Budget of Paradoxes/O

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A Budget of Paradoxes by Augustus De Morgan


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 [ 255 ] 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,[406] 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[407] 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 [ 256 ] feelings of thousands of estimable and well-intentioned men with all the harshness of controversial hostility."

Other doses were administered by Sir J. Bowring,[408] Sir W. Rowan Hamilton,[409] 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 [ 257 ] 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:


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.

[ 258 ]

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 [ 259 ] 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 [ 260 ] 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.[410] 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[411] that his appearance was very like that of a corpse. The John Bull [ 261 ] newspaper—suppose we now say Theodore Hook[412]—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?



"The Writ De Hæretico Commiserando.[413]

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.

[ 262 ]

"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,[414] 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[415] 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."[416]

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: [ 263 ] 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![417]—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 [ 264 ] 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 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[418] Bible of 1599, I saw an [ 265 ] 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[419] 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[420] (by [ 266 ] Mose[421]) 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."

[ 267 ]

No ordinary map would decide these points: so I had to apply to my friend Sir Francis Beaufort,[422] and the charts at the Admiralty decided immediately for Massachusetts.



The French are able paradoxers in their spelling of foreign names. The Abbé Sabatier de Castres,[423] 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[424] and Galileo, references to the works of two Englishmen, the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and Baden Powell].[425]

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 [ 268 ] 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."[426]



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 [ 269 ] 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,[427] 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.



Sometimes a person who has a point to carry will assert a singular fact or prediction for the sake of his point; and [ 270 ] 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[428] wakes a genuine poet's fires,
And modern Britons glory in their sires."[429]

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[430] and Shoberl[431] (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,[432] 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 [ 271 ] 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[433] 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:

[ 272 ]

"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.



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[434] may be excused, as personal satire was his object, for addressing Boswell and Mrs. Piozzi[435] 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:

[ 273 ]

"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's mistake about Hallam in the Pindar story may be worth placing among absurdities. For elucidation, suppose that some poet were now to speak— [ 274 ]

"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,[436] 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 [ 275 ] 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,[437] 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[438] 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 [ 276 ] 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."[439]

[ 277 ] And Quarles[440] 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.



I have come in the way of a work, entitled The Grave of Human Philosophies (1827), translated from the French of R. de Bécourt[441] by A. Dalmas. It supports, but I suspect not very accurately, the views of the old Hindu books. [ 278 ] 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.



There is much private history which will never come to light, caret quia vate sacro,[442] 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 [ 279 ] 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[443] 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[444] bequest of some very good titles [ 280 ] 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.



October 19, 1861. The English Cyclopædia. Conducted by Charles Knight.[445] 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[446] is not absolutely Greek of Greece, we learn from both Pliny[447] and Quintilian[448] that the circle [ 281 ] of the sciences was so called by the Greeks, and Vitruvius[449] 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,[450] 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[451] 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,[452] the same we must suppose, who was confessor to the Emperor Maximilian.[453] 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,[454] which is truly called an Encyclopædia by [ 282 ] 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,[455] 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[456] (1677); but Chambers's[457] (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.

[ 283 ]

We pass on to the Encyclopédie,[458] 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[459] 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[460] 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[461]—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."[462]

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,[463] 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 [ 284 ] 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,[464] 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 [ 285 ] treatises; the part called Miscellaneous and Lexicographical in the Metropolitana[465] 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 [ 286 ] 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 [ 287 ] 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. [ 288 ] 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[466] and Herschel.[467] 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.[468]

The literary excellence of these two extensive undertakings is of the same high character. To many this will [ 289 ] 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[469] 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.[470] 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.

[ 290 ]

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[471] 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[472] informations were laid against the agents in various towns. [ 291 ] 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 [ 292 ] 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,[473] 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 [ 293 ] 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 [ 294 ] 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.[474] 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 [ 295 ] 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[475] died, and left the splendid library which was catalogued by Bouillaud[476] and the brothers Dupuis[477] (Bullialdus and Puteanus), there was a manuscript of De Thou's friend Vieta,[478] the Harmonicon Cœleste, of which it is on record, under Bouillaud's hand, that he himself lent it to Cosmo de' Medici,[479] to which must be added that M. Libri[480] 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,[481] from whom it was procured by some intending plagiarist, who would not give it back. This was repeated by Sherburne,[482] 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 [ 296 ] 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.



October 18, 1862. Correspondence of Scientific Men of the Seventeenth Century, in the Collection of the Earl of Macclesfield.[483] 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,[484] 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,[485] for Trinity College, in 1850.

[ 297 ]

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[486] was in France: as early as 1671, E. Bernard[487] addresses him as "the very Mersennus and intelligence of this age." John Collins[488] 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,[489] 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 [ 298 ] William Jones,[490] 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,[491] the mover and the seconder, and Daval,[492] who drew the bill, were pupils of De Moivre.[493] 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[494] 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,[495] 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 [ 299 ] 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,[496] 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.[497] 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,[498] Oughtred, Charles Cavendish,[499] Gascoigne,[500] Seth Ward,[501] Wallis,[502] [ 300 ] Hu[y]gens,[503] Collins,[504] William Petty,[505] Hooke,[506] Boyle,[507] Pell,[508] Oldenburg,[509] Brancker,[510] Slusius,[511] Bertit,[512] Bernard,[513] Borelli,[514] Mouton,[515] Pardies,[516] Fermat,[517] Towneley,[518] Auzout,[519] [ 301 ] D. Gregory,[520] Halley,[521] Machin,[522] Montmort,[523] Cotes,[524] Jones,[525] Saunderson,[526] Reyneau,[527] Brook Taylor,[528] Maupertuis,[529] Bouguer,[530] La Condamine,[531] Folkes,[532] Macclesfield,[533] [ 302 ] Baker,[534] Barrow,[535] Flamsteed,[536] Lord Brounker,[537] J. Gregory,[538] Newton[539] and Keill.[540] To these the Museum collection adds the names of Thomas Digges,[541] Dee,[542] Tycho Brahe,[543] Harriot,[544] Lydyat,[545] Briggs,[546] Warner,[547] Tarporley, Pell,[548] Lilly,[549] Oldenburg,[550] Collins,[551] Morland.[552]

[ 303 ]

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,[553] 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[554] there contends, and proves it both by Leverrier[555] and by Adams,[556] 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[557] 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 [ 304 ] Simpson[558] 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,[559] 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 [ 305 ] 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,[560] 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,[561] 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.

[ 306 ]

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[562] writes to Collins as follows: "Last week he sent us down the counterpart, which [ 307 ] 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."[563]

There is one mention of "Mr. Cocker,[564] 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 [ 308 ] subsequently forged the famous Arithmetic,[565] 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[566] 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,[567] 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.[568] Murphy chooses Wingate to be the name of an old merchant who [ 309 ] 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.[569] 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 [ 310 ] 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,[570] 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,[571] is now lecturer in Mr. Foster's place." Ward in his work on the Gresham Professors,[572] 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 [ 311 ] 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[573] [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 [ 312 ] 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,[574] afterwards assisted by Pell,[575] commenced a table of antilogarithms, of the kind which Dodson[576] afterwards constructed anew and published. In the Museum collection there is inquiry after inquiry from Charles Cavendish,[577] 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, [ 313 ] 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[578] that the papers had fallen into the hands of Dr. Busby,[579] and Collins[580] writes that they were left in the hands of Dr. Thorndike,[581] a prebendary of Westminster; whence Rigaud[582] seems to say that Thorndike had left them to Dr. Busby. Birch[583] 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 [ 314 ] 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.



Redit labor actus in orbem.[584] 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,[585] already mentioned. It ends with "Quelque objection qu'on fasse touchant les raisonnements ci-dessus on tombera toujours dans l'absurde."[586] 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 [ 315 ] 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,[587] 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.[588] 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[589] steel pens, with engraving of his [ 316 ] premises, and notice of novel application of his unrivalled machinery. The second side begins with "the circle rectified" by W. E. Walker,[590] 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 = 313/80 + 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 [ 317 ] 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[591] 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.



Though I have met with nothing but a little tract from the school of Jacob Behmen[592] (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[593]: 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 [ 318 ] 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[594] 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,[595] 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 [ 319 ] 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,[596] 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 [ 320 ] 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,[597] 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, [ 321 ] 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 [ 322 ] 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[598] and Paracelsus,[599] 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[600] 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, [ 323 ] 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,[601] the name given by Reuchlin[602] 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,[603] 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.

[ 324 ]



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,[604] of Lefèvre d'Étaples,[605] of Pèlerin,[606] and of Etienne.[607] 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 [ 325 ] 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 [ 326 ] Etymology—asked whether he thought it a great new to hear that he was wrong. It was either this Fiddlefaddle, or Lindley Murray[608] 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 [ 327 ] 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.



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 [ 328 ] 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[609] 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 [ 329 ] 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." [ 330 ] 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[610] 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.



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 [ 331 ] 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:[611] 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,[612] 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.[613]

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[614] 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 [ 332 ] 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!"]



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,[615] 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,[616] November 30, 1678: I suppose he lived in England. This [ 333 ] 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,[617] 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,[618] 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 3n2, 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.[619] The only instance I recall is that of M. Cluvier, who (Phil. Trans., 1686, No. 185) refuted M. Mallemont de Messange,[620] who [ 334 ] 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.



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, [ 335 ] 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.


406 ^  See Vol. I, note 119.

407 ^  See Vol. II, note 394.

408 ^  See Vol. I, note 731.

409 ^  See Vol. I, note 709.

410 ^  "The lawyers are brought into court; let them accuse each other."

411 ^  Samuel Rogers (1763-1855), the poet and art connoisseur. He declined the laureateship on the death of Wordsworth (1850). Byron, his pretended friend, wrote a lampoon (1818) ridiculing his cadaverous appearance.

412 ^  Theodore Edward Hook (1788-1841), the well-known wit. He is satirized as Mr. Wagg in Vanity Fair. The John Bull was founded in 1820 and Hook was made editor.

413 ^  "On pitying the heretic."

414 ^  A term of medieval logic. Barbara: All M is P, all S is M, hence all S is P. Celarent: No M is P, all S is M, hence no S is P.

415 ^  "Simply," "According to which," "It does not follow."

416 ^ 

"O sweet soul, what good shall I declare
That heretofore was thine, since such are thy remains!"

417 ^  "Stupid fellow!"

418 ^  Christopher Barker (c. 1529-1599), also called Barkar, was the Queen's printer. He began to publish books in 1569, but did no actual printing until 1576. In 1575 the Geneva Bible was first printed in England, the work being done for Barker. He published 38 partial or complete editions of the Bible from 1575 to 1588, and 34 were published by his deputies (1588-1599).

419 ^  James Franklin (1697-1735) was born in Boston, Mass., and was sent to London to learn the printer's trade. He returned in 1717 and started a printing house. Benjamin, his brother, was apprenticed to him but ran away (1723). James published the New England Courant (1721-1727), and Benjamin is said to have begun his literary career by writing for it.

420 ^  James Hodder was a writing master in Tokenhouse Yard, Lothbury, in 1661, and later kept a boarding school in Bromley-by-Bow. His famous arithmetic appeared at London in 1661 and went through many editions. It was the basis of Cocker's work. (See Vol. I, note 24.) It was long thought to have been the first arithmetic published in America, and it was the first English one. There was, however, an arithmetic published much earlier than this, in Mexico, the Sumario compendioso ... con algunas reglas tocantes al Aritmética, by "Juan Diaz Freyle," in 1556.

421 ^  Henry Mose, Hodder's successor, kept a school in Sherborne Lane, London.

422 ^  Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was printed by the Society for the Diffusion of Useful Knowledge.

423 ^  Antoine Sabatier (1742-1817), born at Castres, was known as the Abbé but was really nothing more than a "clerc tonsuré." He lived at Court and was pensioned to write against the philosophers of the Voltaire group. He posed as the defender of morality, a commodity of which he seems to have possessed not the slightest trace.

424 ^  Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was during his ambitious reign that Galileo was summoned to Rome to make his recantation (1633), the exact nature of which is still a matter of dispute.

425 ^  This Baden Powell (1796-1860) was the Savilian professor of geometry (1827-1860) at Oxford.

426 ^  "Memoirs of the famous bishop of Chiapa, by which it appears that he had butchered or burned or drowned ten million infidels in America in order to convert them. I believe that this bishop exaggerated; but if we should reduce these sacrifices to five million victims, this would still be admirable."

427 ^  Alfonso X (1221-1284), known as El Sabio (the Wise), was interested in astronomy and caused the Alphonsine Tables to be prepared. These table were used by astronomers for a long time. It is said that when the Ptolemaic system of the universe was explained to him he remarked that if he had been present at the Creation he could have shown how to arrange things in a much simpler fashion.

428 ^  George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824), and a poet of no mean ability.

429 ^  The "Aboriginal Britons," an excellent poem, by Richards. (Note by Byron.)—A. De M.

430 ^  John Watkins (d. after 1831), a teacher and miscellaneous writer.

431 ^  Frederic Shoberl (1775-1853), a miscellaneous writer.

432 ^  He wrote, besides the Aboriginal Britons, Songs of the Aboriginal Bards (1792), Modern France: a Poem (1793), Odin, a drama (1804), Emma, a drama on the model of the Greek theatre (1804), Poems (2 volumes, 1804), and a Monody on the Death of Lord Nelson (1806).

433 ^  Henry Kirke White (1785-1806), published his first volume of poems at the age of 18. Southey and William Wilberforce became interested in him and procured for him a sizarship at St. John's College, Cambridge. He at once showed great brilliancy, but he died of tuberculosis at the age of 21.

434 ^  John Wolcot, known as Peter Pindar (1738-1819), was a London physician. He wrote numerous satirical poems. His Bozzy and Piozzi, or the British Biographers, appeared in 1786, and reached the 9th edition in 1788.

435 ^  See Vol. I, note 532.

436 ^  Richard Payne Knight (1750-1824) was a collector of bronzes, gems, and coins, many of his pieces being now in the British Museum. He sat in parliament for twenty-six years (1780-1806), but took no active part in legislation. He opposed the acquisition of the Elgin Marbles, holding them to be of little importance. His Analytical Inquiry into the Principles of Taste appeared in 1808.

437 ^  Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a time professor at the University of Parma. His Observationes in M. Tullium Ciceronem appeared at Pratalboino in 1535. It was revised by his nephew under the title Thesaurus Ciceronianus (Venice, 1570).

438 ^  See Vol. I, note 681.

439 ^ 

To measure the circle, and does not succeed,
Thinking what principle he needs."

440 ^  Francis Quarles (1592-1644), a religious poet. He wrote paraphrases of the Bible and numerous elegies. In the early days of the revolutionary struggle he sided with the Royalists. One of his most popular works was the Emblems (1635), with illustrations by William Marshall.

441 ^  Regnault de Bécourt wrote La Création du monde, ou Système d'organisation primitive suivi de l'interprétation des principaux phénomènes et accidents que se sont opérés dans la nature depuis l'origine de univers jusqu'à nos jours (1816). This may be the work translated by Dalmas.

442 ^  "Because it lacks a holy prophet."

443 ^  Angherà. See Vol. II, note 127.

444 ^  Edmund Curll (1675-1747), a well-known bookseller, publisher, and pamphleteer. He was for a time at "The Peacock without Temple Bar," and later at "The Dial and Bible against St. Dunstan's Church." He was fined repeatedly for publishing immoral works, and once stood in the pillory for it. He is ridiculed in the Dunciad for having been tossed in a blanket by the boys of Westminster School because of an oration that displeased them.

445 ^  See Vol. II, note 206.

446 ^  Encyclopædia.

447 ^  Author of the Historia Naturalis (77 A.D.)

448 ^  Author of the De Institutione Oratorio Libri XII (c. 91 A.D.)

449 ^  His De Architectures Libri X was not merely a work on architecture and building, but on the education of the architect.

450 ^  Cyclophoria.

451 ^  William Caxton (c. 1422-c.1492), sometime Governor of the Company of Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art of printing either at Bruges or Cologne, and between 1471 and 1477 set up a press at Westminster. Tradition says that the first book printed in England was his Game and Playe of Chesse (1474). The Myrrour of the Worlde and th'ymage of the same appeared in 1480. It contains a brief statement on arithmetic, the first mathematics to appear in print in England.

452 ^  See Vol. I, note 40. De Morgan is wrong as to the date of the Margarita Philosophica. The first edition appeared at Freiburg in 1503.

453 ^  Reisch was confessor to Maximilian I (1459-1519), King of the Romans (1486) and Emperor (1493-1519).

454 ^  Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy and mathematics in various cities of France and Germany. His Institutionum astronomicarum libri III appeared at Basel in 1528, his Cosmographia at Paris in 1529, and his Opera at Leyden in 1531.

455 ^  Johannes Heinrich Alsted (1588-1638) was professor of philosophy and theology at his birthplace, Herborn, in Nassau, and later at Weissenberg. He published several works, including the Elementale mathematicum (1611), Systema physicae harmonicae (1612), Methodus admirandorum mathematicorum (1613), Encyclopædia septem tomis distincta (1630), and the work mentioned above.

456 ^  Johann Jakob Hoffmann (1635-1706), professor of Greek and history at his birthplace, Basel. He also wrote the Epitome metrica historiæ universalis civilis et sacræ ab orbe condito (1686).

457 ^  Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but kind-hearted freethinker. His Cyclopædia, or an Universal Dictionary was translated into French and is said to have suggested the great Encyclopédie.

458 ^  Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, par un société de gens de lettres. Mis en ordre et publié par M. Diderot, et quant à la partie mathématique, par M. d'Alembert. Paris, 1751-1780, 35 volumes.

459 ^  "From the egg" (state).

460 ^  See Vol. I, note 785.

461 ^  See Vol. II, note 15.

462 ^  "In morals nothing should serve man as a model but God; in the arts, nothing but nature."

463 ^  Encyclopédie Méthodique, ou par ordre de matières. Paris, 1782-1832, 166½ volumes.

464 ^  See Vol. II, note 336.

465 ^  Encyclopædia Metropolitana; or, Universal Dictionary of Knowledge. London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40 volumes.

466 ^  See Vol. I, note 286.

467 ^  See Vol. I, note 119.

468 ^  De Morgan should be alive to satirize some of the statements on the history of mathematics in the eleventh edition.

469 ^  John Pringle Nichol (1804-1859), Regius professor of astronomy at Glasgow and a popular lecturer on the subject. He lectured in the United States in 1848-1849. His Views of the Architecture of the Heavens (1838) was a very popular work, and his Planetary System (1848, 1850) contains the first suggestion for the study of sun spots by the aid of photography.

470 ^  See Vol. II, note 206.

471 ^  George Long (1800-1879), a native of Poulton, in Lancashire, was called to the University of Virginia when he was only twenty-four years old as professor of ancient languages. He returned to England in 1828 to become professor of Greek at London University. From 1833 to 1849 he edited the twenty-nine volumes of the Penny Cyclopædia. He was an authority on Roman law.

472 ^  A legal phrase, "Qui tam pro domina regina, quam pro se ipso sequitur,"—"Who sues as much on the Queen's account as on his own."

473 ^  Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge (1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen years at the bar he published some two hundred mathematical papers. In 1863 he became professor of mathematics at Cambridge, and so remained until his death. His collected papers, nine hundred in number, were published by the Cambridge Press in 13 volumes (1889-1898). He contributed extensively to the theory of invariants and covariants. De Morgan's reference to his coining of new names is justified, although his contemporary, Professor Sylvester, so far surpassed him in this respect as to have been dubbed "the mathematical Adam."

474 ^  See Vol. II, note 56.

475 ^  See Vol. I, note 207.

476 ^  See Vol. I, note 135.

477 ^  Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With the collaboration of his brother and Nicolas Rigault he published the 1620 and 1626 editions of De Thou's History. He also wrote on law and history. His younger brother, Jacques (died in 1656), edited his works. The two had a valuable collection of books and manuscripts which they bequeathed to the Royal Library at Paris.

478 ^  See Vol. I, note 51.

479 ^  It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.

480 ^  See Vol. I, note 20.

481 ^  See Vol. I, note 188.

482 ^  Sir Edward Sherburne (1618-1702), a scholar of considerable reputation. The reference by De Morgan is to The Sphere of Marcus Manilius, in the appendix to which is a Catalogue of Astronomers, ancient and modern.

483 ^  George Parker, second Earl of Macclesfield (1697-1764). He erected an observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out with the best equipment then available. He was President of the Royal Society in 1752.

484 ^  See Vol. II, note 263.

485 ^  See Vol. I, note 296.

486 ^  See Vol. I, note 188.

487 ^  Edward Bernard (1638-1696), although Savilian professor of astronomy at Oxford, was chiefly interested in archeology.

488 ^  See Vol. I, note 190.

489 ^  See Vol. I, note 190.

490 ^  See Vol. I, note 281.

491 ^  Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well known for the letters written to his son which were published posthumously (1774).

492 ^  Peter Daval (died in 1763), Vice-President of the Royal Society, and an astronomer of some ability.

493 ^  See Vol. I, note 766.

494 ^  William Oughtred (c. 1573-1660), a fellow of King's College, Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known arithmetic and trigonometry of his time. His Arithmeticæ in Numero & Speciebus Institutio ... quasi Clavis Mathematicæ est (1631) went through many editions and appeared in English as The Key to the Mathematicks new forged and filed in 1647.

495 ^  See Vol. I, note 294.

496 ^  Stephen Jordan Rigaud (1816-1859) was senior assistant master of Westminster School (1846) and head master of Queen Elizabeth's School at Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow fever the following year.

497 ^  He also wrote a memoir of his father, privately printed at Oxford in 1883.

498 ^  See Vol. I, note 96.

499 ^  See Vol. I, note 188.

500 ^  William Gascoigne was born at Middleton before 1612 and was killed in the battle of Marston Moor in 1644. He was an astronomer and invented the micrometer with movable threads (before 1639).

501 ^  Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for refusing to sign the covenant. He became professor of astronomy at Oxford (1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor of the Garter (1671). He is best known for his solution of Kepler's problem to approximate a planet's orbit, which appeared in his Astronomia geometrica in 1656.

502 ^  See Vol. I, note 198.

503 ^  See Vol. I, note 172.

504 ^  See Vol. I, note 190.

505 ^  See Vol. I page 114, note 6 220.

506 ^  See Vol. I, note 118.

507 ^  See Vol. I, note 253.

508 ^  See Vol. I, note 186.

509 ^  Heinrich Oldenburgh (1626-1678) was consul in England for the City of Bremen, his birthplace, and afterwards became a private teacher in London. He became secretary of the Royal Society and contributed on physics and astronomy to the Philosophical Transactions.

510 ^  Thomas Brancker, or Branker (1636-1676) wrote the Doctrinæ sphæricæ adumbratio et usus globorum artificialium (1662) and translated the algebra of Rhonius with the help of Pell. The latter work appeared under the title of An Introduction to Algebra (1668), and is noteworthy as having brought before English mathematicians the symbol ÷ for division. The symbol never had any standing on the Continent for this purpose, but thereafter became so popular in England that it is still used in all the English-speaking world.

511 ^  See Vol. I, note 230.

512 ^  Pierre Bertius (1565-1629) was a native of Flanders and was educated at London and Leyden. He became a professor at Leyden, and later held the chair of mathematics at the Collège de France. He wrote chiefly on geography.

513 ^  See Vol. II, note 487.

514 ^  Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome at the Convent of St. Panteleon. He wrote several works on geometry, astronomy, and physics.

515 ^  See Vol. I, note 381.

516 ^  Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient languages and later of mathematics and physics at the Collège of Pau, and afterwards professor of rhetoric at the Collège Louis-le-Grand at Paris. He wrote on geometry, astronomy and physics.

517 ^  Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse, and died in 1665. Although connected with the parliament of Toulouse, his significant work was in mathematics. He was one of the world's geniuses in the theory of numbers, and was one of the founders of the theory of probabilities and of analytic geometry. After his death his son published his edition of Diophantus (1670) and his Varia opera mathematica (1679).

518 ^  This may be Christopher Townley (1603-1674) the antiquary, or his nephew, Richard, who improved the micrometer already invented by Gascoigne.

519 ^  Adrien Auzout a native of Rouen, who died at Rome in 1691. He invented a screw micrometer with movable threads (1666) and made many improvements in astronomical instruments.

520 ^  See Vol. I, note 86.

521 ^  See Vol. I, note 248.

522 ^  John Machin (d. 1751) was professor of astronomy at Gresham College (1713-1751) and secretary of the Royal Society. He translated Newton's Principia into English. His computation of π}} to 100 places is given in William Jones's Synopsis palmariorum matheseos (1706).

523 ^  Pierre Rémond de Montmort (1678-1719) was canon of Notre Dame until his marriage. He was a gentleman of leisure and devoted himself to the study of mathematics, especially of probabilities.

524 ^  Roger Cotes (1682-1716), first Plumian professor of astronomy and physics at Cambridge, and editor of the second edition of Newton's Principia. His posthumous Harmonia Mensurarum (1722) contains "Cotes's Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had lived we had known something."

525 ^  See Vol. I, note 281.

526 ^  See Vol. I, note 769.

527 ^  Charles Réné Reyneau (1656-1728) was professor of mathematics at Angers. His Analyse démontrée, ou Manière de resoudre les problèmes de mathématiques (1708) was a successful attempt to popularize the theories of men like Descartes, Newton, Leibnitz, and the Bernoullis.

528 ^  Brook Taylor (1685-1731), secretary of the Royal Society, and student of mathematics and physics. His Methodus incrementorum directa et inversa (1715) was the first treatise on the calculus of finite differences. It contained the well-known theorem that bears his name.

529 ^  Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut (1735) to measure an arc of a meridian in Lapland. He was head of the physics department in the Berlin Academy from 1745 until 1753. He wrote Sur la figure de la terre (1738) and on geography and astronomy.

530 ^  Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and was one of those sent by the Academy of Sciences to measure an arc of a meridian in Peru (1735). The object of this and the work of Maupertuis was to determine the shape of the earth and see if Newton's theory was supported.

531 ^  Charles Marie de la Condamine (1701-1774) was a member of the Paris Academy of Sciences and was sent with Bouguer to Peru, for the purpose mentioned in the preceding note. He wrote on the figure of the earth, but was not a scientist of high rank.

532 ^  See Vol. I, note 283.

533 ^  See Vol. II, note 483.

534 ^  Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in his Geometrical Key, or Gate of Equations unlocked (1684).

535 ^  See Vol. I, note 350.

536 ^  See Vol. I, note 133.

537 ^  See Vol. I, note 272.

538 ^  See Vol. I, page 118, second note 1 231.

539 ^  The name of Newton is so well known that no note seems necessary. He was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in 1727.

540 ^  John Keill (1671-1721), professor of astronomy at Oxford from 1710, is said to have been the first to teach the Newtonian physics by direct experiment, the apparatus being invented by him for the purpose. He wrote on astronomy and physics. His Epistola de legibus virium centripetarum, in the Philosophical Transactions for 1708, accused Leibnitz of having obtained his ideas of the calculus from Newton, thus starting the priority controversy.

541 ^  Thomas Digges (d. in 1595) wrote An Arithmeticall Militare Treatise, named Stratioticos (1579), and completed A geometrical practise, named Pantometria (1571) that had been begun by his father, Leonard Digges.

542 ^  John Dee (1527-1608), the most famous astrologer of his day, and something of a mathematician, wrote a preface to Billingsley's translation of Euclid into English (1570).

543 ^  See Vol. I, note 112.

544 ^  Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter Raleigh, who sent him to survey Virginia (1585). He was one of the best English algebraists of his time, but his Artis Analyticæ Praxis ad Aequationes Algebraicas resolvendas (1631) did not appear until ten years after his death.

545 ^  Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life chiefly to the study of chronology, writing upon the subject and taking issue with Scaliger (1601).

546 ^  See Vol. I, note 96.

547 ^  Walter Warner edited Harriot's Artis Analyticae Praxis (1631). Tarporley is not known in mathematics.

548 ^  See Vol. I, note 186.

549 ^  See Vol. I, note 224.

550 ^  See Vol. II, note 509.

551 ^  See Vol. I, note 190.

552 ^  Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some years he was assistant to John Pell, then ambassador to Switzerland. He wrote on arithmetical instruments invented by him (1673), on hydrostatics (1697) and on church history (1658).

553 ^  See Vol. I, note 337.

554 ^  See Vol. I, note 129.

555 ^  See Vol. I, note 33.

556 ^  See Vol. I, note 32.

557 ^  See Vol. I, note 786. The history of the subject may be followed in Braunmühl's Geschichte der Trigonometrie.

558 ^  See Vol. I, note 768.

559 ^  See Vol. I, note 192.

560 ^  Michael Dary wrote Dary's Miscellanies (1669), Gauging epitomised (1669), and The general Doctrine of Equation (1664).

561 ^  John Newton (1622-1678), canon of Hereford (1673), educational reformer, and writer on elementary mathematics and astronomy.

562 ^  See Vol. I, note 133.

563 ^  "The average of the two equal altitudes of the sun before and after dinner."

564 ^  See Vol. I, note 24.

565 ^  London, 1678. It went though many editions.

566 ^  "This I who once ..."

567 ^  Arthur Murphy (1727-1805) worked in a banking house until 1754. He then went on the stage and met with some success at Covent Garden. His first comedy, The Apprentice (1756) was so successful that he left the stage and took to play writing. His translation of Tacitus appeared in 1793, in four volumes.

568 ^  Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess Henrietta Maria and remained there several years. He wrote L'usage de la règle de proportion (Paris, 1624, with an English translation in 1626), Arithmétique Logarithmétique (Paris, 1626, with an English translation in 1635), and Of Natural and Artificial Arithmetick (London, 1630, revised in 1650-1652), part I of which was one of the most popular textbooks ever produced in England.

569 ^  John Lambert (1619-1694) was Major-General during the Revolution and helped to draw up the request for Cromwell to assume the protectorate. He was imprisoned in the Tower by the Rump Parliament. He was confined in Guernsey until the clandestine marriage of his daughter Mary to Charles Hatton, son of the governor, after which he was removed (1667) to St. Nicholas in Plymouth Sound.

570 ^  Samuel Foster (d. in 1652) was made professor of astronomy at Gresham College in March, 1636, but resigned in November of that year, being succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and Foster succeeded him. He wrote on dialling and made a number of improvements in geometric instruments.

571 ^  "Twice of the word a minister," that is, twice a minister of the Gospel.

572 ^  This is The Lives of the Professors of Gresham College to which is prefixed the Life of the Founder, Sir Thomas Gresham, London, 1740. It was written by John Ward (c. 1679-1758), professor of rhetoric (1720) at Gresham College and vice-president (1752) of the Royal Society.

573 ^  Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the Treasury in 1692, and was created Baron Halifax in 1700 and Viscount Sunbury and Earl of Halifax in 1714. He introduced the bill establishing the Bank of England, the bill becoming a law in 1694. He had troubles of his own, without considering Newton, for he was impeached in 1701, and was the subject of a damaging resolution of censure as auditor of the exchequer in 1703. Although nothing came of either of these attacks, he was out of office during much of Queen Anne's reign.

574 ^  See Vol. II, note 547.

575 ^  See Vol. I, note 186.

576 ^  James Dodson (d. 1757) was master of the Royal Mathematical School, Christ's Hospital. He was De Morgan's great-grandfather. The Anti-Logarithmic Canon was published in 1742.

577 ^  See Vol. I, note 188.

578 ^  See Vol. I, note 198.

579 ^  Richard Busby, (1606-1695), master of Westminster School (1640) had among his pupils Dryden and Locke.

580 ^  See Vol. I, note 190.

581 ^  Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge (1620-1646), and Prebend of Westminster (1661), was a well-known theological writer of the time.

582 ^  See Vol. I, note 294.

583 ^  See Vol. I, note 192.

584 ^  "Labor performed returns in a circle."

585 ^  See Vol. II, page 208.

586 ^  "Whatever objections one may make to the above arguments, one always falls into an absurdity."

587 ^  See Vol. II. page 11, note 29. The Circle Squared; and the solution of the problem adapted to explain the difference between square and superficial measurement appeared at Brighton in 1865.

588 ^  "And beyond that nothing."

589 ^  Gillott (1759-1873) was the pioneer maker of steel pens by machinery, reducing the price from 1s. each to 4d. a gross. He was a great collector of paintings and old violins.

590 ^  William Edward Walker wrote five works on circle squaring (1853, 1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.

591 ^  Solomon M. Drach wrote An easy Rule for formulizing all Epicyclical Curves (London, 1849), On the Circle area and Heptagon-chord (London, 1864), An easy general Rule for filling up all Magic Squares (London, 1873), and Hebrew Almanack-Signs (London, 1877), besides numerous articles in journals.

592 ^  See Vol. I, note 371.

593 ^  See Vol. I, note 580.

594 ^  See Vol. I, note 163.

595 ^  Robert Fludd or Flud (1574-1637) was a physician with a large London practice. He denied the diurnal rotation of the earth, and was attacked by Kepler and Mersenne, and accused of magic by Gassendi. His Apologia Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis aspersam, veritatis quasi Fluctibus abluens (Leyden, 1616) is one of a large number of works of the mystic type.

596 ^  Consult To the Christianity of the Age. Notes ... comprising an elucidation of the scope and contents of the writings ... of Dionysius Andreas Freher (1854).

597 ^  Sir William Robert Grove (1811-1896), although called to the bar (1835) and to the bench (1853), is best known for his work as a physicist. He was professor of experimental philosophy (1840-1847) at the London Institution, and invented a battery (1839) known by his name. His Correlation of Physical Forces (1846) went through six editions and was translated into French.

598 ^  Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a mystic, closely in touch with the Gottesfreunde of Basel. His Sermons first appeared in print at Leipsic in 1498.

599 ^  Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von Hohenheim, and he took the name by which he is generally known because he held himself superior to Celsus. He was a famous physician and pharmacist, but was also a mystic and neo-Platonist. He lectured in German on medicine at Basel, but lost his position through the opposition of the orthodox physicians and apothecaries.

600 ^  See Vol. I, note 588.

601 ^  Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg. He helped Luther with his translation of the Bible.

602 ^  Johann Reuchlin (1455-1522), the first great German humanist, was very influential in establishing the study of Greek and Hebrew in Germany. His lectures were mostly delivered privately in Heidelberg and Stuttgart. Unlike Melanchthon, he remained in the Catholic Church.

603 ^  Joseph Chitty (1776-1841) published his Precedents of Pleading in 1808 and his Reports of Cases on Practice and Pleading in 1820-23 (2 volumes).

604 ^  See Vol. I, note 35.

605 ^  See Vol. I, note 38.

606 ^  Jean Pèlerin, also known as Viator, who wrote on perspective. His work appeared in 1505, with editions in 1509 and 1521.

607 ^  Henry Stephens. See Vol. I, note 37.

608 ^  The well-known grammarian (1745-1826). He was born at Swatara, in Pennsylvania, and practised law in New York until 1784, after which he resided in England. His grammar (1795) went through 50 editions, and the abridgment (1818) through 120 editions. Murray's friend Dalton, the chemist, said that "of all the contrivances invented by human ingenuity for puzzling the brains of the young, Lindley Murray's grammar was the worst."

609 ^  Robert Recorde (c. 1510-1558) read and probably taught mathematics and medicine at Cambridge up to 1545. After that he taught mathematics at Oxford and practised medicine in London. His Grounde of Artes, published about 1540, was the first arithmetic published in English that had any influence. It went through many editions. The Castle of Knowledge appeared in 1551. It was a textbook on astronomy and the first to set forth the Copernican theory in England. Like Recorde's other works it was written on the catechism plan. His Whetstone of Witte ... containying thextraction of Rootes: The Cosike practise, with the rule of Equation: and the woorkes of Surde Nombres appeared in 1557, and it is in this work that the modern sign of equality first appears in print. The word "Cosike" is an adjective that was used for a long time in Germany as equivalent to algebraic, being derived from the Italian cosa, which stood for the unknown quantity.

610 ^  Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of State under Elizabeth (1596-1603) and under James I (1603-1612).

611 ^  In America the German pronunciation is at present universal among mathematicians, as in the case of most other German names. This is due, no doubt, to the great influence that Germany has had on American education in the last fifty years.

612 ^  The latest transliteration is substantially K'ung-fu-tzǔ.

613 ^  The tendency seems to be, however, to adopt the forms used of individuals or places as rapidly as the mass of people comes to be prepared for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very common in America.

614 ^  Sir Edward Coke (1552-1634), the celebrated jurist.

615 ^  Dethlef Cluvier or Clüver (d. 1708 at Hamburg) was a nephew, not a grandson, of Philippe Cluvier, or Philipp Clüver (1580-c. 1623). Dethlef traveled in France and Italy and then taught mathematics in London. He wrote on astronomy and philosophy and also published in the Acta Eruditorum (1686) his Schediasma geometricum de nova infinitorum scientia. Quadratura circuli infinitis modis demonstrata, and his Monitum ad geometras (1687). Philippe was geographer of the Academy of Leyden. His Introductionis in universam geographiam tam veterem quam novam libri sex appeared at Leyden in 1624, about the time of his death.

616 ^  See Vol. I, note 248.

617 ^  Bernard Nieuwentijt (1654-1718), a physician and burgomaster at Purmerend. His Considerationes circa Analyseos ad quantitates infinite parvas applicatæ Principia et Calculi Differentialis usum (Amsterdam, 1694) was attacked by Leibnitz. He replied in his Considerationes secundæ (1694), and also wrote the Analysis Infinitorum, seu Curvilineorum Proprietates ex Polygonorum Natura deductæ (1695). His most famous work was on the existence of God, Het Regt Gebruik der Werelt Beschouwingen (1718).

618 ^  "From a given line to construct" etc.

619 ^  "Pirates do not fight one another."

620 ^  Claude Mallemens (Mallement) de Messanges (1653-1723) was professor of philosophy at the Collège du Plessis, in Paris, for 34 years. The work to which De Morgan refers is probably the Fameux Problème de la quadrature du cercle, résolu géometriquement par le cercle et a ligne droite that appeared in 1683.