary change of volume in the medium; the transverse from a change of shape. The distance through which an earth-particle moves from its mean position of rest, whether radially or transversely, is called the amplitude of the wave; whilst the double amplitude, or total distance of movement, to and fro or up and down, like the distance from crest to trough of a water wave, may be regarded as the range of the wave. The period of a wave is the time required for the vibrating particle to complete an oscillation. As the rocks of the earth’s crust are very heterogeneous, the earthquake-waves suffer refraction and reflection as they pass from one rock to another differing in density and elasticity. In this way the waves break up and become much modified in course of transmission, thus introducing great complexity into the phenomena. It is known that the normal waves travel more rapidly than the transverse.

Measurements of the surface speed at which earthquake-waves travel require very accurate time-measurers, and these are not generally available in earthquake-shaken regions. Observations during the Charleston earthquake of 1886 were at that time of exceptional value, since they were made over a large area where standard time was kept. Lines drawn through places around the epicentre at which the shock arrives at the same moment are called coseismal lines. The motion of the wave is to be distinguished from the movement of the vibrating particles. The velocity of the earth-particle is its rate of movement, but this is constantly changing during the vibration, and the rate at which the velocity changes is technically called the acceleration of the particle.

Unfelt movements of the ground are registered in the earthquake records, or seismograms, obtained by the delicate instruments used by modern seismologists. From the study of the records of a great earthquake from a distant source, sometimes termed a teleseismic disturbance, some interesting inferences have been drawn with respect to the constitution of the interior of the earth. The complete record shows two phases of “preliminary tremors” preceding the principal waves. It is believed that while the preliminary tremors pass through the body of the earth, the principal waves travel along or parallel to the surface. Probably the first phase represents condensational, and the second phase distortional, waves. Professor Milne concludes from the speed of the waves at different depths that materials having similar physical properties to those at the surface may extend to a depth of about 30 m., below which they pass into a fairly homogeneous nucleus. From the different rates of propagation of the precursors it has been inferred by R.D. Oldham that below the outer crust, which is probably not everywhere of the same thickness, the earth is of practically uniform character to a depth of about six-tenths of the radius, but the remaining four-tenths may represent a core differing physically and perhaps chemically from the outer part. Oldham also suggests, from his study of oceanic and continental wave-paths, that there is probably a difference in the constitution of the earth beneath oceans and beneath continents.

The surface waves, which are waves of great length and long period and are propagated to great distances with practically a constant velocity, have been regarded as quasi-elastic gravitational waves. Further, in a great earthquake the surface of the ground is sometimes visibly agitated in the epifocal district by undulations which may be responsible for severe superficial damage. (See also for elastic waves Elasticity, § 89.)

An old classification of earthquake-shocks, traces of which still linger in popular nomenclature, described them as “undulatory,” when the movement of the ground was mainly in a horizontal direction; “subsultory,” when the motion was vertical, like the effect of a normal wave at the epicentre; and “vorticose,” when the movement was rotatory, apparently due to successive impulses in varying directions.

The sounds which are associated with seismic phenomena, often described as subterranean rumbling and roaring, are not without scientific interest, and have been carefully studied by Davison. “Isacoustic lines” are curves drawn through places where the sound is heard by the same percentage of observers. The sound is always low and often inaudible to many.

The refined instruments which are now used by seismologists for determining the elements of earthquake motion and for recording earthquakes from distant origins are described in the article Seismometer. These instruments were developed as a consequence of the attention given in modern times to the study of earthquakes in the Far East.

(F. W. R.*)

Strange as it may appear, the advances that have been made in the study of earthquakes and the world-wide interest shown in their phenomena were initiated in work commenced in Japan. When the Japanese government, desiring to adopt Western knowledge, invited to its shores bodies of men to act as its instructors, the attention of the newcomers was naturally attracted to the frequent shakings of the ground. Interest in these phenomena increased more rapidly than their frequency, and at length it was felt that something should be done for their systematic study. At midnight on the 22nd of February 1880 movements more violent than usual occurred; chimneys were shattered or rotated, tiles slid down from roofs, and in the morning it was seen that Yokohama had the appearance of a city that had suffered a bombardment. The excitement was intense, and before the ruins had been removed a meeting was convened and the Seismological Society of Japan established. The twenty volumes of original papers published by this body summarize to a large extent the results of the later study of seismology.

The attention of the students of earthquakes in Japan was at first directed almost entirely to seismometry or earthquake measurement. Forms of apparatus which then existed, as for example the seismographs, seismometers and seismoscopes of Mallet, Palmieri and others, were subjected to trial; but inasmuch as they did little more than indicate that an earthquake had taken place—the more elaborate forms recording also the time of its occurrence—they were rapidly discarded, and instruments were constructed to measure earthquake motion. Slightly modified types of the new instruments devised in Japan were adopted throughout the Italian peninsula, and it is fair to say that the seismometry developed in Japan revolutionized the seismometry of the world. The records obtained from the new instruments increased our knowledge of the character of earthquake motion, and the engineer and the architect were placed in a position to construct so that the effects of known movements could be minimized. It was no doubt the marked success, both practical and scientific, attending these investigations that led the Japanese government to establish a chair of seismology at its university, to organize a system of nearly 1000 observing stations throughout the country, and in 1893 to appoint a committee of scientific and practical men to carry out investigations which might palliate the effects of seismic disturbances. In the first year this committee received a grant of £5000, and as liberal sums for the same purpose appear from time to time in the parliamentary estimates, it may be assumed that the work has been fraught with good results. In their publications we find not only records of experiences and experiments in Japan, but descriptions and comments upon earthquake effects in other countries. In two of the volumes there are long and extremely well illustrated accounts of the earthquake which on the 12th of June 1897 devastated Assam, to which country two members of the above-mentioned committee were despatched to gather such information as might be of value to the architect and builder in earthquake-shaken districts.

A great impetus to seismological investigation in Europe and America was no doubt given by the realization of the fact that a large earthquake originating in any one part of the world may be recorded in almost any other. Italy for many years past has had its observatories for recording earthquakes which can be felt, and which are of local origin, but at the present time at all its first-class stations we find instruments to record the unfelt movements due to earthquakes originating at great distances, and as much attention is now paid to the large earthquakes of the world as to the smaller ones originating within Italian territory. The Kaiserliche Akademie der Wissenschaften of Vienna established earthquake observatories in Austria, and the Central Observatorium of St Petersburg has carried out similar work in Russia. Germany attached a seismological observatory to its university at Strassburg, whilst provision has been made for a professorship of Earth Physics (Geophysik) at Göttingen. In accordance with the recommendation of the British Association, seismographs of a similar character have been installed at stations all over the world. The principal objects of this extended and still extending system of stations are to determine the velocity with which motion is propagated over the surface and through the interior of the earth, to locate the positions of sub-oceanic earthquake origins, and generally to extend our knowledge respecting the physical nature of the planet on which we live.

We now know that earthquakes are many times more frequent than was previously supposed. In Japan, for example, between 1885 and 1892 no fewer than 8331 were recorded—that is to say, on the average there were during that time more than 1000 disturbances per year. Although many of these did not cause a sensible shaking over areas exceeding a few hundred square miles, many of them were sufficiently intense to propagate vibrations round and through the globe. If we pick out the well-marked earthquake districts of the world, and give to each of them a seismicity or earthquake frequency per unit area one-third of that in Japan, the conclusion arrived at is that considerable areas of our planet are on the average shaken every half-hour.

The knowledge which we now possess respecting the localities where earthquakes are frequent and the forms of the foci from which they have spread, enables us to speak definitely respecting the originating causes of many of these phenomena. It is found, for example, that although in many countries there may be displays of volcanic and seismic activity taking place almost side by side, it is only rarely that there is direct relationship between the two. Now and then, however, before a volcano breaks into eruption there may be a few ineffectual efforts to form a vent, each of which is accompanied by no more than a slight local shaking of the ground. This is true even for the largest and most violent eruptions, when mountains have with practically a single effort blown off their heads and shoulders. Thus the earthquake which accompanied the eruption of Bandaisan, in central Japan, in 1888 was felt only over a radius of 25 m. The analyses of the seismic registers of Japan clearly indicate that comparatively few shakings originate near to the volcanoes of the country, the majority of them, like those of many other countries, coming from regions where volcanic rocks are absent. The greatest number spread inland from the Pacific seaboard, the movement becoming more and more feeble as it approaches the backbone of the country, which is drilled with numerous volcanic vents. What is true for Japan is generally true for the western coasts of North and South America.

Speaking broadly, earthquakes are most frequent along the steeper flexures in the earth’s surface, and in those regions where there is geological evidence to show that slow secular movements in the earth’s crust are possibly yet in progress. With a unit distance of 2 degrees, or 120 geographical m., we find that the slopes running eastwards from the highlands of Japan and westwards from the Andean ridges down into the Pacific vary from 1 in 20 to 1 in 30, and it is on the faces or near to the bottom of these slopes that seismic efforts are frequent. The slopes running from Australia, eastern America and western Europe into the neighbouring oceans vary between 1 in 70 and 1 in 250, and in these regions earthquakes are of rare occurrence. The seismic activity met with in the Himalayas and the Alps finds its best explanation in the fact that these mountains are geologically recent, and there are no reasons to doubt that the forces which brought their folds into existence are yet in action.

This peculiar association of earthquakes with pronounced topographical configuration and certain geological conditions evidently indicates that the origin of many of them is connected with rock folding. Inasmuch as certain large earthquakes have been accompanied by rock fracture, as for example in 1891, when in central Japan a fault some 50 m. in length was created, whilst the origins of others have been distinctly traced to the line of an existing fault or its continuation, we may conclude that the majority of earthquakes are spasmodic accelerations in the secular movements which are creating (and in some instances possibly obliterating) the more prominent features of the earth’s surface. These secular movements, which include upheavals, subsidences, horizontal displacements—all of which are explained on the assumption of a crust seeking support on a nucleus gradually contracting by loss of heat, are collectively referred to as bradyseismical (βραδύς, slow) movements. To these may be added movements directly attributable to the influence of gravity. Sub-oceanic districts in a state of seismic strain may be so far loaded by the accumulation of sediments that gentle bending may be accompanied by sudden yieldings. This possibly accounts for the frequency of earthquakes off the mouth of the Tonegawa on the eastern side of Japan. The distortions so frequently observed in fossils and pebbles, the varying thickness of contorted strata, and the “creep” in coal-mines, together with other phenomena, indicate that rocks may flow. Observations of this nature lead to the supposition that high plateau-like regions may be gradually subsiding under the influence of their own weight, and that the process of settlement may from time to time be spasmodic in its character. Whether the earthquakes which originate round the submerged basal frontiers of the continents bounding the Pacific are ever attributable to such activities, it is impossible to say. All that we know with certainty is that they are sometimes accompanied by such a vast displacement of material that the ocean has been set into a state of oscillation for periods of 24 hours, that in some instances there have been marked changes in depth, and that enormous sub-oceanic landslips have occurred. These phenomena are, however, equally well explained on the assumption of sudden faulting accompanied by violent shaking, which would dislodge steeply inclined beds of material beneath the ocean as it does upon the land.

Although the proximate cause of earthquake motion is traced to sudden yieldings in the crust of the earth brought about by some form of bradyseismical action, the existence of at least two distinct types of seismic motion indicates that the mechanical conditions accompanying the fracturing of rocks are not always identical. 90 or 95% of the earthquakes which can be recorded consist of elastic or quasi-elastic vibrations. The remainder, including the large earthquakes, not only exhibit the elastic movements, but are accompanied by surface undulations which are propagated most certainly for some hundreds of miles round their origin, and then as horizontal movements sweep over the whole surface of the globe. The former of these may accompany the formation of a new fault or the sudden renewal of movement along an old one; they are cracking or rending effects, without any great displacement. The latter are probably fracturings accompanied by vertical and horizontal displacements of masses of the earth’s crust sufficiently great to set up the observed surface undulations. These shocks are so frequently followed a few minutes later by disturbances, which from their similarity to the movements which have preceded them may be called earthquake echoes, that we are led to the speculation that we are here dealing with the caving-in of ill-supported portions of the earth’s crust, the waves from which are radiated to boundaries and then returned to their origin to coalesce and give rise to a second impulse not unlike the primary. Succeeding the first repetition of motion recorded by the seismograph there is often a rhythmical repetition of similar wave groups, suggesting the existence within our earth of phenomena akin to multiple echoes.

The introduction of new methods into seismometry quickly revolutionized our ideas respecting the character of earthquake motion. Although an earthquake may be strongly felt within a distance of 50 m. from its origin, and although the movements in the upper storeys of buildings within the shaken area may be large, the actual range of the horizontal motion of the ground is usually less than 1⁄10 of an inch. With such earthquakes ordinary seismographs for recording vertical motion do not show any disturbance. When the movement reaches ½ in. it becomes dangerous, and a back-and-forth movement of an inch is usually accompanied by destructive effects. In this latter case the amplitude of the vertical record which indicates the existence of surface waves will vary between ½ and 1⁄100 of an inch. In the earthquake which devastated central Japan on the 26th of October 1891, nearly every building within the epifocal district fell, the ground was fissured, forests slipped down from mountain sides to dam up valleys, whilst the valleys themselves were permanently compressed. The horizontal movements seem to have reached 9 in. or 1 ft., and the surface undulations were visible to the eye.

The rapidity with which the movements are performed varies throughout a disturbance. A typical earthquake usually commences with minute elastic vibrations, the periods of which vary between 1⁄5 and 1⁄20 of a second. These are recorded by seismographs, and are noticed by certain of the lower animals like pheasants, which before the occurrence of movement perceptible to human beings scream as if alarmed. When an earthquake is preceded by a sound we have evidence of preliminary tremors even more rapid than those recorded by seismographs. Following these precursors there is a shock or shocks, the period of which will be 1 or 2 seconds. From this climax the movements, although irregular in character, become slower and smaller until finally they are imperceptible. The duration of a small earthquake usually varies from a few seconds to a minute, but large earthquakes, which are accompanied by surface undulations, may be felt for 2 or 3 minutes, whilst an ordinary seismograph indicates a duration of from 6 to 12 minutes. A free horizontal pendulum tells us that with severe earthquakes the ground comes to rest by a series of more or less rhythmical surgings, continuing over 1 or 2 hours. Although the maximum displacement has a definite direction, the successive vibrations are frequently performed in many different azimuths. The predominating direction at a given station in certain instances is apparently at right angles to the strike of the neighbouring strata, this being the direction of easiest yielding.

Earthquake motion as recorded at stations several thousands of miles distant from its origin exhibits characteristics strikingly different from those just described. The precursors now show periods of from 1 to 5 seconds, whilst the largest movements corresponding to the shocks may have periods of from 20 to 40 seconds. The interval of time by which the first tremors have outraced the maximum movement has also become greater. Within a few hundreds of miles from an origin this interval increases steadily, the velocity of propagation of the first movements being about 2 km. per second, whilst that of the latter may be taken at about 1.6 km. per second. Beyond this distance the velocity of transmission of the first movements rapidly increases, and for great distances, as for example from Japan to England, it is higher than we should expect for waves of compression passing through steel or glass. This observation precludes the idea that these preliminary tremors have travelled through the heterogeneous crust of the earth, and since the average velocity of their transmission increases with the length of the path along which they have travelled, and we but rarely obtain certain evidence that a seismograph has been disturbed by waves which have reached it by travelling in opposite directions round the world, we are led to the conclusion that earthquake precursors pass through our earth and not round its surface. The following table relating to earthquakes, which originated off the coast of Borneo on the 20th and 27th of September 1897, is illustrative of the velocities here considered:—

Localities. Distance
from
origin
in degrees. Velocity
in kms.
per sec. if
on chord. ¼ √ Average
depth of
chord in
kms.

Nicolaieff 81° 8.1 8.0

Potsdam 92° 8.4 9.1

Catania, Ischia, Rocca di Papa, Rome 96° 9.0 9.5

Isle of Wight 103° 9.8 10.2

The chords referred to here are those joining the earthquake origins and distant observing stations, and it will be noted that one-quarter of the square root of the average depths at which these run closely corresponds to observed average velocities if wave paths followed chords. This increase of velocity with average depth shows that the paths followed through the earth must be curved with their convexity towards the centre of the earth. These observations do not directly tell us to what extent a true wave path is deflected from the direction of a chord, but they suggest as an extremely plausible assumption that the square of the speed is a linear function of the depth below the surface of the earth. With this assumption Dr C.G. Knott shows that the square of the speed (v²) can be expressed linearly in terms of the average depth of the chord d, thus: v² = 2.9 + .026 d, the units being miles and seconds. The formula applies with fair accuracy to moderate and high values of d, but it gives too high a value for short chords. It follows that the square of the speed increases 0.9% per mile of descent in the earth. The conclusion we arrive at is that the preliminary tremors which pass through the earth do so in the vicinity of their origin at the rate of almost 2.3 km. per second. This velocity increases as the wave path plunges downwards, attaining in the central regions a velocity of 16 to 17 kms., whilst the highest average velocity which is across a diameter lies between 10 and 12 kms. per second.

The large surface waves radiating from an origin to a distant place have velocities lying between 1.6 and 4 kms. per second, and it has been observed that when the higher velocity has been noted this refers to an observation at a station very remote from the origin. One explanation of this is the assumption that only very large waves indicating a large initial disturbance are capable of travelling to great distances, and as pointed out by R.D. Oldham, large waves under the influence of gravity will travel faster than small waves. These waves (which may be gravitational or distortional) are recorded as slow tiltings of the ground measured by angles of 0.5 to 10 or 15 seconds of arc, or as horizontal displacements of 0.5 or several millimetres. Their calculated lengths have reached 50 kms. (31 m.).

In the section of this article relating to the cause of earthquakes a little has been said about their frequency or the number of times these phenomena are repeated during a given interval of time. It has been shown that all countries are very often moved by earthquakes which have originated at great distances. Great Britain, for example, is crossed about 100 times a year by earthquake waves having durations of from 3 minutes to 3 hours, whilst the vibratory motions which originate in that country are not only small but of rare occurrence. In the earlier stages of the world’s history, because the contraction of its nucleus was more rapid than it is at present, it is commonly inferred that phenomena accompanying bradyseismical activity must have been more pronounced and have shown themselves upon a grander scale than they do at the present time. Now, although the records of our rocks only carry us back over a certain portion of this history, they certainly represent an interval of time sufficiently long to furnish some evidence of such enfeeblement if it ever existed. So far from this being the case, however, we meet with distinct evidences in the later chapters of geological history of plutonic awakenings much more violent than those recorded at its commencement. During Palaeozoic times many mountain ranges were formed, and accompanying these orogenic processes there was marked volcanic activity. In the succeeding Secondary period plutonic forces were quiescent, but during the formation of the early Tertiaries, when some of the largest mountain ranges were created, they awoke with a vigour greater than had ever been previously exhibited. At this period it is not improbable that Scotland was as remarkable for its volcanoes and its earthquakes as Japan is at the present day. If the statement relating to the general decrease in bradyseismical changes referred merely to their frequency, and omitted reference to their magnitude, the views of the geologist and physicist might harmonize. One explanation for this divergence of opinion may rest on the fact that too little attention has been directed to all the conditions which accompany the adaptation of the earth’s crust to its shrinking nucleus. As the latter grows smaller the puckerings and foldings of the former should grow larger. Each succeeding geological epoch should be characterized by mountain formations more stupendous than those which preceded them, whilst the fracturing, dislocation, caving-in of ill-supported regions, and creation of lines of freedom for the exhibition of volcanic activity which would accompany these changes, would grow in magnitude. The written records of many countries reflect but on a smaller scale the crystallized records in their hills. In 1844, at Comrie, in Perthshire, as many as twelve earthquakes were recorded in a single month, whilst now there are but one or two per year. Earthquake frequency varies with time. A district under the influence of hypogenic activities reaches a condition of seismic strain which usually is relieved rapidly at first, but subsequently more slowly.

The small shocks which follow an initial large disturbance are known as after-shocks. The first shock which in 1891 devastated central Japan was accompanied by the formation of a large fault, and the 3364 small shocks which succeeded this during the following two years are regarded as due to intermittent settlements of disjointed material. The decreasing frequency with which after-shocks occur may be represented by a curve. Dr F. Omori points out that the continuation of such a curve gives the means of determining the length of time which will probably elapse before the region to which it refers will return to the same seismic quiescence that it had prior to the initial disturbance.

The positive results that we have respecting the periodicity of earthquakes are but few. Generally earthquakes are somewhat more frequent during winter than during summer, and this applies to both the northern and southern hemispheres. The annual periodicity, which, however, does not show itself if only destructive earthquakes are considered, finds an explanation, according to Dr Knott, in the annual periodicity of long-continued stresses, as for example those due to the accumulation of snow and to barometric gradients. For certain earthquake regions there appears to be a distinct semi-annual period for which no satisfactory explanation has yet been adduced. Although the elaborate registers of Japan, which have enabled us to group earthquakes according to their respective origins and varying intensities, and to separate after-shocks from initial disturbances, have been subjected by Dr Knott to most careful analysis, with the object of discovering periodicities connected with the ebb and flow of the tides, the lunar day or lunar months, nothing of marked character has been found. Certainly there is slight evidence of a periodicity connected with the times of conjunction and opposition of the sun and moon, and a maximum frequency near the time of perigee, but the effect of lunar stresses is comparatively insignificant. Ordinary earthquakes, and especially after-shocks, show a diurnal period, but we cannot say that there are more earthquakes during the night than during the day.

Many experiments and investigations have been made to determine a possible relationship between earthquakes and electrical phenomena, but beyond drawing attention to the fact that luminous appearances may accompany the friction of moving masses of rock, and that a temporary current may be established in a line by the disturbance of an earth-plate, these inquiries have yielded but little of importance. The inquiries respecting a possible relationship between adjustments so frequently taking place within and beneath that region called the crust of the earth and magnetic phenomena are, however, of a more promising nature. We have seen that at or near the origin of earthquakes which for several hours disturb continents, and occasionally cause oceans to oscillate for longer periods, we sometimes have direct evidence of the bodily displacement of many cubic miles of material. When this material is volcanic it is almost invariably magnetic, and we perceive in its sudden rearrangement causes which should produce magnetic effects within an epifocal district. In Japan, where attention is being directed to phenomena of this description, not only have such effects been observed, but unusual magnetic disturbances have been noted prior to the occurrence of large earthquakes. These may, of course, be regarded as mere coincidences, but when we consider volcanic and seismic activities as evidences of physical and chemical changes, together with mechanical displacements of a magnetic magma, it is reasonable to suppose that they should have at least a local influence upon magnetic needles. Another form of disturbance to which magnetic needles are subjected is that which accompanies the passage of large earth-waves beneath certain observatories situated at great distances from earthquake origins. At Utrecht, Potsdam and Wilhelmshaven the magnetographs are frequently disturbed by seismic waves, whilst at many other European observatories such effects are absent or only barely appreciable. To explain these marked differences in the behaviour of magnetic needles at different stations we are at present only in a position to formulate hypotheses. They may be due to the fact that different needles have different periodic times of oscillation; it is possible that at one observatory the mechanical movements of the ground are much greater than at others; we may speculate on the existence of materials beneath and around various observatories which are different in their magnetic characters; and, lastly, we may picture a crust of varying thickness, which from time to time is caused to rise and fall upon a magnetic magma, the places nearest to this being the most disturbed.

A subject to which but little attention has been directed is the effect which displays of seismic and volcanic activities have had upon the human mind. The effects are distinctly dual and opposite in character. In countries like England, where earthquakes are seldom experienced, the prevailing idea is that they are associated with all that is baneful. For certain earthquakes, which fortunately are less than 1% of those which are annually recorded, this is partially true. A disastrous shock may unnerve a whole community. Effects of this nature, however, differ in a marked manner with different nationalities. After the shock of 1891, when Japan lost 9960 of its inhabitants, amongst the wounded indications of mental excitement were shown in spinal and other trouble. Notwithstanding the lightheartedness of this particular nation, it is difficult to imagine that the long series of seismic effects chronicled in Japanese history, which culminated in 1896 in the loss of 29,000 lives by sea-waves, has been without some effect upon its mental and moral character. Several earthquakes are annually commemorated by special services at temples. In bygone times governments have recognized earthquakes as visitations of an angry deity, whom they have endeavoured to appease by repealing stringent laws and taxes. In other countries the sermons which have been preached to show that the tremblings of the world were visitations consequent on impiety, and the prayers which have been formulated to ward off disasters in the future, far exceed in number the earthquakes which gave rise to them. In 1755 many of the English clergy held the view that Lisbon was destroyed because its inhabitants were Catholics, whilst the survivors from that disaster attributed their misfortune to the fact that they had tolerated a few Protestant heretics in their midst. To avoid a recurrence of disaster certain of these were baptized by force. In the myths relating to underground monsters and personages that are said to be the cause of earthquakes we see the direct effects which exhibitions of seismic and volcanic activity have produced upon the imagination. The beliefs, or more properly, perhaps, the poetical fancies, thus engendered have exhibited themselves in various forms. Beneath Japan there is said to be a catfish, which in other countries is replaced by a mole, a hog, an elephant or other living creature, which when it is restless shakes the globe. The Kamchadales picture a subterranean deity called Tuil, who in Scandinavian mythology is represented by the evil genius Loki. We have only to think of the reference in the Decalogue forbidding the making of graven images of that which is in the earth beneath, to see in early Biblical history evidence of a subterranean mythology; and it seems probable that the same causes which led to the creation of Pluto, Vulcan and Poseidon gave rise to practices condemned by Moses.

Perhaps the greatest practical benefits derived from seismological investigations relate to important changes and new principles which have been introduced into the arts of the engineer and builder when constructing in earthquake countries. The new rules and formulae, rather than being theoretical deductions from hypotheses, are the outcome of observation and experiment. True measures of earthquake motion have been given to us by modern seismometers, with the result that seismic destructivity can be accurately expressed in mechanical units. From observation we now know the greatest acceleration and maximum velocity of an earth particle likely to be encountered; and these are measures of the destructivity. The engineer is therefore dealing with known forces, and he has to bear in mind that these are chiefly applied in a horizontal direction. A formula connecting the acceleration requisite to overturn bodies of different dimensions has been given. The acceleration which will fracture or shatter a column firmly fixed at its foundation to the moving earth may be expressed as follows:—

a = 1 gFAB ,

6 fw

where

a = the acceleration per sec. per sec.

F = the force of cohesion, or force per unit surface, which when gradually applied produces fracture.

A = area of base fractured.

B = thickness of the column.

f = height of centre of gravity of column above the fractured base.

w = the weight of the portion broken off.

With this formula and its derivatives we are enabled to state the height to which a wall, for example, may be built capable of resisting any assumed acceleration. Experience has shown that yielding first shows itself at the base of a pier, a wall or a building, and it is therefore clear that the lower portion of such structures should be of greater dimensions or stronger than that above. Piers having these increased dimensions below, and tapering upwards in a proper manner, so that every horizontal section is sufficiently strong to resist the effects of the inertia of its superstructure, are employed to carry railways in Japan. In that country cast-iron piers are things of the past, whilst piers of masonry, together with their foundations, no longer follow the rules of ordinary engineering practice.

After flood, fire, earthquake, or when opportunity presents itself, changes are introduced in the construction of ordinary buildings. In a so-called earthquake-proof house, although externally it is similar to other dwellings, we find rafters running from the ridge pole to the floor sills, an exceedingly light roof, iron straps and sockets replacing mortices and tenons, and many other departures from ordinary rules. Masonry arches for bridges or arched openings in walls (unless protected by lintels), heavy gables, ornamental copings, cappings for chimneys, have by their repeated failure shown that they are undesirable features for construction in earthquake countries. As sites for buildings it is well to avoid soft ground, on which the movement is always greater than on hard ground. Excessive movement also takes place along the face of unsupported openings, and for this reason the edges of scarps, bluffs, cuttings and river-banks are localities to be avoided. In short, the rules and precautions which have to be recognized so as to avoid or mitigate the effects of earthquake movement are so numerous that students of engineering and architecture in Japan receive a special course of lectures on this subject. When it is remembered that a large earthquake may entail a loss of life greater than that which takes place in many wars, and that for the reconstruction of ordinary buildings, factories and public works an expenditure of several million pounds sterling is required, the importance of these studies cannot be overrated. Severe earthquakes are fortunately unknown in the British Isles, but we have simply to turn our eyes to earthquake-shaken colonies and lands in close commercial touch with Great Britain to realize the importance of mitigating such disasters as much as possible, and any endeavour to obviate the wholesale destruction of life should appeal to the civilized communities of the world.

An unexpected application of seismometry has been to record the vibration of railway trains, bridges and steamships. An instrument of suitable construction will give records of the more or less violent jolting and vibratory movements of a train, and so localize irregularities due to changes in the character of ballast and sleepers, to variation in gauge, &c. An instrument placed on a locomotive throws considerable light upon the effects due to the methods of balancing the wheels, and by alterations in this respect a saving of fuel of from 1 to 5 ℔ of coal per mile per locomotive has sometimes been effected.

By mapping the centres from which earthquakes originate off the coast of Japan, we have not only determined districts where geological activity is pronounced, but have placed before the cable engineer well-defined localities which it is advisable to avoid; and in the records of unfelt earthquakes which originate far from land similar information is being collected for the deeper parts of the oceans. Occasionally these records have almost immediately made clear the cause of a cable failure. From lack of such information in 1888, when the cables connecting Australia with the outer world were simultaneously broken, the sudden isolation was regarded as a possible operation of war, and the colonists called out their naval and military reserves. Records of earthquakes originating at great distances have also frequently enabled us to anticipate, to correct, to extend, or to disprove telegraphic accounts of the disasters. Whatever information a seismogram may give is certain, whilst the information gathered from telegrams may in the process of transit become exaggerated or minimized. Otherwise unaccountable disturbances in records from magnetographs, barographs and other instruments employed in observatories are frequently explained by reference to the traces yielded by seismometers. Perhaps the greatest triumph in seismological investigation has been the determination of the varying rates at which motion is propagated through the world. These measurements have already thrown new light upon its effective rigidity, and if we assume that the density of the earth increases uniformly from its surface towards its centre, so that its mean density is 5.5, then, according to Knott, the coefficient of elasticity which governs the transmission of preliminary tremors of an earthquake increases at a rate of nearly 1.2% per mile of descent.

(J. Mi.)

Authorities.—J. Milne, Seismology (London, 1898), Earthquakes (London, 1898), Bakerian Lecture, “Recent Advances in Seismology,” Proc. Roy. Soc., 1906, 77, p. 365; J.A. Ewing, Memoir on Earthquake Measurement (Tokyo, 1883); C.E. Dutton, Earthquakes in the Light of the New Seismology (London, 1904); “The Charleston Earthquake of Aug. 31, 1886,” Ninth Annual Report of the United States Geological Survey, 1889; W.H. Hobbs, Earthquakes, an Introduction to Seismic Geology (London, 1908), “The San Francisco Earthquake and Fire, 1906,” Bull. U.S. Geol. Surv. No. 324; “The California Earthquake of Ap. 18, 1906,” Rep. State Earthq. Com. (Washington, D.C., 1908); R.D. Oldham, “Report on the Great Earthquake of 12 June 1897,” Mem. Geol. Surv. India, xxix. 1899, “On the Propagation of Earthquake Motion to great Distances,” Phil. Trans., 1900, A, vol. 194, p. 135, “The Constitution of the Interior of the Earth as revealed by Earthquakes,” Quar. Jour. Geol. Soc., 1906, 62, p. 456; 1907, 63, p. 344; C. Davison, A Study of Recent Earthquakes (London, 1905); The Hereford Earthquake of December 17, 1896 (Birmingham, 1899), “The Investigation of Earthquakes,” Beiträge z. Geophysik, Bd. ix., 1908, p. 201, and papers on British earthquakes in Quart. Jour. Geol. Soc.; T.J.J. See, “The Cause of Earthquakes, Mountain Formation and Kindred Phenomena connected with the Physics of the Earth,” Proc. Amer. Phil. Soc., 1906, 45, p. 273; F. Frech, “Erdbeben und Gebirgsbau,” Petermann’s Mitteilungen, Bd. 53, 1907, p. 245 (with maps); C.G. Knott, The Physics of Earthquake Phenomena (Oxford, 1908); Comte F. de Montessus de Ballore, Les Tremblements de terre: géographie séismologique (Paris, 1906), La Science séismologique (1907); Transactions of the Seismological Society of Japan; Seismological Journal (Yokohama); Bollettino della Società Sismologica Italiana (Rome); Reports of the British Association, containing the annual reports of the Committee for Seismological Investigations; papers in the Beiträge zur Geophysik and the Ergänzungsbände.

The publications for 1880-1892 were termed the Transactions of the Seismological Society of Japan, and for 1893-1895 the Seismological Journal of Japan. The observations are now published by the Earthquake Investigation Committee of Japan, and edited by F. Omori, professor of seismology at the university of Tokyo.

The chief Italian station is at Rocca di Papa near Rome. It is equipped with delicate instruments designed by its director, Giovanni Agamennone. The records since 1895 are published in the Bollettino della Società Sismologica Italiana, edited by Luigi Palazzo, director of the Central Office for Meteorology and Geodynamics at Rome.

The chief Austrian publications are:—Mittheilungen der Erdbebencommission der k. Akad. der Wissen. in Wien (since 1897); Die Erdbebenwarte (1901-1907); and the “Neueste Erdbebennachrichten, Beilage der Monatsschrift Die Erdbebenwarte.”

The “International Seismological Association” was founded at Strassburg in 1903, and publishes the Beiträge zur Geophysik, edited by George Gerland, director of the Strassburg station; the papers are printed in several languages.

The records of the British Association stations are published (since 1896) in the Reports. Chile has a national earthquake service (founded after the Valparaiso earthquake of August 1906) directed by comte de Montessus de Ballore.

From Strasburger’s Lehrbuch der Botanik, by permission of Gustav Fischer.

Geaster Granulosus, nat. size.

EARTH-STAR (Geaster), in botany, a kind of puff-ball, with a distinct outer coat which, on separating from the inner, splits into several divisions, which become reflexed and spread like a star. The inner coat enveloping the spores is supported, like a ball, either with or without a stalk on the upper face of the star. The spores escape generally by means of a distinct aperture which appears in the top of the ball. There are several species in Britain found on the ground or on decaying leaves. They are rare or local, but more common in the south or south-east of England than in other parts of Britain.