Chapter 5

"Crede ratem ventis corpus ne crede chimistis;Est quævis chimica tutior aura fide."[263]

"Crede ratem ventis corpus ne crede chimistis;

Est quævis chimica tutior aura fide."[263]

Among the smaller paradoxes of the day is that of theTimesnewspaper, which always spells itchymistry: but so, I believe, do Johnson, Walker, and others. The Arabic work is very likely formed from the Greek: but it may be connected either withχημειαor withχυμεια.

Lettre d'un gentil-homme de province à une dame de qualité, sur le sujet de la Comète. Paris, 1681, 4to.

An opponent of astrology, whom I strongly suspect to have been one of the members of the Academy of Sciences under the name of a country gentleman,[264]writes very good sense on the tremors excited by comets.

The Petitioning-Comet: or a brief Chronology of all the famous Comets and their events, that have happened from the birth of Christ to this very day. Together with a modest enquiry into this present comet, London, 1681, 4to.

A satirical tract against the cometic prophecy:

"This present comet (it's true) is of a menacing aspect, but if thenew parliament(for whose convention so many good men pray) continue long to sit, I fear not but the star will lose its virulence and malignancy, or at least its portent be averted from this our nation; which being the humble request to God of all good men, makes me thus entitle it, a Petitioning-Comet."

The following anecdote is new to me:

"Queen Elizabeth (1558) being then at Richmond, and being disswaded from looking on a comet which did then appear, made answer,jacta est alea, the dice are thrown; thereby intimating that the pre-order'd providence of God was above the influence of any star or comet."

The argument was worth nothing: for the comet might have beenon the dicewith the event; the astrologers said no more, at least the more rational ones, who were about half of the whole.

An astrological and theological discourse upon this present great conjunction (the like whereof hath not (likely) been in some ages) ushered in by a great comet. London, 1682, 4to. By C. N.[265]

The author foretells the approaching "sabbatical jubilee," but will not fix the date: he recounts the failures of his predecessors.

A judgment of the comet which became first generally visible to us in Dublin, December 13, about 15 minutes before 5 in the evening,A.D.1680. By a person of quality. Dublin, 1682, 4to.

The author argues against cometic astrology with great ability.

A prophecy on the conjunction of Saturn and Jupiter in this present year 1682. With some prophetical predictions of what is likely to ensue therefrom in the year 1684. By John Case, Student in physic and astrology.[266]London, 1682, 4to.

According to this writer, great conjunctions of Jupiter and Saturn occur "in the fiery trigon," about once in 800 years. Of these there are to be seven: six happened in the several times of Enoch, Noah, Moses, Solomon, Christ, Charlemagne. The seventh, which is to happen at "the lamb's marriage with the bride," seems to be that of 1682; but this is only vaguely hinted.

De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to.Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis. Amsterdam, 1699, 4to.Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam, 1702, 4to.De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.

De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to.

Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis. Amsterdam, 1699, 4to.

Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam, 1702, 4to.

De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.

Who shall contradict Jacob Marcelis?[267]He says the circumference contains the diameter exactly times

10084490873775416798942821848943 ————————————————6997183637540819440035239271702

1008449087377541679894282184894

3 ————————————————

6997183637540819440035239271702

But he does not come very near, as the young arithmetician will find.

MATHEMATICAL THEOLOGY.

Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.[268]London, 1699, 4to.

This is a celebrated speculation, and has been reprinted abroad, and seriously answered. Craig is known in the early history of fluxions, and was a good mathematician.He professed to calculate, on the hypothesis that the suspicions against historical evidence increase with the square of the time, how long it will take the evidence of Christianity to die out. He finds, by formulæ, that had it been oral only, it would have gone out A.D. 800; but, by aid of the written evidence, it will last till A.D. 3150. At this period he places the second coming, which is deferred until the extinction of evidence, on the authority of the question "When the Son of Man cometh, shall he find faith on the earth?" It is a pity that Craig's theory was not adopted: it would have spared a hundred treatises on the end of the world, founded on no better knowledge than his, and many of them falsified by the event. The most recent (October, 1863) is a tract in proof of Louis Napoleon being Antichrist, the Beast, the eighth Head, etc.; and the present dispensation is to close soon after 1864.

In order rightly to judge Craig, who added speculations on the variations of pleasure and pain treated as functions of time, it is necessary to remember that in Newton's day the idea of force, as a quantity to be measured, and as following a law of variation, was very new: so likewise was that of probability, or belief, as an object of measurement.[269]The success of thePrincipiaof Newton put it into many heads to speculate about applying notions of quantity to other things not then brought under measurement. Craig imitated Newton's title, and evidently thought he was making a step in advance: but it is not every one who can plough with Samson's heifer.

It is likely enough that Craig took a hint, directly or indirectly, from Mohammedan writers, who make a reply to the argument that the Koran has not the evidence derivedfrom miracles. They say that, as evidence of Christian miracles is daily becoming weaker, a time must at last arrive when it will fail of affording assurance that they were miracles at all: whence would arise the necessity of another prophet and other miracles. Lee,[270]the Cambridge Orientalist, from whom the above words are taken, almost certainly never heard of Craig or his theory.

THE ARISTOCRAT AS A SCIENTIST.

Copernicans of all sorts convicted ... to which is added a Treatise of the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.

Not all the blood of all the Howards will gain respect for a writer who maintains that eclipses admit no possible explanation under the Copernican hypothesis, and who asks how a man can "go 200 yards to any place if the moving superficies of the earth does carry it from him?" Horace Walpole, at the beginning of hisRoyal and Noble Authors, has mottoed his book with the Cardinal's address to Ariosto, "Dove diavolo, Messer Ludovico, avete pigliato tante coglionerie?"[271]Walter Scott says you could hardly pick out, on any principle of selection—except badness itself, he means of course—the same number of plebeian authors whose works are so bad. But his implied satire on aristocratic writing forgets two points. First, during a large period of our history, when persons of rank condescended to write, they veiled themselves under "a person of honor," "a person of quality," and the like, when not wholly undescribed. Not one of these has Walpole got; he omits,for instance, Lord Brounker's[272]translation of Descartes on Music. Secondly, Walpole only takes the heads of houses: this cuts both ways; he equally eliminates the Hon. Robert Boyle and the precious Edward Howard. The last writer is hardly out of the time in which aristocracy suppressed its names; the avowal was then usually meant to make the author's greatness useful to the book. In our day, literary peers and honorables are very favorably known, and contain an eminent class.[273]They rough it like others, and if such a specimen as Edw. Howard were now to appear, he would be greeted with

"Hereditary noodle! knowest thou notWho would be wise, himself must make him so?"

"Hereditary noodle! knowest thou not

Who would be wise, himself must make him so?"

THE LONGITUDE PROBLEM.

A new and easy method to find the longitude at land or sea. London, 1710, 4to.

This tract is a little earlier than the great epoch of such publications (1714), and professes to find the longitude by the observed altitudes of the moon and two stars.[274]

A new method for discovering the longitude both at sea and land, humbly proposed to the consideration of the public.[275]By Wm. Whiston[276]and Humphry Ditton.[277]London, 1714, 8vo.

This is the celebrated tract, written by the two Arian heretics. Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it the epigram—if, indeed, that be epigram of which the point is pious wish—which has been so often recited for the purity of its style, a purity which transcends modern printing. Perhaps some readers may think that Swift cared little for Whiston and Ditton, except as a chance hearing of their plan pointed them out as good marks. But it was not so: the clique had their eye on the guilty pair before the publication of the tract. The preface is dated July 7; and ten days afterwards Arbuthnot[278]writes as follows to Swift:

"Whiston has at last published his project of the longitude; the most ridiculous thing that ever was thought on. But a pox on him! he has spoiled one of my papers of Scriblerus, which was a proposition for the longitude not very unlike his, to this purpose; that since there was no pole for east and west, that all the princes of Europe should join and build two prodigious poles, upon high mountains,with a vast lighthouse to serve for a polestar. I was thinking of a calculation of the time, charges, and dimensions. Now you must understand his project is by lighthouses, and explosion of bombs at a certain hour."

The plan was certainly impracticable; but Whiston and Ditton might have retorted that they were nearer to the longitude than their satirist to the kingdom of heaven, or even to a bishopric. Arbuthnot, I think, here and elsewhere, reveals himself as the calculator who kept Swift right in his proportions in the matter of the Lilliputians, Brobdingnagians, etc. Swift was very ignorant about things connected with number. He writes to Stella that he has discovered that leap-year comes every four years, and that all his life he had thought it came every three years. Did he begin with the mistake of Cæsar's priests? Whether or no, when I find the person who did not understand leap-year inventing satellites of Mars in correct accordance with Kepler's third law, I feel sure he must have had help.

THE AURORA BOREALIS.

An essay concerning the late apparition in the heavens on the 6th of March. Proving by mathematical, logical, and moral arguments, that it cou'd not have been produced meerly by the ordinary course of nature, but must of necessity be a prodigy. Humbly offered to the consideration of the Royal Society. London, 1716, 8vo.

The prodigy, as described, was what we should call a very decided and unusual aurora borealis. The inference was, that men's sins were bringing on the end of the world. The author thinks that if one of the old "threatening prophets" were then alive, he would give "something like the following." I quote a few sentences of the notion which the author had of the way in which Ezekiel, for instance, would have addressed his Maker in the reign of George the First:

"Begin! Begin! O Sovereign, for once, with aneffectual clap of thunder.... O Deity! either thunder to us no more, or when you thunder, do it home, and strike with vengeance to the mark.... 'Tis not enough to raise a storm, unless you follow it with a blow, and the thunder without the bolt, signifies just nothing at all.... Are then your lightnings of so short a sight, that they don't know how to hit, unless a mountain stands like a barrier in their way? Or perhaps so many eyes open in the firmament make you lose your aim when you shoot the arrow? Is it this? No! but, my dear Lord, it is your custom never to take hold of your arms till you have first bound round your majestic countenance with gathered mists and clouds."

The principles of the Philosophy of the Expansive and Contractive Forces ... By Robert Greene,[279]M.A., Fellow of Clare Hall. Cambridge, 1727, folio.

Sanderson[280]writes to Jones,[281]"The gentleman has been reputed mad for these two years last past, but never gave the world such ample testimony of it before." This was said of a former work of Greene's, on solid geometry, published in 1712, in which he gives a quadrature.[282]He gives the same or another, I do not know which, in the present work, in which the circle is 3-1/5 diameters. This volume is of 981 good folio pages, and treats of all things, mental and material. The author is not at all mad, only wrong onmany points. It is the weakness of the orthodox follower of any received system to impute insanity to the solitary dissentient: which is voted (in due time) a very wrong opinion about Copernicus, Columbus, or Galileo, but quite right about Robert Greene. If misconceptions, acted on by too much self-opinion, be sufficient evidence of madness, it would be a curious inquiry what is the least per-centage of the reigning school which has been insane at any one time. Greene is one of the sources for Newton being led to think of gravitation by the fall of an apple: his authority is the gossip of Martin Folkes.[283]Probably Folkes had it from Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges ashis authority.[284]It is in the draft found among Conduitt's papers of memoranda to be sent to Fontenelle. But Fontenelle, though a great retailer of anecdote, does not mention it in hisélogeof Newton; whence it may be suspected that it was left out in the copy forwarded to France. D'Israeli has got an improvement on the story: the apple "struck him a smart blow on the head": no doubt taking him just on the organ of causality. He was "surprised at the force of the stroke" from so small an apple: but then the apple had a mission; Homer would have saidit was Minerva in the form of an apple. "This led him to consider the accelerating motion of falling bodies," which Galileo had settled long before: "from whence he deduced the principle of gravity," which many had considered before him, but no one haddeduced anything from it. I cannot imagine whence D'Israeli got the rap on the head, I mean got it for Newton: this is very unlike his usual accounts of things. The story is pleasant and possible: its only defect is that various writings, well known to Newton, a verylearnedmathematician, had given more suggestion than a whole sack of apples could have done, if they had tumbled on that mighty head all at once. And Pemberton, speaking from Newton himself, says nothing more than that the idea of the moon being retained by the same force which causes the fall of bodies struck him for the first time while meditating in a garden. One particular tree at Woolsthorpe has been selected as the gallows of the appleshaped goddess: it died in 1820, and Mr. Turnor[285]kept the wood; but Sir D. Brewster[286]brought away a bit of root in 1814, and must have had it on his conscience for 43 years that he may have killed the tree. Kepler's suggestion of gravitation with the inverse distance, and Bouillaud's proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I discovered two anagrams on his name, which are quite conclusive; the notion of gravitation wasnot new; but Newtonwent on. Some wandering spirit, probably whose business it was to resent any liberty taken with Newton's name, put into the head of a friend of mineeighty-oneanagrams on my own pair, some of which hit harder than any apple.

DE MORGAN ANAGRAMS.

This friend, whom I must not name, has since made it up to about 800 anagrams on my name, of which I have seen about 650. Two of them I have joined in the title-page: the reader may find the sense. A few of the others are personal remarks.

"Great gun! do us a sum!"

is a sneer at my pursuits: but,

"Go! great sum! ∫a undu"

is more dignified.

"Sunt agro! gaudemus,"[287]

is happy as applied to one of whom it may be said:

"Ne'er out of town; 'tis such a horrid life;But duly sends his family and wife."

"Ne'er out of town; 'tis such a horrid life;

But duly sends his family and wife."

"Adsum, nugator, suge!"[288]

is addressed to a student who continues talking after the lecture has commenced: oh! the rascal!

"Graduatus sum! nego"[289]

applies to one who declined to subscribe for an M.A. degree.

"Usage mounts guard"

symbolizes a person of very fixed habits.

"Gus! Gus! a mature don!August man! sure, god!And Gus must argue, O!Snug as mud to argue,Must argue on gauds.A mad rogue stung us.Gag a numerous studGo! turn us! damage us!Tug us! O drag us! Amen.Grudge us! moan at us!Daunt us! gag us more!Dog-ear us, man! gut us!D—— us! a rogue tugs!"

"Gus! Gus! a mature don!

August man! sure, god!

And Gus must argue, O!

Snug as mud to argue,

Must argue on gauds.

A mad rogue stung us.

Gag a numerous stud

Go! turn us! damage us!

Tug us! O drag us! Amen.

Grudge us! moan at us!

Daunt us! gag us more!

Dog-ear us, man! gut us!

D—— us! a rogue tugs!"

are addressed to me by the circle-squarers; and,

"O! Gus! tug a mean surd!"

is smart upon my preference of an incommensurable value ofπto 3-1/5, or some such simple substitute. While,

"Gus! Gus! at 'em a' round!"

ought to be the backing of the scientific world to the author of theBudget of Paradoxes.

The whole collection commenced existence in the head of a powerful mathematician during some sleepless nights. Seeing how large a number was practicable, he amused himself by inventing a digested plan of finding more.

Is there any one whose name cannot be twisted into either praise or satire? I have had given to me,

"Thomas Babington MacaulayMouths big: a Cantab anomaly."

"Thomas Babington Macaulay

Mouths big: a Cantab anomaly."

NEWTON'S DE MUNDI SYSTEMATE LIBER.

A treatise of the system of the world. By Sir Isaac Newton. Translated into English. London, 1728, 8vo.

I think I have a right to one little paradox of my own: I greatly doubt that Newton wrote this book. Castiglione,[290]in hisNewtoni Opuscula,[291]gives it in the Latin which appeared in 1731,[292]not for the first time; he saysAngli omnes Newtono tribuunt.[293]It appeared just after Newton's death, without the name of any editor, or any allusion to Newton'srecent departure, purporting to be that popular treatise which Newton, at the beginning of the third book of thePrincipia, says he wrote, intending it to be the third book. It is very possible that some observant turnpenny might construct such a treatise as this from the third book, that it might be ready for publication the moment Newton could not disown it. It has been treated with singular silence: the name of the editor has never been given. Rigaud[294]mentions it without a word: I cannot find it in Brewster'sNewton, nor in theBiographia Britannica. There is no copy in the Catalogue of the Royal Society's Library, either in English or Latin, except in Castiglione. I am open to correction; but I think nothing from Newton's acknowledged works will prove—as laid down in the suspected work—that he took Numa's temple of Vesta, with a central fire, to be intended to symbolize the sun as the center of our system, in the Copernican sense.[295]

Mr. Edleston[296]gives an account of thelectures"de motu corporum," and gives the corresponding pages of theLatin"De Systemate Mundi" of 1731. But no one mentions theEnglishof 1728. This English seems to agree with the Latin; but there is a mystery about it. The preface says, "That this work as here published is genuine will so clearly appear by the intrinsic marks it bears, that it will be but losing words and the reader's time to take pains in giving him any other satisfaction." Surely fewer words would have been lost if the prefator had said at once that the work was from the manuscript preserved at Cambridge. Perhaps it was a mangled copy clandestinely taken and interpreted.

A BACONIAN CONTROVERSY.

Lord Bacon not the author of "The Christian Paradoxes," being a reprint of "Memorials of Godliness and Christianity," by Herbert Palmer, B.D.[297]With Introduction, Memoir, and Notes, by the Rev. Alexander B. Grosart,[298]Kenross. (Private circulation, 1864).

I insert the above in this place on account of a slight connection with the last. Bacon's Paradoxes,—so attributed—were first published as his in some asserted "Remains," 1648.[299]They were admitted into his works in 1730, and remain there to this day. The title is "The Character of a believing Christian, set forth in paradoxes and seeming contradictions." The following is a specimen:

"He believes three to be one and one to be three; a father not to be older than his son; a son to be equal with his father; and one proceeding from both to be equal with both: he believes three persons in one nature, and two natures in one person.... He believes the God of all grace to have been angry with one that never offended Him; and that God that hates sin to be reconciled to himself though sinning continually, and never making or being able to make Him any satisfaction. He believes a most just God to have punished a most just person, and to have justified himself, though a most ungodly sinner. He believes himself freely pardoned, and yet a sufficient satisfaction was made for him."

Who can doubt that if Bacon had written this it must have been wrong? Many writers, especially on theContinent, have taken him as sneering at (Athanasian) Christianity right and left. Many Englishmen have taken him to be quite in earnest, and to have produced a body of edifying doctrine. More than a century ago the Paradoxes were published as a penny tract; and, again, at the same price, in thePenny Sunday Reader, vol. vi, No. 148, a few passages were omitted, astoo strong. But all did not agree: in my copy of Peter Shaw's[300]edition (vol. ii, p. 283) the Paradoxes have been cut out by the binder, who has left the backs of the leaves. I never had the curiosity to see whether other copies of the edition have been served in the same way. The Religious Tract Society republished them recently inSelections from the Writings of Lord Bacon, (no date; bad plan; about 1863, I suppose). No omissions were made, so far as I find.

I never believed that Bacon wrote this paper; it has neither hissparklenor his idiom. I stated my doubts even before I heard that Mr. Spedding, one of Bacon's editors, was of the same mind. (Athenæum, July 16, 1864). I was little moved by the wide consent of orthodox men: for I knew how Bacon, Milton, Newton, Locke, etc., were always claimed as orthodox until almost the present day. Of this there is a remarkable instance.

LOCKE AND SOCINIANISM.

Among the books which in my younger day were in some orthodox publication lists—I think in the list of the Christian Knowledge Society, but I am not sure—was Locke's[301]"Reasonableness of Christianity." It seems to have come down from the eighteenth century, when the battle was belief in Christ against unbelief,simpliciter, as thelogicians say. Now, if ever there was a Socinian[302]book in the world, it is this work of Locke. "These two," says Locke, "faith and repentance, i.e., believing Jesus to be the Messiah, and a good life, are the indispensable conditions of the new covenant, to be performed by all those who would obtain eternal life." All the book is amplification of this doctrine. Locke, in this and many other things, followed Hobbes, whose doctrine, in the Leviathan, isfidem, quanta ad salutem necessaria est, contineri in hoc articulo, Jesus est Christus.[303]For this Hobbes was called an atheist, whichmany still believe him to have been: some of his contemporaries called him, rightly, a Socinian. Locke was known for a Socinian as soon as his work appeared: Dr. John Edwards,[304]his assailant, says he is "Socinianized all over." Locke, in his reply, says "there is not one word of Socinianism in it:" and he was right: the positive Socinian doctrine hasnot one word of Socinianism in it; Socinianism consists in omissions. Locke and Hobbes did not daredenythe Trinity: for such a thing Hobbes might have been roasted, and Locke might have been strangled. Accordingly, the well-known way of teaching Unitarian doctrine was the collection of the asserted essentials of Christianity, without naming the Trinity, etc. This is the plan Newton followed, in the papers which have at last been published.[305]

So I, for one, thought little about the general tendency of orthodox writers to claim Bacon by means of the Paradoxes. I knew that, in his "Confession of Faith"[306]he is a Trinitarian of a heterodox stamp. His second Person takes human nature before he took flesh, not for redemption, but as a condition precedent of creation. "God is so holy, pure, and jealous, that it is impossible for him to be pleased in any creature, though the work of his own hands.... [Gen. i. 10, 12, 18, 21, 25, 31, freely rendered]. But—purposing to become a Creator, and to communicate to his creatures, he ordained in his eternal counsel that one person of the Godhead should be united to one nature, and to one particular of his creatures; that so, in the person of the Mediator, the true ladder might be fixed, whereby God mightdescend to his creatures and his creatures might ascend to God...."

This is republished by the Religious Tract Society, and seems to suit their theology, for they confess to having omitted some things of which they disapprove.

In 1864, Mr. Grosart published his discovery that the Paradoxes are by Herbert Palmer; that they were first published surreptitiously, and immediately afterwards by himself, both in 1645; that the "Remains" of Bacon did not appear until 1648; that from 1645 to 1708, thirteen editions of the "Memorials" were published, all containing the Paradoxes. In spite of this, the Paradoxes were introduced into Bacon's works in 1730, where they have remained.

Herbert Palmer was of good descent, and educated as a Puritan. He was an accomplished man, one of the few of his day who could speak French as well as English. He went into the Church, and was beneficed by Laud,[307]in spite of his puritanism; he sat in the Assembly of Divines, and was finally President of Queens' College, Cambridge, in which post he died, August 13, 1647, in the 46th year of his age.

Mr. Grosart says, speaking of Bacon's "Remains," "All who have had occasion to examine our early literature are aware that it was a common trick to issue imperfect, false, and unauthorized writings under any recently deceased name that might be expected to take. The Puritans, down to John Bunyan, were perpetually expostulating and protesting against such procedure." I have met with instances of all this; but I did not know that there was so much of it: a good collection would be very useful. The work of 1728, attributed to Newton, is likely enough to be one of the class.

Demonstration de l'immobilitez de la Terre.... Par M. de la Jonchere,[308]Ingénieur Français. Londres, 1728, 8vo.

A synopsis which is of a line of argument belonging to the beginning of the preceding century.

TWO FORGOTTEN CIRCLE SQUARERS.

The Circle squared; together with the Ellipsis and several reflections on it. The finding two geometrical mean proportionals, or doubling the cube geometrically. By Richard Locke[309].... London, no date, probably about 1730, 8vo.

According to Mr. Locke, the circumference is three diameters, three-fourths the difference of the diameter and the side of the inscribed equilateral triangle, and three-fourths the difference between seven-eighths of the diameter and the side of the same triangle. This gives, he says, 3.18897. There is an addition to this tract, being an appendix to a book on the longitude.

The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire. London, 1732, 8vo.

Hereπ= 3.0625. No proof is offered.[310]

The longitude discovered by the Eclipses, Occultations, and Conjunctions of Jupiter's planets. By William Whiston. London, 1738.

This tract has, in some copies, the celebrated preface containing the account of Newton's appearance before the Parliamentary Committee on the longitude question, in 1714(Brewster, ii. 257-266). This "historical preface," is an insertion and is dated April 28, 1741, with four additional pages dated August 10, 1741. The short "preface" is by the publisher, John Whiston,[311]the author's son.

THE STEAMSHIP SUGGESTED.

A description and draught of a new-invented machine for carrying vessels or ships out of, or into any harbour, port, or river, against wind and tide, or in a calm. For which, His Majesty has granted letters patent, for the sole benefit of the author, for the space of fourteen years. By Jonathan Hulls.[312]London: printed for the author, 1737. Price sixpence (folding plate and pp. 48, beginning from title).

(I ought to have entered this tract in its place. It is so rare that its existence was once doubted. It is the earliest description of steam-power applied to navigation. The plate shows a barge, with smoking funnel, and paddles at the stem, towing a ship of war. The engine, as described, is Newcomen's.[313]

In 1855, John Sheepshanks,[314]so well known as a friend of Art and a public donor, reprinted this tract, in fac-simile, from his own copy; twenty-seven copies of the original 12mo size, and twelve on old paper, small 4to. I have an original copy, wanting the plate, and with "Price sixpence" carefully erased, to the honor of the book.[315]

It is not known whether Hulls actually constructed a boat.[316]In all probability his tract suggested to Symington, as Symington[317]did to Fulton.)

THE NEWTONIANS ATTACKED.

Le vrai système de physique générale de M. Isaac Newton exposé et analysé en parallèle avec celui de Descartes. By Louis Castel[318][Jesuit and F.R.S.] Paris, 1743, 4to.

This is an elaborate correction of Newton's followers, and of Newton himself, who it seems did not give his own views with perfect fidelity. Father Castel, for instance, assures us that Newton placed the sunat restin the center of the system. Newton left the sun to arrange that matter with the planets and the rest of the universe. In this volume of 500 pages there is right and wrong, both clever.

A dissertation on the Æther of Sir Isaac Newton. By Bryan Robinson,[319]M.D. Dublin, 1743, 8vo.[320]

A mathematical work professing to prove that the assumed ether causes gravitation.

MATHEMATICAL THEOLOGY.

Mathematical principles of theology, or the existence of God geometrically demonstrated. By Richard Jack, teacher of Mathematics. London, 1747, 8vo.[321]

Propositions arranged after the manner of Euclid, with beings represented by circles and squares. But these circles and squares are logical symbols, not geometrical ones. I brought this book forward to the Royal Commission on the British Museum as an instance of the absurdity of attempting aclassedcatalogue from thetitlesof books. The title of this book sends it either to theology or geometry: when, in fact, it is a logical vagary. Some of the houses which Jack built were destroyed by the fortune of war in 1745, at Edinburgh: who will say the rebels did no good whatever? I suspect that Jack copied the ideas of J.B. Morinus, "Quod Deus sit," Paris, 1636,[322]4to, containing an attempt of the same kind, but not stultified with diagrams.

TWO MODEL INDORSEMENTS.

Dissertation, découverte, et démonstrations de la quadrature mathématique du cercle. Par M. de Fauré, géomètre. [s. l., probably Geneva] 1747, 8vo.Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme Suisse. Hague, 1749,[323]4to.

Dissertation, découverte, et démonstrations de la quadrature mathématique du cercle. Par M. de Fauré, géomètre. [s. l., probably Geneva] 1747, 8vo.

Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme Suisse. Hague, 1749,[323]4to.

According to this octavo geometer and quarto gentleman, a diameter of 81 gives a circumference of 256. There is an amusing circumstance about the quarto which has been overlooked, if indeed the book has ever beenexamined. John Bernoulli (the one of the day)[324]and Koenig[325]have both given an attestation: my mathematical readers may stare as they please, such is the fact. But, on examination, there will be reason to think the two sly Swiss played their countryman the same trick as the medical man played Miss Pickle, in the novel of that name. The lady only wanted to get his authority against sousing her little nephew, and said, "Pray, doctor, is it not both dangerous and cruel to be the means of letting a poor tender infant perish by sousing it in water as cold as ice?"—"Downright murder, I affirm," said the doctor; and certified accordingly. De Fauré had built a tremendous scaffolding of equations, quite out of place, and feeling cock-sure that his solutions, if correct, would square the circle, applied to Bernoulli and Koenig—who after his tract of two years before, must have known what he was at—for their approbation of the solutions. And he got it, as follows, well guarded:

"Suivant les suppositions posées dans ce Mémoire, il est si évident quetdoit être = 34,y= 1, etz= 1, que cela n'a besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.[326]"à Basle le 7e Mai 1749.Jean Bernoulli.""Je souscris au jugement de Mr. Bernoulli, en conséquence de ces suppositions.[327]"à la Haye le 21 Juin 1749.S. Koenig."

"Suivant les suppositions posées dans ce Mémoire, il est si évident quetdoit être = 34,y= 1, etz= 1, que cela n'a besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.[326]

"à Basle le 7e Mai 1749.Jean Bernoulli."

"Je souscris au jugement de Mr. Bernoulli, en conséquence de ces suppositions.[327]

"à la Haye le 21 Juin 1749.S. Koenig."

On which de Fauré remarks with triumph—as I have no doubt it was intended he should do—"il conste clairement par ma présente Analyse et Démonstration, qu'ils y ont déjareconnu et approuvé parfaitement que la quadrature du cercle est mathématiquement démontrée."[328]It should seem that it is easier to square the circle than to get round a mathematician.

An attempt to demonstrate that all the Phenomena in Nature may be explained by two simple active principles, Attraction and Repulsion, wherein the attraction of Cohesion, Gravity and Magnetism are shown to be one the same. By Gowin Knight. London, 1748, 4to.

Dr. Knight[329]was Mr. Panizzi's[330]archetype, the first Principal Librarian of the British Museum. He was celebrated for his magnetical experiments. This work was long neglected; but is now recognized as of remarkable resemblance to modern speculations.

THOMAS WRIGHT OF DURHAM.

An original theory or Hypothesis of the Universe. By Thomas Wright[331]of Durham. London, 4to, 1750.

Wright is a speculator whose thoughts are now part of our current astronomy. He took that view—or most of it—of the milky way which afterwards suggested itself to William Herschel. I have given an account of him and his work in thePhilosophical Magazinefor April, 1848.

Wright was mathematical instrument maker to the King,and kept a shop in Fleet Street. Is the celebrated business of Troughton & Simms, also in Fleet Street, a lineal descendant of that of Wright? It is likely enough, more likely that that—as I find him reported to have affirmed—Prester John was the descendant of Solomon and the Queen of Sheba. Having settled it thus, it struck me that I might apply to Mr. Simms, and he informs me that it is as I thought, the line of descent being Wright, Cole, John Troughton, Edward Troughton,[332]Troughton & Simms.[333]

BISHOP HORNE ON NEWTON.

The theology and philosophy in Cicero'sSomnium Scipionisexplained. Or, a brief attempt to demonstrate, that the Newtonian system is perfectly agreeable to the notions of the wisest ancients: and that mathematical principles are the only sure ones. [By Bishop Horne,[334]at the age of nineteen.] London, 1751, 8vo.

This tract, which was not printed in the collected works, and is now excessively rare, is mentioned inNotes and Queries, 1st S., v, 490, 573; 2d S., ix, 15. The boyish satire on Newton is amusing. Speaking of old Benjamin Martin,[335]he goes on as follows:

"But the most elegant account of the matter [attraction] is by that hominiform animal, Mr. Benjamin Martin, who having attended Dr. Desaguliers'[336]fine, raree, gallanty shew for some years [Desaguliers was one of the first who gave public experimental lectures, before the saucy boy was born] in the capacity of a turnspit, has, it seems, taken it into his head to set up for a philosopher."

Thus is preserved the fact, unknown to his biographers, that Benj. Martin was an assistant to Desaguliers in his lectures. Hutton[337]says of him, that "he was well skilled in the whole circle of the mathematical and philosophical sciences, and wrote useful books on every one of them": this is quite true; and even at this day he is read by twenty where Horne is read by one; see the stalls,passim. All that I say of him, indeed my knowledge of the tract, is due to this contemptuous mention of a more durable man than himself. My assistant secretary at the Astronomical Society, the late Mr. Epps,[338]bought the copy at a stall because his eye was caught by the notice of "Old Ben Martin," of whom he was a great reader. Old Ben could not be a Fellow of the Royal Society, because he kept a shop: even though the shop sold nothing but philosophical instruments. Thomas Wright, similarly situated as to shop and goods, never was a Fellow. The Society of our day has greatly degenerated: those of the old time would be pleased, no doubt, that the glories of their dayshould be commemorated. In the early days of the Society, there was a similar difficulty about Graunt, the author of the celebrated work on mortality. But their royal patron, "who never said a foolish thing," sent them a sharp message, and charged them if they found any more such tradesmen, they should "elect them without more ado."

Horne's first pamphlet was published when he was but twenty-one years old. Two years afterwards, being then a Fellow of his college, and having seen more of the world, he seems to have felt that his manner was a little too pert. He endeavored, it is said, to suppress his first tract: and copies are certainly of extreme rarity. He published the following as his maturer view:

A fair, candid, and impartial state of the case between Sir Isaac Newton and Mr. Hutchinson.[339]In which is shown how far a system of physics is capable of mathematical demonstration; how far Sir Isaac's, as such a system, has that demonstration; and consequently, what regard Mr. Hutchinson's claim may deserve to have paid to it. By George Horne, M.A. Oxford, 1753, 8vo.

It must be remembered that the successors of Newton were very apt to declare that Newton had demonstrated attraction as aphysicalcause: he had taken reasonable pains to show that he did not pretend to this. If any one had said to Newton, I hold that every particle of matter is a responsible being of vast intellect, ordered by the Creator to move as it would do if every other particle attracted it, and gifted with power to make its way in true accordance with that law, as easily as a lady picks her way across the street; what have you to say against it?—Newton must have replied, Sir! if you really undertake to maintain this asdemonstrable, your soul had better borrow a little powerfrom the particles of which your body is made: if you merely ask me to refute it, I tell you that I neither can nor need do it; for whether attraction comes in this way or in any other,it comes, and that is all I have to do with it.

The reader should remember that the word attraction, as used by Newton and the best of his followers, only meant adrawing towards, without any implication as to the cause. Thus whether they said that matter attracts matter, or that young lady attracts young gentleman, they were using one word in one sense. Newton found that the law of the first is the inverse square of the distance: I am not aware that the law of the second has been discovered; if there be any chance, we shall see it at the year 1856 in this list.

In this point young Horne made a hit. He justly censures those who fixed upon Newton a more positive knowledge of what attraction is than he pretended to have. "He has owned over and over he did not know what he meant by it—it might be this, or it might be that, or it might be anything, or it might be nothing." With the exception of thenothingclause, this is true, though Newton might have answered Horne by "Thou hast said it."

(I thought everybody knew the meaning of "Thou hast said it": but I was mistaken. In three of the evangelistsΣὺ λέγειςis the answer to "Art thou a king?" The force of this answer, as always understood, is "That is your way of putting it." The Puritans, who lived in Bible phrases, so understood it: and Walter Scott, who caught all peculiarities of language with great effect, makes a marked instance, "Were you armed?—I was not—I went in my calling, as a preacher of God's word, to encourage them that drew the sword in His cause. In other words, to aid and abet the rebels, said the Duke.Thou hast spoken it, replied the prisoner.")

Again, Horne quotes Rowning[340]as follows:

"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon this same subject of attraction, about every particle of a fluid being intrenched in three spheres of attraction and repulsion, one within another, 'the innermost of which (he says) is a sphere of repulsion, which keeps them from approaching into contact; the next, a sphere of attraction, diffused around this of repulsion, by which the particles are disposed to run together into drops; and the outermost of all, a sphere of repulsion, whereby they repel each other, when removed out of the attraction.' So that between theurgings, andsolicitations, of one and t'other, a poor unhappy particle must ever be at his wit's end, not knowing which way to turn, or whom to obey first."

Rowning has here started the notion which Boscovich[341]afterwards developed.

I may add to what precedes that it cannot be settled that, as Granger[342]says, Desaguliers was the first who gave experimental lectures in London. William Whiston gave some, and Francis Hauksbee[343]made the experiments. The prospectus, as we should now call it, is extant, a quarto tract of plates and descriptions, without date. Whiston, in his life,gives 1714 as the first date of publication, and therefore, no doubt, of the lectures. Desaguliers removed to London soon after 1712, and commenced his lectures soon after that. It will be rather a nice point to settle which lectured first; probabilities seem to go in favor of Whiston.

FALLACIES IN A THEORY OF ANNUITIES.

An Essay to ascertain the value of leases, and annuities for years and lives. By W[eyman] L[ee]. London, 1737, 8vo.A valuation of Annuities and Leases certain, for a single life. By Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition, 1773.

An Essay to ascertain the value of leases, and annuities for years and lives. By W[eyman] L[ee]. London, 1737, 8vo.

A valuation of Annuities and Leases certain, for a single life. By Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition, 1773.

Every branch of exact science has its paradoxer. The world at large cannot tell with certainty who is right in such questions as squaring the circle, etc. Mr. Weyman Lee[344]was the assailant of what all who had studied called demonstration in the question of annuities. He can be exposed to the world: for his error arose out of his not being able to see that the whole is the sum of all its parts.

By an annuity, say of £100, now bought, is meant that the buyer is to have for his money £100 in a year, if he be then alive, £100 at the end of two years, if then alive, and so on. It is clear that he would buy a life annuity if he should buy the first £100 in one office, the second in another, and so on. All the difference between buying the whole from one office and buying all the separate contingent payments at different offices, is immaterial to calculation. Mr. Lee would have agreed with the rest of the world about the payments to be made to the several different offices, in consideration of their several contracts: but he differed from every one else about the sum to be paid tooneoffice. He contended that the way to value an annuity is to find out the term of years which the individual has an even chance of surviving, and to charge for the life annuity the value of an annuity certain for that term.

It is very common to say that Lee took the average life, or expectation, as it is wrongly called, for his term: and this I have done myself, taking the common story. Having exposed the absurdity of this second supposition, taking it for Lee's, in myFormal Logic,[345]I will now do the same with the first.

A mathematical truth is true in its extreme cases. Lee's principle is that an annuity on a life is the annuity made certain for the term within which it is an even chance the life drops. If, then, of a thousand persons, 500 be sure to die within a year, and the other 500 be immortal, Lee's price of an annuity to any one of these persons is the present value of one payment: for one year is the term which each one has an even chance of surviving and not surviving. But the true value is obviously half that of a perpetual annuity: so that at 5 percent Lee's rule would give less than the tenth of the true value. It must be said for the poor circle-squarers, that they never err so much as this.

Lee would have said, if alive, that I have put anextreme case: but anyuniversaltruth is true in its extreme cases. It is not fair to bring forward an extreme case against a person who is speaking as of usual occurrences: but it is quite fair when, as frequently happens, the proposer insists upon a perfectly general acceptance of his assertion. And yet many who go the whole hog protest against being tickled with the tail. Counsel in court are good instances: they are paradoxers by trade. June 13, 1849, at Hertford, there was an action about a ship, insured against atotalloss: some planks were saved, and the underwriters refused to pay. Mr. Z. (for deft.) "There can be no degrees of totality; and some timbers were saved."—L. C. B. "Then if the vessel were burned to the water's edge, and some rope saved in the boat, there would be no total loss."—Mr. Z. "This is putting a very extreme case."—L. C. B. "The argumentwould go that length." What wouldJudgeZ.—as he now is—say to the extreme case beginning somewhere between six planks and a bit of rope?

MONTUCLA'S WORK ON THE QUADRATURE.

Histoire des recherches sur la quadrature du cercle ... avec une addition concernant les problèmes de la duplication du cube et de la trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]

This isthehistory of the subject.[346]It was a little episode to the great history of mathematics by Montucla, of which the first edition appeared in 1758. There was much addition at the end of the fourth volume of the second edition; this is clearly by Montucla, though the bulk of the volume is put together, with help from Montucla's papers, by Lalande.[347]There is also a second edition of the history of the quadrature, Paris, 1831, 8vo, edited, I think, by Lacroix; of which it is the great fault that it makes hardly any use of the additional matter just mentioned.

Montucla is an admirable historian when he is writing from his own direct knowledge: it is a sad pity that he did not tell us when he was depending on others. We are not to trust a quarter of his book, and we must read many other books to know which quarter. The fault is common enough, but Montucla's good three-quarters is so good that the fault is greater in him than in most others: I mean the fault of not acknowledging; for an historian cannot read everything. But it must be said that mankind give little encouragement to candor on this point. Hallam, in hisHistory of Literature, states with his own usual instinct of honesty every case in which he depends upon others: Montucla does not. And what is the consequence?—Montucla is trusted, and believed in, and cried up in the bulk; while the smallest talker can lament that Hallam should be so unequal and apt to depend on others, without remembering to mention that Hallam himself gives the information. As to a universal history of any great subject being written entirely upon primary knowledge, it is a thing of which the possibility is not yet proved by an example. Delambre attempted it with astronomy, and was removed by death before it was finished,[348]to say nothing of the gaps he left.

Montucla was nothing of a bibliographer, and his descriptions of books in the first edition were insufficient. The Abbé Rive[349]fell foul of him, and as the phrase is, gave it him. Montucla took it with great good humor, tried to mend, and, in his second edition, wished his critic had lived to see thevernis de bibliographewhich he had given himself.

I have seen Montucla set down as anesprit fort, more than once: wrongly, I think. When he mentions Barrow's[350]address to the Almighty, he adds, "On voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il croyait en l'immortalité de l'âme, et en une Divinité autre que la natureuniverselle."[351]This is irony, not an expression of opinion. In the book of mathematical recreations which Montucla constructed upon that of Ozanam,[352]and Ozanam upon that of Van Etten,[353]now best known in England by Hutton's similar treatment of Montucla, there is an amusing chapter on the quadrators. Montucla refers to his own anonymous book of 1754 as a curious book published by Jombert.[354]He seems to have been a little ashamed of writing about circle-squarers: what a slap on the face for an unborn Budgeteer!

Montucla says, speaking of France, that he finds three notions prevalent among the cyclometers: (1) that there is a large reward offered for success; (2) that the longitude problem depends on that success; (3) that the solution is the great end and object of geometry. The same threenotions are equally prevalent among the same class in England. No reward has ever been offered by the government of either country. The longitude problem in no way depends upon perfect solution; existing approximations are sufficient to a point of accuracy far beyond what can be wanted.[355]And geometry, content with what exists, has long passed on to other matters. Sometimes a cyclometer persuades a skipper who has made land in the wrong place that the astronomers are in fault, for using a wrong measure of the circle; and the skipper thinks it a very comfortable solution! And this is the utmost that the problem ever has to do with longitude.

ANTINEWTONIANISMUS.

Antinewtonianismus.[356]By Cælestino Cominale,[357]M.D. Naples, 1754 and 1756, 2 vols. 4to.

The first volume upsets the theory of light; the second vacuum, vis inertiæ, gravitation, and attraction. I confess I never attempted these big Latin volumes, numbering 450 closely-printed quarto pages. The man who slays Newton in a pamphlet is the man for me. But I will lend them to anybody who will give security, himself in £500, and two sureties in £250 each, that he will read them through, and give a full abstract; and I will not exact security for their return. I have never seen any mention of this book: it has a printer, but not a publisher, as happens with so many unrecorded books.

OFFICIAL BLOW TO CIRCLE SQUARERS.

1755. The French Academy of Sciences came to the determination not to examine any more quadratures or kindred problems. This was the consequence, no doubt, of the publication of Montucla's book: the time was well chosen; for that book was a full justification of the resolution. The Royal Society followed the same course, I believe, a few years afterwards. When our Board of Longitude was in existence, most of its time was consumed in listening to schemes, many of which included the quadrature of the circle. It is certain that many quadrators have imagined the longitude problem to be connected with theirs: and no doubt the notion of a reward offered by Government for a true quadrature is a result of the reward offered for the longitude. Let it also be noted that this longitude reward was not a premium upon excogitation of a mysterious difficulty. The legislature was made to know that the rational hopes of the problem were centered in the improvement of the lunar tables and the improvement of chronometers. To these objects alone, and by name, the offer was directed: several persons gained rewards for both; and the offer was finally repealed.

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