Volume II (part 2)

Does 2½d. never pass from hand to hand? And is 2½d. so precisely the modulus of popular wants, that an alteration of 4 per cent. would make it useless? Of all the values which 2½d. measures, from three pounds of potatoes down to certain arguments used in the House of Commons, there is not one for which a cent would not do just as well. Mr. Lowe has fallen into the misconception of the person who admired the dispensation of Providence by which large rivers are made to run through cities so great and towns so many. If the cent were to be introduced to-morrow, straightway the buns and cakes, the soda-water bottles, the short omnibus fares, the bunches of radishes, etc. etc. etc., would adapt themselves to the coin.

"If the proposed system were adopted, they would all be compelled to live in decimals for ever; if a man dined at a public house he would have to pay for his dinner in decimal fractions. (Hear, hear.) He objected to that, for he thought that a man ought to be able to pay for his dinner in integers." (Hear, hear, and a laugh.)

The confusion of ideas here exhibited is most instructive. The speaker is under the impression that we are introducing fractions: the truth is, that we only want to abandon the more difficult fractions which we have got, and to introduce easier fractions. Does he deny this? Let us trace his denial to its legitimate consequences. A man ought to pay for his dinner in integers.

Now, if Mr. Lowe insists on it that our integer is the pound, he is bound to admit that the present integer is the pound, of which a shilling, etc., are fractions. The next time he has a chop and a pint of stout in the city, the waiter should say—"A pound, sir, to you," and should add, "Please to remember the waiter in integers." Mr. Lowe fancies that when he pays one and sixpence, he pays in integers, and so he does, if his integer be a penny or a sixpence. Let him bring his mind to contemplate a mil as the integer, the lowest integer, and the seven cents five mils which he would pay under the new system would be payment in integers also. But, as it happens with some others, he looks up the present system, with Cocker, and Walkingame, and always looks down the proposed system. The word decimal is obstinately associated with fractions, for which there is no need. Hence it becomes so much of a bugbear, that, to parody the lines of Pope, which probably suggested one of Mr. Lowe's phrases—

"Dinner he finds too painful an endeavor,

Condemned to pay in decimals for ever."

"The present system, however, had not yet been changed into decimal system. That change might appear very easy to accomplished mathematicians and men of science, but it was one which it would be very difficult to carry out. (Hear, hear). What would have to be done? Every sum would have to be reduced into a vulgar fraction of a pound, and then divided by the decimal of a pound—a pleasant sum for an old applewoman to work out!" (Hear, hear, and laughter.)

A pleasant sum even for an accomplished mathematician. What does divided by the decimal of a pound mean? Perhaps it means reduced to the decimal of a pound! Mr. Lowe supposes, as many others do, that, after the change, all calculations will be proposed in old money, and then converted into new. He cannot hit the idea that the new coins will take the place of the old. This lack of apprehension will presently appear further.

"It would not be an agreeable task, even for some members of that House, to reduce 4½d., or nine half-pence, to mils." (Hear, hear.)

Let the members be assured that nine half-pence will be, for every practical purpose, 18 mils. But now to the fact asserted. Davies Gilbert used to maintain that during the long period he sat in the House, he never knew more than three men in it, at one time, who had a tolerable notion of fractions. [I heard him give the names of three at the time when he spoke: they were Warburton, Pollock, and Hume. He himself was then out of Parliament.] Joseph Hume affirmed that he had never met with more than ten members who were arithmeticians. But both these gentlemen had a high standard. Mr. Lowe has given a much more damaging opinion. He evidently means that the general run of members could not do his question. It is done as follows: Since farthings gain on mils, at the rate of a whole mil in 24 farthings (24 farthings being 25 mils), it is clear that 18 farthings being three-quarters of 24 farthings, will gain three-quarters of a mil; that is, 18 farthings are eighteen mils and three-quarters of a mil. Any number of farthings is as many mils and as many twenty-fourths of a mil. To a certain extent, we feel able to protest against the manner in which Kidderminster has treated the other constituencies. We do not hold it impossible to give the Members of the House in general a sufficient knowledge of the meaning and consequences of the decimal succession of units, tens, hundreds, thousands, etc.; and we believe that there are in the House itself competent men, in number enough to teach all the rest. All that is wanted is the power of starting from the known to arrive at the unknown. Now there is one kind of decimals with which every member is acquainted—the Chiltern Hundreds. If public opinion would enable the competent minority to start from this in their teaching, not as a basis, but as an alternative, in three weeks the fundamentals would be acquired, and members in general would be as fit to turn 4½d. into mils, as any boys on the lower forms of a commercial school.

For a long period of years, allusion to the general ignorance of arithmetic, has been a standing mode of argument, and has always been well received: whenever one member describes others as knownothings, those others cry Hear to the country in a transport of delight. In the meanwhile the country is gradually arriving at the conclusion that a true joke is no joke.

"The main objection was, if they went below 6d., that the new scale of coins would not be commensurate in any finite ratio with anything in this new currency of mils."

Fine words, wrongly used. The new coins are commensurable with, and in a finite ratio to, the old ones. The farthing is to the mil as 25 to 24. The speaker has something here in the bud, which we shall presently meet with in the flower; and fallacies are more easily nipped in flower than in bud.

"No less than five of our present coins must be called in, or else—which would be worse—new values must be given to them."

This dreadful change of value consists in sixpence farthing going to the half-shilling instead of sixpence. Whether the new farthings be called mils or not is of no consequence.

"If a poor man put a penny in his pocket, it would come out a coin of different value, which he would not understand. Suppose he owed another man a penny, how was he to pay him ? Was he to pay him in mils? Four mils would be too little, and five mils would be too much. The hon. gentlemen said there would be only a mil between them. That was exactly it. He believed there would be a 'mill' between them." (Much laughter.)

Mr. Lowe, who cannot pass a half-crown for more than a florin, or get in a florin at less than half-a-crown, has such a high faith in the sterner stuff of his fellow countrymen, that he believes any two of them would go to fisty cuffs for the 25th part of a farthing. He reasons thus: He has often heard in the streets, "I'd fight you for the fiftieth part of a farden:" and having (that is, for a Member) a notion both of fractions and logic, he infers that those who would fight for the 50th of a farthing would, a fortiori, fight for a 25th. His mistake arises from his not knowing that when a person offers to fight another for 1/200d., he really means to fight for love; and that the stake is merely a matter of form, a feigned issue, a pro forma report of progress. Do the Members of the House think they have all the forms to themselves?

"What would be the present expression for four-pence? Why, 0.166 (a laugh); for threepence? .0125; for a penny? .004166, and so on ad infinitum (a laugh); for a half-penny? .002083 ad infinitum. (A laugh). What would be the present expression for a farthing? Why, .0010416 ad infinitum. (A laugh). And this was the system which was to cause such a saving in figures, and these were the quantities into which the poor would have to reduce the current coin of the realm. (Cheers). With every respect for decimal fractions, of which he boasted no profound knowledge, he doubted whether the poor were equal to mental arithmetic of this kind, (hear, hear) and he hoped the adoption of the system would be deferred until there were some proof that they would be able to understand it; for, after all, this was the question of the poor, and the whole weight of the change would fall upon them. Let the rich by all means have permission to perplex themselves by any division of a pound they pleased; but do not let them, by any experiment like this, impose difficulties upon the poor and compel men to carry ready-reckoners in their pocket to give them all these fractional quantities." (Hear, hear.)

We should hardly believe all this to be uttered in earnest, if we had not known that several persons who have not Mr. Lowe's humor, nevertheless have his impressions on this point. It must therefore be answered; but how is this to be done seriously?

Dialogue between a member of Parliament and an orange-boy, three days after the introduction of the complete decimal system. The member, going down to the House, wants oranges to sustain his voice in a two hours' speech on moving that 100000l. be placed at the disposal of Her Majesty, to supply the poor with ready-reckoners.

Boy. Fine oranges! two a penny! two a penny!

Member. Here boy, two! Now, how am I to pay you?

Boy. Give you change, your honor.

Member. Ah! but how? Where's your ready-reckoner?

Boy. I sells a better sort nor them. Mine's real Cheyny.

Member. But you see a farthing is now .0014166666 ad infinitum, and if we multiply this by 4——

Boy. Hold hard, Guv'ner; I sees what you're arter. Now what'll you stand if I puts you up to it? which Bill Smith he put me up in two minutes, cause he goes to the Ragged School.

Member. You don't mean that you do without a book!

Boy. Book be blowed. Come now, old un, here's summut for both on us. I got a florin, you gives me a half-a-crown for it, and I larns you the new money, gives you your oranges, and calls you a brick into the bargain.

Member (to himself). Never had such a chance of getting off half-a-crown for value since that —— fellow Bowring carried his crochet. (Aloud.) Well, boy, it's a bargain. Now!

Boy. Why, look 'e here, my trump, its a farden more to the tizzy—that's what it is.

Member. What's that?

Boy. Why, you knows a sixpence when you sees it. (Aside). Blest if I think he does! Well, its six browns and a farden now. A lady buys two oranges, and forks out a sixpence; well in coorse, I hands over fippence farden astead of fippence. I always gives a farden more change, and takes according.

Member (in utter surprise, lets his oranges tumble into the gutter). Never mind! They won't be wanted now. (Walks off one way. Boy makes a pass of naso-digital mesmerism, and walks off the other way).

To the poor, who keep no books, the whole secret is "Sixpence farthing to the half shilling, twelve pence halfpenny to the shilling." The new twopence halfpenny, or cent, will be at once five to the shilling.

In conclusion, we remark that three very common misconceptions run through the hon. Member's argument; and, combined in different proportions, give variety to his patterns.

First, he will have it that we design to bring the uneducated into contact with decimal fractions. If it be so, it will only be as M. Jourdain was brought into contact with prose. In fact, Quoi! quand je dis, Nicole, apportez-moi mes pantoufles, c'est de la prose? may be rendered: "What! do you mean that ten to the florin is a cent a piece must be called decimal reckoning?" If we had to comfort a poor man, horror-struck by the threat of decimals, we should tell him what manner of fractions had been inflicted upon him hitherto; nothing less awful than quarto-duodecimo-vicesimals, we should assure him.

Secondly, he assumes that the penny, such as it now is, will remain, as a coin of estimation, after it has ceased to be a coin of exchange; and that the mass of the people will continue to think of prices in old pence, and to calculate them in new ones, or else in new mils. No answer is required to this, beyond the mere statement of the nature of the assumption and denial.

Thirdly, he attributes to the uneducated community a want of perception and of operative power which really does not belong to them. The evidence offered to the Committee of the House shows that no fear is entertained on this point by those who come most in contact with farthing purchasers. And this would seem to be a rule,—that is, fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them, no fear at all in the minds of those who are.

A remarkable instance of this distinction happened five-and-twenty years ago. The Admiralty requested the Astronomical Society to report on the alterations which should be made in the Nautical Almanac, the seaman's guide-book over the ocean. The greatest alteration proposed was the description of celestial phenomena in mean (or clock time), instead of apparent (or sundial) time, till then always employed. This change would require that in a great many operations the seaman should let alone what he formerly altered by addition or subtraction, and alter by addition or subtraction what he formerly let alone; provided always that what he formerly altered by addition he should, when he altered at all, alter by subtraction, and vice versa. This was a tolerably difficult change for uneducated skippers, working by rules they had only learned by rote. The Astronomical Society appointed a Committee of forty, of whom nine were naval officers or merchant seamen [I was on this Committee]. Some men of science were much afraid of the change. They could not trust an ignorant skipper or mate to make those alterations in their routine, on the correctness of which the ship might depend. Had the Committee consisted of men of science only, the change might never have been ventured on. But the naval men laughed, and said there was nothing to fear; and on their authority the alteration was made. The upshot was, that, after the new almanacs appeared, not a word of complaint was ever heard on the matter. Had the House of Commons had to decide this question, with Mr. Lowe to quote the description given by Basil Hall (who, by the way, was one of the Committee) of an observation on which the safety of the ship depended, worked out by the light of a lantern in a gale of wind off a lee shore, this simple and useful change might at this moment have been in the hands of its tenth Government Commission.

[Aug. 14, 1866. The Committee was appointed in the spring of 1830: it consisted of forty members. Death, of course, has been busy; there are now left Lord Shaftesbury, Mr. Babbage, Sir John Herschel, Sir Thomas Maclear (Astronomer Royal at the Cape of Good Hope), Dr. Robinson (of Armagh), Sir James South, Lord Wrottesley, and myself].

THE TONAL SYSTEM.

Project of a new system of arithmetic, weight, measure, and coins, proposed to be called the tonal system, with sixteen to the base. By J. W. Mystrom. Philadelphia, 1862, 8vo.

That is to say, sixteen is to take the place of ten, and to be written 10. The whole language is to be changed; every man of us is to be sixteen-stringed Jack and every woman sixteen-stringed Jill. Our old one, two, three, up to sixteen, are to be (Noll going for nothing, which will please those who dislike the memory of Old Noll) replaced by An, De, Ti, Go, Su, By, Ra, Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an, Ton-de, etc. for 17, 18, etc. The number which in the system has the symbol

28(13)5(11)7(14)0(15)

(using our present compounds instead of new types) is to be pronounced

Detam-memill-lasan-suton-hubong-ramill-posanfy.

The year is to have sixteen months, and here they are:

Anuary, Debrian, Timander, Gostus,

Suvenary, Bylian, Ratamber, Mesudius,

Nictoary, Kolumbian, Husamber, Vyctorius,

Lamboary, Polian, Fylander, Tonborius.

Surely An-month, De-month, etc. would do as well. Probably the wants of poetry were considered. But what are we to do with our old poets? For example—

"It was a night of lovely June,

High rose in cloudless blue the moon."

Let us translate—

"It was a night of lovely Nictoary,

High rose in cloudless blue the (what, in the name of all that is absurd?)."

And again, Fylander thrown into our December! What is to become of those lines of Praed, which I remember coming out when I was at Cambridge,—

"Oh! now's the time of all the year for flowers and fun, the Maydays;

To trim your whiskers, curl your hair, and sinivate the ladies."

If I were asked which I preferred, this system or that of Baron Ferrari already mentioned, proceeding by twelves, I should reply, with Candide, when he had the option given of running the gauntlet or being shot: Les volontés sont libres, et je ne veux ni l'un ni l'autre. We can imagine a speculator providing such a system for Utopia as it would be in the mind of a Laputan: but to explain how an engineer who has surveyed mankind from Philadelphia to Rostof on the Don should for a moment entertain the idea of such a system being actually adopted, would beat a jury of solar-system-makers, though they were shut up from the beginning of Anuary to the end of Tonborius. When I see such a scheme as this imagined to be practicable, I admire the wisdom of Providence in providing the quadrature of the circle, etc., to open a harmless sphere of action to the possessors of the kind of ingenuity which it displays. Those who cultivate mathematics have a right to speak strongly on such efforts of arithmetic as this: for, to my knowledge, persons who have no knowledge are frequently disposed to imagine that their makers are true brothers of the craft, a little more intelligible than the rest.

SOME SMALL PARADOXERS.

Vis inertiae victa, or Fallacies affecting science. By James Reddie. London, 1862, 8vo.

An attack on the Newtonian mechanics; revolution by gravitation demonstrably impossible; much to be said for the earth being the immovable center. A good analysis of contents at the beginning, a thing seldom found. The author has followed up his attack in a paper submitted to the British Association, but which it appears the Association declined to consider. It is entitled—

Victoria Toto Cœlo; or, Modern Astronomy recast. London, 1863, 8vo.

At the end is a criticism of Sir G. Lewis's History of Ancient Astronomy.

On the definition and nature of the Science of Political Economy. By H. Dunning Macleod, Esq. Cambridge, 1862, 8vo.

A paper read—but, according to the report, not understood—at the British Association. There is a notion that political economy is entirely mathematical; and its negative quantity is strongly recommended for study: it contains "the whole of the Funds, Credit, 32 parts out of 33 of the value of Land...." The mathematics are described as consisting of—first, number, or Arithmetic; secondly, the theory of dependent quantities, subdivided into dependence by cause and effect, and dependence by simultaneous variations; thirdly, "independent quantities or unconnected events, which is the theory of probabilities." I am not ashamed, having the British Association as a co-non-intelligent, to say I do not understand this: there is a paradox in it, and the author should give further explanation, especially of his negative quantity. Mr. Macleod has gained praise from great names for his political economy; but this, I suspect, must have been for other parts of his system.

On the principles and practice of just Intonation, with a view to the abolition of temperament.... By General Perronet Thompson. Sixth Edition. London, 1862, 8vo.

Here is General Thompson again, with another paradox: but always master of the subject, always well up in what his predecessors have done, and always aiming at a useful end. He desires to abolish temperament by additional keys, and has constructed an enharmonic organ with forty sounds in the octave. If this can be introduced, I, for one, shall delight to hear it: but there are very great difficulties in the way, greater than stood even in the way of the repeal of the bread-tax.

In a paper on the beats of organ-pipes and on temperament published some years ago, I said that equal temperament appeared to me insipid, and not so agreeable as the effect of the instrument when in progress towards being what is called out of tune, before it becomes offensively wrong. There is throughout that period unequal temperament, determined by accident. General Thompson, taking me one way, says I have launched a declaration which is likely to make an epoch in musical practice; a public musical critic, taking me another way, quizzes me for preferring music out of tune. I do not think I deserve either one remark or the other. My opponent critic, I suspect, takes equally tempered and in tune to be phrases of one meaning. But by equal temperament is meant equal distribution among all the keys of the error which an instrument must have, which, with twelve sounds only in the octave, professes to be fit for all the keys. I am reminded of the equal temperament which was once applied to the postmen's jackets. The coats were all made for the average man: the consequence was that all the tall men had their tails too short; all the short men had them too long. Some one innocently asked why the tall men did not change coats with the short ones.

A diagram illustrating a discovery in the relation of circles to right-lined geometrical figures. London, 1863, 12mo.

The circle is divided into equal sectors, which are joined head and tail: but a property is supposed which is not true.

An attempt to assign the square roots of negative powers; or what is √ -1? By F.H. Laing. London, 1863, 8vo.

If I understand the author, -a and +a are the square roots of -a, as proved by multiplying them together. The author seems quite unaware of what has been done in the last fifty years.

BYRNE'S DUAL ARITHMETIC.

Dual Arithmetic. A new art. By Oliver Byrne. London, 1863, 8vo.

The plan is to throw numbers into the form a(1.1)b (1.01)c (1.001)d... and to operate with this form. This is an ingenious and elaborate speculation; and I have no doubt the author has practised his method until he could surprise any one else by his use of it. But I doubt if he will persuade others to use it. As asked of Wilkins's universal language, Where is the second man to come from?

An effective predecessor in the same line of invention was the late Mr. Thomas Weddle, in his "New, simple, and general method of solving numeric equations of all orders," 4to, 1842. The Royal Society, to which this paper was offered, declined to print it: they ought to have printed an organized method, which, without subsidiary tables, showed them, in six quarto pages, the solution (x=8.367975431) of the equation

1379.664 x + 2686034 × 10 x - 17290224 × 10 x + 2524156 × 10 = 0.

The method proceeds by successive factors of the form, a being the first approximation, a × 1.b × 1.0c × 1.00d.... In my copy I find a few corrections made by me at the time in Mr. Weddle's announcement. "It was read before that learned body [the R. S.] and they were pleased [but] to transmit their thanks to the author. The en[dis]couragement which he received induces [obliges] him to lay the result of his enquiries in this important branch of mathematics before the public [, at his own expense; he being an usher in a school at Newcastle]." Which is most satirical, Mr. Weddle or myself? The Society, in the account which it gave of this paper, described it as a "new and remarkably simple method" possessing "several important advantages." Mr. Rutherford's extended value of π was read at the very next meeting, and was printed in the Transactions; and very properly: Mr. Weddle's paper was excluded, and very very improperly.

HORNER'S METHOD.

I think it may be admited that the indisposition to look at and encourage improvements of calculation which once marked the Royal Society is no longer in existence. But not without severe lessons. They had the luck to accept Horner's now celebrated paper, containing the method which is far on the way to become universal: but they refused the paper in which Horner developed his views of this and other subjects: it was printed by T. S. Davies after Horner's death. I make myself responsible for the statement that the Society could not reject this paper, yet felt unwilling to print it, and suggested that it should be withdrawn; which was done.

But the severest lesson was the loss of Barrett's Method, now the universal instrument of the actuary in his highest calculations. It was presented to the Royal Society, and refused admission into the Transactions: Francis Baily printed it. The Society is now better informed: "live and learn," meaning "must live, so better learn," ought to be the especial motto of a corporation, and is generally acted on, more or less.

Horner's method begins to be introduced at Cambridge: it was published in 1820. I remember that when I first went to Cambridge (in 1823) I heard my tutor say, in conversation, there is no doubt that the true method of solving equations is the one which was published a few years ago in the Philosophical Transactions. I wondered it was not taught, but presumed that it belonged to the higher mathematics. This Horner himself had in his head: and in a sense it is true; for all lower branches belong to the higher: but he would have stared to have been told that he, Horner, was without a European predecessor, and in the distinctive part of his discovery was heir-at-law to the nameless Brahmin—Tartar—Antenoachian—what you please—who concocted the extraction of the square root.

It was somewhat more than twenty years after I had thus heard a Cambridge tutor show sense of the true place of Horner's method, that a pupil of mine who had passed on to Cambridge was desired by his college tutor to solve a certain cubic equation—one of an integer root of two figures. In a minute the work and answer were presented, by Horner's method. "How!" said the tutor, "this can't be, you know." "There is the answer, Sir!" said my pupil, greatly amused, for my pupils learnt, not only Horner's method, but the estimation it held at Cambridge. "Yes!" said the tutor, "there is the answer certainly; but it stands to reason that a cubic equation cannot be solved in this space." He then sat down, went through a process about ten times as long, and then said with triumph: "There! that is the way to solve a cubic equation!"

I think the tutor in this case was never matched, except by the country organist. A master of the instrument went into the organ-loft during service, and asked the organist to let him play the congregation out; consent was given. The stranger, when the time came, began a voluntary which made the people open their ears, and wonder who had got into the loft: they kept their places to enjoy the treat. When the organist saw this, he pushed the interloper off the stool, with "You'll never play 'em out this side Christmas." He then began his own drone, and the congregation began to move quietly away. "There," said he, "that's the way to play 'em out!"

I have not scrupled to bear hard on my own university, on the Royal Society, and on other respectable existences: being very much the friend of all. I will now clear the Royal Society from a very small and obscure slander, simply because I know how. This dissertation began with the work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer published, in 1849, a method of calculating logarithms. First, a long list of instances in which, as he alleges, foreign discoverers have been pillaged by Englishmen, or turned into Englishmen: for example, O'Neill, so called by Mr. Byrne, the rectifier of the semi-cubical parabola claimed by the Saxons under the name of Neal: the grandfather of this mathematician was conspicuous enough as Neal; he was archbishop of York. This list, says the writer, might be continued without end; but he has mercy, and finishes with his own case, as follows:—"About twenty years ago, I discovered this method of directly calculating logarithms. I could generally find the logarithm of any number in a minute or two without the use of books or tables. The importance of the discovery subjected me to all sorts of prying. Some asserted that I committed a table of logarithms to memory; others attributed it to a peculiar mental property; and when Societies and individuals failed to extract my secret, they never failed to traduce the inventor and the invention. Among the learned Societies, the Royal Society of London played a very base part. When I have more space and time at my disposal, I will revert to this subject again."

Such a trumpery story as this remains unnoticed at the time; but when all are gone, a stray copy from a stall falls into hands which, not knowing what to make of it, make history of it. It is a very curious distortion. The reader may take it on my authority, that the Royal Society played no part, good or bad, nor had the option of playing a part. But I myself pars magna fui: and when the author has "space and time" at his disposal, he must not take all of them; I shall want a little of both.

ARE ATOMS WORLDS?

The mystery of being; or are ultimate atoms inhabited worlds? By Nicholas Odgers. Redruth and London, 1863, 8vo.

This book, as a paradox, beats quadrature, duplication, trisection, philosopher's stone, perpetual motion, magic, astrology, mesmerism, clairvoyance, spiritualism, homœopathy, hydropathy, kinesipathy, Essays and Reviews, and Bishop Colenso, all put together. Of all the suppositions I have given as actually argued, this is the one which is hardest to deny, and hardest to admit. Reserving the question—as beyond human discussion—whether our particles of carbon, etc. are clusters of worlds, the author produces his reasons for thinking that they are at least single worlds. Of course—though not mentioned—the possibility is to be added of the same thing being true of the particles which make up our particles, and so down, for ever: and, on the other hand, of our planets and stars as being particles in some larger universe, and so up, for ever.

"Great fleas have little fleas upon their backs to bite 'em,

And little fleas have lesser fleas, and so ad infinitum.

And the great fleas themselves, in turn, have greater fleas to go on;

While these again have greater still, and greater still, and so on."

I have often had the notion that all the nebulæ we see, including our own, which we call the Milky Way, may be particles of snuff in the box of a giant of a proportionately larger universe. Of course the minim of time—a million of years or whatever the geologists make it—which our little affair has lasted, is but a very small fraction of a second to the great creature in whose nose we shall all be in a few tens of thousands of millions of millions of millions of years.

All this is quite possible, and the probabilities for and against are quite out of reach. Perhaps also all the worlds, both above and below us, are fac-similes of our own. If so, away goes free will for good and all; unless, indeed, we underpin our system with the hypothesis that all the fac-simile bodies of different sizes are actuated by a common soul. These acute supplementary notions of mine go far to get rid of the difficulty which some have found in the common theory that the soul inhabits the body: it has been stated that there is, somewhere or another, a world of souls which communicate with their bodies by wondrous filaments of a nature neither mental nor material, but of a tertium quid fit to be a go-between; as it were a corporispiritual copper encased in a spiritucorporeal gutta-percha. My theory is that every soul is everywhere in posse, as the schoolmen said, but not anywhere in actu, except where it finds one of its bodies. These a priori difficulties being thus removed, the system of particle-worlds is reduced to a dry question of fact, and remitted to the decision of the microscope. And a grand field may thus be opened, as optical science progresses! For the worlds are not fac-similes of ours in time: there is not a moment of our past, and not a moment of our future, but is the present of one or more of the particles. A will write the death of Cæsar, and B the building of the Pyramids, by actual observation of the processes with a power of a thousand millions; C will discover the commencement of the Millennium, and D the termination of Ersch and Gruber's Lexicon, as mere physical phenomena. Against this glorious future there is a sad omen: the initials of the forerunner of this discovery are—NO!

THE SUPERNATURAL.

The History of the Supernatural in all ages and nations, and in all Churches, Christian and Pagan: demonstrating a universal faith. By Wm. Howitt. London, 2 vols. 8vo. 1863.

Mr. Howitt is a preacher of spiritualism. He cements an enormous collection of alleged facts with a vivid outpouring of exhortation, and an unsparing flow of sarcasm against the scorners of all classes. He and the Rev. J. Smith (ante, 1854) are the most thoroughgoing universalists of all the writers I know on spiritualism. If either can insert the small end of the wedge, he will not let you off one fraction of the conclusion that all countries, in all ages, have been the theaters of one vast spiritual display. And I suspect that this consequence cannot be avoided, if any part of the system be of truly spiritual origin. Mr. Howitt treats the philosophers either as ignorant babies, or as conscious spirit-fearers: and seems much inclined to accuse the world at large of dreading, lest by the actual presence of the other world their Christianity should imbibe a spiritual element which would unfit it for the purposes of their lives.

FROM MATTER TO SPIRIT.

From Matter to Spirit. By C. D. With a preface by A. B. London, 1863, 8vo.

This is a work on Spiritual Manifestations. The author upholds the facts for spiritual phenomena: the prefator suspends his opinion as to the cause, though he upholds the facts. The work begins systematically with the lower class of phenomena, proceeds to the higher class, and offers a theory, suggested by the facts, of the connection of the present and future life. I agree in the main with A. B.; but can, of course, make none but horrescent reference to his treatment of the smaller philosophers. This is always the way with your paradoxers: they behave towards orthodoxy as the thresher fish behaves towards the whale. But if true, as is said, that the drubbing clears the great fish of parasites which he could not otherwise get rid of, he ought to bear no malice. This preface retorts a little of that contempt which the "philosophical world" has bestowed with heaped measure upon those who have believed their senses, and have drawn natural, even if hasty, inferences. There is philosophercraft as well as priestcraft, both from one source, both of one spirit. In English cities and towns, the minister of religion has been tamed: so many weapons are bared against him when he obtrudes his office in a dictatory manner, that, as a rule, there is no more quiet and modest member of society than the urban clergyman. Domination over religious belief is reserved for the exclusive use of those who admit the right: the rare exception to this mode of behavior is laughed at as a bigot, or shunned as a nuisance. But the overbearing minister of nature, who snaps you with unphilosophical as the clergyman once frightened you with infidel, is still a recognized member of society, wants taming, and will get it. He wears the priest's cast-off clothes, dyed to escape detection: the better sort of philosophers would gladly set him to square the circle.

The book just named appeared about the same time as this Budget began in the Athenæum. It was commonly attributed, the book to my wife, the preface to myself. Some time after, our names were actually announced by the publisher, who ought to know. It will be held to confirm this statement that I announce our having in our possession some twenty reviews of different lengths, and of all characters: who ever collects a number of reviews of a book, except the author?

A great many of these reviews settle the matter a priori. If there had been spirits in the matter, they would have done this, and they would not have done that. Jean Meslier said there could be no God over all, for, if there had been one, He would have established a universal religion. If J. M. knew that, J. M. was right: but if J. M. did not know that, then J. M. was on the "high priori road," and may be left to his course. The same to all who know what spirits would do and would not do.

A. B. very distinctly said that he knew some of the asserted facts, believed others on testimony, but did not pretend to know whether they were caused by spirits, or had some unknown and unimagined origin. This he said as clearly as I could have said it myself. But a great many persons cannot understand such a frame of mind: their own apparatus is a kind of spirit-level, and their conclusion on any subject is the little bubble, which is always at one end or the other. Many of the reviewers declare that A. B. is a secret believer in the spirit-hypothesis: and one of them wishes that he had "endorsed his opinion more boldly." According to this reviewer, any one who writes "I boldly say I am unable to choose," contradicts himself. In truth, a person who does say it has a good deal of courage, for each side believes that he secretly favors the other; and both look upon him as a coward. In spite of all this, A. B. boldly repeats that he feels assured of many of the facts of spiritualism, and that he cannot pretend to affirm or deny anything about their cause.

The great bulk of the illogical part of the educated community—whether majority or minority I know not; perhaps six of one and half-a-dozen of the other—have not power to make a distinction, cannot be made to take a distinction, and of course, never attempt to shake a distinction. With them all such things are evasions, subterfuges, come-offs, loopholes, etc. They would hang a man for horse-stealing under a statute against sheep-stealing; and would laugh at you if you quibbled about the distinction between a horse and a sheep. I divide the illogical—I mean people who have not that amount of natural use of sound inference which is really not uncommon—into three classes:—First class, three varieties: the Niddy, the Noddy, and the Noodle. Second class, three varieties: the Niddy-Noddy, the Niddy-Noodle, and the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-Noodle. No person has a right to be angry with me for more than one of these subdivisions.

The want of distinction was illustrated to me, when a boy, about 1820, by the report of a trial which I shall never forget: boys read newspapers more keenly than men. Every now and then a bench of country magistrates rather astonishes the town populations, accustomed to rub their brains against one another. Such a story as the following would, in our day, bring down grave remarks from above: but I write of the olden (or Eldon) time, when nothing but conviction in a court of record would displace a magistrate. In that day the third-class amalgamator of distinct things was often on the bench of quarter-sessions.

An attorney was charged with having been out at night poaching. A clear alibi was established; and perjury had certainly been committed. The whole gave reason to suspect that some ill-willers thought the bench disliked the attorney so much that any conviction was certain on any evidence. The bench did dislike the attorney: but not to the extent of thinking he could snare any partridges in the fields while he was asleep in bed, except the dream-partridges which are not always protected by the dream-laws. So the chairman said, "Mr. ——, you are discharged; but you should consider this one of the most fortunate days of your life." The attorney indignantly remonstrated, but the magistrate was right; for he said, "Mr. ——, you have frequently been employed to defend poachers: have you been careful to impress upon them the enormity of their practices?" It appeared in a wrangling conversation that the magistrates saw little moral difference between poaching and being a poacher's professional defender without lecturing him on his wickedness: but they admitted with reluctance, that there was a legal distinction; and the brain of N could no further go. This is nearly fifty years ago; and Westernism was not quite extinct. If the present lords of the hills and the valleys want to shine, let them publish a true history of their own order. I am just old enough to remember some of the last of the squires and parsons who protested against teaching the poor to read and write. They now write books for the working classes, give them lectures, and the like. There is now no class, as a class, more highly educated, broadly educated, and deeply educated, than those who were, in old times, best described as partridge-popping squireens. I have myself, when a boy, heard Old Booby speaking with pride of Young Booby as having too high a spirit to be confined to books: and I suspected that his dislike to teaching the poor arose in fact from a feeling that they would, if taught a little, pass his heir.

A. B. recommended the spirit-theory as an hypothesis on which to ground inquiry; that is, as the means of suggestion for the direction of inquiry. Every person who knows anything of the progress of physics understands what is meant; but not the reviewers I speak of. Many of them consider A. B. as adopting the spirit-hypothesis. The whole book was written, as both the authors point out, to suggest inquiry to those who are curious; C. D. firmly believing, A. B. as above. Neither C. D. nor A. B. make any other pretence. Both dwell upon the absence of authentications and the suppression of names as utterly preventive of anything like proof. And A. B. says that his reader "will give him credit, if not himself a goose, for seeing that the tender of an anonymous cheque would be of equal effect, whether drawn on the Bank of England or on Aldgate Pump." By this test a number of the reviewers are found to be geese: for they take the authors as offering proof, and insist, against the authors, on the very point on which the authors had themselves insisted beforehand.

Leaving aside imperceptions of this kind, I proceed to notice a clerical and medical review. I have lived much in the middle ages, especially since the invention of printing; and from thence I have brought away a high respect for and grateful recollection of—the priest in everything but theology, and the physician in everything but medicine. The professional harness was unfavorable to all progress, except on a beaten road; the professional blinkers prevented all but the beaten road from being seen: the professional reins were pulled at the slightest attempt to quicken pace, even on the permitted path; and the professional whip was heavily laid on at the slightest attempt to diverge. But when the intelligent man of either class turned his attention out of his ordinary work, he had, in most cases, the freshness and vigor of a boy at play, and like the boy, he felt his freedom all the more from the contrast of school-restraint.

In the case of medicine, and physics generally, the learned were, in some essential points, more rational than many of their present impugners. They pass for having put a priori obstacles in the way of progress: they might rather be reproved for too much belief in progress obtained by a priori means. They would have shouted with laughter at a dunce who—in a review I read, but without making a note—declared that he would not believe his senses except when what they showed him was capable of explanation upon some known principle. I have seen such stuff as this attributed to the schoolmen; but only by those who knew nothing about them. The following, which I wrote some years ago, will give a notion of a distinction worth remembering. It is addressed to the authorities of the College of Physicians.

"The ignominy of the word empiric dates from the ages in which scholastic philosophy deduced physical consequences a priori;—the ages in which, because a lion is strong, rubbing with lion's fat would have been held an infallible tonic. In those happy days, if a physician had given decoction of a certain bark, only because in numberless instances that decoction had been found to strengthen the patient, he would have been a miserable empiric. Not that the colleges would have passed over his returns because they were empirical: they knew better. They were as skilful in finding causes for facts, as facts for causes. The president and the elects of that day would have walked out into the forest with a rope, and would have pulled heartily at the tree which yielded the bark: nor would they ever have left it until they had pulled out a legitimate reason. If the tree had resisted all their efforts, they would have said, 'Ah! no wonder now; the bark of a strong tree makes a strong man.' But if they had managed to serve the tree as you would like to serve homœopathy, then it would have been 'We might have guessed it; all the virtus roborativa has settled in the bark.' They admitted, as we know from Molière, the virtus dormitiva of opium, for no other reason than that opium facit dormire. Had the medicine not been previously known, they would, strange as it may seem to modern pharmacopœists, have accorded a virtus dormitiva to the new facit dormire. On this point they have been misapprehended. They were prone to infer facit from a virtus imagined a priori; and they were ready in supplying facit in favor of an orthodox virtus. They might have gone so far, for example, under pre-notional impressions, as the alliterative allopath, who, when maintenance of truth was busy opposing the progress of science called vaccination, declared that some of its patients coughed like cows, and bellowed like bulls; but they never refused to find virtus when facit came upon them, no matter whence. They would rather have accepted Tenterden steeple than have rejected the Goodwin Sands. They would have laughed their modern imitators to scorn: but as they are not here, we do it for them.

"The man of our day—the a priori philosopher—tries the question whether opium can cause sleep by finding out in the recesses of his own noddle whether the drug can have a dormitive power: Well! but did not the schoolman do the same? He did; but mark the distinction. The schoolman had recourse to first principles, when there was no opium to try it by: our man settles the point in the same way with a lump of opium before him. The schoolman shifted his principles with his facts: the man of our drawing-rooms will fight facts with his principles, just as an old physician would have done in actual practice, with the rod of his Church at his back.

"The story about Galileo—which seems to have been either a joke made against him, or by him—illustrates this. Nature abhors a vacuum was the explanation of the water rising in a pump: but they found that the water would not rise more than 32 feet. They asked for explanation: what does the satirist make the schoolmen say? That the stoppage is not a fact, because nature abhors a vacuum? No! but that the principle should be that nature abhors a vacuum as far as 32 feet. And this is what would have been done.

"There are still among us both priests and physicians who would have belonged, had they lived three or four centuries ago, to the glorious band of whom I have spoken, the majority of the intelligent, working well for mankind out of the professional pursuit. But we have a great many who have helped to abase their classes. Go where we may, we find specimens of the lower orders of the ministry of religion and the ministry of health showing themselves smaller than the small of other pursuits. And how is this? First, because each profession is entered upon a mere working smack of its knowledge, without any depth of education, general or professional. Not that this is the whole explanation, nor in itself objectionable: the great mass of the world must be tended, soul and body, by those who are neither Hookers nor Harveys: let such persons not venture ultra crepidam, and they are useful and respectable. But, secondly, there is a vast upheaving of thought from the depths of commonplace learning. I am a clergyman! Sir! I am a medical man! Sir! and forthwith the nature of things is picked to pieces, and there is a race, with the last the winner, between Philosophy mounted on Folly's donkey, and Folly mounted on Philosophy's donkey. How fortunate it is for Law that her battles are fought by politicians in the Houses of Parliament. Not that it is better done: but then politics bears the blame."

I now come to the medical review. After a quantity of remark which has been already disposed of, the writer shows Greek learning, a field in which the old physician would have had a little knowledge. A. B., for the joke's sake, had left untranslated, as being too deep, a remarkably easy sentence of Aristotle, to the effect that what has happened was possible, for if impossible it would not have happened. The reviewer, in "simple astonishment,"—it was simple—at the pretended incapacity—I was told by A. B. that the joke was intended to draw out a reviewer—translates:—He says that this sentence is A. B.'s summing up of the evidence of Spiritualism. Now, being a sort of alter ego of A. B., I do declare that he is not such a fool as to rest the evidence of Spiritualism—the spirit explanation—upon the occurrence of certain facts proving the possibility of those very facts. In truth, A. B. refuses to receive spiritualism, while he receives the facts: this is the gist of his whole preface, which simply admits spiritualism among the qualified candidates, and does not know what others there may be.

The reviewer speaks of Aristotle as "that clear thinker and concise writer." I strongly suspect that his knowledge of Aristotle was limited to the single sentence which he had translated or got translated. Aristotle is concise in phrase, not in book, and is powerful and profound in thought: but no one who knows that his writing, all we have of him, is the very opposite of clear, will pretend to decide that he thought clearly. As his writing, so probably was his thought; and his books are, if not anything but clear, at least anything good but clear. Nobody thinks them clear except a person who always clears difficulties: which I have no doubt was the reviewer's habit; that is, if he ever took the field at all. The gentleman who read Euclid, all except the As and Bs and the pictures of scratches and scrawls, is the type of a numerous class.

The reviewer finds that the word amosgepotically, used by A. B., is utterly mysterious and incomprehensible. He hopes his translation of the bit of Greek will shield him from imputation of ignorance: and thinks the word may be referred to the "obscure dialect" out of which sprung aneroid, kalos geusis sauce, and Anaxyridian trousers. To lump the first two phrases with the third smacks of ignorance in a Greek critic; for ἀναξυριδια, breeches, would have turned up in the lexicon; and kalos geusis, though absurd, is not obscure. And ἀμωσγεπως, somehow or other, is as easily found as ἀναξυριδια. The word aneroid, I admit, has puzzled better scholars than the critic: but never one who knows the unscholarlike way in which words ending in ειδης have been rendered. The aneroid barometer does not use a column of air in the same way as the old instrument. Now ἀεροειδης—properly like the atmosphere—is by scientific non-scholarship rendered having to do with the atmosphere; and ἀναεροειδης—say anaëroid—denies having to do with the atmosphere; a nice thing to say of an instrument which is to measure the weight of the atmosphere. One more absurdity, and we have aneroid, and there you are. The critic ends with a declaration that nothing in the book shakes his faith in a Quarterly reviewer who said that suspension of opinion, until further evidence arrives, is justifiable: a strange summing up for an article which insists upon utter rejection being unavoidable. The expressed aim of both A. B. and C. D. was to excite inquiry, and get further evidence: until this is done, neither asks for a verdict.

Oh where! and oh where! is old Medicine's learning gone! There was some in the days of yore, when Popery was on! And it's oh! for some Greek, just to find a word upon! The reviewer who, lexicon in hand, can neither make out anaxyridical, amosgepotical, kalos geusis, nor distinguish them from aneroid, cannot be trusted when he says he has translated a sentence of Aristotle. He may have done it; but, as he says of spiritualism, we must suspend our opinion until further evidence shall arrive.

We now come to the theological review. I have before alluded to the faults of logic which are Protestant necessities: but I never said that Protestant argument had nothing but paralogism. The writer before me attains this completeness: from beginning to end he is of that confusion and perversion which, as applied to interpretation of the New Testament, is so common as to pass unnoticed by sermon-hearers; but which, when applied out of church, is exposed with laughter in all subjects except theology. I shall take one instance, putting some words in italics.

A. B.

My state of mind, which refers the whole either to unseen intelligence, or something which man has never had any conception of, proves me to be out of the pale of the Royal Society.

Theological Critic.

... he proceeds to argue that he himself is outside its sacred pale because he refers all these strange phenomena to unseen spiritual intelligence.

The possibility of a yet unimagined cause is insisted on in several places. On this ground it is argued by A. B. that spiritualists are "incautious" for giving in at once to the spirit doctrine. But, it is said, they may be justified by the philosophers, who make the flint axes, as they call them, to be the works of men, because no one can see what else they can be. This kind of adoption, condemned as a conclusion, is approved as a provisional theory, suggestive of direction of inquiry: experience having shown that inquiry directed by a wrong theory has led to more good than inquiry without any theory at all. All this A. B. has fully set forth, in several pages. On it the reviewer remarks that "with infinite satisfaction he tries to justify his view of the case by urging that there is no other way of accounting for it; after the fashion of the philosophers of our own day, who conclude that certain flints found in the drift are the work of men, because the geologist does not see what else they can be." After this twist of meaning, the reviewer proceeds to say, and A. B. would certainly join him, "There is no need to combat any such mode of reasoning as this, because it would apply with equal force and justice to any theory whatever, however fantastic, profane, or silly." And so, having shown how the reviewer has hung himself, I leave him funipendulous.

One instance more, and I have done. A reviewer, not theological, speaking of the common argument that things which are derided are not therefore to be rejected, writes as follows:—"It might as well be said that they who laughed at Jenner and vaccination were, in a certain but very unsatisfactory way, witnesses to the possible excellence of the system of St. John Long." Of course it might: and of course it is said by all people of common sense. In introducing the word "possible," the reviewer has hit the point: I suspect that this word was introduced during revision, to put the sentence into fighting order; hurry preventing it being seen that the sentence was thus made to fight on the wrong side. Jenner, who was laughed at, was right; therefore, it is not impossible—that is, it is possible—that a derided system may be right. Mark the three gradations: in medio tutissimus ibis.

Reviewer.—If a system be derided, it is no ground of suspense that derided systems have turned out true: if it were, you would suspend your opinion about St. John Long on account of Jenner.—Ans. You ought to do so, as to possibility; and before examination; not with the notion that J. proves St. J. probable; only possible.

Common Sense.—The past emergence of truths out of derided systems proves that there is a practical certainty of like occurrence to come. But, inasmuch as a hundred speculative fooleries are started for one truth, the mind is permitted to approach the examination of any one given novelty with a bias against it of a hundred to one: and this permission is given because so it will be, leave or no leave. Every one has licence not to jump over the moon.

Paradoxer.—Great men have been derided, and I am derided: which proves that my system ought to be adopted. This is a summary of all the degrees in which paradoxers contend for the former derision of truths now established, giving their systems probability. I annex a paragraph which D [e &c.] inserted in the Athenæum of October 23, 1847.

"Discoverers and Discoveries.

"Aristotle once sent his servant to the cellar to fetch wine:—and the fellow brought him back small beer. The Stagirite (who knew the difference) called him a blockhead. 'Sir,' said the man, 'all I can say is, that I found it in the cellar.' The philosopher muttered to himself that an affirmative conclusion could not be proved in the second figure,—and Mrs. Aristotle, who was by, was not less effective in her remark, that small beer was not wine because it was in the same cellar. Both were right enough: and our philosophers might take a lesson from either—for they insinuate an affirmative conclusion in the second figure. Great discoverers have been little valued by established schools,—and they are little valued. The results of true science are strange at first,—and so are their's. Many great men have opposed existing notions,—and so do they. All great men were obscure at first,—and they are obscure. Thinking men doubt,—and they doubt. Their small beer, I grant, has come out of the same cellar as the wine; but this is not enough. If they had let it stand awhile in the old wine-casks, it might have imbibed a little of the flavor."

There are better reviews than I have noticed; which, though entirely dissenting, are unassailable on their own principles. What I have given represents five-sixths of the whole. But it must be confessed that the fraction of fairness and moderation and suspended opinion which the doctrine of Spirit Manifestations has met with—even in the lower reviews—is strikingly large compared to what would have been the case fifty years ago. It is to be hoped that our popular and periodical literatures are giving us one thinker created for twenty geese double-feathered: if this hope be realized, we shall do! Seeing all that I see, I am not prepared to go the length of a friend of mine who, after reading a good specimen of the lower reviewing, exclaimed—Oh! if all the fools in the world could be rolled up into one fool, what a reviewer he would make!

Calendrier Universel et Perpétuel; par le Commandeur P. J. Arson. Publié par ses Enfans (Œuvre posthume). Nice, 1863, 4to.

I shall not give any account of this curious calendar, with all its changes and symbols. But there is one proposal, which, could we alter the general notions of time—a thing of very dubious possibility—would be convenient. The week is made to wax and wane, culminating on the Sunday, which comes in the middle. Thursday, Friday, Saturday, are ascending or waxing days; Monday, Tuesday, Wednesday, are descending or waning days. Our six days, lumped together after the great distinguishing day, Sunday, are too many to be distinctly thought of together: a division of three preceding and three following the day of most note would be much more easily used. But all this comes too late. It may be, nevertheless, that some individuals may be able to adjust their affairs with advantage by referring Thursday, Friday, Saturday, to the following Sunday, and Monday, Tuesday, Wednesday, to the preceding Sunday. But M. Arson's proposal to alter the names of the days is no more necessary than it is practicable.

CYCLOMETRY.

I am not to enter anything I do not possess. The reader therefore will not learn from me the feats of many a man-at-arms in these subjects. He must be content, unless he will bestir himself for himself, not to know how Mr. Patrick Cody trisects the angle at Mullinavat, or Professor Recalcati squares the circle at Milan. But this last is to be done by subscription, at five francs a head: a banker is named who guarantees restitution if the solution be not perfectly rigorous; the banker himself, I suppose, is the judge. I have heard of a man of business who settled the circle in this way: if it can be reduced to a debtor and creditor account, it can certainly be done; if not, it is not worth doing. Montucla will give the accounts of the lawsuits which wagers on the problem have produced in France.

Neither will I enter at length upon the success of the new squarer who advertises (Nov. 1863) in a country paper that, having read that the circular ratio was undetermined, "I thought it very strange that so many great scholars in all ages should have failed in finding the true ratio, and have been determined to try myself.... I am about to secure the benefit of the discovery, so until then the public cannot know my new and true ratio." I have been informed that this trial makes the diameter to the circumference as 64 to 201, giving π = 3.140625 exactly. The result was obtained by the discoverer in three weeks after he first heard of the existence of the difficulty. This quadrator has since published a little slip, and entered it at Stationers' Hall. He says he has done it by actual measurement; and I hear from a private source that he uses a disk of 12 inches diameter, which he rolls upon a straight rail. Mr. James Smith did the same at one time; as did also his partisan at Bordeaux. We have, then, both 3.125 and 3.140625, by actual measurement. The second result is more than the first by about one part in 200. The second rolling is a very creditable one; it is about as much below the mark as Archimedes was above it. Its performer is a joiner, who evidently knows well what he is about when he measures; he is not wrong by 1 in 3,000.

The reader will smile at the quiet self-sufficiency with which "I have been determined to try myself" follows the information that "so many great scholars in all ages" have failed. It is an admirable spirit, when accompanied by common sense and uncommon self-knowledge. When I was an undergraduate there was a little attendant in the library who gave me the following,—"As to cleaning this library, Sir, if I have spoken to the Master once about it, I have spoken fifty times: but it is of no use; he will not employ littery men; and so I am obliged to look after it myself."

I do not think I have mentioned the bright form of quadrature in which a square is made equal to a circle by making each side equal to a quarter of the circumference. The last squarer of this kind whom I have seen figures in the last number of the Athenæum for 1855: he says the thing is no longer a problem, but an axiom. He does not know that the area of the circle is greater than that of any other figure of the same circuit. This any one might see without mathematics. How is it possible that the figure of greatest area should have any one length in its circuit unlike in form to any other part of the same length?

The feeling which tempts persons to this problem is that which, in romance, made it impossible for a knight to pass a castle which belonged to a giant or an enchanter. I once gave a lecture on the subject: a gentleman who was introduced to it by what I said remarked, loud enough to be heard by all around, "Only prove to me that it is impossible, and I will set about it this very evening."

This rinderpest of geometry cannot be cured, when once it has seated itself in the system: all that can be done is to apply what the learned call prophylactics to those who are yet sound. When once the virus gets into the brain, the victim goes round the flame like a moth; first one way and then the other, beginning where he ended, and ending where he begun: thus verifying the old line

"In girum imus nocte, ecce! et consumimur igni."

Every mathematician knows that scores of methods, differing altogether from each other in process, all end in this mysterious 3.14159..., which insists on calling itself the circumference to a unit of diameter. A reader who is competent to follow processes of arithmetic may be easily satisfied that such methods do actually exist. I will give a sketch, carried out to a few figures, of three: the first two I never met with in my reading; the third is the old method of Vieta. [I find that both the first and second methods are contained in a theorem of Euler.]

What Mr. James Smith says of these methods is worth noting. He says I have given three "fancy proofs" of the value of π: he evidently takes me to be offering demonstration. He proceeds thus:—

"His first proof is traceable to the diameter of a circle of radius 1. His second, to the side of any inscribed equilateral triangle to a circle of radius 1. His third, to a radius of a circle of diameter 1. Now, it may be frankly admitted that we can arrive at the same result by many other modes of arithmetical calculation, all of which may be shown to have some sort of relation to a circle; but, after all, these results are mere exhibitions of the properties of numbers, and have no more to do with the ratio of diameter to circumference in a circle than the price of sugar with the mean height of spring tides. (Corr. Oct. 21, 1865)."

I quote this because it is one of the few cases—other than absolute assumption of the conclusion—in which Mr. Smith's conclusions would be true if his premise were true. Had I given what follows as proof, it would have been properly remarked, that I had only exhibited properties of numbers. But I took care to tell my reader that I was only going to show him methods which end in 3.14159.... The proofs that these methods establish the value of π are for those who will read and can understand.

200000000 31415 3799

66666667 2817

26666667 1363

11428571 661

5079365 321

2308802 156

1065601 76

497281 37

234014 18

110849 9

52785 5

25245 2

12118 1

5834

314153799 31415 9265

1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on. The sum of all is the circumference of that diameter. The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure. Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

2. To the square root of 3 add its half. Take half the third part of this; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum is the circumference to a unit of diameter.

Square root of 3.... 1.73205081

.86602540

2.59807621

.43301270

.08660254

1855768

412393

93726

21629

5047

1188

281

67

16

4

1

3.14159265

3. Take the square root of ½; the square root of half of one more than this; the square root of half of one more than the last; and so on, until we come as near to unity as the number of figures chosen will permit. Multiply all the results together, and divide 2 by the product: the quotient is an approximation to the circumference when the diameter is unity. Taking aim at four figures, that is, working to five figures to secure accuracy in the fourth, we have .70712 for the square root of ½; .92390 for the square root of half one more than .70712; and so on, through .98080, .99520, .99880, .99970, .99992, .99998. The product of the eight results is .63667; divide 2 by this, and the quotient is 3.1413..., of which four figures are correct. Had the product been .636363... instead of .63667..., the famous result of Archimedes, 22-7ths, would have been accurately true. It is singular that no cyclometer maintains that Archimedes hit it exactly.

A literary journal could hardly admit as much as the preceding, if it stood alone. But in my present undertaking it passes as the halfpennyworth of bread to many gallons of sack. Many more methods might be given, all ending in the same result, let that result mean what it may.

Now since dozens of methods, to which dozens more might be added at pleasure, concur in giving one and the same result; and since these methods are declared by all who have shown knowledge of mathematics to be demonstrated: it is not asking too much of a person who has just a little knowledge of the first elements that he should learn more, and put his hand upon the error, before he intrudes his assertion of the existence of error upon those who have given more time and attention to it than himself, and who are in possession, over and above many demonstrations, of many consequences verifying each other, of which he can know nothing. This is all that is required. Let any one square the circle, and persuade his friends, if he and they please: let him print, and let all read who choose. But let him abstain from intruding himself upon those who have been satisfied by existing demonstration, until he is prepared to lay his finger on the point in which existing demonstration is wrong. Let him also say what this mysterious 3.14159... really is, which comes in at every door and window, and down every chimney, calling itself the circumference to a unit of diameter. This most impudent and successful impostor holds false title-deeds in his hands, and invites examination: surely those who can find out the rightful owner are equally able to detect the forgery. All the quadrators are agreed that, be the right what it may, 3.14159... is wrong. It would be well if they would put their heads together, and say what this wrong result really means. The mathematicians of all ages have tried all manner of processes, with one object in view, and by methods which are admitted to yield demonstration in countless cases. They have all arrived at one result. A large number of opponents unite in declaring this result wrong, and all agree in two points: first, in differing among themselves; secondly, in declining to point out what that curious result really is which the mathematical methods all agree in giving.

Most of the quadrators are not aware that it has been fully demonstrated that no two numbers whatsoever can represent the ratio of the diameter to the circumference with perfect accuracy. When therefore we are told that either 8 to 25 or 64 to 201 is the true ratio, we know that it is no such thing, without the necessity of examination. The point that is left open, as not fully demonstrated to be impossible, is the geometrical quadrature, the determination of the circumference by the straight line and circle, used as in Euclid. The general run of circle-squarers, hearing that the quadrature is not pronounced to be demonstratively impossible, imagine that the arithmetical quadrature is open to their ingenuity. Before attempting the arithmetical problem, they ought to acquire knowledge enough to read Lambert's demonstration (last given in Brewster's translation of Legendre's Geometry) and, if they can, to refute it. [It will be given in an Appendix.] Probably some have begun this way, and have caught a Tartar who has refused to let them go: I have never heard of any one who, in producing his own demonstration, has laid his finger on the faulty part of Lambert's investigation. This is the answer to those who think that the mathematicians treat the arithmetical squarers too lightly, and that as some person may succeed at last, all attempts should be examined. Those who have so thought, not knowing that there is demonstration on the point, will probably admit that a person who contradicts a theorem of which the demonstration has been acknowledged for a century by all who have alluded to it as read by themselves, may reasonably be required to point out the error before he demands attention to his own result.

Apopempsis of the Tutelaries.—Again and again I am told that I spend too much time and trouble upon my two tutelaries: but when I come to my summing-up I shall make it appear that I have a purpose. Some say I am too hard upon them: but this is quite a mistake. Both of them beat little Oliver himself in the art and science of asking for more; but without Oliver's excuse, for I had given good allowance. Both began with me, not I with them: and both knew what they had to expect when they applied for a second helping.

On July 31, the Monday after the publication of my remarks on my 666 correspondent, I found three notes in separate envelopes, addressed to me at "7A, University College." When I saw the three new digits I was taken rhythmopoetic, as follows—

Here's the Doctor again with his figs, and by Heavens!

He was always at sixes, and now he's at sevens.

To understand this fully the reader must know that the greater part of Apocalyptic interpretation has long been condensed, in my mind, into the Turkish street-cry—In the name of the Prophet! figs! I make a few extracts. The reader will observe that Dr. Thorn grumbles at his private letters being publicly ridiculed. A man was summoned for a glutolactic assault; he complained of the publication of his proceeding: I kicked etc. in confidence, he said.

"After reading your last, which tries in every way to hold me up to public ridicule for daring to write you privately ['that you would be d——d,' omitted by accident] one would say, Why have anything to do with such a testy person? [Wrong word; no testy person can manage cool and consecutive ridicule. Quære, what is this word? Is it anything but a corruption of the obsolete word tetchy of the same meaning? Some think touchy is our modern form of tetchy, which I greatly doubt]. My answer is, the poor man is lamentably ignorant; he is not only so, but 'out of the way' [quite true; my readers know me by this time for an out-of-the-way person. What other could tackle my squad of paradoxers? What other would undertake the job?] Can he be brought back and form one of those who in Ezekiel 37 ch. have the Spirit breathed into them and live.... Have I any other feeling towards you except that of peace and goodwill? [Not to your distinct knowledge; but in all those who send people to 'the other place' for contempt of their interpretations, there is a lurking wish which is father to the thought; 'you will be d——d' and 'you be d—d' are Siamese twins]. Of course your sneer at 666 brought plain words; but when men meddle with what they do not understand (not having the double Vahu) they must be dealt with faithfully by those who do.... [They must; which justifies the Budget of Paradoxes: but no occasion to send them anywhere; no preachee and floggee too, as the negro said]. Many will find the text Prov. i. 26 fully realized. [All this contains distinct assumption of a right 'of course' to declare accursed those who do not respect the writer's vagary].... If I could but get the א, the Ox-head, which in Old Hebrew was just the Latin Digamma, F, out of your name, and could then Thau you with the Thau of Ezekiel ix, 4, the χ, then you would bear the number of a man! But this is too hard for me, although not so for the Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in so solemn a matter as the discussion of Holy Writ? [Is food for ridicule the right thing? Did I discuss Holy Writ? I did not: I concussed profane scribble. Even the Doctor did not discuss; he only enunciated and denunciated out of the mass of inferences which a mystical head has found premises for in the Bible]."

M 40

O 70

R 100

G 6

N 50

266

ת= χ 400

[That ill opinions are near relations of ill wishes, will be detected by those who are on the look out. The following was taken down in a Scotch Church by Mr. Cobden, who handed it to a Roman friend of mine, for his delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope into trouble; and we pray that thou wouldst be mercifully pleased to increase the same."]

Here is a martyr who quarrels with his crown; a missionary who reviles his persecutor: send him to New Zealand, and he would disagree with the Maoris who ate him. Man of unilateral reciprocity! have you, who write to a stranger with hints that that stranger and his wife are children of perdition, the bad taste to complain of a facer in return? As James Smith—the Attorney-wit, not the Dock-cyclometer—said, or nearly said,

"A pretty thing, forsooth!

Is he to burn, all scalding hot,

Me and my wife, and am I not

To job him out a tooth?"

Those who think parody vulgar will be pleased to substitute for the above a quotation from Butler:—

"There's nothing so absurd or vain

Or barbarous or inhumane,

But if it lay the least pretence

To piety and godliness,

Or tender-hearted conscience,

And zeal for gospel truths profess,—

Does sacred instantly commence,

And all that dare but question it are straight

Pronounced th' uncircumcised and reprobate,

As malefactors that escape and fly

Into a sanctuary for defence,

Must not be brought to justice thence,

Although their crimes be ne'er so great and high.

And he that dares presume to do't

Is sentenced and delivered up

To Satan that engaged him to't."

THE NUMBER OF THE BEAST.

Of all the drolleries of controversy none is more amusing than the manner in which those who provoke a combat expect to lay down the laws of retaliation. You must not strike this way! you must not parry that way! If you don't take care, we shall never meddle with you again! We were not prepared for such as this! Why did we have anything to do with such a testy person? M. Jourdain must needs show Nicole, his servant-maid, how good a thing it was to be sure of fighting without being killed, by care and tierce. "Et cela n'est il pas beau d'être assuré de son fait quand on se bat contre quelqu'un? Là, pousse moi un peu, pour voir. Nicole. Eh bien! quoi? M. Jourdain. Tout beau. Hola! Ho! doucement. Diantre soit la coquine! Nicole. Vous me dites de pousser. M. Jourdain. Oui; mais tu me pousses en tierce, avant que de pousser en quarte, et tu n'as pas la patience que je pare."

His colleague, my secular tutelary, who also made an anachronistic onset, with his repartees and his retorts, before there was anything to fire at, takes what I give by way of subsequent provocation with a good humor which would make a convert of me if he could afford .01659265 ... of a grain of logic. He instantly sent me his photograph for the asking, and another letter in proof. The Thor-hammerer does nothing but grumble, except when he tells a good story, which he says he had from Dr. Abernethy. A Mr. James Dunlop was popping at the Papists with a 666-rifled gun, when Dr. Chalmers quietly said, "Why, Dunlop, you bear it yourself," and handed him a paper on which the numerals in

I A C O B V S D V N L O P V S

1 100 5 500 5 50 5

were added up. This is almost as good as the Filii Dei Vicarius, the numerical letters of which also make 666. No more of these crazy—I first wrote puerile, but why should young cricketers be libelled?—attempts to extract religious use from numerical vagaries, and to make God over all a proposer of salvation conundrums: and no more of the trumpery hints about future destiny which is too great a compliment to call blasphemous. If the Doctor will cipher upon the letter in ἐν ᾡ μετρῳ μετρειτε μετρηθησεται ὑμιν with double Vahu cubic measure, he will perhaps learn to leave off trying to frighten me into gathering grapes from thorns.

Mystical hermeneutics may be put to good use by out-of-the-way people. They may be made to call the attention of the many to a distinction well known among the learned. The books of the New Testament have been for 1,500 years divided into two classes: the acknowledged (ὁμολογουμενα), which it has always been paradox not to receive; and the controverted (ἀντιλεγομενα), about which there has always been that difference of opinion which no scholar overlooks, however he may decide for himself after balance of evidence. Eusebius, who first (l. 3, c. 25) recorded the distinction—which was much insisted on by the early Protestants—states the books which are questioned as doubtful, but which yet are approved and acknowledged by many—or the many, it is not easy to say which he means—to be the Epistles of James and Jude, the second of Peter and the second and third of John. In other places he speaks doubtingly of the Epistle to the Hebrews. The Apocalypse he does not even admit into this class, for he proceeds as follows—I use the second edition of the English folio translation (1709), to avert suspicion of bias from myself:—

"Among the spurious [νοθοι] let there be ranked both the work entitled the Acts of Paul, and the book called Pastor, and the Revelation of Peter: and moreover, that which is called the Epistle of Barnabas, and that named the Doctrines of the Apostles: and moreover, as I said, the Revelation of John (if you think good), which some, as I have said, do reject, but others allow of, and admit among those books which are received as unquestionable and undoubted."

Eusebius, though he will not admit the Apocalypse even into the controverted list, but gives permission to call it spurious, yet qualifies his permission in a manner which almost annihilates the distinctive force of νοθος, and gives the book a claim to rank (if you think good, again) in the controverted list. And this is the impression received by the mind of Lardner, who gives Eusebius fully and fairly, but when he sums up, considers his author as admitting the Apocalypse into the second list. A stick may easily be found to beat the father of ecclesiastical history. There are whole faggots in writers as opposite as Baronius and Gibbon, who are perhaps his two most celebrated sons. But we can hardly imagine him totally misrepresenting the state of opinion of those for whom and among whom he wrote. The usual plan, that of making an author take the views of his readers, is more easy in his case than in that of any other writer: for, as the riddle says, he is You-see-by-us; and to this reading of his name he has often been subjected. Dr. Nathaniel Lardner, who, though heterodox in doctrine, tries hard to be orthodox as to the Canon, is "sometimes apt to think" that the list should be collected and divided as in Eusebius. He would have no one of the controverted books to be allowed, by itself, to establish any doctrine. Even without going so far, a due use of early opinion and long continued discussion would perhaps prevent rational people from being induced by those who have the double Vahu to place the Apocalypse above the Gospels, which all the Bivahuites do in effect, and some are said to have done in express words. But my especial purpose is to point out that an easy way of getting rid of 665 out of 666 of the mystics is to require them to establish the Apocalypse before they begin. See if they even know so much as that there is a crowd of testimonies for and against, running through the first four centuries, which makes this book the most difficult of the whole Canon. Try this method, and you will escape beautiful, as the French say. Dean Alford, in Vol. IV, p. 8, of his New Testament, gives an elaborate handling of this question. He concludes by saying that he cannot venture to refuse his consent to the tradition that the Apostle is the author. This modified adherence, or non-nonadherence, pretty well represents the feeling of orthodox Protestants, when learning and common sense come together.

I have often, in former days, had the attempt made to place the Apocalypse on my neck as containing prophecies yet unfulfilled. The preceding method prevents success; and so does the following. It may almost be taken for granted that theological system-fighters do not read the New Testament: they hunt it for detached texts; they listen to it in church in that state of quiescent nonentity which is called reverent attention: but they never read it. When it is brought forward, you must pretend to find it necessary to turn to the book itself: you must read "The revelation ... to show unto his servants things which must shortly come to pass.... Blessed is he that readeth ... for the time is at hand." You must then ask your mystic whether things deferred for 1800 years were shortly to come to pass, etc.? You must tell him that the Greek ἐν ταχει, rendered "shortly," is as strong a phrase as the language has to signify soon. The interpreter will probably look as if he had never read this opening: the chances are that he takes up the book to see whether you have been committing a fraud. He will then give you some exquisite evasion: I have heard it pleaded that the above was a mere preamble. This word mere is all-sufficient: it turns anything into nothing. Perhaps he will say that the argument is that of the Papists: if so, tell him that there is no Christian sect but bears true witness against some one or more absurdities in other sects.

An anonyme suggests that ἐν ταχει may not be "soon," it may be "quickly, without reference to time when:" he continues thus, "May not time be 'at hand' when it is ready to come, no matter how long delayed?" I now understand what *** and *** meant when they borrowed my books and promised to return them quickly, it was "without reference to time when." As to time at hand—provided you make a long arm—I admire the quirk, but cannot receive it: the word is ἐγγυς, which is a word of closeness in time, in place, in reckoning, in kindred, etc.

Another gentleman is not surprised that Apocalyptic reading leads to a doubt of the "canonicity" of the book: it ought not to rest on church testimony, but on visible miracle. He offers me, or any reader of the Athenæum, the "sight of a miracle to that effect, and within forty-eight hours' journey (fare paid)." I seldom travel, and my first thought was whether my carpet-bag would be found without a regular hunt: but, on reading further, I found that it was only a concordance that would be wanted. Forty hours' collection and numerical calculation of Greek nouns would make it—should I happen to agree with the writer—many hundred millions to one that Revelation xiii is superhuman. There is but one verse (the fifth) which the writer does not see verified. I looked at this verse, and was much startled. The Budget began in October 1863: should it last until March 1867—it is now August 1866—it is clear that I am the first Beast, and my paradoxers are the saints whom I persecute.

[The Budget did terminate in March 1867: I hope the gentleman will be satisfied with the resulting interpretation.]

The same opponent is surprised that I should suppose a thing which "comes to pass" must be completed, and cannot contain what is to happen 1800 years after. All who have any knowledge of English idiom know that a thing comes to pass when it happens, and came to pass afterwards. But as the original is Greek, we must look at the Greek: it is δει γενεσθαι for "must come to pass," and we know that ἐγενετο is what is usually translated "came to pass." No word of more finished completion exists in Greek.

And now for a last round of biter-bit with the Thor-hammerer, of whom, as in the other case, I shall take no more notice until he can contrive to surpass himself, which I doubt his being able to do. He informs me that by changing A into ת in my name he can make a 666 of me; adding, "This is too hard for me, although not so for the Lord!" Sheer nonsense! He could just as easily have directed to "Prof. De Morgתn" as have assigned me apartment 7A in University College. It would have been seen for whom it was intended: and if not, it would still have reached me, for my colleagues have for many a year handed all out-of-the-way things over to me. There is no 7A: but 7 is the Museum of Materia Medica. I took the only hint which the address gave: I inquired for hellebore, but they told me it was not now recognized, that the old notion of its value was quite obsolete, and that they had nothing which was considered a specific in senary or septenary cases. The great platitude is the reference of such a difficulty as writing ת for A to the Almighty! Not childish, but fatuous: real childishness is delightful. I knew an infant to whom, before he could speak plain, his parents had attempted to give notions of the Divine attributes: a wise plan, many think. His father had dandled him up-side-down, ending with, There now! Papa could not dance on his head! The mannikin made a solemn face, and said, But Dod tood! I think the Doctor has rather mistaken the way of becoming as a little child, intended in Matt. xviii. 3: let us hope the will may be taken for the deed.

Two poets have given images of transition from infancy to manhood: Dryden,—for the Hind is Dryden himself on all fours! and Wordsworth, in his own character of broad-nailed, featherless biped:

"The priest continues what the nurse began,

And thus the child imposes on the man."

"The child's the father of the man,

And I could wish my days to be
Bound each to each by natural piety."

In Wordsworth's aspiration it is meant that sense and piety should grow together: in Dryden's description a combination of Mysticism And Bigotry (can this be the double Vahu?), personified as "the priest,"—who always catches it on this score, though the same spirit is found in all associations,—succeeds the boguey-teaching of the nurse. Never was the contrast of smile and scowl, of light and darkness, better seen than in the two pictures. But an acrostic distinction may be drawn. When mysticism predominates over bigotry, we have the grotesque picturesque, and the natural order of words gives us Mab, an appropriate suggestion. But when bigotry has the upper hand, we see Bam, which is just as appropriate; for bigotry nearly always deals with facts and logic so as to require the application of at least one of the minor words by which dishonesty is signified. I think that M is the Doctor's initial, and that Queen Mab tickles him in his sleep with the sharp end of a 6.

(Monday, August 21.) Three weeks having elapsed without notice from me of the Doctor, I receive a reminder of his existence, in which I find that as I am the Daniel who judges the Magi of Babylon, it is to be pointed out that Daniel "bore a certain number, that of a man (beloved), Daniel, ch. 10. v. 11, and which you certainly do not." Then, "by Greek power," Belteshazzar is made = 666. Here is another awkward imitation of the way of a baby child. When you have sported with the tiny creature until it runs away offended, by the time you have got into conversation again you will find the game is to be renewed: a little head peeps out from a hiding-place with "I don't love you." The proper rejoinder is, "Very well! then I'll have pussy." But in the case before me there is a rule of three sums to do; as baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I can.

The squaring of the circle and the discovery of the Beast are the two goals—and goals also—of many unbalanced intellects, and of a few instances of the better kind. I might have said more of 666, but I am not deep in its bibliography. A work has come into my hands which contains a large number of noted cases: to some of my readers it will be a treat to see the collection; and the sight will perhaps be of some use to those who have read controversy on the few celebrated cases which are of general notoriety. It is written by a learned decipherer, a man who really knew the history of the subject, the Rev. David Thom, of Bold Street Chapel, Liverpool, who died, I am told, a few years ago.

Anybody who reads his book will be inclined to parody a criticism which was once made on Paley's Evidences—"Well! if there be anything in Christianity, this man is no fool." And, if he should chance to remember it, he will be strongly reminded of a sentence in my opening chapter,—"The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, especially as to the mode of doing it, a preliminary to inventing knowledge for himself." And this is reinforced by the fact that Mr. Thom, though a scholar, was not conspicuous for learning, except in this his great pursuit. He was a paradoxer on other points. He reconciled Calvinism and eternal reprobation with Universalism and final salvation; showing these two doctrines to be all one.

This gentleman must not be confounded with the Rev. John Hamilton Thom (no relation), at or near the same time and until recently, of Renshaw Street Chapel, Liverpool who was one of the minority in the Liverpool controversy when, nearly thirty years ago, three heretical Unitarian schooners exchanged shotted sermons with thirteen Orthodox ships of the line, and put up their challengers' dander—an American corruption of d—d anger—to such an extent, by quiet and respectful argument, that those opponents actually addressed a printed intercession to the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and Heretics." So much for the distinction, which both gentlemen would thank me for making very clear: I take it quite for granted that a guesser at 666 would feel horrified at being taken for a Unitarian, and that a Unitarian would feel queerified at being taken for a guesser at 666. Mr. David Thom's book is The Number and Names of the Apocalyptic Beasts, Part I, 1848, 8vo.: I think the second part was never published. I give the Greek and Latin solutions, omitting the Hebrew: as usual, all the Greek letters are numeral, but only M D C L X V I of the Latin. I do not give either the decipherers or their reasons: I have not room for this; nor would I, if I could, bias my reader for one rather than another.

D. F. Julianus Cæsar Atheus (or Aug.); Diocles Augustus; Ludovicus; Silvester Secundus; Linus Secundus; Vicarius Filii Dei; Doctor et Rex Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse Catholicæ Ecclesiæ Visibile Caput; Dux Cleri; Una, Vera, Catholica, Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina will also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres; Dic Lux ; Ludvvic; Will. Laud; Λατεινος; ἡ λατινη βασιλεια; ἐκκλησια ἰταλικα; εὐανθας; τειταν; ἀρνουμε; λαμπετις; ὁ νικητης; κακος ὁδηγος; ἀληθης βλαβερος; παλαι βασκανος; ἀμνος ἀδικος; ἀντεμος; γενσηρικος; εὐινας; Βενεδικτος; Βονιβαζιος γ. παπα ξ. η. ε. ε. α., meaning Boniface III. Pope 68th, bishop of bishops the first! οὐλπιος; διος εἰμι ἡ ἡρας; ἡ μισσα ἡ παπικη; λουθερανα; σαξονειος; Βεζζα ἀντιθεος (Beza); ἡ ἀλαζονεια βιου; Μαομετις; Μαομετης β.; θεος εἰμι ἐπι γαιης; ἰαπετος; παπεισκος; διοκλασιανος; χεινα; βρασκι; Ιον Παυνε; κουποκς; (cowpox, ς being the vau; certainly the vaccinated have the mark of the Beast); Βοννεπαρτη; Ν. Βονηπαρτε; εὐπορια; παραδοσις; το μεγαθηριον.

All sects fasten this number on their opponents. It is found in Martin Lauter, affirmed to be the true way of writing the name, by carrying numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn, found it in ישו נצרי Jesus of Nazareth. I find on inquiry that this satire was actually put forth by some medieval rabbis, but that it is not idiomatic: it represents quite fairly "Jesus Nazarene," but the Hebrew wants an article quite as much as the English wants "the."

Mr. David Thom's own solution hits hard at all sides: he finds a 666 for both beasts; ἡ φρην (the mind) for the first, and ἐκκλησιαι σαρκικαι (fleshly churches) for the second. A solution which embodies all mental philosophy in one beast and all dogmatic theology in the other, is very tempting: for in these are the two great supports of Antichrist. It will not, however, mislead me, who have known the true explanation a long time. The three sixes indicate that any two of the three subdivisions, Roman, Greek, and Protestant, are, in corruption of Christianity, six of one and half a dozen of the other: the distinctions of units, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and Concordance at ten, hundred, thousand) of symbolizing differences of number in the subdivisions.

It may be good to know that, even in speculations on 666, there are different degrees of unreason. All the diviners, when they get a colleague or an opponent, at once proceed to reckon him up: but some do it in play and some in earnest. Mr. David Thom found a young gentleman of the name St. Claire busy at the Beast number: he forthwith added the letters in στ κλαιρε and found 666: this was good fun. But my spiritual tutelary, when he found that he could not make a beast of me, except by changing א into ת, solemnly referred the difficulty to the Almighty: this was poor earnest.

I am glad I did not notice, in time to insert it in the Athenæum, a very remarkable paradoxer brought forward by Mr. Thom, his friend Mr. Wapshare: it is a little too strong for the general public. In the Athenæum they would have seen and read it: but this book will be avoided by the weaker brethren. It is as follows:

"God, the Elohim, was six days in creating all things, and having made MAN he entered into his rest. He is no more seen as a Creator, as Elohim, but as Jehovah, the Lord of the Sabbath, and the Spirit of life in Man, which Spirit worketh sin in the flesh; for the Spirit of Love, in all flesh, is Lust, or the spirit of a beast, So Rom. vii. And which Spirit is crucified in the flesh. He then, as Jehovah—as the power of the Law, in and over all flesh, John viii. 44—increases that which he has made as the Elohim, and his power shall last for 6 days, or 6 periods of time, computed at a millennium of years; and at the end of which six days, he who is the Spirit of all flesh shall manifest himself as the Holy Spirit of Almighty Love, and of all truth; and so shall the Church have her Sabbath of Rest—all contention being at an end. This is, as well as I may now express it, my solution of the mystery in Hebrew, and in Greek, and also in Latin, IHS. For he that was lifted up is King of the Jews, and is the Lord of all Life, working in us, both to will and to do; as is manifest in the Jews—they slaying him that his blood might be good for the healing of the nations, of all people and tongues. As the Father of all natural flesh, he is the Spirit of Lust, as in all beasts; as the Father, or King of the Jews, he is the Devil, as he himself witnesseth in John viii., already referred to. As lifted up, he is transformed into the Spirit of Love, a light to the Gentiles, and the glory of his people Israel.... For there is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was Satan, the Spirit of life in that body, is, in Christ crucified, seen in the Spirit that is in all, and through all and over all, God blessed for ever."

All this seems well meant, and Mr. Thom prints it as convinced of its piety, and "pronounces no opinion." Mystics of all sorts! see what you may come to, or what may come to you! I have inserted the above for your good.

There is nothing in this world so steady as some of the paradoxers. They are like the spiders who go on spinning after they have web enough to catch all the flies in the neighborhood, if the flies would but come. They are like the wild bees who go on making honey which they never can eat, proving sic vos non vobis to be a physical necessity of their own contriving. But nobody robs their hives: no, unlike the bees, they go about offering their ware to any who will take it as a gift. I had just written the last sentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received this morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out of the above account of the Rev. D. Thom, published Oct. 27: three notes had arrived before.

For curiosity I give one day's allowance, supposing these to be all: more may arrive before night.

29th Oct. 1866.

"Dear Sir,—

In re .

"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern Tau' Φανεροω—To make manifest, shew, or explain; and this may satisfy the House of Joseph in Amos 5c. While Belteshazzar = 666 may be also satisfactory to the House of David, and so we may have Zech. 10c. 6v. in operation when Ezekiel 37c. 16v. has been realised;—but there, what is the use of writing, it is all Coptic to a man who has not , The Thau of the North, the double Vahu וָו. Look at Jeremiah 3c. 8v. and then to Psalm 83 for 'hidden ones' צְפוּנֶי יְהוָה—The Zephoni Jehovah, and say whether they have any connection with the Zephon Thau. The Hammer of Thor of Jeremiah 23c. 29v. as I gave you in No. 3 of my present edition.

Yours truly

Le Chevalier Au Cin."

By Greek Power.

C = 20

H = 8

E = 5

V = 6

A = 1

L = 30

I = 10

E = 5

R = 100

A = 1

U = 400

C = 20

I = 10

N = 50

666

There will be thousands of Morgans who will be among the wise and prudent of Hosea 14c. 9v. when the Seventh Angel sounds, let me number that One by Greek, Rev. 17c. 1v:

S = 200

E = 5

× V = 6

E = 5

N = 50

T = 300

H = 8

A = 1

N = 50

× G = 6

E = 5

L = 30

666

V and G = 12 ought to be equal to one Gammadion or 3 × 4 = 12, what say you?

London, October 29, 1866.

"Dear Sir,—

In re versus .

However pretentious the X or may be, and it is peculiarly so just now in this land; after all it is only made of two Roman V's—and so is only = (10)—and therefore is not the perfect number 12 of Reveln, but is the mark of the goddess Decima!

Yours truly

Wm. Thorn."

Had the one who sent forth a pastoral (Romish) the other day, remained amongst the faithful expectants, see how he would have numbered, whereas he sold himself for the privilege of signing

Henry E. Manning.

By English Key. H = 8

E = 5

N = 40

R = 80

Y = 140

E = 5

D = 4

W = 120

A = 1

R = 80

D = 4

M = 30

A = 1

N = 40

N = 40

I = 9

N = 40

G = 7

= 12

666

Can you now understand the difference between and or X? Look to my challenge.

Cutting from newspaper:—

ITALY.

Rome (via Marseilles), October

Mr. Gladstone has paid a visit to the Pope.

By Greek Power. G = 6

L = 30

A = 1

D = 4

S = 200

T = 300

O = 70

N = 50

E = 5

666

And what then ?

In other letters John Stuart Mill is 666 if the a be left out; Chasuble is perfect. John Brighte is a fait accompli; and I am asked whether intellect can account for the final e. Very easily: this Beast is not the M. P., but another person who spells his name differently. But if John Sturt Mill and John Brighte choose so to write themselves, they may.

A curious collection; a mystical phantasmagoria! There are those who will try to find meaning: there are those who will try to find purpose.

"And some they said—What are you at?

And some—What are you arter?"

My account of Mr. Thom and his 666 appeared on October 27: and on the 29th I received from the editor a copy of Mr. Thom's sermons published in 1863 (he died Feb. 27, 1862) with best wishes for my health and happiness. The editor does not name himself in the book; but he signed his name in my copy: and may my circumference never be more than 3⅛ of my diameter if the signature, name and writing both, were not that of my ing friend Mr. James Smith! And so I have come in contact with him on 666 as well as on π! I should have nothing left to live for, had I not happened to hear that he has a perpetual motion on hand. I returned thanks and kind regards: and Miss Miggs's words—"Here's forgivenesses of injuries! here's amicablenesses!"—rang in my ears. But I was made slightly uncomfortable: how could the war go on after this armistice? Could I ever make it understood that the truce only extended to the double Vahu and things thereunto relating? It was once held by seafaring men that there was no peace with Spaniards beyond the line: I was determined that there must be no concord with J. S. inside the circle; that this must be a special exception, like Father Huddleston and old Grouse in the gun-room. I was not long in anxiety; twenty-four hours after the book of sermons there came a copy of the threatened exposure—The British Association in Jeopardy, and Professor De Morgan in the Pillory without hope of escape. By James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This exposure consists of reprints from the Athenæum and Correspondent: of things new there is but one. In a short preface Mr. J. S. particularly recommends to "read to the end." At the end is an appendix of two pages, in type as large as the work; a very prominent peroration. It is an article from the Athenæum, left out of its place. In the last sentence Mr. J. Smith, who had asked whether his character as an honest Geometer and Mathematician was not at stake, is warned against the fallacia plurium interrogationum. He is told that there is not a more honest what's-his-name in the world: but that as to the counter which he calls his character as a mathematician, he is assured that it has been staked years ago, and lost. And thus truth has the last word. There is no occasion to say much about reprints. One of them is a letter [that given above] of August 25, 1865, written by Mr. J. S. to the Correspondent. It is one of his quadratures; and the joke is that I am made to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to write in the Athenæum and forestall him. When I saw myself thus quoted—yes! quoted! double commas, first person—I felt as I suppose did Wm. Wilberforce when he set eyes on the affectionate benediction of the potato which waggish comrades had imposed on a raw Irish reporter as part of his speech. I felt as Martin of Galway—kind friend of the poor dumb creatures!—when he was told that the newspapers had put him in Italics. "I appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics? Do I ever speak in Italics?" I appeal to editor and readers, whether I ever squared the circle until a week or two ago, when I gave my charitable mode of reconciling the discrepant cyclometers.

The absurdity of the imitation of symbolic reasoning is so lusciously rich, that I shall insert it when I make up my final book. Somebody mastered Spanish merely to read Don Quixote: it would be worth while to learn a little algebra merely to enjoy this a b-istical attack on the windmills. The principle is, Prove something in as roundabout a way as possible, mention the circle once or twice irrelevantly in the course of your proof, and then make an act of Q. E. D. in words at length. The following is hardly caricature:—

To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of the House: let d = 666, the number of the Beast. Then of necessity d = a + b + c + 1; so that 1 is a harmonious and logical quantification of the number of which we are to take care. Now, b, the middle of our digital system, is, by mathematical and geometrical combination, a mean between 5 + 1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real mathematician can refuse without serious injury to his mathematical and geometrical reputation. It follows of necessity that 2 + 2 = 5, quod erat demonstrumhorrendum. If Simpkin & Marshall have not, after my notice, to account for a gross of copies more than would have gone off without me, the world is not worthy of its James Smith!

The only fault of the above is, that there is more connection than in the process of Faber Cyclometricus: so much, in fact, that the blunders are visible. The utter irrelevance of premises to conclusion cannot be exhibited with the requisite obscurity by any one who is able to follow reasoning: it is high art displayed in a certain toning down of the ægri somnia, which brings them to a certain look of reproach to reasoning which I can only burlesque. Mr. J. S. produces something which resembles argument much as a chimpanzee in dolor, because balked of his dinner, resembles a thinking man at his studies. My humble attempt at imitation of him is more like a monkey hanging by his tail from a tree and trying to crack a cocoa-nut by his chatter.

I could forgive Mr. J. S. anything, properly headed. I would allow him to prove—for himself—that the Quadrature of the Circle is the child of a private marriage between the Bull Unigenitus and the Pragmatic Sanction, claiming tithe of onions for repeal of the Mortmain Act, before the Bishops in Committee under the kitchen table: his mode of imitating reason would do this with ease. But when he puts his imitation into my mouth, to make me what he calls a "real mathematician," my soul rises in epigram against him. I say with the doll's dressmaker—such a job makes me feel like a puppet's tailor myself—"He ought to have a little pepper? just a few grains? I think the young man's tricks and manners make a claim upon his friends for a little pepper?" De Fauré and Joseph Scaliger come into my head: my reader may look back for them.

"Three circlesquarers to the manner born,

Switzerland, France, and England did adorn,

De Fauré in equations did surpass,

Joseph at contradictions was an ass.

Groaned Folly, I'm used up! What shall I do

To make James Smith? Grinned Momus, Join the two!"

As to my locus pœnitentiæ, the reader who is fit to enjoy the letter I have already alluded to will see that I have a soft and easy position; that the thing is really a pillowry; and that I am, like Perrette's pot of milk,

"Bien posé sur un coussinet."

Joanna Southcott never had a follower who believed in her with more humble piety than Mr. James Smith believes in himself. After all that has happened to him, he asks me with high confidence to "favor the writer with a proof" that I still continue of opinion that "the best of the argument is in my jokes, and the best of the joke is in his arguments." I will not so favor him. At the very outset I told him in plain English that he has the whiphand of all the reasoners in the world, and in plain French that il a perdu le droit d'être frappé de l'évidence; I might have said pendu. To which I now add, in plain Latin, Sapienti pauca, indocto nihil. The law of Chancery says that he who will have equity must do equity: the law of reasoning says that he who will have proof must see proof.

The introduction of things quite irrelevant, by way of reproach, is an argument in universal request: and it often happens that the argument so produced really tells against the producer. So common is it that we forget how boyish it is; but we are strikingly reminded when it actually comes from a boy. In a certain police court, certain small boys were arraigned for conspiring to hoot an obnoxious individual on his way from one of their school exhibitions. This proceeding was necessary, because there seemed to be a permanent conspiracy to annoy the gentleman; and the masters did not feel able to interfere in what took place outside the school. So the boys were arraigned; and their friends, as silly in their way as themselves, allowed one of them to make the defence, instead of employing counsel; and did not even give them any useful hints. The defence was as follows; and any one who does not see how richly it sets off the defences of bigger boys in bigger matters has much to learn. The innocent conviction that there was answer in the latter part is delightful. Of course fine and recognizance followed.

A—— said the boys had received great provocation from B——. He was constantly threatening them with a horsewhip which he carried in his hand [the boy did not say what had passed to induce him to take such a weapon], and he had repeatedly insulted the master, which the boys could not stand. B—— had in his own drawing-room told him (A——) that he had drawn his sword against the master and thrown away the scabbard. B—— knew well that if he came to the college he would catch it, and then he went off through a side door—which was no sign of pluck; and then he brought Mrs. B—— with him, thinking that her presence would protect him.

My readers may expect a word on Mr. Thom's sermons, after my account of his queer doings about 666. He is evidently an honest and devout man, much wanting in discrimination. He has a sermon about private judgment, in which he halts between the logical and legal meanings of the word. He loathes those who apply their private judgment to the word of God: here he means those who decide what it ought to be. He seems in other places aware that the theological phrase means taking right to determine what it is. He uses his own private judgment very freely, and is strong in the conclusion that others ought not to use theirs except as he tells them how; he leaves all the rest of mankind free to think with him. In this he is not original: his fame must rest on his senary tripod.

JAMES SMITH ONCE MORE.

Mr. James Smith's procedures are not caricature of reasoning; they are caricature of blundering. The old way of proving that 2 = 1 is solemn earnest compared with his demonstrations. As follows:

Let x = 1

Then x = x

And x - 1 = x - 1

Divide both sides by x - 1; then

x + 1 = 1; but x = 1, whence 2 = 1.

When a man is regularly snubbed, bullied, blown up, walked into, and put down, there is usually some reaction in his favor, a kind of deostracism, which cannot bear to hear him always called the blunderer. I hope it will be so in this case. There is nothing I more desire than to see sects of paradoxers. There are fully five thousand adults in England who ought to be the followers of some one false quadrature. And I have most hope of 3⅛, because I think Mr. James Smith better fitted to be the leader of an organized infatuation than any one I know of. He wants no pity, and will get none. He has energy, means, good humor, strong conviction, character, and popularity in his own circle. And, most indispensable point of all, he sticks at nothing;

"In cœlum jusseris, ibit."

When my instructor found I did not print an acceptance of what I have quoted, he addressed me as follows (Corr., Sept 23):—

"In this life, however, we must do our duty, and, when necessary, use the rod, not in a spirit of revenge, but for the benefit of the culprit and the good of society. Now, Sir, the opportunity has been thrown in your way of slipping out of the pillory without risk of serious injury; but, like an obstinate urchin, you have chosen to quarrel with your opportunity and remain there, and thus you compel me to deal with you as schoolmasters used to do with stupid boys in bygone days—that is to say, you force me to the use of the critic's rod, compel me to put you where little Jack Horner sat, and, as a warning to other naughty boys, to ornament you with a dunce's cap. The task I set you was a very simple one, as I shall make manifest at the proper time."

In one or more places, as well as this, Mr. Smith shows that he does not know the legend of little Jack Horner, whom he imagines to be put in the corner as a bad boy. This is curious; for there had been many allusions to the story in the journal he was writing in, and the Christmas pie had become altered into the Seaforth π.

Mr. Smith is satisfied at last that—what between argument and punishment he has convinced me. He says (Corr., Jan. 27, 1866): "I tell him without hesitation that he knows the true ratio of diameter to circumference as well as I do, and if he be wise he will admit it." I should hope I do, and better; but there is no occasion to admit what everybody knows.

I have often wished that we could have a slight glimpse of the reception which was given to some of the old cyclometers: but we have nothing, except the grave disapprobation of historians. I am resolved to give the New Zealander a chance of knowing a little more than this about one of them at least; and, by the fortunate entrance into life of the Correspondent, I am able to do it. I omit sober mathematical answers, of which there were several. The following letter is grave earnest:

"Sir,—I have watched Mr. James Smith's writings on this subject from the first, and I did hope that, as the more he departs from truth the more easy it must be to refute him, [this by no means always true] some of your correspondents would by this time have done so. I own that I am unable to detect the fallacy of his argument; and I am quite certain that 'Π' is wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the very elements of mathematical truth.' I have observed an immense amount of geometrical reasoning on his part, and I cannot see that it is either fair or honest to deny this, which may be regarded as the 'elements' of mathematical truth. Would it not be better for 'Π' to answer Mr. Smith, to refute his arguments, to point out their fallacies, and to save learners from error, than to plunge into gross insult and unmanly abuse? Would it not be well, also, that Professor De Morgan should favour us with a little reasoning?

"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I trust that this will not continue, since the subject is one of immense importance to science in general, especially to nautical science, and all that thereto belongs.

Yours, etc.,

A Captain, R.N."

On looking at this homœopathic treatment of the 3⅛ quadrature—remember, homœopathic, similia similibus, not infinitesimal—and at the imputation thrown upon it, I asked myself, what is vulgarity? No two agree, except in this, that every one sees vulgarity in what is directed against himself. Mark the world, and see if anything be so common as the description of the other side's remarks as "vulgar attempt at wit." "I suppose you think that very witty:" the answer is "No my friend! your remark shows that you feel it as wit, so that the purpose is answered; I keep my razor for something else than cutting blocks;" I am inclined to think that "out of place" is a necessary attribute of true vulgarity. And further, it is to be noticed that nothing is unproducible—salvo pudore—which has classical authority, modern or ancient, in its favor. "He is a vulgar fellow; I asked him what he was upon, and what do you think he answered, My legs!"—"Well, and has he not justification? what do you find in Terence? Quid agitur? Statur." I do not even blench from my principle where I find that it brings what is called "taking a sight" within permissible forms of expression: Rabelais not only establishes its antiquity, but makes it English. Our old translation has it thus (book 2. ch. 19):

"Then made the Englishman this sign. His left hand, all open, he lifted up into the air, then instantly shut into his fist the four fingers thereof; and his thumb extended at length he placed upon the tip of his nose. Presently after he lifted up his right hand all open and abased and bent it downwards, putting the thumb thereof in the very place where the little finger of the left hand did close in the fist, and the four right hand fingers he softly moved in the air. Then contrarily he did with the right hand what he had done with the left, and with the left what he had done with the right."

An impressive sight! The making of a fist of the left hand is a great addition of power, and should be followed in modern practice. The gentle sullation of the front fingers, with the clenched fist behind them, says as plainly as possible, Put suaviter in modo in the van, but don't forget to have fortiter in re in the rear.

My Budget was announced (March 23, 1867) for completion on the 30th. Mr. James Smith wrote five letters, one before the completion, four after it; the five contained 68 pages of quarto letter paper. Mr. J. S. had picked up a clerical correspondent, with whom he was in the heat of battle.

"March 27.—Dear Sir. Very truly yours. Duty; for my own sake; just time left to retrieve my errors; sends copy of letter to clergyman; new proof never before thought of; merest tyro would laugh if I were to stifle it, whether by rhodomontade or silent contempt; keep your temper. I shall be convinced; and if world be right in supposing me incapable of a foul act, I shall proclaim glorious discovery in the Athenæum.

"April 15.—Sir,... My dear Sir, Your sincere tutelary. Copy of another letter to clergyman; discovery tested by logarithms; reasons such as none but a knave or a sinner can resist. Let me advise you to take counsel before it is too late! Keep your temper. Let not your pride get the better of your discretion! Screw up your courage, my good friend, and resolve to show the world that you are an honest man....

"April 20.—Sir ... Your very sincere and favorite tutelary. I have long played the cur, snapping and snarling...; suddenly lost my power, and became half-starved dog without spirit to bark; try if air cannot restore me; calls himself the thistle in allusion to my other tutelary, the thorn; Would I prefer his next work to be, 'A whip for the Mathematical Cur, Prof. De M.' In some previous letter which I have mislaid, he told me his next would be 'a muzzle for the Mathematical Bull dog, Prof. De M.'

"April 23.—Sir. Very sincerely yours. More letters to clergyman; you may as well knock your head against a stone wall to improve your intellect as attempt to controvert my proofs. [I thought so too; and tried neither].

"May 6.—My dear Sir. Very sincerely yours. All to myself, and nothing to note.

"July 2.—No more in this interval. All that precedes is a desperate attempt to induce me to continue my descriptions: notoriety at any price."

I dare say the matter is finished: the record of so marked an instance of self-delusion will be useful.

I append to the foregoing a letter from Dr. Whewell to Mr. James Smith. The Master of Trinity was conspicuous as a rough customer, an intellectual bully, an overbearing disputant: the character was as well established as that of Sam Johnson. But there was a marked difference. It was said of Johnson that if his pistol missed fire, he would knock you down with the butt end of it: but Whewell, in like case, always acknowledged the miss, and loaded again or not, as the case might be. He reminded me of Dennis Brulgruddery, who says to Dan, Pacify me with a good reason, and you'll find me a dutiful master. I knew him from the time when he was my teacher at Cambridge, more than forty years. As a teacher, he was anything but dictatorial, and he was perfectly accessible to proposal of objections. He came in contact with me in his slashing way twice in our after joint lives, and on both occasions he acknowledged himself overcome, by that change of manner, and apologetic mode of continuance, which I had seen him employ towards others under like circumstances.

I had expressed my wish to have a thermometer of probability, with impossibility at one end, as 2 and 2 make 5, and necessity at the other, as 2 and 2 make 4, and a graduated rise of examples between them. Down came a blow: "What! put necessary and contingent propositions together! It's absurd!" I pointed out that the two kinds of necessity are but such extremes of probability as 0 and ∞ are of number, and illustrated by an urn with 1 white and n black balls, n increasing without limit. It was frankly seen, and the point yielded; a large company was present.

Again, in a large party, after dinner, and politics being the subject, I was proceeding, in discussion with Mr. Whewell, with "I think"...—"Ugh! you think!" was the answer. I repeated my phrase, and gave as a reason the words which Lord Grey had used in the House of Lords the night before (the celebrated advice to the Bishops to set their houses in order). He had not heard of this, and his manner changed in an instant: he was the rational discutient all the rest of the evening, having previously been nothing but a disputant with all the distinctions strongly marked.

I have said that Whewell was gentle with his pupils; it was the same with all who wanted teaching: it was only on an armed enemy that he drew his weapon. The letter which he wrote to Mr. J. Smith is an instance: and as it applies with perfect fidelity to the efforts of unreasoning above described, I give it here. Mr. James Smith is skilfully exposed, and felt it; as is proved by "putting the writer in the stocks."

"The Lodge, Cambridge, September 14th, 1862.

"Sir,—I have received your explanation of your proposition that the circumference of the circle is to its diameter as 25 to 8. I am afraid I shall disappoint you by saying that I see no force in your proof: and I should hope that you will see that there is no force in it if you consider this: In the whole course of the proof, though the word cycle occurs, there is no property of the circle employed. You may do this: you may put the word hexagon or dodecagon, or any other word describing a polygon in the place of Circle in your proof, and the proof would be just as good as before. Does not this satisfy you that you cannot have proved a property of that special figure—a circle?

"Or you may do this: calculate the side of a polygon of 24 sides inscribed in a circle. I think you are a Mathematician enough to do this. You will find that if the radius of the circle be one, the side of this polygon is .264 etc. Now, the arc which this side subtends is according to your proposition 3.125/12 = .2604, and therefore the chord is greater than its arc, which you will allow is impossible.

"I shall be glad if these arguments satisfy you, and

"I am, Sir, your obedient Servant,

"W. Whewell."

AN M.P.'S ARITHMETIC.

In the debate of May, 1866, on Electoral Qualifications, a question arose about arithmetical capability. Mr. Gladstone asked how many members of the House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and fifty-eight, answered one member; the thing cannot be done, answered another. There is an old paradox to which this relates: it arises out of the ignorance of the distinction between abstract and concrete arithmetic. Magnitude may be divided by magnitude; and the answer is number: how often does 12d. contain 4d.; answer three times. Magnitude may be divided by number, and the answer is magnitude: 12d. is divided in four equal parts, what is each part? Answer three pence. The honorable objector, whose name I suppress, trusting that he has mended his ways, gave the following utterance:

"With regard to the division sum, it was quite possible to divide by a sum, but not by money. How could any one divide money by 2l. 16s. 8d.? (Laughter.) The question might be asked, 'How many times 2s. will go into 1l.?' but that was not dividing by money; it was simply dividing 20 by 2. He might be asked, 'How many times will 6s. 8d. go into a pound?' but it was only required to divide 240 by 80. If the right hon. gentleman were to ask the hon. member for Brighton (Professor Fawcett), or any other authority, he would receive the same answer—viz., that it was possible to divide by a sum, but not by money. (Hear.)"

I shall leave all comment for the second edition, if I publish one. I shall be sure to have something to laugh at. Anything said from a respectable quarter, or supposed to be said, is sure to find defenders. Sam Johnson, a sound arithmetician, comparing himself, and what he alone had done in three years, with forty French Academicians and their forty years, said it proved that an Englishman is to a Frenchman as 40 × 40 to 3, or as 1600 to 3. Boswell, who was no great hand at arithmetic, made him say that an Englishman is to a Frenchman as 3 to 1600. When I pointed this out, the supposed Johnson was defended through thick and thin in Notes and Queries.

I am now curious to see whether the following will find a palliator. It is from "Tristram Shandy," book V. chapter 3. There are two curious idioms, "for for" and "half in half"; but these have nothing to do with my point:

"A blessing which tied up my father's tongue, and a misfortune which set it loose with a good grace, were pretty equal: sometimes, indeed, the misfortune was the better of the two; for, for instance, where the pleasure of harangue was as ten, and the pain of the misfortune but as five, my father gained half in half; and consequently was as well again off as if it had never befallen him."

This is a jolly confusion of ideas; and wants nothing but a defender to make it perfect. A person who invests five with a return of ten, and one who loses five with one hand and gains ten with the other, both leave off five richer than they began, no doubt. The first gains "half in half," more properly "half on half," that is, of the return, 10, the second 5 is gain upon the first 5 invested. "Half in half" is a queer way of saying cent. per cent. If the 5l. invested be all the man had in the world, he comes out, after the gain, twice as well off as he began, with reference to his whole fortune. But it is very odd to say that balance of 5l. gain is twice as good as if nothing had befallen, either loss or gain. A mathematician thinks 5 an infinite number of times as great as 0. The whole confusion is not so apparent when money is in question: for money is money whether gained or lost. But though pleasure and pain stand to one another in the same algebraical relation as money gained and lost, yet there is more than algebra can take account of in the difference.

Next, Ri. Milward (Richard, no doubt, but it cannot be proved) who published Selden's Table Talk, which he had collected while serving as amanuensis, makes Selden say, "A subsidy was counted the fifth part of a man's estate; and so fifty subsidies is five and forty times more than a man is worth." For times read subsidies, which seems part of the confusion, and there remains the making all the subsidies equal to the first, though the whole of which they are to be the fifths is perpetually diminished.

Thirdly, there is the confusion of the great misomath of our own day, who discovered two quantities which he avers to be identically the same, but the greater the one the less the other. He had a truth in his mind, which his notions of quantity were inadequate to clothe in language. This erroneous phraseology has not found a defender; and I am almost inclined to say, with Falstaff, The poor abuses of the time want countenance.

ERRONEOUS ARITHMETICAL NOTIONS.

"Shallow numerists," as Cocker is made to call them, have long been at work upon the question how to multiply money by money. It is, I have observed, a very common way of amusing the tedium of a sea voyage: I have had more than one bet referred to me. Because an oblong of five inches by four inches contains 5 × 4 or 20 square inches, people say that five inches multiplied by four inches is twenty square inches: and, thinking that they have multiplied length by length, they stare when they are told that money cannot be multiplied by money. One of my betters made it an argument for the thing being impossible, that there is no square money: what could I do but suggest that postage-stamps should be made legal tender. Multiplication must be repetition: the repeating process must be indicated by number of times. I once had difficulty in persuading another of my betters that if you repeat five shillings as often as there are hairs in a horse's tail, you do not multiply five shillings by a horsetail.

I am very sorry to say that these wrong notions have found support—I think they do so no longer—in the University of Cambridge. In 1856 or 1857, an examiner was displaced by a vote of the Senate. The pretext was that he was too severe an examiner: but it was well known that great dissatisfaction had been expressed, far and wide through the Colleges, at an absurd question which he had given. He actually proposed such a fraction as

6s. 3d.
/
17s. 4d. .

As common sense gained a hearing very soon, there is no occasion to say more. In 1858, it was proposed at a college examination, to divide 22557 days, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also to explain the fraction

32l. 18s. 8d.
/
62l. 12s. 9d. .

All paradoxy, in matters of demonstration, arises out of muddle about first principles. Who can say how much of it is to be laid at the door of the University of Cambridge, for not taking care of the elements of arithmetical thought?

ON LITERARY BARGAINS.

The phenomena of the two ends of society, when brought together, give interesting comparisons: I mean the early beginnings of thought and literature, and our own high and finished state, as we think it. There is one very remarkable point. In the early day, the letter was matter of the closest adherence, and implied meanings were not admitted.

The blessing of Isaac meant for Esau, went to false Jacob, in spite of the imposition; and the writer of Genesis seems to intend to give the notion that Isaac had no power to pronounce it null and void. And "Jacob's policy, whereby he became rich"—as the chapter-heading puts it—in speckled and spotted stock, is not considered as a violation of the agreement, which contemplated natural proportions. In the story of Lycurgus the lawgiver is held to have behaved fairly when he bound the Spartans to obey his laws until he returned—intimating a short absence—he intending never to return. And Vishnoo, when he asked the usurper for three steps of territory as a dwarf, and then enlarged himself until he could bring heaven and earth under the bargain, was thought clever, certainly, but quite fair.

There is nothing of this kind recognized in our day: so far good. But there is a bad contrary: the age is apt, in interpretation, to upset the letter in favor of the view—very often the after thought—of one side only. The case of John Palmer, the improver of the mail coach system, is smothered. He was to have an office and a salary, and 2½ per cent for life on the increased revenue of the Post-Office. His rights turned out so large, that Government would not pay them. For misconduct, real or pretended, they turned him out of his office: but his bargain as to the percentage had nothing to do with his future conduct; it was payment for his plan. I know nothing, except from the debates of 1808 in the two Houses: if any one can redeem the credit of the nation, the field is open. When I was young, the old stagers spoke of this transaction sparingly, and dismissed it speedily.

The government did not choose to remember what private persons must remember, and are made to remember, if needful. When Dr. Lardner made his bargain with the publishers for the Cabinet Cyclopædia he proposed that he, as editor, should have a certain sum for every hundred sold above a certain number: the publishers, who did not think there was any chance of reaching the turning sale of this stipulation, readily consented. But it turned out that Dr. Lardner saw further than they: the returns under this stipulation gave him a very handsome addition to his other receipts. The publishers stared; but they paid. They had no idea of standing out that the amount was too much for an editor; they knew that, though the editor had a percentage, they had all the rest; and they would not have felt aggrieved if he had received ten times as much. But governments, which cannot be brought to book before a sworn jury, are ruled only by public opinion. John Palmer's day was also the day of Thomas Fyshe Palmer, and the governments, in their prosecutions for sedition, knew that these would have a reflex action upon the minds of all who wrote about public affairs.

DECLARATION OF BELIEF

1864-65.—It often happens that persons combine to maintain and enforce an opinion; but it is, in our state of society, a paradox to unite for the sole purpose of blaming the opposite side. To invite educated men to do this, and above all, men of learning or science, is the next paradoxical thing of all. But this was done by a small combination in 1864. They got together and drew up a declaration, to be signed by "students of the natural sciences," who were to express their "sincere regret that researches into scientific truth are perverted by some in our own times into occasion for casting doubt upon the truth and authenticity of the Holy Scriptures." In words of ambiguous sophistry, they proceeded to request, in effect, that people would be pleased to adopt the views of churches as to the complete inspiration of all the canonical books. The great question whether the Word of God is in the Bible, or whether the Word of God is all the Bible, was quietly taken for granted in favor of the second view; to the end that men of science might be induced to blame those who took the first view. The first public attention was drawn to the subject by Sir John Herschel, who in refusing to sign the writ sent to him, administered a rebuke in the Athenæum, which would have opened most eyes to see that the case was hopeless. The words of a man whose suaviter in modo makes his fortiter in re cut blocks with a razor are worth preserving:

"I consider the act of calling upon me publicly to avow or disavow, to approve or disapprove, in writing, any religious doctrine or statement, however carefully or cautiously drawn up (in other words, to append my name to a religious manifesto) to be an infringement of that social forbearance which guards the freedom of religious opinion in this country with especial sanctity.... I consider this movement simply mischievous, having a direct tendency (by putting forward a new Shibboleth, a new verbal test of religious partisanship) to add a fresh element of discord to the already too discordant relations of the Christian world.... But no nicety of wording, no artifice of human language, will suffice to discriminate the hundredth part of the shades of meaning in which the most world-wide differences of thought on such subjects may be involved; or prevent the most gentle worded and apparently justifiable expression of regret, so embodied, from grating on the feelings of thousands of estimable and well-intentioned men with all the harshness of controversial hostility."

Other doses were administered by Sir J. Bowring, Sir W. Rowan Hamilton, and myself. The signed declaration was promised for Christmas, 1864: but nothing presentable was then ready; and it was near Midsummer, 1865, before it was published. Persons often incautiously put their names without seeing the character of a document, because they coincide in its opinions. In this way, probably, fifteen respectable names were procured before printing; and these, when committed, were hawked as part of an application to "solicit the favor" of other signatures. It is likely enough no one of the fifteen saw that the declaration was, not maintenance of their own opinion, but regret (a civil word for blame) that others should think differently.

When the list appeared, there were no fewer than 716 names! But analysis showed that this roll was not a specimen of the mature science of the country. The collection was very miscellaneous: 38 were designated as "students of the College of Chemistry," meaning young men who attended lectures in that college. But as all the Royal Society had been applied to, a test results as follows. Of Fellows of the Royal Society, 600 in number, 62 gave their signatures; of writers in the Philosophical Transactions, 166 in number, 19 gave their signatures. Roughly speaking, then, only one out of ten could be got to express disapprobation of the free comparison of the results of science with the statements of the canonical books. And I am satisfied that many of these thought they were signing only a declaration of difference of opinion, not of blame for that difference. The number of persons is not small who, when it comes to signing printed documents, would put their names to a declaration that the coffee-pot ought to be taken down-stairs, meaning that the teapot ought to be brought up-stairs. And many of them would defend it. Some would say that the two things are not contradictory; which, with a snort or two of contempt, would be very effective. Others would, in the candid and quiet tone, point out that it is all one, because coffee is usually taken before tea, and it keeps the table clear to send away the coffee-pot before the teapot is brought up.

The original signatures were decently interred in the Bodleian Library: and the advocates of scattering indefinite blame for indefinite sins of opinion among indefinite persons are, I understand, divided in opinion about the time at which the next attempt shall be made upon men of scientific studies: some are for the Greek Calends, and others for the Roman Olympiads. But, with their usual love of indefiniteness, they have determined that the choice shall be argued upon the basis that which comes first cannot be settled, and is of no consequence.

I give the declaration entire, as a curiosity: and parallel with it I give a substitute which was proposed in the Athenæum, as worthy to be signed both by students of theology, and by students of science, especially in past time. When a new attempt is made, it will be worth while to look at both:

Declaration.

We, the undersigned Students of the Natural Sciences, desire to express our sincere regret, that researches into scientific truth are perverted by some in our own times into occasion for casting doubt upon the Truth and Authenticity of the Holy Scriptures.

Proposed Substitute.

We, the undersigned Students of Theology and of Nature, desire to express our sincere regret, that common notions of religious truth are perverted by some in our own times into occasion for casting reproach upon the advocates of demonstrated or highly probable scientific theories.

We conceive that it is impossible for the Word of God, as written in the book of nature, and God's Word written in Holy Scripture, to contradict one another, however much they may appear to differ.

We conceive that it is impossible for the Word of God, as correctly read in the Book of Nature, and the Word of God, as truly interpreted out of the Holy Scripture, to contradict one another, however much they may appear to differ.

We are not forgetful that Physical Science is not complete, but is only in a condition of progress, and that at present our finite reason enables us only to see as through a glass darkly,

We are not forgetful that neither theological interpretation nor physical knowledge is yet complete, but that both are in a condition of progress; and that at present our finite reason enables us only to see both one and the other as through a glass darkly [the writers of the original declaration have distinctively applied to physical science the phrase by which St. Paul denotes the imperfections of theological vision, which they tacitly assume to be quite perfect],

and we confidently believe, that a time will come when the two records will be seen to agree in every particular. We cannot but deplore that Natural Science should be looked upon with suspicion by many who do not make a study of it, merely on account of the unadvised manner in which some are placing it in opposition to Holy Writ.

and we confidently believe, that a time will come when the two records will be seen to agree in every particular. We cannot but deplore that Religion should be looked upon with suspicion by some and Science by others, of the students of either who do not make a study of the other, merely on account of the unadvised manner in which some are placing Religion in opposition to Science, and some are placing Science in opposition to Religion.

We believe that it is the duty of every Scientific Student to investigate nature simply for the purpose of elucidating truth,

We believe that it is the duty of every theological student to investigate the Scripture, and of every scientific student to investigate Nature, simply for the purpose of elucidating truth.

and that if he finds that some of his results appear to be in contradiction to the Written Word, or rather to his own interpretations of it, which may be erroneous, he should not presumptuously affirm that his own conclusions must be right, and the statements of Scripture wrong;

And if either should find that some of his results appear to be in contradiction, whether to Scripture or to Nature, or rather to his own interpretation of one or the other, which may be erroneous, he should not affirm as with certainty that his own conclusion must be right, and the other interpretation wrong:

rather, leave the two side by side till it shall please God to allow us to see the manner in which they may be reconciled;

but should leave the two side by side for further inquiry into both, until it shall please God to allow us to arrive at the manner in which they may be reconciled.

and, instead of insisting upon the seeming differences between Science and the Scriptures, it would be as well to rest in faith upon the points in which they agree.

In the mean while, instead of insisting, and least of all with acrimony or injurious statements about others, upon the seeming differences between Science and the Scriptures, it would be a thousand times better to rest in faith as to our future state, in hope as to our coming knowledge, and in charity as to our present differences.

The distinctness of the fallacies is creditable to the composers, and shows that scientific habits tend to clearness, even to sophistry. Nowhere does it so plainly stand out that the Written Word means the sense in which the accuser takes it, while the sense of the other side is their interpretation. The infallible church on one side, arrayed against heretical pravity on the other, is seen in all subjects in which men differ. At school there were various games in which one or another advantage was the right of those who first called for it. In adult argument the same thing is often attempted: we often hear—I cried Church first!

I end with the answer which I myself gave to the application: its revival may possibly save me from a repetition of the like. If there be anything I hate more than another it is the proposal to place any persons, especially those who allow freedom to me, under any abridgment of their liberty to think, to infer, and to publish. If they break the law, take the law; but do not make the law: ἀγοραιοι ἀγονται ἐγκαλειτωσαν ἀλληλοις. I would rather be asked to take shares in an argyrosteretic company (with limited liability) for breaking into houses by night on fork and spoon errands. I should put aside this proposal with nothing but laughter. It was a joke against Sam Rogers that his appearance was very like that of a corpse. The John Bull newspaper—suppose we now say Theodore Hook—averred that when he hailed a coach one night in St. Paul's Churchyard, the jarvey said, "Ho! ho! my man; I'm not going to be taken in that way: go back to your grave!" This is the answer I shall make for the future to any relics of a former time who shall want to call me off the stand for their own purposes. What obligation have I to admit that they belong to our world?

"SCRIPTURE AND SCIENCE.

"The Writ De Hæretico Commiserando.

Nov. 14, 1864.

"This document was sent to me four days ago. It 'solicits the favor'—I thought at first it was a grocer's supplication for tea and sugar patronage—of my signature to expression of 'sincere regret' that some persons unnamed—general warrants are illegal—differ from what I am supposed—by persons whom it does not concern—to hold about Scripture and Science in their real or alleged discrepancies.

"No such favor from me: for three reasons. First, I agree with Sir. J. Herschel that the solicitation is an intrusion to be publicly repelled. Secondly, I do not regret that others should differ from me, think what I may: those others are as good as I, and as well able to think, and as much entitled to their conclusions. Thirdly, even if I did regret, I should be ashamed to put my name to bad chemistry made to do duty for good reasoning. The declaration is an awkward attempt to saturate sophism with truism; but the sophism is left largely in excess.

"I owe the inquisitors a grudge for taking down my conceit of myself. For two months I have crowed in my own mind over my friend Sir J. Herschel, fancying that the promoters instinctively knew better than to bring their fallacies before a writer on logic. Ah! my dear Sir John! thought I, if you had shown yourself to be well up in Barbara Celarent, and had ever and anon astonished the natives with the distinction between simpliciter and secundum quid, no autograph-hunters would have baited a trap with non sequitur to catch your signature. What can I say now? I hide my diminished head, diminished by the horns which I have been compelled to draw in.

"Those who make personal solicitation for support to an opinion about religion are bound to know their men. The king had a right to Brother Neale's money, because Brother Neale offered it. Had he put his hand into purse after purse by way of finding out all who were of Brother Neale's mind, he would have been justly met by a rap on the knuckles whenever he missed his mark.

"The kind of test before me is the utmost our time will allow of that inquisition into opinion which has been the curse of Christianity ever since the State took Providence under its protection. The writ de hæretico commiserando is little more than the smell of the empty cask: and those who issue it may represent the old woman with her

"O suavis anima, quale in te dicam bonum

Antehac fuisse; tales cum sint reliquiæ."

It is no excuse that the illegitimate bantling is a very little one. Its parents may think themselves hardly treated when they are called lineal successors of Tony Fire-the-faggot: but, degenerate though they be, such is their ancestry. Let every allowance be made for them: but their unholy fire must be trodden out; so long as a spark is left, nothing but fuel is wanted to make a blaze. If this cannot be done, let the flame be confined to theology, though even there it burns with diminished vigor: and let charity, candor, sense, and ridicule, be ready to play upon it whenever there is any chance of its extending to literature and science.

"What would be the consequence if this test-signing absurdity were to grow? Deep would call unto deep; counter-declaration would answer declaration, each stronger than the one before. The moves would go on like the dispute of two German students, of whom each is bound to a sharper retort on a graduated scale, until at last comes dummer Junge!—and then they must fight. There is a gentleman in the upper fifteen of the signers of the writ—the hawking of whose names appears to me very bad taste—whom I met in cordial cooperation for many a year at a scientific board. All I knew about his religion was that he, as a clergyman, must in some sense or other receive the 39 Articles:—all that he could know about mine was that I was some kind of heretic, or so reputed. If we had come to signing opposite manifestoes, turn-about, we might have found ourselves in the lowest depths of party discussion at our very council-table. I trust the list of subscribers to the declaration, when it comes to be published, will show that the bulk of those who have really added to our knowledge have seen the thing in its true light.

"The promoters—I say nothing about the subscribers—of the movement will, I trust, not feel aggrieved at the course I have taken or the remarks I have made. Walter Scott says that before we judge Napoleon by the temptation to which he yielded, we ought to remember how much he may have resisted: I invite them to apply this rule to myself; they can have no idea of the feeling with which I contemplate all attempts to repress freedom of inquiry, nor of the loathing with which I recoil from the proposal to be art and part. They have asked me to give a public opinion upon a certain point. It is true that they have had the kindness to tender both the opinion they wish me to form, and the shape in which they would have it appear: I will let them draw me out, but I will not let them take me in. If they will put an asterisk to my name, and this letter to the asterisk, they are welcome to my signature. As I do not expect them to relish this proposal, I will not solicit the favor of its adoption. But they have given a right to think, for they have asked me to think; to publish, for they have asked me to allow them to publish; to blame them, for they have asked me to blame their betters. Should they venture to find fault because my direction of disapproval, publicly given, is half a revolution different from theirs, they will be known as having presented a loaded document at the head of a traveler in the highway of discussion, with—Your signature or your silence!"

THE FLY-LEAF PARADOX.

The paradox being the proposition of something which runs counter to what would generally be thought likely, may present itself in many ways. There is a fly-leaf paradox, which puzzled me for many years, until I found a probable solution. I frequently saw, in the blank leaves of old books, learned books, Bibles of a time when a Bible was very costly, etc., the name of an owner who, by the handwriting and spelling, must have been an illiterate person or a child, followed by the date of the book itself. Accordingly, this uneducated person or young child seemed to be the first owner, which in many cases was not credible. Looking one day at a Barker's Bible of 1599, I saw an inscription in a child's writing, which certainly belonged to a much later date. It was "Martha Taylor, her book, giuen me by Granny Scott to keep for her sake." With this the usual verses, followed by 1599, the date of the book. But it so chanced that the blank page opposite the title, on which the above was written, was a verso of the last leaf of a prayer book, which had been bound before the Bible; and on the recto of this leaf was a colophon, with the date 1632. It struck me immediately that uneducated persons and children, having seen dates written under names, and not being quite up in chronology, did frequently finish off with the date of the book, which stared them in the face.

Always write in your books. You may be a silly person—for though your reading my book is rather a contrary presumption, yet it is not conclusive—and your observations may be silly or irrelevant, but you cannot tell what use they may be of long after you are gone where Budgeteers cease from troubling.

I picked up the following book, printed by J. Franklin at Boston, during the period in which his younger brother Benjamin was his apprentice. And as Benjamin was apprenticed very early, and is recorded as having learned the mechanical art very rapidly, there is some presumption that part of it may be his work, though he was but thirteen at the time. As this set of editions of Hodder (by Mose) is not mentioned, to my knowledge, I give the title in full:

"Hodder's Arithmetick: or that necessary art made most easy: Being explained in a way familiar to the capacity of any that desire to learn it in a little time. By James Hodder, Writing-master. The Five and twentieth edition, revised, augmented, and above a thousand faults amended, by Henry Mose, late servant and successor to the author. Boston: printed by J. Franklin, for S. Phillips, N. Buttolph, B. Elliot, D. Henchman, G. Phillips, J. Elliot, and E. Negus, booksellers in Boston, and sold at their shops. 1719."

The book is a very small octavo, the type and execution are creditable, the woodcut at the beginning is clumsy. It is a perfect copy, page for page, of the English editions of Mose's Hodder, of which the one called seventeenth is of London, 1690. There is not a syllable to show that the edition above described might not be of Boston in England. Presumptions, but not very strong ones, might be derived from the name of Franklin, and from the large number of booksellers who combined in the undertaking. It chanced, however, that a former owner had made the following note in my copy:

"Wednessday, July ye 14, 1796, att ten in ye forenoon we saild from Boston, came too twice, once in King Rode, and once in ye Narrows. Saild by ye lighthouse in ye eveng."

No ordinary map would decide these points: so I had to apply to my friend Sir Francis Beaufort, and the charts at the Admiralty decided immediately for Massachusetts.

PARADOXES OF ORTHOGRAPHY AND COMPUTATION.

The French are able paradoxers in their spelling of foreign names. The Abbé Sabatier de Castres, in 1772, gives an account of an imaginary dialogue between Swif, Adisson, Otwai, and Bolingbrocke. I had hoped that this was a thing of former days, like the literal roasting of heretics; but the charity which hopeth all things must hope for disappointments. Looking at a recent work on the history of the popes, I found referred to, in the matter of Urban VIII and Galileo, references to the works of two Englishmen, the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and Baden Powell].

I must not forget the "moderate computation" paradox. This is the way by which large figures are usually obtained. Anything surprisingly great is got by the "lowest computation," anything as surprisingly small by the "utmost computation"; and these are the two great subdivisions of "moderate computation." In this way we learn that 70,000 persons were executed in one reign, and 150,000 persons burned for witchcraft in one century. Sometimes this computation is very close. By a card before me it appears that all the Christians, including those dispersed in heathen countries, those of Great Britain and Ireland excepted, are 198,728,000 people, and pay their clergy 8,852,000l. But 6,400,000 people pay the clergy of the Anglo-Irish Establishment 8,896,000l.; and 14,600,000 of other denominations pay 1,024,000l. When I read moderate computations, I always think of Voltaire and the "mémoires du fameux évêque de Chiapa, par lesquels il paraît qu'il avait égorgé, ou brulé, ou noyé dix millions d'infidèles en Amérique pour les convertir. Je crus que cet évêque exaggérait; mais quand on réduisait ces sacrifices à cinq millions de victimes, cela serait encore admirable."

CENTRIFUGAL FORCE.

My Budget has been arranged by authors. This is the only plan, for much of the remark is personal: the peculiarities of the paradoxer are a large part of the interest of the paradox. As to subject-matter, there are points which stand strongly out; the quadrature of the circle, for instance. But there are others which cannot be drawn out so as to be conspicuous in a review of writers: as one instance, I may take the centrifugal force.

When I was about nine years old I was taken to hear a course of lectures, given by an itinerant lecturer in a country town, to get as much as I could of the second half of a good, sound, philosophical omniscience. The first half (and sometimes more) comes by nature. To this end I smelt chemicals, learned that they were different kinds of gin, saw young wags try to kiss the girls under the excuse of what was called laughing gas—which I was sure was not to blame for more than five per cent of the requisite assurance—and so forth. This was all well so far as it went; but there was also the excessive notion of creative power exhibited in the millions of miles of the solar system, of which power I wondered they did not give a still grander idea by expressing the distances in inches. But even this was nothing to the ingenious contrivance of the centrifugal force. "You have heard what I have said of the wonderful centripetal force, by which Divine Wisdom has retained the planets in their orbits round the Sun. But, ladies and gentlemen, it must be clear to you that if there were no other force in action, this centripetal force would draw our earth and the other planets into the Sun, and universal ruin would ensue. To prevent such a catastrophe, the same wisdom has implanted a centrifugal force of the same amount, and directly opposite," etc. I had never heard of Alfonso X of Castile, but I ventured to think that if Divine Wisdom had just let the planets alone it would come to the same thing, with equal and opposite troubles saved. The paradoxers deal largely in speculation conducted upon the above explanation. They provide external agents for what they call the centrifugal force. Some make the sun's rays keep the planets off, without a thought about what would become of our poor eyes if the push of the light which falls on the earth were a counterpoise to all its gravitation. The true explanation cannot be given here, for want of room.

CAMBRIDGE POETS.

Sometimes a person who has a point to carry will assert a singular fact or prediction for the sake of his point; and this paradox has almost obtained the sole use of the name. Persons who have reputation to care for should beware how they adopt this plan, which now and then eventuates a spanker, as the American editor said. Lord Byron, in "English Bards, etc." (1809), ridiculing Cambridge poetry, wrote as follows:

"But where fair Isis rolls her purer wave,

The partial muse delighted loves to lave;

On her green banks a greener wreath she wove,

To crown the bards that haunt her classic grove;

Where Richards wakes a genuine poet's fires,

And modern Britons glory in their sires."

There is some account of the Rev. Geo. Richards, Fellow of Oriel and Vicar of Bampton, (M.A. in 1791) in the Living Authors by Watkins and Shoberl (1816). In Rivers's Living Authors, of 1798, which is best fitted for citation, as being published before Lord Byron wrote, he is spoken of in high terms. The Aboriginal Britons was an Oxford (special) prize poem, of 1791. Charles Lamb mentions Richards as his school-fellow at Christ's Hospital, "author of the Aboriginal Britons, the most spirited of the Oxford Prize Poems: a pale, studious Grecian."

As I never heard of Richards as a poet, I conclude that his fame is defunct, except in what may prove to be a very ambiguous kind of immortality, conferred by Lord Byron. The awkwardness of a case which time has broken down is increased by the eulogist himself adding so powerful a name to the list of Cambridge poets, that his college has placed his statue in the library, more conspicuously than that of Newton in the chapel; and this although the greatness of poetic fame had some serious drawbacks in the moral character of some of his writings. And it will be found on inquiry that Byron, to get his instance against Cambridge, had to go back eighteen years, passing over seven intermediate productions, of which he had either never heard, or which he would not cite as waking a genuine poet's fires.

The conclusion seems to be that the Aboriginal Britons is a remarkable youthful production, not equalled by subsequent efforts.

To enhance the position in which the satirist placed himself, two things should be remembered. First, the glowing and justifiable terms in which Byron had spoken,—a hundred and odd lines before he found it convenient to say no Cambridge poet could compare with Richards,—of a Cambridge poet who died only three years before Byron wrote, and produced greatly admired works while actually studying in the University. The fame of Kirke White still lives; and future literary critics may perhaps compare his writings and those of Richards, simply by reason of the curious relation in which they are here placed alongside of each other. And it is much to Byron's credit that, in speaking of the deceased Cambridge poet, he forgot his own argument and its exigencies, and proved himself only a paradoxer pro re nata.

Secondly, Byron was very unfortunate in another passage of the same poem:

"What varied wonders tempt us as they pass!

The cow-pox, tractors, galvanism, and gas.

In turns appear, to make the vulgar stare,

Till the swoln bubble bursts—and all is air!"

Three of the bubbles have burst to mighty ends. The metallic tractors are disused; but the force which, if anything, they put in action, is at this day, under the name of mesmerism, used, prohibited, respected, scorned, assailed, defended, asserted, denied, declared utterly obscure, and universally known. It was hard lines to select for candidates for oblivion not one of whom got in. I shall myself, I am assured, be some day cited for laughing at the great discovery of ——: the blank is left for my reader to fill up in his own way; but I think I shall not be so unlucky in four different ways.

FALSIFIED PREDICTION.

The narration before the fact, as prophecy has been called, sometimes quite as true as the narration after the fact, is very ridiculous when it is wrong. Why, the pre-narrator could not know; the post-narrator might have known. A good collection of unlucky predictions might be made: I hardly know one so fit to go with Byron's as that of the Rev. Daniel Rivers, already quoted, about Johnson's biographers. Peter Pindar may be excused, as personal satire was his object, for addressing Boswell and Mrs. Piozzi as follows:

"Instead of adding splendor to his name,

Your books are downright gibbets to his fame;

You never with posterity can thrive,

'Tis by the Rambler's death alone you live."

But Rivers, in prose narrative, was not so excusable. He says:

"As admirers of the learning and moral excellence of their hero, we glow at almost every page with indignation that his weaknesses and his failings should be disclosed to public view.... Johnson, after the luster he had reflected on the name of Thrale ... was to have his memory tortured and abused by her detested itch for scribbling. More injury, we will venture to affirm, has been done to the fame of Johnson by this Lady and her late biographical helpmate, than his most avowed enemies have been able to effect: and if his character becomes unpopular with some of his successors, it is to those gossiping friends he is indebted for the favor."

Poor dear old Sam! the best known dead man alive! clever, good-hearted, logical, ugly bear! Where would he have been if it had not been for Boswell and Thrale, and their imitators? What would biography have been if Boswell had not shown how to write a life?

Rivers is to be commended for not throwing a single Stone at Mrs. Thrale's second marriage. This poor lady begins to receive a little justice. The literary world seems to have found out that a blue-stocking dame who keeps open house for a set among them has a right, if it so please her, to marry again without taking measures to carry on the cake-shop. I was before my age in this respect: as a boy-reader of Boswell, and a few other things that fell in my way, I came to a clearness that the conduct of society towards Mrs. Piozzi was blackguard. She wanted nothing but what was in that day a woman's only efficient protection, a male relation with a brace of pistols, and a competent notion of using them.

BYRON AND WORDSWORTH.

Byron's mistake about Hallam in the Pindar story may be worth placing among absurdities. For elucidation, suppose that some poet were now to speak—

"Of man's first disobedience, and the fruit

Eve gave to Adam in his birthday suit—"

and some critic were to call it nonsense, would that critic be laughing at Milton? Payne Knight, in his Taste, translated part of Gray's Bard into Greek. Some of his lines are

θερμὰ δ' ὁ τὲγγων δάκρυα στοναχαῖς

οὖλον μέλος φοβερᾷ

ηἔιδε φωνᾷ.

Literally thus:

"Wetting warm tears with groans,

Continuous chant with fearful

Voice he sang."

On which Hallam remarks: "The twelfth line [our first] is nonsense." And so it is, a poet can no more wet his tears with his groans than wet his ale with his whistle. Now this first line is from Pindar, but is only part of the sense; in full it is:

θερμὰ δὲ τέγγων δάκρυα στοναχαῖς

ὅρθιον φώνασε.

Pindar's τέγγων must be Englished by shedding, and he stands alone in this use. He says, "shedding warm tears, he cried out loud, with groans." Byron speaks of

"Classic Hallam, much renowned for Greek:"

and represents him as criticising the Greek of all Payne's lines, and not discovering that "the lines" were Pindar's until after publication. Byron was too much of a scholar to make this blunder himself: he either accepted the facts from report, or else took satirical licence. And why not? If you want to laugh at a person, and he will not give occasion, whose fault is it that you are obliged to make it? Hallam did criticise some of Payne Knight's Greek; but with the caution of his character, he remarked that possibly some of these queer phrases might be "critic-traps" justified by some one use of some one author. I remember well having a Latin essay to write at Cambridge, in which I took care to insert a few monstrous and unusual idioms from Cicero: a person with a Nizolius, and without scruples may get scores of them. So when my tutor raised his voice against these oddities, I was up to him, for I came down upon him with Cicero, chapter and verse, and got round him. And so my own solecisms, many of them, passed unchallenged.

Byron had more good in his nature than he was fond of letting out: whether he was a soured misanthrope, or whether his vein lay that way in poetry, and he felt it necessary to fit his demeanor to it, are matters far beyond me. Mr. Crabb Robinson told me the following story more than once. He was at Charles Lamb's chambers in the Temple when Wordsworth came in, with the new Edinburgh Review in his hand, and fume on his countenance. "These reviewers," said he, "put me out of patience! Here is a young man—they say he is a lord—who has written a volume of poetry; and these fellows, just because he is a lord, set upon him, laugh at him, and sneer at his writing. The young man will do something, if he goes on as he has begun. But these reviewers seem to think that nobody may write poetry, unless he lives in a garret." Crabb Robinson told this long after to Lady Byron, who said, "Ah! if Byron had known that, he would never have attacked Wordsworth. He went one day to meet Wordsworth at dinner; when he came home I said, 'Well, how did the young poet get on with the old one?' 'Why, to tell you the truth,' said he, 'I had but one feeling from the beginning of the visit to the end, and that was—reverence!'" Lady Byron told my wife that her husband had a very great respect for Wordsworth. I suppose he would have said—as the Archangel said to his Satan—"Our difference is po[li = e]tical."

I suspect that Fielding would, if all were known, be ranked among the unlucky railers at supposed paradox. In his Miscellanies (1742, 8vo) he wrote a satire on the Chrysippus or Guinea, an animal which multiplies itself by division, like the polypus. This he supposes to have been drawn up by Petrus Gualterus, meaning the famous usurer, Peter Walter. He calls it a paper "proper to be read before the R——l Society": and next year, 1743, a quarto reprint was made to resemble a paper in the Philosophical Transactions. So far as I can make out, one object is ridicule of what the zoologists said about the polypus: a reprint in the form of the Transactions was certainly satire on the Society, not on Peter Walter and his knack of multiplying guineas.

Old poets have recognized the quadrature of the circle as a well-known difficulty. Dante compares himself, when bewildered, to a geometer who cannot find the principle on which the circle is to be measured:

"Quale è 'l geometra che tutto s' affige

Per misurar lo cerchio, e non ritruova,

Pensando qual principio ond' egli indige."

And Quarles speaks as follows of the summum bonum:

"Or is't a tart idea, to procure

An edge, and keep the practic soul in ure,

Like that dear chymic dust, or puzzling quadrature?"

The poetic notion of the quadrature must not be forgotten. Aristophanes, in the Birds, introduces a geometer who announces his intention to make a square circle. Pope, in the Dunciad, delivers himself as follows, with a Greek pronunciation rather strange in a translator of Homer. Probably Pope recognized, as a general rule, the very common practice of throwing back the accent in defiance of quantity, seen in o´rator, au´ditor, se´nator, ca´tenary, etc.

"Mad Mathesis alone was unconfined,

Too mad for mere material chains to bind,—

Now to pure space lifts her ecstatic stare,

Now, running round the circle, finds it square."

The author's note explains that this "regards the wild and fruitless attempts of squaring the circle." The poetic idea seems to be that the geometers try to make a square circle. Disraeli quotes it as "finds its square," but the originals do not support this reading.

DE BECOURT.

I have come in the way of a work, entitled The Grave of Human Philosophies (1827), translated from the French of R. de Bécourt by A. Dalmas. It supports, but I suspect not very accurately, the views of the old Hindu books. That the sun is only 450 miles from us, and only 40 miles in diameter, may be passed over; my affair is with the state of mind into which persons of M. Bécourt's temperament are brought by a fancy. He fully grants, as certain, four millions of years as the duration of the Hindu race, and 1956 as that of the universe. It must be admitted he is not wholly wrong in saying that our errors about the universe proceed from our ignorance of its origin, antiquity, organization, laws, and final destination. Living in an age of light, he "avails himself of that opportunity" to remove this veil of darkness, etc. The system of the Brahmins is the only true one: he adds that it has never before been attempted, as it could not be obtained except by him. The author requests us first, to lay aside prejudice; next, to read all he says in the order in which he says it: we may then pronounce judgment upon a work which begins by taking the Brahmins for granted. All the paradoxers make the same requests. They do not see that compliance would bring thousands of systems before the world every year: we have scores as it is. How is a poor candid inquirer to choose. Fortunately, the mind has its grand jury as well as its little one: and it will not put a book upon its trial without a prima facie case in its favor. And with most of those who really search for themselves, that case is never made out without evidence of knowledge, standing out clear and strong, in the book to be examined.

BEQUEST OF A QUADRATURE.

There is much private history which will never come to light, caret quia vate sacro, because no Budgeteer comes across it. Many years ago a man of business, whose life was passed in banking, amused his leisure with quadrature, was successful of course, and bequeathed the result in a sealed book, which the legatee was enjoined not to sell under a thousand pounds. The true ratio was 3.1416: I have the anecdote from the legatee's executor, who opened the book. That a banker should square the circle is very credible: but how could a City man come by the notion that a thousand pounds could be got for it? A friend of mine, one of the twins of my zodiac, will spend a thousand pounds, if he have not done it already, in black and white cyclometry: but I will answer for it that he, a man of sound business notions, never entertained the idea of π recouping him, as they now say. I speak of individual success: of course if a company were formed, especially if it were of unlimited lie-ability, the shares would be taken. No offence; there is nothing but what a pun will either sanctify, justify, or nullify:

"It comes o'er the soul like the sweet South

That breathes upon a bank of vile hits."

The shares would be at a premium of 3⅛ on the day after issue. If they presented me with the number of shares I deserve, for suggestion and advertisement, I should stand up for the Archpriest of St. Vitus and 3-1/5, with a view to a little more gold on the bridge.

I now insert a couple of reviews, one about Cyclopædias, one about epistolary collections. Should any reader wish for explanation of this insertion, I ask him to reflect a moment, and imagine me set to justify all the additions now before him! In truth these reviews are the repositories of many odds and ends: they were not made to the books; the materials were in my notes, and the books came as to a ready-made clothes shop, and found what would fit them. Many remember Curll's bequest of some very good titles which only wanted treatises written to them. Well! here were some tolerable reviews—as times go—which only wanted books fitted to them. Accordingly, some tags were made to join on the books; and then as the reader sees.

I should find it hard to explain why the insertion is made in this place rather than another. But again, suppose I were put to make such an explanation throughout the volume. The improver who laid out grounds and always studied what he called unexpectedness, was asked what name he gave it for those who walked over his grounds a second time. He was silenced; but I have an answer: It is that which is given by the very procedure of taking up my book a second time.

REVIEW OF CYCLOPÆDIAS.

October 19, 1861. The English Cyclopædia. Conducted by Charles Knight. 22 vols.: viz., Geography, 4 vols.; Biography, 6 vols.; Natural History, 4 vols.; Arts and Sciences, 8 vols. (Bradbury & Evans.)

The Encyclopædia Britannica: a Dictionary of Arts, Sciences, and General Literature. Eighth Edition. 21 vols. and Index. (Black.)

The two editions above described are completed at the same time: and they stand at the head of the two great branches into which pantological undertakings are divided, as at once the largest and the best of their classes.

When the works are brought together, the first thing that strikes the eye is the syllable of difference in the names. The word Cyclopædia is a bit of modern purism. Though ἐγκυκλοπαιδεια is not absolutely Greek of Greece, we learn from both Pliny and Quintilian that the circle of the sciences was so called by the Greeks, and Vitruvius has thence naturalized encyclium in Latin. Nevertheless we admit that the initial en would have euphonized but badly with the word Penny: and the English Cyclopædia is the augmented, revised, and distributed edition of the Penny Cyclopædia. It has indeed been said that Cyclopædia should mean the education of a circle, just as Cyropædia is the education of Cyrus. But this is easily upset by Aristotle's word κυκλοφορία, motion in a circle, and by many other cases, for which see the lexicon.

The earliest printed Encyclopædia of this kind was perhaps the famous "myrrour of the worlde," which Caxton translated from the French and printed in 1480. The original Latin is of the thirteenth century, or earlier. This is a collection of very short treatises. In or shortly after 1496 appeared the Margarita Philosophica of Gregory Reisch, the same we must suppose, who was confessor to the Emperor Maximilian. This is again a collection of treatises, of much more pretension: and the estimation formed of it is proved by the number of editions it went through. In 1531 appeared the little collection of works of Ringelberg, which is truly called an Encyclopædia by Morhof, though the thumbs and fingers of the two hands will meet over the length of its one volume. There are more small collections; but we pass on to the first work to which the name of Encyclopædia is given. This is a ponderous Scientiarum Omnium Encyclopædia of Alsted, in four folio volumes, commonly bound in two: published in 1629 and again in 1649; the true parent of all the Encyclopædias, or collections of treatises, or works in which that character predominates. The first great dictionary may perhaps be taken to be Hofman's Lexicon Universale (1677); but Chambers's (so called) Dictionary (1728) has a better claim. And we support our proposed nomenclature by observing that Alsted accidentally called his work Encyclopædia, and Chambers simply Cyclopædia.

We shall make one little extract from the myrrour, and one from Ringelberg. Caxton's author makes a singular remark for his time; and one well worthy of attention. The grammar rules of a language, he says, must have been invented by foreigners: "And whan any suche tonge was perfytely had and usyd amonge any people, than other people not used to the same tonge caused rulys to be made wherby they myght lerne the same tonge ... and suche rulys be called the gramer of that tonge." Ringelberg says that if the right nostril bleed, the little finger of the right hand should be crooked, and squeezed with great force; and the same for the left.

We pass on to the Encyclopédie, commenced in 1751; the work which has, in many minds, connected the word encyclopædist with that of infidel. Readers of our day are surprised when they look into this work, and wonder what has become of all the irreligion. The truth is, that the work—though denounced ab ovo on account of the character of its supporters—was neither adapted, nor intended, to excite any particular remark on the subject: no work of which D'Alembert was co-editor would have been started on any such plan. For, first, he was a real sceptic: that is, doubtful, with a mind not made up. Next, he valued his quiet more than anything; and would as soon have gone to sleep over an hornet's nest as have contemplated a systematic attack upon either religion or government. As to Diderot—of whose varied career of thought it is difficult to fix the character of any one moment, but who is very frequently taken among us for a pure atheist—we will quote one sentence from the article "Encyclopédie," which he wrote himself:—"Dans le moral, il n'y a que Dieu qui doit servir de modèle a 1'homme; dans les art, que la nature."

A great many readers in our country have but a very hazy idea of the difference between the political Encyclopædia, as we may call it, and the Encyclopédie Méthodique, which we always take to be meant—whether rightly or not we cannot tell—when we hear of the "great French Encyclopædia." This work, which takes much from its predecessor, professing to correct it, was begun in 1792, and finished in 1832. There are 166 volumes of text, and 6439 plates, which are sometimes incorporated with the text, sometimes make about 40 more volumes. This is still the monster production of the kind; though probably the German Cyclopædia of Ersch and Gruber, which was begun in 1818, and is still in progress, will beat it in size. The great French work is a collection of dictionaries; it consists of Cyclopædias of all the separate branches of knowledge. It is not a work, but a collection of works, one or another department is to be bought from time to time; but we never heard of a complete set for sale in one lot. As ships grow longer and longer, the question arises what limit there is to the length. One answer is, that it will never do to try such a length that the stern will be rotten before the prow is finished. This wholesome rule has not been attended to in the matter before us; the earlier parts of the great French work were antiquated before the whole were completed: something of the kind will happen to that of Ersch and Gruber.

The production of a great dictionary of either of the kinds is far from an easy task. There is one way of managing the Encyclopædia which has been largely resorted to; indeed, we may say that no such work has been free from it. This plan is to throw all the attention upon the great treatises, and to resort to paste and scissors, or some process of equally easy character, for the smaller articles. However it may be done, it has been the rule that the Encyclopædia of treatises should have its supplemental Dictionary of a very incomplete character. It is true that the treatises are intended to do a good deal; and that the Index, if it be good, knits the treatises and the dictionary into one whole of reference. Still there are two stools, and between them a great deal will fall to the ground. The dictionary portion of the Britannica is not to be compared with its treatises; the part called Miscellaneous and Lexicographical in the Metropolitana is a great failure. The defect is incompleteness. The biographical portion, for example, of the Britannica is very defective: of many names of note in literature and science, which become known to the reader from the treatises, there is no account whatever in the dictionary. So that the reader who has learnt the results of a life in astronomy, for example, must go to some other work to know when that life began and ended. This defect has run through all the editions; it is in the casting of the work. The reader must learn to take the results at their true value, which is not small. He must accustom himself to regard the Britannica as a splendid body of treatises on all that can be called heads of knowledge, both greater and smaller; with help from the accompanying dictionary, but not of the most complete character. Practically, we believe, this defect cannot be avoided: two plans of essentially different structure cannot be associated on the condition of each or either being allowed to abbreviate the other.

The defect of all others which it is most difficult to avoid is inequality of performance. Take any dictionary you please, of any kind which requires the association of a number of contributors, and this defect must result. We do not merely mean that some will do their work better than others; this of course: we mean that there will be structural differences of execution, affecting the relative extent of the different parts of the whole, as well as every other point by which a work can be judged. A wise editor will not attempt any strong measures of correction: he will remember that if some portions be below the rest, which is a disadvantage, it follows that some portions must be above the rest, which is an advantage. The only practical level, if level there must be, is that of mediocrity, if not of absolute worthlessness: any attempt to secure equality of strength will result in equality of weakness. Efficient development may be cut down into meager brevity, and in this way only can apparent equality of plan be secured throughout. It is far preferable to count upon differences of execution, and to proceed upon the acknowledged expectation that the prominent merits of the work will be settled by the accidental character of the contributors; it being held impossible that any editorial efforts can secure a uniform standard of goodness. Wherever the greatest power is found, it should be suffered to produce its natural effect. There are, indeed, critics who think that the merit of a book, like the strength of a chain, is that of its weakest part: but there are others who know that the parallel does not hold, and who will remember that the union of many writers must show exaggeration of the inequalities which almost always exist in the production of one person. The true plan is to foster all the good that can be got, and to give development in the directions in which most resources are found: a Cyclopædia, like a plant, should grow towards the light.

The Penny Cyclopædia had its share of this kind of defect or excellence, according to the way in which the measure is taken. The circumstance is not so much noticed as might be expected, and this because many a person is in the habit of using such a dictionary chiefly with relation to one subject, his own; and more still want it for the pure dictionary purpose, which does not go much beyond the meaning of the word. But the person of full and varied reference feels the differences; and criticism makes capital of them. The Useful Knowledge Society was always odious to the organs of religious bigotry; and one of them, adverting to the fact that geography was treated with great ability, and most unusual fullness, in the Penny Cyclopædia, announced it by making it the sole merit of the work that, with sufficient addition, it would make a tolerably good gazetteer.

Some of our readers may still have hanging about them the feelings derived from this old repugnance of a class to all that did not associate direct doctrinal teaching of religion with every attempt to communicate knowledge. I will take one more instance, by way of pointing out the extent to which stupidity can go. If there be an astronomical fact of the telescopic character which, next after Saturn's ring and Jupiter's satellites, was known to all the world, it was the existence of multitudes of double stars, treble stars, etc. A respectable quarterly of the theological cast, which in mercy we refrain from naming, was ignorant of this common knowledge,—imagined that the mention of such systems was a blunder of one of the writers in the Penny Cyclopædia, and lashed the presumed ignorance of the statement in the following words, delivered in April, 1837:

"We have forgotten the name of that Sidrophel who lately discovered that the fixed stars were not single stars, but appear in the heavens like soles at Billingsgate, in pairs; while a second astronomer, under the influence of that competition in trade which the political economists tell us is so advantageous to the public, professes to show us, through his superior telescope, that the apparently single stars are really three. Before such wondrous mandarins of science, how continually must homunculi like ourselves keep in the background, lest we come between the wind and their nobility."

Certainly these little men ought to have kept in the background; but they did not: and the growing reputation of the work which they assailed has chronicled them in literary history; grubs in amber.

This important matter of inequality, which has led us so far, is one to which the Encyclopædia is as subject as the Cyclopædia; but it is not so easily recognized as a fault. We receive the first book as mainly a collection of treatises: we know their authors, and we treat them as individuals. We see, for instance, the names of two leading writers on Optics, Brewster and Herschel. It would not at all surprise us if either of these writers should be found criticising the other by name, even though the very view opposed should be contained in the same Encyclopædia with the criticism. And in like manner, we should hold it no wonder if we found some third writer not comparable to either of those we have named. It is not so in the Cyclopædia: here we do not know the author, except by inference from a list of which we never think while consulting the work. We do not dissent from this or that author: we blame the book.

The Encyclopædia Britannica is an old friend. Though it holds a proud place in our present literature, yet the time was when it stood by itself, more complete and more clear than anything which was to be found elsewhere. There must be studious men alive in plenty who remember when they were studious boys, what a literary luxury it was to pass a few days in the house of a friend who had a copy of this work. The present edition is a worthy successor of those which went before. The last three editions, terminating in 1824, 1842, and 1861, seem to show that a lunar cycle cannot pass without an amended and augmented edition. Detailed criticism is out of the question; but we may notice the effective continuance of the plan of giving general historical dissertations on the progress of knowledge. Of some of these dissertations we have had to take separate notice; and all will be referred to in our ordinary treatment of current literature.

The literary excellence of these two extensive undertakings is of the same high character. To many this will need justification: they will not easily concede to the cheap and recent work a right to stand on the same shelf with the old and tried magazine, newly replenished with the best of everything. Those who are cognizant by use of the kind of material which fills the Penny Cyclopædia will need no further evidence: to others we shall quote a very remarkable and certainly very complete testimony. The Cyclopædia of the Physical Sciences, published by Dr. Nichol in 1857 (noticed by us, April 4), is one of the most original of our special dictionaries. The following is an extract from the editor's preface:

"When I assented to Mr. Griffin's proposal that I should edit such a Cyclopædia, I had it in my mind that I might make the scissors eminently effective. Alas! on narrowly examining our best Cyclopædias, I found that the scissors had become blunted through too frequent and vigorous use. One great exception exists: viz., the Penny Cyclopædia of Charles Knight. The cheapest and the least pretending, it is really the most philosophical of our scientific dictionaries. It is not made up of a series of treatises, some good and many indifferent, but is a thorough Dictionary, well proportioned and generally written by the best men of the time. The more closely it is examined, the more deeply will our obligation be felt to the intelligence and conscientiousness of its projector and editor."

After Dr. Nichol's candid and amusing announcement of his scissorial purpose, it is but fair to state that nothing of the kind was ultimately carried into effect, even upon the work in which he found so much to praise. I quote this testimony because it is of a peculiar kind.

The success of the Penny Magazine led Mr. Charles Knight in 1832 to propose to the Useful Knowledge Society a Cyclopædia in weekly penny numbers. These two works stamp the name of the projector on the literature of our day in very legible characters. Eight volumes of 480 pages each were contemplated; and Mr. Long and Mr. Knight were to take the joint management. The plan embraced a popular account of Art and Science, with very brief biographical and geographical information. The early numbers of the work had some of the Penny Magazine character: no one can look at the pictures of the Abbot and Abbess in their robes without seeing this. By the time the second volume was completed, it was clearly seen that the plan was working out its own extension: a great development of design was submitted to, and Mr. Long became sole editor. Contributors could not be found to make articles of the requisite power in the assigned space. One of them told us that when he heard of the eight volumes, happening to want a shelf to be near at hand for containing the work as it went on, he ordered it to be made to hold twenty-five volumes easily. But the inexorable logic of facts beat him after all: for the complete work contained twenty-six volumes and two thick volumes of Supplement.

The penny issue was brought to an end by the state of the law, which required, in 1833, that the first and last page of everything sold separately should contain the name and address of the printer. The penny numbers contained this imprint on the fold of the outer leaf: and qui tam informations were laid against the agents in various towns. It became necessary to call in the stock; and the penny issue was abandoned. Monthly parts were substituted, which varied in bulk, as the demands of the plan became more urgent, and in price from one sixpence to three. The second volume of Supplement appeared in 1846, and during the fourteen years of issue no one monthly part was ever behind its time. This result is mainly due to the peculiar qualities of Mr. Long, who unites the talents of the scholar and the editor in a degree which is altogether unusual. If any one should imagine that a mixed mass of contributors is a punctual piece of machinery, let him take to editing upon that hypothesis, and he shall see what he shall see and learn what he shall learn.

The English contains about ten per cent more matter than the Penny Cyclopædia and its supplements; including the third supplementary volume of 1848, which we now mention for the first time. The literary work of the two editions cost within 500l. and 50,000l.: that of the two editions of the Britannica cost 41,000l. But then it is to be remembered that the Britannica had matter to begin upon, which had been paid for in the former editions. Roughly speaking, it is probable that the authorship of a page of the same size would have cost nearly the same in one as in the other.

The longest articles in the Penny Cyclopædia were "Rome" in 98 columns and "Yorkshire" in 86 columns. The only article which can be called a treatise is the Astronomer Royal's "Gravitation," founded on the method of Newton in the eleventh section, but carried to a much greater extent. In the English Cyclopædia, the longest article of geography is "Asia," in 45 columns. In natural history the antelopes demand 36 columns. In biography, "Wellington" uses up 42 columns, and his great military opponent 41 columns. In the division of Arts and Sciences, which includes much of a social and commercial character, the length of articles often depends upon the state of the times with regard to the subject. Our readers would not hit the longest article of this department in twenty guesses: it is "Deaf and Dumb" in 60 columns. As other specimens, we may cite Astronomy, 19; Banking, 36; Blind, 24; British Museum, 35; Cotton, 27; Drama, 26; Gravitation, 50; Libraries, 50; Painting, 34; Railways, 18; Sculpture, 36; Steam, etc., 37; Table, 40; Telegraph, 30; Welsh language and literature, 39; Wool, 21. These are the long articles of special subdivisions: the words under which the Encyclopædia gives treatises are not so prominent. As in Algebra, 10; Chemistry, 12; Geometry, 8; Logic, 14; Mathematics, 5; Music, 9. But the difference between the collection of treatises and the dictionary may be illustrated thus: though "Mathematics" have only five columns, "Mathematics, recent terminology of," has eight: and this article we believe to be by Mr. Cayley, who certainly ought to know his subject, being himself a large manufacturer of the new terms which he explains. Again, though "Music" in genere, as the schoolmen said, has only nine columns, "Temperament and Tuning," has eight, and "Chord" alone has two. And so on.

In a dictionary of this kind it is difficult to make a total clearance of personality: by which we mean that exhibition of peculiar opinion which is offensive to taste when it is shifted from the individual on the corporate book. The treatise of the known author may, as we have said, carry that author's controversies on its own shoulders: and even his crotchets, if we may use such a word. But the dictionary should not put itself into antagonism with general feeling, nor even with the feelings of classes. We refer particularly to the ordinary and editorial teaching of the article. If, indeed, the writer, being at issue with mankind, should confess the difference, and give abstract of his full grounds, the case is altered: the editor then, as it were, admits a correspondent to a statement of his own individual views. The dictionary portion of the Britannica is quite clear of any lapses on this point, so far as we know: the treatises and dissertations rest upon their authors. The Penny Cyclopædia was all but clear: and great need was there that it should have been so. The Useful Knowledge Society, starting on the principle of perfect neutrality in politics and religion, was obliged to keep strict watch against the entrance of all attempt even to look over the hedge. There were two—we believe only two—instances of what we have called personality. The first was in the article "Bunyan." It is worth while to extract all that is said—in an article of thirty lines—about a writer who is all but universally held to be the greatest master of allegory that ever wrote:

"His works were collected in two volumes, folio, 1736-7: among them 'The Pilgrim's Progress' has attained the greatest notoriety. If a judgment is to be formed of the merits of a book by the number of times it has been reprinted, and the many languages into which it has been translated, no production in English literature is superior to this coarse allegory. On a composition which has been extolled by Dr. Johnson, and which in our own times has received a very high critical opinion in its favor [probably Southey], it is hazardous to venture a disapproval, and we, perhaps, speak the opinion of a small minority when we confess that to us it appears to be mean, jejune and wearisome."

—If the unfortunate critic who thus individualized himself had been a sedulous reader of Bunyan, his power over English would not have been so jejune as to have needed that fearful word. This little bit of criticism excited much amusement at the time of its publication: but it was so thoroughly exceptional and individual that it was seldom or never charged on the book. The second instance occurred in the article "Socinians." It had been arranged that the head-words of Christian sects should be intrusted to members of the sects themselves, on the understanding that the articles should simply set forth the accounts which the sects themselves give of their own doctrines. Thus the article on the Roman Church was written by Dr. Wiseman. But the Unitarians were not allowed to come within the rule: as in other quarters, they were treated as the gypsies of Christianity. Under the head "Socinians"—a name repudiated by themselves—an opponent was allowed not merely to state their alleged doctrines in his own way, but to apply strong terms, such as "audacious unfairness," to some of their doings. The protests which were made against this invasion of the understanding produced, in due time, the article "Unitarians," written by one of that persuasion. We need not say that these errors have been amended in the English Cyclopædia: and our chief purpose in mentioning them is to remark, that this is all we can find on the points in question against twenty-eight large volumes produced by an editor whose task was monthly, and whose issue was never delayed a single hour. How much was arrested before publication none but himself can say. We have not alluded to one or two remonstrances on questions of absolute fact, which are beside the present purpose.

Both kinds of encyclopædic works have been fashioned upon predecessors, from the very earliest which had a predecessor to be founded upon; and the undertakings before us will be themselves the ancestors of a line of successors. Those who write in such collections should be careful what they say, for no one can tell how long a mis-statement may live. On this point we will give the history of a pair of epithets. When the historian De Thou died, and left the splendid library which was catalogued by Bouillaud and the brothers Dupuis (Bullialdus and Puteanus), there was a manuscript of De Thou's friend Vieta, the Harmonicon Cœleste, of which it is on record, under Bouillaud's hand, that he himself lent it to Cosmo de' Medici, to which must be added that M. Libri found it in the Magliabecchi Library at Florence in our own day. Bouillaud, it seems, entirely forgot what he had done. Something, probably, that Peter Dupuis said to Bouillaud, while they were at work on the catalogue, remained on his memory, and was published by him in 1645, long after; to the effect that Dupuis lent the manuscript to Mersenne, from whom it was procured by some intending plagiarist, who would not give it back. This was repeated by Sherburne, in 1675, who speaks of the work, which "being communicated to Mersennus was, by some perfidious acquaintance of that honest-minded person, surreptitiously taken from him, and irrecoverably lost or suppressed, to the unspeakable detriment of the lettered world." Now let the reader look through the dictionaries of the last century and the present, scientific or general, at the article, "Vieta," and he will be amused with the constant recurrence of "honest-minded" Mersenne, and his "surreptitious" acquaintance. We cannot have seen less than thirty copies of these epithets.

REVIEW OF MACCLESFIELD LETTERS.

October 18, 1862. Correspondence of Scientific Men of the Seventeenth Century, in the Collection of the Earl of Macclesfield. 2 vols. (Oxford, University Press.)

Though the title-page of this collection bears the date 1841, it is only just completed by the publication of its Table of Contents and Index. Without these, a work of the kind is useless for consultation, and cannot make its way. The reason of the delay will appear: its effect is well known to us. We have found inquirers into the history of science singularly ignorant of things which this collection might have taught them.

In the same year, 1841, the Historical Society of Science, which had but a brief existence, published a collection of letters, eighty-three in number, edited by Mr. Halliwell, of English men of science, which dovetails with the one before us, and is for the most part of a prior date. The two should be bound up together. The smaller collection runs from 1562 to 1682; the larger, from 1606 to past 1700. We shall speak of the two as the Museum collection and the Macclesfield collection. And near them should be placed, in every scientific library, the valuable collection published, by Mr. Edleston, for Trinity College, in 1850.

The history of these letters runs back to famous John Collins, the attorney-general of the mathematics, as he has been called, who wrote to everybody, heard from everybody, and sent copies of everybody's letter to everybody else. He was in England what Mersenne was in France: as early as 1671, E. Bernard addresses him as "the very Mersennus and intelligence of this age." John Collins was never more than accountant to the Excise Office, to which he was promoted from teaching writing and ciphering, at the Restoration: he died in 1682. We have had a man of the same office in our own day, the late Prof. Schumacher, who made the little Danish Observatory of Altona the junction of all the lines by which astronomical information was conveyed from one country to another. When the collision took place between Denmark and the Duchies, the English Government, moved by the Astronomical Society, instructed its diplomatic agents to represent strongly to the Danish Government, when occasion should arise, the great importance of the Observatory of Altona to the astronomical communications of the whole world. But Schumacher had his own celebrated journal, the Astronomische Nachrichten, by which to work out part of his plan; private correspondence was his supplementary assistant. Collins had only correspondence to rely on. Nothing is better known than that it was Collins's collection which furnished the materials put forward by the Committee of the Royal Society in 1712, as a defence of Newton against the partisans of Leibnitz. The noted Commercium Epistolicum is but the abbreviation of a title which runs on with "D. Johannis Collins et aliorum ..."

The whole of this collection passed into the hands of William Jones, the father of the Indian Judge of the same name, who died in 1749. Jones was originally a teacher, but was presented with a valuable sinecure by the interest of George, second Earl of Macclesfield, the mover of the bill for the change of style in Britain, who died President of the Royal Society. This change of style may perhaps be traced to the union of energies which were brought into concert by the accident of a common teacher: Lord Macclesfield and Lord Chesterfield, the mover and the seconder, and Daval, who drew the bill, were pupils of De Moivre. Jones, who was a respectable mathematician though not an inventor, collected the largest mathematical library of his day, and became possessor of the papers of Collins, which contained those of Oughtred and others. Some of these papers passed into the custody of the Royal Society: but the bulk was either bequeathed to, or purchased by, Lord Macclesfield; and thus they found their way to Shirburn Castle, where they still remain.

A little before 1836, this collection attracted the attention of a searching inquirer into points of mathematical history, the late Professor Rigaud, who died in 1839. He examined the whole collection of letters, obtained Lord Macclesfield's consent to their publication, and induced the Oxford Press to bear the expense. It must be particularly remembered that there still remains at Shirburn Castle a valuable mass of non-epistolary manuscripts. So far as we can see, the best chance of a further examination and publication lies in public encouragement of the collection now before us: the Oxford Press might be induced to extend its operations if it were found that the results were really of interest to the literary and scientific world. Rigaud died before the work was completed, and the publication was actually made by one of his sons, S. Jordan Rigaud, who died Bishop of Antigua. But this publication was little noticed, for the reasons given. The completion now published consists of a sufficient table of contents, of the briefest kind, by Professor De Morgan, and an excellent index by the Rev. John Rigaud. The work is now fairly started on its career.

If we were charged to write a volume with the title "Small things in their connection with great," we could not do better than choose the small part of this collection of letters as our basis. The names, as well as the contents, are both great and small: the great names, those which are known to every mathematician who has any infusion of the history of his pursuit, are Briggs, Oughtred, Charles Cavendish, Gascoigne, Seth Ward, Wallis, Hu[y]gens, Collins, William Petty, Hooke, Boyle, Pell, Oldenburg, Brancker, Slusius, Bertit, Bernard, Borelli, Mouton, Pardies, Fermat, Towneley, Auzout, D. Gregory, Halley, Machin, Montmort, Cotes, Jones, Saunderson, Reyneau, Brook Taylor, Maupertuis, Bouguer, La Condamine, Folkes, Macclesfield, Baker, Barrow, Flamsteed, Lord Brounker, J. Gregory, Newton and Keill. To these the Museum collection adds the names of Thomas Digges, Dee, Tycho Brahe, Harriot, Lydyat, Briggs, Warner, Tarporley, Pell, Lilly, Oldenburg, Collins, Morland.

The first who appears on the scene is the celebrated Oughtred, who is related to have died of joy at the Restoration: but it should be added, by way of excuse, that he was eighty-six years old. He is an animal of extinct race, an Eton mathematician. Few Eton men, even of the minority which knows what a sliding rule is, are aware that the inventor was of their own school and college: but they may be excused, for Dr. Hutton, so far as his Dictionary bears witness, seems not to have known it any more than they. A glance at one of his letters reminds us of a letter from the Astronomer Royal on the discovery of Neptune, which we printed March 20, 1847. Mr. Airy there contends, and proves it both by Leverrier and by Adams, that the limited publication of a private letter is more efficient than the more general publication of a printed memoir. The same may be true of a dead letter, as opposed to a dead book. Our eye was caught by a letter of Oughtred (1629), containing systematic use of contractions for the words sine, cosine, etc., prefixed to the symbol of the angle. This is so very important a step, simple as it is, that Euler is justly held to have greatly advanced trigonometry by its introduction. Nobody that we know of has noticed that Oughtred was master of the improvement, and willing to have taught it, if people would have learnt. After looking at his dead letter, we naturally turned to his dead book on trigonometry, and there we found the abbreviations s, sco, t, tco, se, seco, regularly established as part of the system of the work. But not one of those who have investigated the contending claims of Euler and Thomas Simpson has chanced to know of Oughtred's "Trigonometrie": and the present revival is due to his letter, not to his book.

A casual reader, turning over the pages, would imagine that almost all the letters had been printed, either in the General Dictionary, or in Birch, etc.: so often does the supplementary remark begin with "this letter has been printed in ——." For ourselves we thought, until we counted, that a large majority of the letters had been given, either in whole or in part. But the positive strikes the mind more forcibly than the negative: we find that all of which any portion has been in type makes up very little more than a quarter; the cases in which the whole letter is given being a minority of this quarter. The person who has been best ransacked is Flamsteed: of 36 letters from him, 34 had been previously given in whole or in part. Of 59 letters to and from Newton, only 17 have been culled.

The letters have been modernized in spelling, and, to some extent, in algebraical notation; it also seems that conjectural methods of introducing interpolations into the text have been necessary. For all this we are sorry: the scientific value of the collection is little altered, but its literary value is somewhat lowered. But it could not be helped: the printers could not work from the originals, and Professor Rigaud had to copy everything himself. A fac-simile must have been the work of more time than he had to give: had he attempted it, his death would have cut short the whole undertaking, instead of allowing him to prepare everything but a preface, and to superintend the printing of one of the volumes. We may also add, that we believe we have notices of all the letters in the Macclesfield collection. We judge this because several which are too trivial to print are numbered and described; and those would certainly not have been noticed if any omissions had been made. And we know that every letter was removed from Shirburn Castle to Oxford.

Two persons emerge from oblivion in this series of letters. The first is Michael Dary, an obscure mathematician, who was in correspondence with Newton and other stars. He was a gauger at Bristol, by the interest of Collins; afterwards a candidate for the mathematical school at Christ's Hospital, with a certificate from Newton: he was then a gunner in the Tower, and is lastly described by Wallis as "Mr. Dary, the tobacco-cutter, a knowing man in algebra." In 1674, Dary writes to Newton at Cambridge, as follows:—"Although I sent you three papers yesterday, I cannot refrain from sending you this. I have had fresh thoughts this morning." Two months afterwards poor Newton writes to Collins, "Mr. Dary is very solicitous about mathematics": but in spite of the persecution, he subscribes himself to Dary "your loving friend." Dary's problem is that of finding the rate of interest of an annuity of which the value and term are given. Dary's theorem, which he seems to have invented specially for the solution of his problem, though it is of wide range, can be exhibited to mathematical readers even in our columns. In modern language, it is that the limit of φnx, when n increases without limit, is a solution of φx = x. We have mentioned the I. Newton to whom Dary looked up; we add a word about the one on whom he looked down. Dr. John Newton, a sedulous publisher of logarithms, tables of interest, etc., who began his career before Isaac Newton, sometimes puzzles those who do not know him, when described as I. Newton. The scientific world was of opinion that all that was valuable in one of his works was taken from Dary's private communications.

The second character above alluded to is one who carried mathematical researches a far greater length than Newton himself: the assistance which he rendered in this respect, even to Newton, has never been acknowledged in modern times: though the work before us shows that his contemporaries were fully aware of it, and never thought of concealing it. In his theory of gravitation, in which, so far as he went, we have every reason to believe he was prior to Newton, he did not extend his calculations to the distance of the moon; his views in this matter were purely terrestrial, and led him to charge according to weight. He was John Stiles, the London and Cambridge carrier: his name is a household word in the Macclesfield Letters, and is even enshrined in the depths of Birch's quartos. Dary informs Newton—let us do his memory this justice—that he had paid John Stiles for the carriage. At the time when the railroad to Cambridge was opened, a correspondent recommended the directors, in our columns, to call an engine by the name of John Stiles, and never to let that name go off the road. We do not know whether the advice was followed: if not, we repeat it.

Little points of life and manners come out occasionally. Baker, the author of a work on algebra much esteemed at the time, wrote to Collins that their circumstances are alike, "having a just and equal number of chargeable olive-branches, and being in the same predicament and blessed condemnation with you, not more preaching than unpaid, and preaching the art of contentment to others, am forced to practise it." But the last sentence of his letter runs as follows: "I have sent by the bearer ... twenty shillings, as a token to you; desiring you to accept of it, as a small taste from Yours, Thos. Baker." In our day, men of a station to pay parish taxes do not offer their friends hard money to buy liquor. But Flamsteed writes to Collins as follows: "Last week he sent us down the counterpart, which my father has scaled, and I return up to you by the carrier, with 5l. to be paid to Mr. Leneve for the writing, I have added 2s. 6d. over, which will pay the expenses and serve to drink, with him." This would seem as odd to us as it would have seemed thirty years ago that half-a-crown should pay carriage for a deed from Derby to London, and leave margin for a bottle of wine: in our day, the Post-office and the French treaty would just manage it between them. But Flamsteed does not limit his friend to one bottle; he adds, "If you expend more than the half-crown, I will make it good after Whitsuntide." Collins does not remember exactly where he had met James Gregory, and mentions two equally likely places thus: "Sir, it was once my good hap to meet with you in an alehouse or in Sion College." There is a little proof how universally the dinner-hour was twelve o'clock. Astronomers well know the method of finding time by equal altitudes of the sun before and after noon: Huyghens calls it "le moyen de deux égales hauteurs du soleil devant et après dîner."

There is one mention of "Mr. Cocker, our famous English graver and writer, now a schoolmaster at Northampton." This is the true Cocker: his genuine works are specimens of writing, such as engraved copy-books, including some on arithmetic, with copper-plate questions and space for the working; also a book of forms for law-stationers, with specimens of legal handwriting. It is recorded somewhere that Cocker and another, whose name we forget, competed with the Italians in the beauty of their flourishes. This was his real fame: and in these matters he was great. The eighth edition of his book of law forms (1675), published shortly after Cocker's death, has a preface signed "J. H." This was John Hawkins, who became possessed of Cocker's papers—at least he said so—and subsequently forged the famous Arithmetic, a second work on Decimal Arithmetic, and an English dictionary, all attributed to Cocker. The proofs of this are set out in De Morgan's Arithmetical Books. Among many other corroborative circumstances, the clumsy forger, after declaring that Cocker to his dying day resisted strong solicitation to publish his Arithmetic, makes him write in the preface Ille ego qui quondam of this kind: "I have been instrumental to the benefit of many, by virtue of those useful arts, writing and engraving; and do now, with the same wonted alacrity, cast this my arithmetical mite into the public treasury." The book itself is not comparable in merit to at least half-a-dozen others. How then comes Cocker to be the impersonation of Arithmetic? Unless some one can show proof, which we have never found, that he was so before 1756, the matter is to be accounted for thus.

Arthur Murphy, the dramatist, was by taste a man of letters, and ended by being the translator of Tacitus; though many do not know that the two are one. His friends had tried to make him a man of business; and no doubt he had been well plied with commercial arithmetic. His first dramatic performance, the farce of "The Apprentice," produced in 1756, is about an idle young man who must needs turn actor. Two of the best known books of the day in arithmetic were those of Cocker and Wingate. Murphy chooses Wingate to be the name of an old merchant who delights in vulgar fractions, and Cocker to be his arithmetical catchword—"You read Shakespeare! get Cocker's Arithmetic! you may buy it for a shilling on any stall; best book that ever was wrote!" and so on. The farce became very popular, and, as we believe, was the means of elevating Cocker to his present pedestal, where Wingate would have been, if his name had had the droller sound of the two to English ears.

A notoriety of an older day turns up, Major-General Lambert. The common story is that he was banished to Guernsey, where he passed thirty years in confinement, rearing and painting flowers. But Baker, in 1678, represents him as a prisoner at Plymouth, sending equations for solution as a challenge: probably his place of confinement was varied, and his occupation also.

[General Lambert was removed to Plymouth, probably about 1668. His daughter captured the son of the Governor of Guernsey, who therefore probably was reckoned an unsafe custodier thenceforward; though he assured the king that he had turned the young couple out of doors, and had never given them a penny. Great importance was attached to Lambert's safe detention: probably the remaining republicans looked upon him as to be their next Cromwell, if such a thing were to be. There were standing orders to shoot him at once on the first appearance of any enemy before the island. See Notes and Queries, 3d S. iv. 89.]

Collins informs James Gregory that "some of the Royal Academy wrote over to Mr. Oldenburg, who was desired to impart the same to the Council of the Royal Society, that the French King was willing to allow pensions to one or two learned Englishmen, but they never made any answer to such a proposal." This was written in 1671, and the thing probably happened several years before. Mr. De Morgan communicated the account of the proposal to Lord Macaulay, who replied that he did not think that any Englishman received a literary pension from Louis; but that there is a curious letter, about 1664, from the French Ambassador, in which he says that he has, by his master's orders, been making inquiries as to the state of learning in England, and that he is sorry to find that the best writer is the infamous Miltonus. On two such independent testimonies it may be held proved that the French King had attempted to buy a little adherence from English literature and science; and the silent contempt of the Royal Society is an honorable fact in their history.

Another little bit of politics is as follows. Oughtred is informed that "Mr. Foster, our Lecturer on Astronomy at Gresham College, is put out because he will not kneel down at the communion-table. A Scotsman [Mungo Murray], one that is verbi bis minister, is now lecturer in Mr. Foster's place." Ward in his work on the Gresham Professors, suppresses the reason, and the suppression lowers the character of his book. Foster was expelled in 1636, and re-elected on a vacancy in 1641, when Puritanism had gained strength.

The correspondence of Newton would require deeper sifting than could be given in such an article as the present. The first of the letters (1669) is curious, as presenting the appearance of forms belonging to the great calculus which, in this paragraph, we ought to call that of fluxions. We find, of the date February 18, 1669-70, what we believe is the earliest manifestation of that morbid part of Newton's temperament which has been so variously represented. He had solved a problem—being that which we have called Dary's—on which he writes as follows: "The solution of the annuity problem, if it will be of any use, you have my leave to insert into the Philosophical Transactions, so it be without my name to it. For I see not what there is desirable in public esteem, were I able to acquire and maintain it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline."

Three letters touch upon "the experiment of glass rubbed to cause various motions in bits of paper underneath": they are supplements to the account given by Newton to the Royal Society, and printed by Birch. It was Newton, so far as appears, who added glass to the substances known to be electric. Soon afterwards we come to a little bit of the history of the appointment to the Mint. It has appeared from the researches of late years that Newton was long an aspirant for public employment: the only coolness which is known to have taken place between him and Charles Montague [Halifax] arose out of his imagining that his friend was not in earnest about getting him into the public service. March 14, 1696, Newton writes thus to Halley: "And if the rumour of preferment for me in the Mint should hereafter, upon the death of Mr. Hoar [the comptroller], or any other occasion, be revived, I pray that you would endeavour to obviate it by acquainting your friends that I neither put in for any place in the Mint, nor would meddle with Mr. Hoar's place, were it offered to me." This means that Mr. Hoar's place had been suggested, which Newton seems to have declined. Five days afterwards, Montague writes to Newton that he is to have the Wardenship. It is fair to Newton to say that in all probability this was not—or only in a smaller degree—a question of personal dignity, or of salary. It must by this time have been clear to him that the minister, though long bound to make him an object of patronage, was actually seeking him for the Mint, because he wanted both Newton's name and his talents for business—which he knew to be great—in the weighty and dangerous operation of restoring the coinage. It may have been, and probably was, the case that Newton had a tolerably accurate notion of what he would have to do, and of what degree of power would be necessary to enable him to do it in his own way.

We have said that the non-epistolary manuscripts are still unexamined. There is a chance that one of them may answer a question of two centuries' standing, which is worth answering, because it has been so often asked. About 1640, Warner, afterwards assisted by Pell, commenced a table of antilogarithms, of the kind which Dodson afterwards constructed anew and published. In the Museum collection there is inquiry after inquiry from Charles Cavendish, first, as to when the Analogics, as he called them, would be finished; next, when they would be printed. Pell answers, in 1644, that Warner left his papers to a kinsman, who had become bankrupt, and proceeds thus:

"I am not a little afraid that all Mr. Warner's papers, and no small share of my labours therein, are seazed upon, and most unmathematically divided between the sequestrators and creditors, who (not being able to ballance the account where there appeare so many numbers, and much troubled at the sight of so many crosses and circles in the superstitious Algebra and that black art of Geometry) will, no doubt, determine once in their lives to become figure-casters, and so vote them all to be throwen into the fire, if some good body doe not reprieve them for pye-bottoms, for which purposes you know analogicall numbers are incomparably apt, if they be accurately calculated."

Pell afterwards told Wallis that the papers had fallen into the hands of Dr. Busby, and Collins writes that they were left in the hands of Dr. Thorndike, a prebendary of Westminster; whence Rigaud seems to say that Thorndike had left them to Dr. Busby. Birch says that he procured for the Royal Society four boxes from Busby's trustees, containing papers of Warner and Pell: but there is no other tradition of such things in the Society. But in the Birch manuscripts at the British Museum, there turns up, as printed in what we call the Museum collection, a list of Warner's papers, with Collins's receipt to Dr. Thorndike at the bottom, and engagement to restore them on demand. The date is December 14, 1667; Wallis's statement being in 1693. It is possible that Busby may be a mistake altogether: he was very unlikely to have had charge of any mathematical papers: there may have been a confusion between the Prebendary of Westminster and the Head Master of Westminster School. If so, in all probability Thorndike handed the cumbrous lot over to the notorious collector of mathematical papers, blessing himself that he got rid of them in a manner which would insure their return if he were called upon by the owners to restore them. It is much against this hypothesis that Dodson, who certainly recalculated, can say nothing more about Warner than a repetition of Wallis's story: though, had Collins kept the papers, they would probably have been in Jones's possession at the very time when Dodson, who was a friend of Jones and a user of his library, was engaged on his own computations. But even books, and still more manuscripts, are often singularly overlooked; and it remains not very improbable that Warner's table is now at Shirburn Castle, among the unexamined manuscripts.

CYCLOMETRY AND STEEL PENS.

Redit labor actus in orbem. Among the matters which have come to me since the Budget opened, there is a pamphlet of quadrature of two pages and a half from Professor Recalcati, already mentioned. It ends with "Quelque objection qu'on fasse touchant les raisonnements ci-dessus on tombera toujours dans l'absurde." A civil engineer—so he says—has made the quadrature "no longer a problem, but an axiom." As follows: "Take the quadrant of a circle whose circumference is given, square the quadrant which gives the true square of the circle. Because 30 ÷ 4 = 7.5 × 7.5 = 56.25 = the positive square of a circle whose circumference is 30." Brevity, the soul of wit, is the "wings of mighty-winds" to quadrature, and sends it "flying all abroad." A surbodhicary—something like M.A. or LL.D., I understand—at Calcutta, published in 1863 the division of an angle into any odd number of parts, demonstration and all in—when the diagram is omitted—one page, good-sized, well-leaded type, small duodecimo. But in the Preface he acknowledges "sheer inability" to execute his task. Mr. William Dean, of Todmorden, in 1863, announced 3-9/64 as proved both practically and geometrically: he has been already mentioned anonymously. Next I have the tract of Don Juan Larriva, published at Leiria in 1856, and dedicated to Queen Victoria. Mr. W. Peters, already mentioned, who has for some months been circulating diagrams on a card, publishes (August, 1865) The Circle Squared. He agrees with the Archpriest of St. Vitus. He hints that a larger publication will depend partly on the support he receives, and partly on the castigation, for which last, of course, he looks to me. Cyclometers have their several styles of wit; so have anticyclometers too, for that matter. Mr. Peters will not allow me any extra-journal being: I am essentially a quotation from the Athenæum; "A. De Morgan" et præterea nihil. If he had to pay for keeping me set up, he would find out his mistake, and would be glad to compound handsomely for a stereotype. Next comes a magnificent sheet of pasteboard, printed on both sides. Having glanced at it and detected quadrature, I began methodically at the beginning—"By Royal Command," with the lion and unicorn, and all that comes between. Mercy on us! thought I to myself: has Her Majesty referred the question to the Judicial Committee of the Privy Council, where all the great difficulties go now-a-days, and is this proclamation the result? On reading further I was relieved by finding that the first side is entirely an advertisement of Joseph Gillott's steel pens, with engraving of his premises, and notice of novel application of his unrivalled machinery. The second side begins with "the circle rectified" by W. E. Walker, who finds π = 3.141594789624155.... This is an off-shoot from an accurate geometrical rectification, on which is to be presumed Mr. Gillott's new machinery is founded. I have no doubt that Mr. Walker's error, which is only in the sixth place of decimals, will not hurt the pens, unless it be by the slightest possible increase of the tendency to open at the points. This arises from Mr. Walker having rectified above proof by .000002136034362....

Lastly, I, even I myself, who have long felt that I was a quadrature below par, have solved the problem by means which, in the present state of the law of libel, I dare not divulge. But the result is permitted; and it goes far to explain all the discordances. The ratio of the circumference to the diameter is not always the same! Not that it varies with the radius; the geometers are right enough on that point: but it varies with the time, in a manner depending upon the difference of the true longitudes of the Sun and Moon. A friend of mine—at least until he misbehaved—insisted on the mean right ascensions: but I served him as Abraham served his guest in Franklin's parable. The true formula is, A and a being the Sun's and Moon's longitudes,

π = 3-13/80 + 3/80 cos(A - a).

Mr. James Smith obtained his quadrature at full moon; the Archpriest of St. Vitus and some others at new moon. Until I can venture to publish the demonstration, I recommend the reader to do as I do, which is to adopt 3.14159..., and to think of the matter only at the two points of the lunar month at which it is correct. The Nautical Almanac will no doubt give these points in a short time: I am in correspondence with the Admiralty, with nothing to get over except what I must call a perverse notion on the part of the Superintendent of the Almanac, who suspects one correction depending on the Moon's latitude; and the Astronomer Royal leans towards another depending on the date of the Queen's accession. I have no patience with these men: what can the Moon's node of the Queen's reign possibly have to do with the ratio in question? But this is the way with all the regular men of science; Newton is to them etc. etc. etc. etc.

The following method of finding the circumference of a circle (taken from a paper by Mr. S. Drach in the Phil. Mag., Jan. 1863, Suppl.) is as accurate as the use of 3.14159265. From three diameters deduct 8-thousandths and 7-millionths of a diameter; to the result add five per cent. We have then not quite enough; but the shortcoming is at the rate of about an inch and a sixtieth of an inch in 14,000 miles.

JACOB BEHMEN.

Though I have met with nothing but a little tract from the school of Jacob Behmen (or Böhme; I keep to the old English version of his name), yet there has been more, and of a more recent date. I am told of an "Introduction to Theosophy [Theo private, I suppose, as in theological]; or, the Science of the Mystery of Christ," published in 1854, mostly from the writings of William Law: and also of a volume of 688 pages, of the same year, printed for private circulation, containing notes for a biography of William Law. The editor of the first work wishes to grow "a generation of perfect Christians" by founding a Theosophic College, for which he requests the public to raise a hundred thousand pounds. There is a good account of Jacob Behmen in the Penny Cyclopædia. The author mentions inaccurate accounts, one of which he quotes, as follows: "He derived all his mystical and rapturous doctrine from Wood's Athenæ Oxonienses, Vol. I, p. 610, and Hist. et Antiq. Acad. Oxon., Vol. II, p. 308." On which the author remarks that Wood was born after Behmen's death. There must have been a few words which slipped out: what is meant is that Behmen "derived his doctrine from Robert Fludd, for whom see Wood's etc. etc." Even this is absurd enough: for Behmen began to publish in 1610, and Fludd in 1616. Fludd was a Rosicrucian, and a mystic of a different type from Behmen. I have some of his works, and could produce out of them paradoxes enough, according to our ways of thinking, to fit out a host. But the Rosicrucian system was a recognized school of its day, and Fludd, a man of great learning, had abettors enough in all which he advanced, and predecessors in most of it.

[A Correspondent has recently sent a short summary of the claims of Jacob Behmen to rank higher than I have placed him. I shall gladly insert this summary in the book I contemplate, as a statement of what is said of Behmen far less liable to suspicion of exaggeration than anything I could write. I shall add a few extracts from Behmen himself, in support of his right to be in my list.]

"Jacob Behmen.—That Prof. De Morgan classes Jacob Behmen among paradoxers can only be attributed to the fact of his being avowedly unacquainted with the writings of that author. Perhaps you may think a few words from one who knows them well of sufficient interest to the learned Professor, and your readers in general, to be worthy of space in your columns. The metaphysical system of Behmen—the most perfect and only true one—still awaits a qualified commentator. Behmen's countryman, Dionysius Andreas Freher, who spent the greater part of his life in this country, and whose exposition of Behmen exists only in MS., filling many volumes, written in English, with the exception of two, written in German, with numerous beautiful, highly ingenious, and elaborate illustrations,—copies of some of which are in the British Museum, but all the originals of which are in the possession of the gentleman who is the editor of the two works alluded to by Professor De Morgan,—this Freher was the first to philosophically expound Behmen's system, which was afterwards, with the help of these MSS., as it were, popularized by William Law; but both Freher and Law confined themselves chiefly to its theological aspect. In Behmen, however, is to be found, not only the true ground of all theology, but also that of all physical science. He demonstrated with a fullness, accuracy, completeness and certainty that leave nothing to be desired, the innermost ground of Deity and Nature; and, confining myself to the latter, I can from my own knowledge assert, that in Behmen's writings is to be found the true and clear demonstration of every physical fact that has been discovered since his day. Thus, the science of electricity, which was not yet in existence when he wrote, is there anticipated; and not only does Behmen describe all the now known phenomena of that force, but he even gives us the origin, generation and birth of electricity itself. Again, positive evidence can be adduced that Newton derived all his knowledge of gravitation and its laws from Behmen, with whom gravitation or attraction is, and very properly so, as he shows us, the first of the seven properties of Nature. The theory defended by Mr. Grove, at the Nottingham meeting of last year, that all the apparently distinct causes of moral and physical phenomena are but so many manifestations of one central force, and that Continuity is the law of nature, is clearly laid down, and its truth demonstrated, by Behmen, as well as the distinction between spirit and matter, and that the moral and material world is pervaded by a sublime unity. And though all this was not admitted in Behmen's days, because science was not then sufficiently advanced to understand the deep sense of our author, many of his passages, then unintelligible, or apparently absurd, read by the light of the present age, are found to contain the positive enunciation of principles at whose discovery and establishment science has only just arrived by wearisome and painful investigations. Every new scientific discovery goes to prove his profound and intuitive insight into the most secret workings of nature; and if scientific men, instead of sharing the prejudice arising from ignorance of Behmen's system, would place themselves on the vantage ground it affords, they would at once find themselves on an eminence whence they could behold all the arcana of nature. Behmen's system, in fact, shows us the inside of things, while modern physical science is content with looking at the outside. Behmen traces back every outward manifestation or development to its one central root,—to that one central energy which, as yet, is only suspected; every link in the chain of his demonstration is perfect, and there is not one link wanting. He carries us from the out-births of the circumference, along the radius to the center, or point, and beyond that even to the zero, demonstrating the constitution of the zero, or nothing, with mathematical precision. C. W. H."

And so Behmen is no subject for the Budget! I waited until I should chance to light on one of his volumes, knowing that any volume would do, and almost any page. My first hap was on the second volume of the edition of 1664 (4to, published by M. Richardson) and opening near the beginning, a turn or two brought me to page 13, where I saw about sulphur and mercurius as follows:

"Thus SUL is the soul, in an herb it is the oil, and in man also, according to the spirit of this world in the third principle, which is continually generated out of the anguish of the will in the mind, and the Brimstone-worm is the Spirit, which hath the fire and burneth: PHUR is the sour wheel in itself which causeth that.

"Mercurius comprehendeth all the four forms, even as the life springeth up, and yet hath not its dark beginning in the Center as the PHUR hath, but after the flash of fire, when the sour dark form is terrified, where the hardness is turned into pliant sharpness, and where the second will (viz. the will of nature, which is called the Anguish) ariseth, there Mercurius hath its original. For MER is the shivering wheel, very horrible, sharp, venomous, and hostile; which assimulateth it thus in the sourness in the flash of fire, where the sour wrathful life ariseth. The syllable CU is the pressing out, of the Anxious will of the mind, from Nature: which is climbing up, and willeth to be out aloft. RI is the comprehension of the flash of fire, which in MER giveth a clear sound and tune. For the flash maketh the tune, and it is the Salt-Spirit which soundeth, and its form (or quality) is gritty like sand, and herein arise noises, sounds and voices, and thus CU comprehendeth the flash, and so the pressure is as a wind which thrusteth, and giveth a spirit to the flash, so that it liveth and burneth. Thus the syllable US is called the burning fire, which with the spirit continually driveth itself forth: and the syllable CU presseth continually upon the flash."

Shades of Tauler and Paracelsus, how strangely you do mix! Well may Hallam call Germany the native soil of Mysticism. Had Behmen been the least of a scholar, he would not have divided sulph-ur and merc-ur-i-us as he has done: and the inflexion us, that boy of all work, would have been rejected. I think it will be held that a writer from whom hundreds of pages like the above could be brought together, is fit for the Budget. If Sampson Arnold Mackay had tied his etymologies to a mystical Christology, instead of a mystical infidelity, he might have had a school of followers. The nonsense about Newton borrowing gravitation from Behmen passes only with those who know neither what Newton did, nor what was done before him.

The above reminds me of a class of paradoxers whom I wonder that I forgot; they are without exception the greatest bores of all, because they can put the small end of their paradox into any literary conversation whatever. I mean the people who have heard the local pronunciation of celebrated names, and attempt not only to imitate it, but to impose on others their broken German or Arabic, or what not. They also learn the vernacular names of those who are generally spoken of in their Latin forms; at least, they learn a few cases, and hawk them as evidences of erudition. They are miserably mistaken: scholarship, as a rule, always accepts the vernacular form of a name which has vernacular celebrity. Hallam writes Behmen: his index-maker, rather superfluously, gives "Behmen or Boehm." And he retains Melanchthon, the name given by Reuchlin to his little kinsman Schwartzerd, because the world has adopted it: but he will none of Capnio, the name which Reuchlin fitted on to himself, because the world has not adopted it. He calls the old forms pedantry: but he sees that the rejection of well-established results of pedantry would be greater pedantry still. The paradoxers assume the question that it is more correct to sound a man by lame imitation of his own countrymen than as usual in the country in which the sound is to be made. Against them are, first, the world at large; next, an overpowering majority of those who know something about surnames and their history. Some thirty years ago—a fact—there appeared at the police-office a complainant who found his own law. In the course of his argument, he asked, "What does Kitty say?"—"Who's Kitty?" said the magistrate, "your wife, or your nurse?"—"Sir! I mean Kitty, the celebrated lawyer."—"Oh!" said the magistrate, "I suspect you mean Mr. Chitty, the author of the great work on pleading."—"I do sir! But Chitty is an Italian name, and ought to be pronounced Kitty." This man was a full-blown flower: but there is many a modest bud; and all ought either to blush when seen or to waste their pronunciation on the desert air.

A PLEA FOR KING CUSTOM.

I stand up for King Custom, or Usus, as Horace called him, with whom is arbitrium the decision, and jus the right, and norma the way of deciding, simply because he has potestas the power. He may admit one and another principle to advise: but Custom is not a constitutional king; he may listen to his cabinet, but he decides for himself: and if the ministry should resign, he blesses his stars and does without them. We have a glorious liberty in England of owning neither dictionary, grammar, nor spelling-book: as many as choose write by either of the three, and decide all disputed points their own way, those following them who please.

Throughout this book I have called people by the names which denote them in their books, or by our vernacular names. This is the intelligible way of proceeding. I might, for instance (Vol. I, p. 44), have spoken of Charles de Bovelles, of Lefèvre d'Étaples, of Pèlerin, and of Etienne. But I prefer the old plan. Those who like another plan better, are welcome to substitute with a pen, when they know what to write; when they do not, it is clear that they would not have understood me if I had given modern names.

The principal advisers of King Custom are as follows. First, there is Etymology, the chiffonnier, or general rag-merchant, who has made such a fortune of late years in his own business that he begins to be considered highly respectable. He gives advice which is more thought of than followed, partly on account of the fearful extremes into which he runs. He lately asked some boys of sixteen, at a matriculation examination in English, to what branch of the Indo-Germanic family they felt inclined to refer the Pushto language, and what changes in the force of the letters took place in passing from Greek into Mœso-Gothic. Because all syllables were once words, he is a little inclined to insist that they shall be so still. He would gladly rule English with a Saxon rod, which might be permitted with a certain discretion which he has never attained: and when opposed, he defends himself with analogies of the Aryan family until those who hear him long for the discovery of an Athanasyus. He will transport a word beyond seas—he is recorder of Rhematopolis—on circumstantial evidence which looks like mystery gone mad; but, strange to say, something very often comes to light after sentence is passed which proves the soundness of the conviction.

The next adviser is Logic, a swearing old justice of peace, quorum, and rotulorum, whose excesses brought on such a fit of the gout that for many years he was unable to move. He is now mending, and his friends say he has sown his wild oats. He has some influence with the educated subjects of Custom, and will have more, if he can learn the line at which interference ought to stop: with them he has succeeded in making an affirmative of two negatives; but the vulgar won't never have nothing to say to him. He has always railed at Milton for writing that Eve was the fairest of her daughters; but has never satisfactorily shown what Milton ought to have said instead.

The third adviser has more influence with the mass of the subjects of King Custom than the other two put together; his name is Fiddlefaddle, the toy-shop keeper; and the other two put him forward to do their worst work. In return, he often uses their names without authority. He took Etymology to witness that means to an end must be plural: and he would have any one method to be a mean. But Etymology proved him wrong, King Custom referred him to his Catechism, in which is "a means whereby we receive the same," and Analogy—a subordinate of Etymology—asked whether he thought it a great new to hear that he was wrong. It was either this Fiddlefaddle, or Lindley Murray his traveler, who persuaded the Miss Slipslops, of the Ladies Seminary, to put "The Misses Slipslop" over the gate. Sixty years ago, this bagman called at all the girls' schools, and got many of the teachers to insist on the pupils saying "Is it not" and "Can I not" for "Isn't it" and "Can't I": of which it came that the poor girls were dreadfully laughed at by their irreverent brothers when they went home for the holidays. Had this bad adviser not been severely checked, he might by this time have proposed our saying "The Queen's of England son," declaring, in the name of Logic, that the prince was the Queen's son, not England's.

Lastly, there is Typography the metallurgist, an executive officer who is always at work in secret, and whose lawless mode of advising is often done by carrying his notions into effect without leave given. He it is who never ceases suggesting that the same word is not to occur in a second place within sight of the first. When the Authorized Version was first printed, he began this trick at the passage, "Let there be light, and there was light;" he drew a line on the proof under the second light, and wrote "luminosity?" opposite. He is strongest in the punctuations and other signs; he has a pepper-box full of commas always by his side. He puts everything under marks of quotation which he has ever heard before. An earnest preacher, in a very moving sermon, used the phrase Alas! and alack a day! Typography stuck up the inverted commas because he had read the old Anglo-Indian toast, "A lass and a lac a day!" If any one should have the sense to leave out of his Greek the unmeaning scratches which they call accents, he goes to a lexicon and puts them in. He is powerful in routine; but when two routines interlace or overlap, he frequently takes the wrong one.

Subject to bad advice, and sometimes misled for a season, King Custom goes on his quiet way and is sure to be right at last.

"Treason does never prosper: what's the reason?

Why, when it prospers, none dare call it treason."

Language is in constant fermentation, and all that is thrown in, so far as it is not fit to assimilate, is thrown off; and this without any obvious struggle. In the meanwhile every one who has read good authors, from Shakspeare downward, knows what is and what is not English; and knows, also, that our language is not one and indivisible. Two very different turns of phrase may both be equally good, and as good as can be: we may be relieved of the consequences of contempt of one court by habeas corpus issuing out of another.

TEST OF LANGUAGE.

Hallam remarks that the Authorized Version of the Bible is not in the language of the time of James the First: that it is not the English of Raleigh or of Bacon. Here arises the question whether Raleigh and Bacon are the true expositors of the language of their time; and whether they were not rather the incipient promoters of a change which was successfully resisted by—among other things—the Authorized Version of the Testaments. I am not prepared to concede that I should have given to the English which would have been fashioned upon that of Bacon by imitators, such as they usually are, the admiration which is forced from me by Bacon's English from Bacon's pen. On this point we have a notable parallel. Samuel Johnson commands our admiration, at least in his matured style: but we nauseate his followers. It is an opinion of mine that the works of the leading writers of an age are seldom the proper specimens of the language of their day, when that language is in its state of progression. I judge of a language by the colloquial idiom of educated men: that is, I take this to be the best medium between the extreme cases of one who is ignorant of grammar and one who is perched upon a style. Dialogue is what I want to judge by, and plain dialogue: so I choose Robert Recorde and his pupil in the Castle of Knowledge, written before 1556. When Dr. Robert gets into his altitudes of instruction, he differs from his own common phraseology as much as probably did Bacon when he wrote morals and philosophy. But every now and then I come to a little plain talk about a common thing, of which I propose to show a specimen. Anything can be made to look old by such changes as makes into maketh, with a little old spelling. I shall invert these changes, using the newer form of inflexion, and the modern spelling: with no other variation whatever.

"Scholar. Yet the reason of that is easy enough to be conceived, for when the day is at the longest the Sun must needs shine the more time, and so must it needs shine the less time when the day is at the shortest: this reason I have heard many men declare.

Master. That may be called a crabbed reason, for it goes backward like a crab. The day makes not the Sun to shine, but the Sun shining makes the day. And so the length of the day makes not the Sun to shine long, neither the shortness of the day causes not [sic] the Sun to shine the lesser time, but contrariwise the long shining of the Sun makes the long day, and the short shining of the Sun makes the lesser day: else answer me what makes the days long or short?

Scholar. I have heard wise men say that Summer makes the long days, and Winter makes the long nights.

Master. They might have said more wisely, that long days make summer and short days make winter.

Scholar. Why, all that seems one thing to me.

Master. Is it all one to say, God made the earth, and the earth made God? Covetousness overcomes all men, and all men overcome covetousness?

Scholar. No, not so; for here the effect is turned to be the cause, and the agent is made the patient.

Master. So is it to say Summer makes long days, when you should say: Long days make summer.

Scholar. I perceive it now: but I was so blinded with the vulgar error, that if you had demanded of me further what did make the summer, I had been like to have answered that green leaves do make summer; and the sooner by remembrance of an old saying that a year should come in which the summer should not be known but by the green leaves.

Master. Yet this saying does not import that green leaves do make summer, but that they betoken summer; so are they the sign and not the cause of summer."

I have taken a whole page of our author, without omission, that the reader may see that I do not pick out sentences convenient for my purpose. I have done nothing but alter the third person of the verb and the spelling: but great is the effect thereof. We say "the Sun shining makes the day"; Recorde, "the Sonne shynynge maketh the daye." These points apart, we see a resemblance between our English and that of three hundred years ago, in the common talk of educated persons, which will allow us to affirm that the language of the authorized Bible must have been very close to that of its time. For I cannot admit that much change can have taken place in fifty years: and the language of the version represents both our common English and that of Recorde with very close approximation. Take sentences from Bacon and Raleigh, and it will be apparent that these writers will be held to differ from all three, Recorde, the version, and ourselves, by differences of the same character. But we speak of Recorde's conversation, and of our own. We conclude that it is the plain and almost colloquial character of the Authorized Version which distinguishes it from the English of Bacon and Raleigh, by approximating it to the common idiom of the time. If any one will cast an eye upon the letters of instruction written by Cecil and the Bishop of London to the translators themselves, or to the general directions sent to them in the King's name, he will find that these plain business compositions differ from the English of Bacon and Raleigh by the same sort of differences which distinguish the version itself.

PRONUNCIATION.

The foreign word, or the word of a district, or class of people, passes into the general vernacular; but it is long before the specially learned will acknowledge the right of those with whom they come in contact to follow general usage. The rule is simple: so long as a word is technical or local, those who know its technical or local pronunciation may reasonably employ it. But when the word has become general, the specialist is not very wise if he refuse to follow the mass, and perfectly foolish if he insist on others following him. There have been a few who demanded that Euler should be pronounced in the German fashion: Euler has long been the property of the world at large; what does it matter how his own countrymen pronounce the letters? Shall we insist on the French pronouncing Newton without that final tong which they never fail to give him? They would be wise enough to laugh at us if we did. We remember that a pedant who was insisting on all the pronunciations being retained, was met by a maxim in contradiction, invented at the moment, and fathered upon Kaen-foo-tzee, an authority which he was challenged to dispute. Whom did you speak of? said the bewildered man of accuracy. Learn your own system, was the answer, before you impose it on others; Confucius says that too.

The old English has fote, fode, loke, coke, roke, etc., for foot, etc. And above rhymes in Chaucer to remove. Suspecting that the broader sounds are the older, we may surmise that remove and food have retained their old sounds, and that cook, once coke, would have rhymed to our Luke, the vowel being brought a little nearer, perhaps, to the o in our present coke, the fuel, probably so called as used by cooks. If this be so, the Chief Justice Cook of our lawyers, and the Coke (pronounced like the fuel) of the greater part of the world, are equally wrong. The lawyer has no right whatever to fasten his pronunciation upon us: even leaving aside the general custom, he cannot prove himself right, and is probably wrong. Those who know the village of Rokeby (pronounced Rookby) despise the world for not knowing how to name Walter Scott's poem: that same world never asked a question about the matter, and the reception of the parody of Jokeby, which soon appeared, was a sufficient indication of their notion. Those who would fasten the hodiernal sound upon us may be reminded that the question is, not what they call it now, but what it was called in Cromwell's time. Throw away general usage as a lawgiver, and this is the point which emerges. Probably Rūke-by would be right, with a little turning of the Italian ū towards ō of modern English.

[Some of the above is from an old review. I do not always notice such insertions: I take nothing but my own writings. A friend once said to me, "Ah! you got that out of the Athenæum!" "Excuse me," said I. "the Athenæum got that out of me!"]

APOLOGIES TO CLUVIER.

It is part of my function to do justice to any cyclometers whose methods have been wrongly described by any orthodox sneerers (myself included). In this character I must notice Dethlevus Cluverius, as the Leipzig Acts call him (probably Dethleu Cluvier), grandson of the celebrated geographer, Philip Cluvier. The grandson was a Fellow of the Royal Society, elected on the same day as Halley, November 30, 1678: I suppose he lived in England. This man is quizzed in the Leipzig Acts for 1686; and, if Montucla insinuate rightly, by Leibnitz, who is further suspected of wanting to embroil Cluvier with his own opponent Nieuwentiit, on the matter of infinitesimals. So far good: I have nothing against Leibnitz, who though he was ironical, told us what he laughed at. But Montucla has behaved very unfairly: he represents Cluvier as placing the essence of his method in the solution of the problem construere mundum divinæ menti analogum, to construct a world corresponding to the divine mind. Nothing to begin with: no way of proceeding. Now, it ought to have been ex data linea construere, etc.: there is a given line, which is something to go on. Further, there is a way of proceeding: it is to find the product of 1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier with unsquaring the parabola, which Archimedes had squared as tight as a glove. But he never mentions how very nearly Cluvier agrees with the Greek: they only differ by 1 divided by 3n, where n is the infinite number of parts of which a parabola is composed. This must have been the conceit that tickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should fight it out. Cluvier, was admitted, on terms of irony, into the Leipzig Acts: he appeared on a more serious footing in London. It is very rare for one cyclometer to refute another: les corsaires ne se battent pas. The only instance I recall is that of M. Cluvier, who (Phil. Trans., 1686, No. 185) refuted M. Mallemont de Messange, who published at Paris in 1686. He does it in a very serious style, and shows himself a mathematician. And yet in the year in which, in the Phil. Trans., he was a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in that very year he was the visionary who, in the Leipzig Acts, professed to build a world resembling the divine mind by multiplying together 1, 2, 3, 4, etc. up to infinity.

THE RAINBOW PARADOX.

There is a very pretty opening for a paradox which has never found its paradoxer in print. The philosophers teach that the rainbow is not material: it comes from rain-drops, but those rain-drops do not take color. They only give it, as lenses and mirrors; and each one drop gives all the colors, but throws them in different directions. Accordingly, the same drop which furnishes red light to one spectator will furnish violet to another, properly placed. Enter the paradoxer whom I have to invent. The philosopher has gulled you nicely. Look into the water, and you will see the reflected rainbow: take a looking-glass held sideways, and you see another reflection. How could this be, if there were nothing colored to reflect? The paradoxer's facts are true: and what are called the reflected rainbows are other rainbows, caused by those other drops which are placed so as to give the colors to the eye after reflection, at the water or the looking-glass. A few years ago an artist exhibited a picture with a rainbow and its apparent reflection: he simply copied what he had seen. When his picture was examined, some started the idea that there could be no reflection of a rainbow; they were right: they inferred that the artist had made a mistake; they were wrong. When it was explained, some agreed and some dissented. Wanted, immediately, an able paradoxer: testimonials to be forwarded to either end of the rainbow, No. 1. No circle-squarer need apply, His Variegatedness having been pleased to adopt 3.14159... from Noah downwards.

TYCHO BRAHE REVIVED.

The system of Tycho Brahé, with some alteration and addition, has been revived and contended for in our own day by a Dane, W. Zytphen, who has published The Motion of the Sun in the Universe, (second edition) Copenhagen, 1865, 8vo, and Le Mouvement Sidéral, 1865, 8vo. I make an extract.

"How can one explain Copernically that the velocity of the Moon must be added to the velocity of the Earth on the one place in the Earth's orbit, to learn how far the Moon has advanced from one fixed star to another; but in another place in the orbit these velocities must be subtracted (the movements taking place in opposite directions) to attain the same result? In the Copernican and other systems, it is well known that the Moon, abstracting from the insignificant excentricity of the orbit, always in twenty-four hours performs an equally long distance. Why has Copernicus never been denominated Fundamentus or Fundator? Because he has never convinced anybody so thoroughly that this otherwise so natural epithet has occurred to the mind."

Really the second question is more effective against Newton than against Copernicus; for it upsets gravity: the first is of great depth.

JAMES SMITH WILL NOT DOWN.

The Correspondent journal makes a little episode in the history of my Budget (born May, 1865, died April, 1866). It consisted entirely of letters written by correspondents. In August, a correspondent who signed "Fair Play"—and who I was afterwards told was a lady—thought it would be a good joke to bring in the Cyclometers. Accordingly a letter was written, complaining that though Mr. Sylvester's demonstration of Newton's theorem—then attracting public attention—was duly lauded, the possibly greater discovery of the quadrature seemed to be blushing unseen, and wasting etc. It went on as follows:

"Prof. De Morgan, who, from his position in the scientific world, might fairly afford to look favourably on less practised efforts than his own, seems to delight in ridiculing the discoverer. Science is, of course, a very respectable person when he comes out and makes himself useful in the world [it must have been a lady; each sex gives science to the other]: but when, like a monk of the Middle Ages, he shuts himself up [it must have been a lady; they always snub the bachelors] in his cloistered cell, repeating his mumpsimus from day to day, and despising the labourers on the outside, we begin to think of Galileo, Jenner, Harvey, and other glorious trios, who have been contemned ..."

The writer then called upon Mr. James Smith to come forward. The irony was not seen; and that day fortnight appeared the first of more than thirty letters from his pen. Mr. Smith was followed by Mr. Reddie, Zadkiel, and others, on their several subjects. To some of the letters I have referred; to others I shall come. The Correspondent was to become a first-class scientific journal; the time had arrived at which truth had an organ: and I received formal notice that I could not stifle it by silence, nor convert it into falsehood by ridicule. When my reader sees my extracts, he will readily believe my declaration that I should have been the last to stifle a publication which was every week what James Mill would call a dose of capital for my Budget. A few anti-paradoxers brought in common sense: but to the mass of the readers of the journal it all seemed to be the difference between Tweedledum and Tweedledee. Some said that the influx of scientific paradoxes killed the journal: but my belief is that they made it last longer than it otherwise would have done. Twenty years ago I recommended the paradoxers to combine and publish their views in a common journal: with a catholic editor, who had no pet theory, but a stern determination not to exclude anything merely for absurdity. I suspect it would answer very well. A strong title, or motto, would be wanted: not so coarse as was roared out in a Cambridge mob when I was an undergraduate—"No King! No Church! No House of Lords! No nothing, blast me!"—but something on that principle.

At the end of 1867 I addressed the following letter to the Athenæum:

Pseudomath, Philomath, and Graphomath.

December 31, 1867

Many thanks for the present of Mr. James Smith's letters of Sept. 28 and of Oct. 10 and 12. He asks where you will be if you read and digest his letters: you probably will be somewhere first. He afterwards asks what the WE of the Athenæum will be if, finding it impossible to controvert, it should refuse to print. I answer for you, that We-We of the Athenæum, not being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what controverts itself to print itself, if it please.

Philomath is a good old word, easier to write and speak than mathematician. It wants the words between which I have placed it. They are not well formed: pseudomathete and graphomathete would be better: but they will do. I give an instance of each.

The pseudomath is a person who handles mathematics as the monkey handled the razor. The creature tried to shave himself as he had seen his master do; but, not having any notion of the angle at which the razor was to be held, he cut his own throat. He never tried a second time, poor animal! but the pseudomath keeps on at his work, proclaims himself clean-shaved, and all the rest of the world hairy. So great is the difference between moral and physical phenomena! Mr. James Smith is, beyond doubt, the great pseudomath of our time. His 3⅛ is the least of a wonderful chain of discoveries. His books, like Whitbread's barrels, will one day reach from Simpkin & Marshall's to Kew, placed upright, or to Windsor laid length-ways. The Queen will run away on their near approach, as Bishop Hatto did from the rats: but Mr. James Smith will follow her were it to John o' Groats.

The philomath, for my present purpose, must be exhibited as giving a lesson to presumption. The following anecdote is found in Thiébault's Souvenirs de vingt ans de séjours à Berlin, published in 1804. The book itself got a high character for truth. In 1807 Marshal Mollendorff answered an inquiry of the Duc de Bassano, by saying that it was the most veracious of books, written by the most honest of men. Thiébault does not claim personal knowledge of the anecdote, but he vouches for its being received as true all over the north of Europe.

Diderot paid a visit to Russia at the invitation of Catherine the Second. At that time he was an atheist, or at least talked atheism: it would be easy to prove him either one thing or the other from his writings. His lively sallies on this subject much amused the Empress, and all the younger part of her Court. But some of the older courtiers suggested that it was hardly prudent to allow such unreserved exhibitions. The Empress thought so too, but did not like to muzzle her guest by an express prohibition: so a plot was contrived. The scorner was informed that an eminent mathematician had an algebraical proof of the existence of God, which he would communicate before the whole Court, if agreeable. Diderot gladly consented. The mathematician, who is not named, was Euler. He came to Diderot with the gravest air, and in a tone of perfect conviction said, "Monsieur!

a + bn
/
n = x

donc Dieu existe; répondez!" Diderot, to whom algebra was Hebrew, though this is expressed in a very roundabout way by Thiébault—and whom we may suppose to have expected some verbal argument of alleged algebraical closeness, was disconcerted; while peals of laughter sounded on all sides. Next day he asked permission to return to France, which was granted. An algebraist would have turned the tables completely, by saying, "Monsieur! vous savez bien que votre raisonnement demande le développement de x suivant les puissances entières de n". Goldsmith could not have seen the anecdote, or he might have been supposed to have drawn from it a hint as to the way in which the Squire demolished poor Moses.

The graphomath is a person who, having no mathematics, attempts to describe a mathematician. Novelists perform in this way: even Walter Scott now and then burns his fingers. His dreaming calculator, Davy Ramsay, swears "by the bones of the immortal Napier." Scott thought that the the philomaths worshiped relics: so they do, in one sense. Look into Hutton's Dictionary for Napier's Bones, and you shall learn all about the little knick-knacks by which he did multiplication and division. But never a bone of his own did he contribute; he preferred elephants' tusks. The author of Headlong Hall makes a grand error, which is quite high science: he says that Laplace proved the precession of the equinoxes to be a periodical inequality. He should have said the variation of the obliquity. But the finest instance is the following: Mr. Warren, in his well-wrought tale of the martyr-philosopher, was incautious enough to invent the symbols by which his savant satisfied himself Laplace was right on a doubtful point. And this is what he put together—

√-3a, y / z + 9 - n = 9, n × log e.

Now, to Diderot and the mass of mankind this might be Laplace all over: and, in a forged note of Pascal, would prove him quite up to gravitation. But I know of nothing like it, except in the lately received story of the American orator, who was called on for some Latin, and perorated thus: "Committing the destiny of the country to your hands, Gentlemen, I may without fear declare, in the language of the noble Roman poet,

E pluribus unum,

Multum in parvo,

Ultima Thule,

Sine qua non."

But the American got nearer to Horace than the martyr-philosopher to Laplace. For all the words are in Horace, except Thule, which might have been there. But is not a symbol wanted by Laplace; nor can we see how it could have been; in fact, it is not recognized in algebra. As to the junctions, etc., Laplace and Horace are about equally well imitated.

Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and Nov. 4, 15. The last of these letters has two curious discoveries. First, Mr. Smith declares that he has seen the editor of the Athenæum: in several previous letters he mentions a name. If he knew a little of journalism he would be aware that editors are a peculiar race, obtained by natural selection. They are never seen, even by their officials; only heard down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of circles. Mr. Smith has got hold of the construction I was taught, when a boy, for a pretty four-arc oval. But my teachers knew better than to call it an ellipse: Mr. Smith does not; but he produces from it such confirmation of 3⅛ as would convince any honest editor.

Surely the cyclometer is a Darwinite development of a spider, who is always at circles, and always begins again when his web is brushed away. He informs you that he has been privileged to discover truths unknown to the scientific world. This we know; but he proceeds to show that he is equally fortunate in art. He goes on to say that he will make use of you to bring those truths to light, "just as an artist makes use of a dummy for the purpose of arranging his drapery." The painter's lay-figure is for flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith should read Sam Weller's pathetic story of the "four wax dummies." As to his use of a dummy, it is quite correct. When I was at University College, I walked one day into a room in which my Latin colleague was examining. One of the questions was, "Give the lives and fates of Sp. Mælius, and Sp. Cassius." Umph! said I, surely all know that Spurius Mælius was whipped for adulterating flour, and that Spurius Cassius was hanged for passing bad money. Now, a robe arranged on a dummy would look just like the toga of Cassius on the gallows. Accordingly, Mr. Smith is right in the drapery-hanger which he has chosen: he has been detected in the attempt to pass bad circles. He complains bitterly that his geometry, instead of being read and understood by you, is handed over to me to be treated after my scurrilous fashion. It is clear enough that he would rather be handled in this way than not handled at all, or why does he go on writing? He must know by this time that it is a part of the institution that his "untruthful and absurd trash" shall be distilled into mine at the rate of about 3⅛ pages of the first to one column of the second. Your readers will never know how much they gain by the process, until Mr. James Smith publishes it all in a big book, or until they get hold of what he has already published. I have six pounds avoirdupois of pamphlets and letters; and there is more than half a pound of letters written to you in the last two months. Your compositor must feel aggrieved by the rejection of these clearly written documents, without erasures, and on one side only. Your correspondent has all the makings of a good contributor, except the knowledge of his subject and the sense to get it. He is, in fact, only a mask: of whom the fox

"O quanta species, inquit, cerebrum non habet."

I do not despair of Mr. Smith on any question which does not involve that unfortunate two-stick wicket at which he persists in bowling. He has published many papers; he has forwarded them to mathematicians: and he cannot get answers; perhaps not even readers. Does he think that he would get more notice if you were to print him in your journal? Who would study his columns? Not the mathematician, we know; and he knows. Would others? His balls are aimed too wide to be blocked by any one who is near the wicket. He has long ceased to be worth the answer which a new invader may get. Rowan Hamilton, years ago, completely knocked him over; and he has never attempted to point out any error in the short and easy method by which that powerful investigator condescended to show that, be right who may, he must be wrong. There are some persons who feel inclined to think that Mr. Smith should be argued with: let those persons understand that he has been argued with, refuted, and has never attempted to stick a pen into the refutation. He stated that it was a remarkable paradox, easily explicable; and that is all. After this evasion, Mr. James Smith is below the necessity of being told that he is unworthy of answer. His friends complain that I do nothing but chaff him. Absurd! I winnow him; and if nothing but chaff results, whose fault is that? I am usefully employed: for he is the type of a class which ought to be known, and which I have done much to make known.

Nothing came of this until July 1869, when I received a reprint of the above letter, with a comment, described as Appendix D of a work in course of publication on the geometry of the circle. The Athenæum journal received the same: but the Editor, in his private capacity, received the whole work, being The Geometry of the Circle and Mathematics as applied to Geometry by Mathematicians, shown to be a mockery, delusion, and a snare, Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor Whitworth, and Mr. Wilson, the author of the alleged amendment of Euclid. How these accomplished mathematicians could be inveigled into continued discussion is inexplicable. Mr. Whitworth began by complaining of Mr. Smith's attacks upon mathematicians, continued to correspond after he was convinced that J. S. proved an arc and its chord to be equal, and only retreated when J. S. charged him with believing in 3⅛, and refusing acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense of his geometry from the assaults of the Athenæum. This the editor would not publish; so J. S. sent a copy to Mr. Wilson himself. Some correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.

There is a little derision of the Athenæum and a merited punishment for "that unscrupulous critic and contemptible mathematical twaddler, De Morgan."

MR. REDDIE'S ASTRONOMY.

At p. 183 I mentioned Mr. Reddie, the author of Vis Inertiæ Victa and of Victoria toto cœlo, which last is not an address to the whole heaven, either from a Roman Goddess or a British Queen, whatever a scholar may suppose. Between these Mr. Reddie has published The Mechanics of the Heavens, 8vo, 1862: this I never saw until he sent it to me, with an invitation to notice it, he very well knowing that it would catch. His speculations do battle with common notions of mathematics and of mechanics, which, to use a feminine idiom, he blasphemes so you can't think! and I suspect that if you do not blaspheme them too, you can't think. He appeals to the "truly scientific," and would be glad to have readers who have read what he controverts, i.e., Newton's Principia: I wish he may get them; I mean I hope he may obtain them. To none but these would an account of his speculations be intelligible: I accordingly disposed of him in a very short paragraph of description. Now many paradoxers desire notice, even though it be disparaging. I have letters from more than one—besides what have been sent to the Editor of the Athenæum—complaining that they are not laughed at; although they deserve it, they tell me, as much as some whom I have inserted. Mr. Reddie informs me that I have not said a single word against his books, though I have given nearly a column to sixteen-string arithmetic, and as much to animalcule universes. What need to say anything to readers of Newton against a book from which I quoted that revolution by gravitation is demonstrably impossible? It would be as useless as evidence against a man who has pleaded guilty. Mr. Reddie derisively thanks me for "small mercies"; he wrote me private letters; he published them, and more, in the Correspondent. He gave me, pro viribus suis, such a dressing you can't think, both for my Budget non-notice, and for reviews which he assumed me to have written. He outlawed himself by declaring (Correspondent, Nov. 11, 1856) that I—in a review—had made a quotation which was "garbled, evidently on purpose to make it appear that" he "was advocating solely a geocentric hypothesis, which is not true." In fact, he did his best to get larger "mercy." And he shall have it; and at a length which shall content him, unless his mecometer be an insatiable apparatus. But I fear that in other respects I shall no more satisfy him than the Irish drummer satisfied the poor culprit when, after several times changing the direction of the stroke at earnest entreaty, he was at last provoked to call out, "Bad cess to ye, ye spalpeen! strike where one will, there's no plasing ye!"

Mr. Reddie attaches much force to Berkeley's old arguments against the doctrine of fluxions, and advances objections to Newton's second section, which he takes to be new. To me they appear "such as have been often made," to copy a description given in a review: though I have no doubt Mr. Reddie got them out of himself. But the whole matter comes to this: Mr. Reddie challenged answer, especially from the British Association, and got none. He presumes that this is because he is right, and cannot be answered: the Association is willing to risk itself upon the counter-notion that he is wrong, and need not be answered; because so wrong that none who could understand an answer would be likely to want one.

Mr. Reddie demands my attention to a point which had already particularly struck me, as giving the means of showing to all readers the kind of confusion into which paradoxers are apt to fall, in spite of the clearest instruction. It is a very honest blunder, and requires notice: it may otherwise mislead some, who may suppose that no one able to read could be mistaken about so simple a matter, let him be ever so wrong about Newton. According to his own mis-statement, in less than five months he made the Astronomer Royal abandon the theory of the solar motion in space. The announcement is made in August, 1865, as follows: the italics are not mine:

"The third (Victoria ...), although only published in September, 1863, has already had its triumph. It is the book that forced the Astronomer Royal of England, after publicly teaching the contrary for years, to come to the conclusion, "strange as it may appear," that "the whole question of solar motion in space is at the present time in doubt and abeyance." This admission is made in the Annual Report of the Council of the Royal Astronomical Society, published in the Society's Monthly Notices for February, 1864."

It is added that solar motion is "full of self-contradiction, which "the astronomers" simply overlooked, but which they dare not now deny after being once pointed out."

The following is another of his accounts of the matter, given in the Correspondent, No. 18, 1865:

"... You ought, when you came to put me in the 'Budget,' to have been aware of the Report of the Council of the Royal Astronomical Society, where it appears that Professor Airy, with a better appreciation of my demonstrations, had admitted—'strange,' say the Council, 'as it may appear,'—that 'the whole question of solar motion in space [and here Mr. Reddie omits some words] is now in doubt and abeyance.' You were culpable as a public teacher of no little pretensions, if you were 'unaware' of this. If aware of it, you ought not to have suppressed such an important testimony to my really having been 'very successful' in drawing the teeth of the pegtops, though you thought them so firmly fixed. And if you still suppress it, in your Appendix, or when you reprint your 'Budget,' you will then be guilty of a suppressio veri, also of further injury to me, who have never injured you...."

Mr. Reddie must have been very well satisfied in his own mind before he ventured such a challenge, with an answer from me looming in the distance. The following is the passage of the Report of the Council, etc., from which he quotes: