Chapter 4

In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, permissio, et correctio," dated 1620 without the month or day, permission is given to reprint the work of Copernicus with certain alterations; and, by implication, to read existing copies after correction in writing. In the preamble the author is callednobilis astrologus; not a compliment to his birth, which was humble, but to his fame. The suspension was because:

"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi repugnantia (quod in homine Christiano minime tolerandum) nonper hypothesintractare, sedut verissimaadstruere non dubitat!"[141]

And the corrections relate:

"Locis in quibus nonex hypothesi, sedasserendode situ et motu Terræ disputat."[142]

That is, the earth's motion may be an hypothesis for elucidation of the heavenly motions, but must not be asserted as a fact.

(In Pref. circa finem.) "Copernicus.Si fortasse eruntματαιόλογοι, qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi summunt, propter aliquem locum scripturæ, male ad suum propositum detortum, ausi fuerint meumhoc institutum reprehendere ac insectari: illos nihil moror adeo ut etiam illorum judicium tanquam temerarium contemnam. Non enim obscurum est Lactantium, celebrem alioqui scriptorem, sed Mathematicum parum, admodum pueriliter de forma terræ loqui, cum deridet eos, qui terram globi formam habere prodiderunt. Itaque non debet mirum videri studiosis, si qui tales nos etiam videbunt. Mathemata Mathematicis scribuntur, quibus et hi nostri labores, si me non fallit opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid....Emend.Ibisi fortassedele omnia, usque ad verbumhi nostri laboreset sic accommoda—Cœterum hi nostri labores."[143]

All the allusion to Lactantius, who laughed at the notion of the earth being round, which was afterwards found true, is to be struck out.

(Cap. 5. lib. i. p. 3) "Copernicus.Si tamen attentius rem consideremus, videbitur hæc quæstio nondum absoluta, et ideireo minime contemnenda.Emend.Si tamen attentius rem consideremus, nihil refert an Terram in medio Mundi, an extra Medium existere, quoad solvendas cœlestium motuum apparentias existimemus."[144]

We must not say the question is not yet settled, but only that it may be settled either way, so far as mere explanation of the celestial motions is concerned.

(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo tractat de veritate motus Terræ, dum solvit veterum rationes probantes ejus quietem. Cum tamen problematice videatur loqui; ut studiosis satisfiat, seriesque et ordo libri integer maneat; emendetur ut infra."[145]

A chapter which seems to assert the motion should perhaps be expunged; but it may perhaps be problematical; and, not to break up the book, must be amended as below.

(p. 6.) "Copernicus.Cur ergo hesitamus adhuc, mobilitatem illi formæ suæ a natura congruentem concedere, magisquam quod totus labatur mundus, cujus finis ignoratur, scirique nequit, neque fateamur ipsius cotidianæ revolutionis in cœlo apparentiam esse, et in terra veritatem? Et hæc perinde se habere, ac si diceret Virgilianus Æneas: Provehimur portu ...Emend.Cur ergo non possum mobilitatem illi formæ suæ concedere, magisque quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quæ apparent in cœlo, perinde se habere ac si ..."[146]

"Why should we hesitate to allow the earth's motion," must be altered into "I cannot concede the earth's motion."

(p. 7.) "Copernicus.Addo etiam, quod satis absurdum videretur, continenti sive locanti motum adscribi, et non potius contento et locato, quod est terra.Emend.Addo etiam difficilius non esse contento et locato, quod est Terra, motum adscribere, quam continenti."[147]

We must not say it is absurd to refuse motion to thecontainedandlocated, and to give it to the containing and locating; say that neither is more difficult than the other.

(p. 7.) "Copernicus.Vides ergo quod ex his omnibus probabilior sit mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione, tanquam terræ maxime propria.Emend.Vides... delendus est usque ad finem capitis."[148]

Strike out the whole of the chapter from this to the end; it says that the motion of the earth is the most probable hypothesis.

(Cap. 9. lib. i. p. 7.) "Copernicus.Cum igitur nihil prohibeat mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus conveniant, ut possit una errantium syderum existimari.Emend.Cum igitur Terram moveri assumpserim, videndum nunc arbitror, an etiam illi plures possint convenire motus."[149]

We must not say that nothing prohibits the motion of the earth, only that havingassumedit, we may inquire whether our explanations require several motions.

(Cap. 10. lib. i. p. 9.) "Copernicus.Non pudet nos fateri ... hoc potius in mobilitate terræ verificari.Emend.Non pudet nos assumere ... hoc consequenter in mobilitate verificari."[150]

(Cap. 10. lib. i. p. 10.) "Copernicus.Tanta nimirum est divina hæc. Opt. Max. fabrica.Emend.Dele illa verba postrema."[151]

(Cap. ii. lib. i.[152]) "Copernicus.De triplici motu telluris demonstratio.Emend.De hypothesi triplicis motus Terræ, ejusque demonstratione."[153]

(Cap. 10. lib. iv. p. 122.[154]) "Copernicus.De magnitudine horum trium siderum, Solis, Lunæ, et Terræ.Emend.Dele verbahorum trium siderum, quia terra non est sidus, ut facit eam Copernicus."[155]

We must not say we are not ashamed toacknowledge;assumeis the word. We must not call this assumption aDivine work. A chapter must not be headeddemonstration, buthypothesis. The earth must not be called astar; the word implies motion.

It will be seen that it does not take much to reduce Copernicus to pure hypothesis. No personal injury being done to the author—who indeed had been 17 years out ofreach—the treatment of his book is now an excellent joke. It is obvious that the Cardinals of the Index were a little ashamed of their position, and made a mere excuse of a few corrections. Their mode of dealing with chap. 8, thisproblematice videtur loqui, ut studiosis satisfiat,[156]is an excuse to avoid corrections. But they struck out the stinging allusion to Lactantius[157]in the preface, little thinking, honest men, for they really believed what they said—that the light of Lactantius would grow dark before the brightness of their own.

THE CONVOCATION AT OXFORD EQUALLY AT FAULT.

1622. I make no reference to the case of Galileo, except this. I have pointed out (Penny Cycl. Suppl."Galileo";Engl. Cycl."Motion of the Earth") that it is clear the absurdity was the act of theItalianInquisition—for the private and personal pleasure of the Pope, whoknewthat the course he took would not commit him asPope—and not of the body which calls itself theChurch. Let the dirty proceeding have its right name. The Jesuit Riccioli,[158]the stoutest and most learned Anti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican and Pope-hater, are equally positive that the RomanChurchnever pronounced any decision: and this in the time immediately following the ridiculous proceeding of the Inquisition. In like manner a decision of the Convocation of Oxford is not a law of theEnglishChurch; which is fortunate, for that Convocation, in 1622, came to a decision quite as absurd, and a great dealmore wicked than the declaration against the motion of the earth. The second was a foolish mistake; the first was a disgusting surrender of right feeling. The story is told without disapprobation by Anthony Wood, who never exaggerated anything against the university of which he is writing eulogistic history.

In 1622, one William Knight[159]put forward in a sermon preached before the University certain theses which, looking at the state of the times, may have been improper and possibly of seditious intent. One of them was that the bishop might excommunicate the civil magistrate: this proposition the clerical body could not approve, and designated it by the termerronea,[160]the mildest going. But Knight also declared as follows:

"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in ipsos faciat impetum, et ipsi nec potestatem ordinariam implorare, nec alia ratione effugere periculum possint, in presenti periculo se et suos contra tyrannum, sicut contra privatum grassatorem, defendere licet."[161]

That is, a man may defend his purse or a woman her honor, against the personal attack of a king, as against that of a private person, if no other means of safety can be found. The Convocation sent Knight to prison, declared the proposition"falsa, periculosa, etimpia," and enacted that all applicants for degrees should subscribe this censure, and make oath that they would neither hold, teach, nor defend Knight's opinions.

The thesis, in the form given, was unnecessary and improper. Though strong opinions of the king's rights were advanced at the time, yet no one ventured to say that,ministers and advisers apart, the king mightpersonallybreak the law; and we know that the first and only attempt which his successor made brought on the crisis which cost him his throne and his head. But the declaration that the proposition wasfalsefar exceeds in all that is disreputable the decision of the Inquisition against the earth's motion. We do not mention this little matter in England. Knight was a Puritan, and Neal[162]gives a short account of his sermon. From comparison with Wood,[163]I judge that the theses, as given, were not Knight's words, but the digest which it was customary to make in criminal proceedings against opinion. This heightens the joke, for it appears that the qualifiers of the Convocation took pains to present their condemnation of Knight in the terms which would most unequivocally make their censure condemn themselves. This proceeding took place in the interval between the two proceedings against Galileo: it is left undetermined whether we must say pot-kettle-pot or kettle-pot-kettle.

Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis. Antwerp, 1631, 8vo.[164]

This book contains the evidence of an ardent opponent of Galileo to the fact, that Roman Catholics of the day did not consider the decree of theIndexor of theInquisitionas a declaration of theirChurch. Fromond would have been glad to say as much, and tries to come near it, but confesses he must abstain. SeePenny Cyclop. Suppl."Galileo," andEng. Cycl."Motion of the Earth." The author of a celebrated article in theDublin Review, in defence of theChurch of Rome, seeing that Drinkwater Bethune[165]makes use of the authority of Fromondus, but for another purpose, sneers at him for bringing up a "musty old Professor." If he had known Fromondus, and used him he would have helped his own case, which is very meagre for want of knowledge.[166]

Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la Proposition faicte par le Sieur Morin pour l'invention des longitudes. Paris, 1634, 8vo.[167]

This is the Official Report of the Commissioners appointed by the Cardinal, of whom Pascal is the one now best known, to consider Morin's plan. See the full account in Delambre,Hist. Astr. Mod.ii. 236, etc.

THE METIUS APPROXIMATION.

Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640, 4to.[168]

This book contains the celebrated approximationguessed atby his father, Peter Metius,[169]namely that the diameter isto the circumference as 113 to 355. The errorisat the rate of about a foot in 2,000 miles. Peter Metius, having his attention called to the subject by the false quadrature of Duchesne, found that the ratio lay between 333/106 and 377/120. He then took the liberty of taking the mean of both numerators and denominators, giving 355/113. He had no right to presume that this mean was better than either of the extremes; nor does it appear positively that he did so. He published nothing; but his son Adrian,[170]when Van Ceulen's work showed how near his father's result came to the truth, first made it known in the work above. (SeeEng. Cyclop., art. "Quadrature.")

ON INHABITABLE PLANETS.

A discourse concerning a new world and another planet, in two books. London, 1640, 8vo.[171]Cosmotheoros: or conjectures concerning the planetary worlds and their inhabitants. Written in Latin, by Christianus Huyghens. This translation was first published in 1698. Glasgow, 1757, 8vo. [The original is also of 1698.][172]

A discourse concerning a new world and another planet, in two books. London, 1640, 8vo.[171]

Cosmotheoros: or conjectures concerning the planetary worlds and their inhabitants. Written in Latin, by Christianus Huyghens. This translation was first published in 1698. Glasgow, 1757, 8vo. [The original is also of 1698.][172]

The first work is by Bishop Wilkins, being the third edition, [first in 1638] of the first book, "That the Moon may be a Planet"; and the first edition of the second work,"That the Earth may be a Planet." [See more under the reprint of 1802.] Whether other planets be inhabited or not, that is, crowded with organisations some of them having consciousness, is not for me to decide; but I should be much surprised if, on going to one of them, I should find it otherwise. The whole dispute tacitly assumes that, if the stars and planets be inhabited, it must be by things of which we can form some idea. But for aught we know, what number of such bodies there are, so many organisms may there be, of which we have no way of thinking nor of speaking. This is seldom remembered. In like manner it is usually forgotten that thematterof other planets may be of different chemistry from ours. There may be no oxygen and hydrogen in Jupiter, which may havegensof its own.[173]But this must not be said: it would limit the omniscience of thea priorischool of physical inquirers, the larger half of the whole, and would be veryunphilosophical. Nine-tenths of my best paradoxers come out from among this larger half, because they are just a little more than of it at their entrance.

There was a discussion on the subject some years ago, which began with

The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm. Whewell, Master of Trinity College, Cambridge]. A dialogue on the plurality of worlds, being a supplement to the Essay on that subject. [First found in the second edition, 1854; removed to the end in subsequent editions, and separate copies issued.][174]

A work of skeptical character, insisting on analogies which prohibit the positive conclusion that the planets, stars, etc., are what we should callinhabitedworlds. It producedseveral works and a large amount of controversy in reviews. The last predecessor of whom I know was

Plurality of Worlds.... By Alexander Maxwell. Second Edition. London, 1820, 8vo.

This work is directed against the plurality by an author who does not admit modern astronomy. It was occasioned by Dr. Chalmers's[175]celebrated discourses on religion in connection with astronomy. The notes contain many citations on the gravity controversy, from authors now very little read: and this is its present value. I find no mention of Maxwell, not even in Watt.[176]He communicated with mankind without the medium of a publisher; and, from Vieta till now, this method has always been favorable to loss of books.

A correspondent informs me that Alex. Maxwell, who wrote on the plurality of worlds, in 1820, was a law-bookseller and publisher (probably his own publisher) in Bell Yard. He had peculiar notions, which he was fond of discussing with his customers. He was a bit of a Swedenborgian.

INHABITED PLANETS IN FICTION.

There is a class of hypothetical creations which do not belong to my subject, because they areacknowledgedto be fictions, as those of Lucian,[177]Rabelais,[178]Swift, FrancisGodwin,[179]Voltaire, etc. All who have more positive notions as to either the composition or organization of other worlds, than the reasonable conclusion that our Architect must be quite able to construct millions of other buildings on millions of other plans, ought to rank with the writers just mentioned, in all but self-knowledge. Of every one of their systems I say, as the Irish Bishop said of Gulliver's book,—I don't believe half of it. Huyghens had been preceded by Fontenelle,[180]who attracted more attention. Huyghens is very fanciful and very positive; but he gives a true account of his method. "But since there's no hopes of a Mercury to carry us such a journey, we shall e'en be contented with what's in our power: we shall suppose ourselves there...." And yet he says, "We have proved that they live in societies, have hands and feet...." Kircher[181]had gone to the stars before him, but would not find any life in them, either animal or vegetable.

The question of the inhabitants of a particular planet is one which has truth on one side or the other: either there are some inhabitants, or there are none. Fortunately, it is of no consequence which is true. But there are many cases where the balance is equally one of truth and falsehood, in which the choice is a matter of importance. My work selects, for the most part, sins against demonstration: but the world is full of questions of fact or opinion, in which a struggling minority will become a majority, or else willbe gradually annihilated: and each of the cases subdivides into results of good, and results of evil. What is to be done?

"Periculosum est credere et non credere;Hippolitus obiit quia novercæ creditum est;Cassandræ quia non creditum ruit Ilium:Ergo exploranda est veritas multum priusQuam stulta prove judicet sententia."[182]

"Periculosum est credere et non credere;

Hippolitus obiit quia novercæ creditum est;

Cassandræ quia non creditum ruit Ilium:

Ergo exploranda est veritas multum prius

Quam stulta prove judicet sententia."[182]

Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.[183]

No magnetic body can move about its poles: the earth is a magnetic body, therefore, etc. The iron and its magnetism are typical of two natures in one person; so it is said, "Si exaltatus fuero à terra, omnia traham ad me ipsum."[184]

A VENETIAN BUDGET OF PARADOXES.

Le glorie degli incogniti, o vero gli huomini illustri dell' accademia de' signori incogniti di Venetia. Venice, 1647, 4to.

This work is somewhat like a part of my own: it is a budget of Venetian nobodies who wished to be somebodies; but paradox is not the only means employed. It is of a serio-comic character, gives genuine portraits in copperplate, and grave lists of works; but satirical accounts. The astrologer Andrew Argoli[185]is there, and his son; both of whom, with some of the others, have place in modern workson biography. Argoli's discovery that logarithms facilitate easy processes, but increase the labor of difficult ones, is worth recording.

Controversiæ de vera circuli mensura ... inter ... C. S. Longomontanum et Jo. Pellium.[186]Amsterdam, 1647, 4to.

Longomontanus,[187]a Danish astronomer of merit, squared the circle in 1644: he found out that the diameter 43 gives the square root of 18252 for the circumference; which gives 3.14185... for the ratio. Pell answered him, and being a kind of circulating medium, managed to engage in the controversy names known and unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish, Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri and Golius.[188]Among them, of course, Longomontanus was mademincemeat: but he is said to have insisted on the discovery of his epitaph.[189]

THE CIRCULATING MEDIA OF MATHEMATICS.

The great circulating mediums, who wrote to everybody, heard from everybody, and sent extracts to everybody else, have been Father Mersenne, John Collins, and the late Professor Schumacher: all "late" no doubt, but only the last recent enough to be so styled. If M.C.S. should ever again stand for "Member of the Corresponding Society," it should raise an acrostic thought of the three. There is an allusion to Mersenne's occupation in Hobbes's reply to him. He wanted to give Hobbes, who was very ill at Paris, the Roman Eucharist: but Hobbes said, "I have settled all that long ago; when did you hear from Gassendi?" We are reminded of William's answer to Burnet. John Collins disseminated Newton, among others. Schumacher ought to have been called the postmaster-general of astronomy, as Collins was called the attorney-general of mathematics.[190]

THE SYMPATHETIC POWDER.

A late discourse ... by Sir Kenelme Digby.... Rendered into English by R. White. London, 1658, 12mo.

On this work seeNotes and Queries, 2d series, vii. 231, 299, 445, viii. 190. It contains the celebrated sympathetic powder. I am still in much doubt as to the connection of Digby with this tract.[191]Without entering on the subject here, I observe that in Birch'sHistory of the Royal Society,[192]to which both Digby and White belonged, Digby, though he brought many things before the Society, never mentioned the powder, which is connected only with the names of Evelyn[193]and Sir Gilbert Talbot.[194]The sympathetic powder was that which cured by anointing the weapon with its salve instead of the wound. I have long been convinced that it was efficacious. The directions were to keep thewound clean and cool, and to take care of diet, rubbing the salve on the knife or sword.[195]If we remember the dreadful notions upon drugs which prevailed, both as to quantity and quality, we shall readily see that any way ofnotdressing the wound would have been useful. If the physicians had taken the hint, had been careful of diet etc., and had poured the little barrels of medicine down the throat of a practicable doll,theywould have had their magical cures as well as the surgeons.[196]Matters are much improved now; the quantity of medicine given, even by orthodox physicians, would have been called infinitesimal by their professional ancestors. Accordingly, the College of Physicians has a right to abandon its motto, which isArs longa, vita brevis, meaningPractice is long, so life is short.

HOBBES AS A MATHEMATICIAN.

Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. London, 1666, 4to.

In six dialogues: the sixth contains a quadrature of the circle.[197]But there is another edition of this work, without place or date on the title-page, in which the quadrature is omitted. This seems to be connected with the publicationof another quadrature, without date, but about 1670, as may be judged from its professing to answer a tract of Wallis, printed in 1669.[198]The title is "Quadratura circuli, cubatio sphæræ, duplicatio cubi," 4to.[199]Hobbes, who began in 1655, was very wrong in his quadrature; but, though not a Gregory St. Vincent,[200]he was not the ignoramus in geometry that he is sometimes supposed. His writings, erroneous as they are in many things, contain acute remarks on points of principle. He is wronged by being coupled with Joseph Scaliger, as the two great instances of men of letters who have come into geometry to help the mathematicians out of their difficulty. I have never seen Scaliger's quadrature,[201]except in the answers of Adrianus Romanus,[202]Vieta and Clavius, and in the extracts of Kastner.[203]Scaliger had no right to such strong opponents: Erasmus or Bentley might just as well have tried the problem, and either would have done much better in any twenty minutes of his life.[204]

AN ESTIMATE OF SCALIGER.

Scaliger inspired some mathematicians with great respect for his geometrical knowledge. Vieta, the first man of his time, who answered him, had such regard for his opponentas made him conceal Scaliger's name. Not that he is very respectful in his manner of proceeding: the following dry quiz on his opponent's logic must have been very cutting, being true. "In grammaticis, dare navibus Austros, et dare naves Austris, sunt æque significantia. Sed in Geometricis, aliud est adsumpsisse circulumBCDnon esse majorem triginta sex segmentisBCDF, aliud circuloBCDnon esse majora triginta sex segmentaBCDF. Illa adsumptiuncula vera est, hæc falsa."[205]Isaac Casaubon,[206]in one of his letters to De Thou,[207]relates that, he and another paying a visit to Vieta, the conversation fell upon Scaliger, of whom the host said that he believed Scaliger was the only man who perfectly understood mathematical writers, especially the Greek ones: and that he thought more of Scaliger when wrong than of many others when right; "pluris se Scaligerum vel errantem facere quam multosκατορθούντας."[208]This must have been before Scaliger's quadrature (1594). There is an old story of some one saying, "Mallem cum Scaligero errare, quam cum Clavio recte sapere."[209]This I cannot help suspecting to have been a version of Vieta's speech with Clavius satirically inserted, on account of the great hostility which Vieta showed towards Clavius in the latter years of his life.

Montucla could not have read with care either Scaliger's quadrature or Clavius's refutation. He gives the first a wrong date: he assures the world that there is no question about Scaliger's quadrature being wrong, in the eyes of geometers at least: and he states that Clavius mortified himextremely by showing that it made the circle less than its inscribed dodecagon, which is, of course, equivalent to asserting that a straight line is not always the shortest distance between two points. DidClaviusshow this? No, it was Scaliger himself who showed it, boasted of it, and declared it to be a "noble paradox" that a theorem false in geometry is true in arithmetic; a thing, he says with great triumph, not noticed by Archimedes himself! He says in so many words that the periphery of the dodecagon is greater than that of the circle; and that the more sides there are to the inscribed figure, the more does it exceed the circle in which it is. And herearethe words, on the independent testimonies of Clavius and Kastner:

"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum, tanto plus poterit ambitus polygoni quam ambitus circuli."[210]

There is much resemblance between Joseph Scaliger and William Hamilton,[211]in a certain impetuousity of character, and inaptitude to think of quantity. Scaliger maintained that the arc of a circle is less than its chord in arithmetic, though greater in geometry; Hamilton arrived at two quantities which are identical, but the greater the one the less the other. But, on the whole, I liken Hamilton rather to Julius than to Joseph. On this last hero of literature I repeat Thomas Edwards,[212]who says that a man is unlearned who, be his other knowledge what it may, does notunderstand the subject he writes about. And now one of many instances in which literature gives to literature character in science. Anthony Teissier,[213]the learned annotator of De Thou's biographies, says of Finæus, "Il se vanta sans raison avoir trouvé la quadrature du cercle; la gloire de cette admirable découverte était réservée à Joseph Scalinger, comme l'a écrit Scévole de St. Marthe."[214]

JOHN GRAUNT AS A PARADOXER.

Natural and Political Observations ... upon the Bills of Mortality. By John Graunt, citizen of London. London, 1662, 4to.[215]

This is a celebrated book, the first great work upon mortality. But the author, goingultra crepidam, has attributed to the motion of the moon in her orbit all the tremors which she gets from a shaky telescope.[216]But there is another paradox about this book: the above absurd opinion is attributed to that excellent mechanist, Sir William Petty, who passed his days among the astronomers. Graunt did not write his own book! Anthony Wood[217]hints that Petty "assisted, or put into a way" his old benefactor: no doubt the two friends talked the matter over many a time. Burnet and Pepys[218]state that Petty wrote the book. It is enough for me thatGraunt, whose honesty was never impeached, uses the plainest incidental professions of authorship throughout; that he was elected into the Royal Society because he was the author; that Petty refers to him as author in scores of places, and published an edition, as editor, after Graunt's death, with Graunt's name of course. The note on Graunt in theBiographia Britannicamay be consulted; it seems to me decisive. Mr. C. B. Hodge, an able actuary, has done the best that can be done on the other side in theAssurance Magazine, viii. 234. If I may say what is in my mind, without imputation of disrespect, I suspect some actuaries have a bias: they would rather have Petty the greater for their Coryphæus than Graunt the less.[219]

Pepys is an ordinary gossip: but Burnet's account has an animus which is of a worse kind. He talks of "one Graunt, a Papist, under whose name Sir William Petty[220]published his observations on the bills of mortality." He then gives the cock without a bull story of Graunt being a trustee of the New River Company, and shutting up the cocks and carrying off their keys, just before the fire of London, by which a supply of water was delayed.[221]It was one of the first objections made to Burnet's work, that Graunt wasnota trustee at the time; and Maitland, the historian of London, ascertained from the books of the Company that he was not admitted until twenty-three days after the breaking out of the fire. Graunt's first admissionto the Company took place on the very day on which a committee was appointed to inquire into the cause of the fire. So much for Burnet. I incline to the view that Graunt's setting London on fire strongly corroborates his having written on the bills of mortality: every practical man takes stock before he commences a grand operation in business.

MANKIND A GULLIBLE LOT.

De Cometis: or a discourse of the natures and effects of Comets, as they are philosophically, historically, and astrologically considered. With a brief (yet full) account of the III late Comets, or blazing stars, visible to all Europe. And what (in a natural way of judicature) they portend. Together with some observations on the nativity of the Grand Seignior. By John Gadbury,Φιλομαθηματικός. London, 1665, 4to.

Gadbury, though his name descends only in astrology, was a well-informed astronomer.[222]D'Israeli[223]sets down Gadbury, Lilly, Wharton, Booker, etc., as rank rogues: I think him quite wrong. The easy belief in roguery and intentional imposture which prevails in educated society is, to my mind, a greater presumption against the honesty of mankind than all the roguery and imposture itself. Putting aside mere swindling for the sake of gain, and looking at speculation and paradox, I find very little reason to suspect wilful deceit.[224]My opinion of mankind is founded upon themournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in, judging by experience. I do not say anything against Isaac D'Israeli for talking his time. We are all in the team, and we all go the road, but we do not all draw.

A FORERUNNER OF A WRITTEN ESPERANTO.

An essay towards a real character and a philosophical language. By John Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225]London, 1668, folio.

This work is celebrated, but little known. Its object gives it a right to a place among paradoxes. It proposes a language—if that be the proper name—in whichthingsand their relations shall be denoted by signs, notwords: so that any person, whatever may be his mother tongue, may read it in his own words. This is an obvious possibility, and, I am afraid, an obvious impracticability. One man may construct such a system—Bishop Wilkins has done it—but where is the man who will learn it? The second tongue makes a language, as the second blow makes a fray. There has been very little curiosity about his performance, the work is scarce; and I do not know where to refer the reader for any account of its details, except, to the partial reprint of Wilkins presently mentioned under 1802, in which there is an unsatisfactory abstract. There is nothing in theBiographia Britannica, except discussion of Anthony Wood's statement that the hint was derived from Dalgarno's book,De Signis, 1661.[226]Hamilton (Discussions, Art. 5, "Dalgarno") does not say a word on this point, beyond quoting Wood; and Hamilton, though he did now and then write about his countrymen with a rough-nibbed pen, knew perfectly well how to protect their priorities.

GREGOIRE DE ST. VINCENT.

Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.—Opus Geometricum posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668, folio.[227]

The first book has more than 1200 pages, on all kinds of geometry. Gregory St. Vincent is the greatest of circle-squarers, and his investigations led him into many truths: he found the property of the area of the hyperbola[228]which led to Napier's logarithms being calledhyperbolic. Montucla says of him, with sly truth, that no one has ever squared the circle with so much genius, or, excepting his principal object, with so much success.[229]His reputation, and the many merits of his work, led to a sharp controversy on his quadrature, which ended in its complete exposure by Huyghens and others. He had a small school of followers, who defended him in print.

RENE DE SLUSE.

Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668, 4to.[230]

The Mesolabum is the solution of the problem of finding two mean proportionals, which Euclid's geometry does not attain. Slusius is a true geometer, and uses the ellipse, etc.: but he is sometimes ranked with the trisecters, for which reason I place him here, with this explanation.

The finding of two mean proportionals is the preliminary to the famous old problem of the duplication of the cube, proposed by Apollo (not Apollonius) himself. D'Israeli speaks of the "six follies of science,"—the quadrature, the duplication, the perpetual motion, the philosopher's stone, magic, and astrology. He might as well have added the trisection, to make the mystic number seven: but had he done so, he would still have been very lenient; only seven follies in all science, from mathematics to chemistry! Science might have said to such a judge—as convicts used to say who got seven years, expecting it for life, "Thank you, my Lord, and may you sit there till they are over,"—may the Curiosities of Literature outlive the Follies of Science!

JAMES GREGORY.

1668. In this year James Gregory, in hisVera Circuli et Hyperbolæ Quadratura,[231]held himself to have proved thatthegeometricalquadrature of the circle is impossible. Few mathematicians read this very abstruse speculation, and opinion is somewhat divided. The regular circle-squarers attempt thearithmeticalquadrature, which has long been proved to be impossible. Very few attempt the geometrical quadrature. One of the last is Malacarne, an Italian, who published hisSolution Géométrique, at Paris, in 1825. His method would make the circumference less than three times the diameter.

BEAULIEU'S QUADRATURE.

La Géométrie Françoise, ou la Pratique aisée.... La quadracture du cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died in 1674].[232]

If this book had been a fair specimen, I might have pointed to it in connection with contemporary English works, and made a scornful comparison. But it is not a fair specimen. Beaulieu was attached to the Royal Household, and throughout the century it may be suspected that the household forced a royal road to geometry. Fifty years before, Beaugrand, the king's secretary, made a fool of himself, and [so?] contrived to pass for a geometer. He had interest enough to get Desargues, the most powerful geometer of his time,[233]the teacher and friend of Pascal, prohibited fromlecturing. See some letters on the History of Perspective, which I wrote in theAthenæum, in October and November, 1861. Montucla, who does not seem to know the true secret of Beaugrand's greatness, describes him as "un certain M. de Beaugrand, mathématicien, fort mal traité par Descartes, et à ce qu'il paroit avec justice."[234]

Beaulieu's quadrature amounts to a geometrical construction[235]which givesπ= √10. His depth may be ascertained from the following extracts. First on Copernicus:

"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la force de ses Problèmes, si sa trop grande présomption ne l'avoit porté à avancer en cette Science une proposition aussi absurde, qu'elle est contre la Foy et raison, en faisant la circonférence d'un Cercle fixe, immobile, et le centre mobile, sur lequel principe Géométrique, il a avancé en son Traitté Astrologique le Soleil fixe, et la Terre mobile."[236]

I digress here to point out that though our quadrators, etc., very often, and our historians sometimes, assert that men of the character of Copernicus, etc., were treated with contempt and abuse until their day of ascendancy came, nothing can be more incorrect. From Tycho Brahé[237]to Beaulieu, there is but one expression of admiration for the genius of Copernicus. There is an exception, which, Ibelieve, has been quite misunderstood. Maurolycus,[238]in hisDe Sphæra, written many years before its posthumous publication in 1575, and which it is not certain he would have published, speaking of the safety with which various authors may be read after his cautions, says, "Toleratur et Nicolaus Copernicus qui Solem fixum et Terramin girum circumvertiposuit: et scutica potius, aut flagello, quam reprehensione dignus est."[239]Maurolycus was a mild and somewhat contemptuous satirist, when expressing disapproval: as we should now say, he pooh-poohed his opponents; but, unless the above be an instance, he was never savage nor impetuous. I am fully satisfied that the meaning of the sentence is, that Copernicus, who turned the earth like a boy's top, ought rather to have a whip given him wherewith to keep up his plaything than a serious refutation. To speak oftoleratinga personas beingmore worthy of a flogging than an argument, is almost a contradiction.

I will now extract Beaulieu's treatise on algebra, entire.

"L'Algebre est la science curieuse des Sçavans et specialement d'un General d'Armée ou Capitaine, pour promptement ranger une Armée en bataille, et nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a 5 figures particulieres en cette sorte. P signifieplusau commerce, et à l'ArméePiquiers. M signifiemoins, etMousquetaireen l'Art des bataillons. [It is quite true that P and M were used forplusandminusin a great many old works.] R signifieracineen la mesure du Cube, et en l'Arméerang. Q signifiequaréen l'un et l'autre usage. C signifiecubeen la mesure, etCavallerieen la composition des bataillons et escadrons. Quant à l'operation de cette science, c'estd'additionner unplusd'avecplus, la somme seraplus, etmoinsd'avecplus, on soustrait le moindre duplus, et la reste est la somme requise ou nombre trouvé. Je dis seulement cecy en passant pour ceux qui n'en sçavent rien du tout."[240]

This is the algebra of the Royal Household, seventy-three years after the death of Vieta. Quære, is it possible that the fame of Vieta, who himself held very high stations in the household all his life, could have given people the notion that when such an officer chose to declare himself an algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu, and all thebeaux. Beaugrand—not only secretary to the king, but "mathematician" to the Duke of Orleans—I wonder what his "fool" could have been like, if indeed he kept the offices separate,—would have been in my list if I had possessed hisGeostatique, published about 1638.[241]He makes bodies diminish in weight as they approach the earth, because the effect of a weight on a lever is less as it approaches the fulcrum.

SIR MATTHEW HALE.

Remarks upon two late ingenious discourses.... By Dr. Henry More.[242]London, 1676, 8vo.

In 1673 and 1675, Matthew Hale,[243]then Chief Justice, published two tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the Torricellian experiment. Here are the answers by the learned and voluminous Henry More. The whole would be useful to any one engaged in research about ante-Newtonian notions of gravitation.

Observations touching the principles of natural motions; and especially touching rarefaction and condensation.... By the author ofDifficiles Nugæ. London, 1677, 8vo.

This is another tract of Chief Justice Hale, published the year after his death. The reader will remember thatmotion, in old philosophy, meant any change from state to state: what we now describe asmotionwaslocal motion. This is a very philosophical book, aboutfluxandmateria prima,virtus activaandessentialis, and other fundamentals. I think Stephen Hales, the author of the "Vegetable Statics," has the writings of the Chief Justice sometimes attributed to him, which is very puny justice indeed.[244]Matthew Hale died in 1676, and from his devotion to science it probably arose that his famousPleas of the Crown[245]and other law works did not appear until after his death. One of hiscontemporaries was the astronomer Thomas Street, whoseCaroline Tables[246]were several times printed: another contemporary was his brother judge, Sir Thomas Street.[247]But of the astronomer absolutely nothing is known: it is very unlikely that he and the judge were the same person, but there is not a bit of positive evidence either for or against, so far as can be ascertained. Halley[248]—no less a person—published two editions of theCaroline Tables, no doubt after the death of the author: strange indeed that neither Halley nor any one else should leave evidence that Street was born or died.

Matthew Hale gave rise to an instance of the lengths a lawyer will go when before a jury who cannot detect him. Sir Samuel Shepherd,[249]the Attorney General, in opening Hone's[250]first trial, calls him "one who was the most learned man that ever adorned the Bench, the most even man that ever blessed domestic life, themost eminent man that ever advanced the progress of science, and one of the [very moderate] best and most purely religious men that ever lived."

ON THE DISCOVERY OF ANTIMONY.

Basil Valentine his triumphant Chariot of Antimony, with annotations of Theodore Kirkringius, M.D. With the true book of the learned Synesius, a Greek abbot, taken out of the Emperour's library, concerning the Philosopher's Stone. London, 1678, 8vo.[251]

There are said to be three Hamburg editions of the collected works of Valentine, who discovered the common antimony, and is said to have given the nameantimoine, in a curious way. Finding that the pigs of his convent throve upon it, he gave it to his brethren, who died of it.[252]The impulse given to chemistry by R. Boyle[253]seems to have brought out a vast number of translations, as in the following tract:

ON ALCHEMY.

Collectanea Chymica: A collection of ten several treatises in chymistry, concerning the liquor Alkehest, the Mercury of Philosophers, and other curiosities worthy the perusal. Written by Eir. Philaletha,[254]Anonymus, J. B. Van-Helmont,[255]Dr. Fr.Antonie,[256]Bernhard Earl of Trevisan,[257]Sir Geo. Ripley,[258]Rog. Bacon,[259]Geo. Starkie,[260]Sir Hugh Platt,[261]and the Tomb of Semiramis. See more in the contents. London, 1684, 8vo.

In the advertisements at the ends of these tracts there are upwards of a hundred English tracts, nearly all of the period, and most of them translations. Alchemy looks up since the chemists have found perfectly different substances composed of the same elements and proportions. It is true the chemists cannot yettransmute; but they may in time: they poke about most assiduously. It seems, then, that the conviction that alchemymustbe impossible was a delusion: but we do not mention it.

The astrologers and the alchemists caught it in company in the following, of which I have an unreferenced note.

"Mendacem et futilem hominem nominare qui volunt, calendariographum dicunt; at qui sceleratum simul ac impostorem, chimicum.[262]

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