Chapter IV: Part 4

Passing over the success of Bacon's own endeavors to improve the details of physical science, which was next to nothing, and of his method as a whole, which has never been practised, we might say much of the good influence of his writings. Sound wisdom, set in sparkling wit, must instruct and amuse to the end of time: and, as against error, we repeat that Bacon is soundly wise, so far as he goes. There is hardly a form of human error within his scope which he did not detect, expose, and attach to a satirical metaphor which never ceases to sting. He is largely indebted to a very extensive reading; but the thoughts of others fall into his text with such a close-fitting compactness that he can make even the words of the Sacred Writers pass for his own. A saying of the prophet Daniel, rather a hackneyed quotation in our day, _Multi pertransibunt, et augebitur scientia_, stands in the title-page of the first edition {90} of Montucla's _History of Mathematics_ as a quotation from Bacon--and it is not the only place in which this mistake occurs. When the truth of the matter, as to Bacon's system, is fully recognized, we have little fear that there will be a reaction against the man. First, because Bacon will always live to speak for himself, for he will not cease to be read: secondly, because those who seek the truth will find it in the best edition of his works, and will be most ably led to know what Bacon was, in the very books which first showed at large what he _was not_.

THE CONGREGATION OF THE INDEX, ON COPERNICUS.

In this year (1620) appeared the corrections under which the Congregation of the Index--i.e., the Committee of Cardinals which superintended the _Index_ of forbidden books--proposed to allow the work of Copernicus to be read. I insert these conditions in full, because they are often alluded to, and I know of no source of reference accessible to a twentieth part of those who take interest in the question.

By a decree of the Congregation of the Index, dated March 5, 1616, the work of Copernicus, and another of Didacus Astunica,[137] are suspended _donec corrigantur_, as teaching:

"Falsam illam doctrinam Pythagoricam, divinae que Scripturae omnino adversantem, de mobilitate Terrae et immobilitate Solis."[138]

But a work of the Carmelite Foscarini[139] is:

{91}

"Omnino prohibendum atque damnandum," because "ostendere conatur praefatam doctrinam ... consonam esse veritati et non adversari Sacrae Scripturae."[140]

Works which teach the false doctrine of the earth's motion are to be corrected; those which declare the doctrine conformable to Scripture are to be utterly prohibited.

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 called _nobilis astrologus_; not a compliment to his birth, which was humble, but to his fame. The suspension was because:

"Sacrae Scripturae, ejusque verae et Catholicae interpretationi repugnantia (quod in homine Christiano minime tolerandum) non _per hypothesin_ tractare, sed _ut verissima_ adstruere non dubitat!"[141]

And the corrections relate:

"Locis in quibus non _ex hypothesi_, sed _asserendo_ de situ et motu Terrae 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 erunt [Greek: mataiologoi], qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi summunt, propter aliquem locum scripturae, male ad suum propositum detortum, ausi fuerint meum {92} hoc 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 terrae 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. ecclesiasticae conducere aliquid.... _Emend._ Ibi _si fortasse_ dele omnia, usque ad verbum _hi nostri labores_ et sic accommoda--_Coeterum 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 haec quaestio 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 coelestium motuum apparentias existimemus."[144]

{93}

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 Terrae, 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 formae suae a natura congruentem concedere, magisquam quod totus labatur mundus, cujus finis ignoratur, scirique nequit, neque fateamur ipsius cotidianae revolutionis in coelo apparentiam esse, et in terra veritatem? Et haec perinde se habere, ac si diceret Virgilianus AEneas: Provehimur portu ... _Emend._ Cur ergo non possum mobilitatem illi formae suae concedere, magisque quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quae apparent in coelo, perinde se habere ac si ..."[146]

{94}

"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 the _contained_ and _located_, 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 Terrae, quam ejus quies, praesertim in cotidiana revolutione, tanquam terrae 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 Terrae, 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]

{95}

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

(Cap. 10. lib. i. p. 9.) "_Copernicus._ Non pudet nos fateri ... hoc potius in mobilitate terrae verificari. _Emend._ Non pudet nos assumere ... hoc consequenter in mobilitate verificari."[150]

(Cap. 10. lib. i. p. 10.) "_Copernicus._ Tanta nimirum est divina haec. 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 Terrae, ejusque demonstratione."[153]

(Cap. 10. lib. iv. p. 122.[154]) "_Copernicus._ De magnitudine horum trium siderum, Solis, Lunae, et Terrae. _Emend._ Dele verba _horum trium siderum_, quia terra non est sidus, ut facit eam Copernicus."[155]

We must not say we are not ashamed to _acknowledge_; _assume_ is the word. We must not call this assumption a _Divine work_. A chapter must not be headed _demonstration_, but _hypothesis_. The earth must not be called a _star_; 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 of {96} reach--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, this _problematice 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 the _Italian_ Inquisition--for the private and personal pleasure of the Pope, who _knew_ that the course he took would not commit him as _Pope_--and not of the body which calls itself the _Church_. 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 Roman _Church_ never 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 the _English_ Church; which is fortunate, for that Convocation, in 1622, came to a decision quite as absurd, and a great deal {97} more 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 term _erronea_,[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, et _impia_," 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, {98} ministers and advisers apart, the king might _personally_ break 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 was _false_ far 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 terrae 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 the _Index_ or of the _Inquisition_ as a declaration of their _Church_. Fromond would have been glad to say as much, and tries to come near it, but confesses he must abstain. See _Penny Cyclop. Suppl._ "Galileo," and _Eng. Cycl._ "Motion of the Earth." The author of a celebrated article in the _Dublin Review_, in defence of the {99} Church 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 a 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 approximation _guessed at_ by his father, Peter Metius,[169] namely that the diameter is {100} to the circumference as 113 to 355. The error is at 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. (See _Eng. 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]

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, {101} "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 the _matter_ of other planets may be of different chemistry from ours. There may be no oxygen and hydrogen in Jupiter, which may have _gens_ of its own.[173] But this must not be said: it would limit the omniscience of the _a priori_ school of physical inquirers, the larger half of the whole, and would be very _unphilosophical_. 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 call _inhabited_ worlds. It produced {102} several 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 are _acknowledged_ to be fictions, as those of Lucian,[177] Rabelais,[178] Swift, Francis {103} Godwin,[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 will {104} be 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 novercae creditum est;
Cassandrae quia non creditum ruit Ilium:
Ergo exploranda est veritas multum prius
Quam stulta prove judicet sententia."[182]

Nova Demonstratio immobilitatis terrae petita ex virtute magnetica. By
Jacobus Grandamicus. Flexiae (La Fleche), 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 a 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 works {105} on biography. Argoli's discovery that logarithms facilitate easy processes, but increase the labor of difficult ones, is worth recording.

Controversiae 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 made {106} mincemeat: but he is said to have insisted on the discovery of his epitaph.[189]

{107}

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]

{108}

THE SYMPATHETIC POWDER.

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

On this work see _Notes 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's _History 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 the {109} wound 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 of _not_ dressing 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, _they_ would 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 is _Ars longa, vita brevis_, meaning _Practice is long, so life is short_.

HOBBES AS A MATHEMATICIAN.

Examinatio et emendatio Mathematicae Hodiernae. 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 publication {110} of 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 sphaerae, 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 opponent {111} as 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 aeque significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora triginta sex segmenta BCDF. Illa adsumptiuncula vera est, haec 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 multos [Greek: katorthountas]."[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 him {112} extremely 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. Did _Clavius_ show 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 here _are_ the 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 not {113} understand 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 Finaeus, "Il se vanta sans raison avoir trouve la quadrature du cercle; la gloire de cette admirable decouverte etait reservee a Joseph Scalinger, comme l'a ecrit Scevole 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, going _ultra 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 that {114} Graunt, 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 the _Biographia Britannica_ may 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 the _Assurance 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 Coryphaeus 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 was _not_ a 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 admission {115} to 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, [Greek: Philomathematikos]. 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 the {116} mournful 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 which _things_ and their relations shall be denoted by signs, not _words_: 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 the _Biographia Britannica_, except discussion of Anthony Wood's statement that the hint was derived from Dalgarno's book, {117} _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 called _hyperbolic_. 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.

{118}

RENE DE SLUSE.

Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liege], 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 his _Vera Circuli et Hyperbolae Quadratura_,[231] held himself to have proved that {119} the _geometrical_ quadrature of the circle is impossible. Few mathematicians read this very abstruse speculation, and opinion is somewhat divided. The regular circle-squarers attempt the _arithmetical_ quadrature, which has long been proved to be impossible. Very few attempt the geometrical quadrature. One of the last is Malacarne, an Italian, who published his _Solution Geometrique_, at Paris, in 1825. His method would make the circumference less than three times the diameter.

BEAULIEU'S QUADRATURE.

La Geometrie Francoise, ou la Pratique aisee.... La quadracture du
cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe 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 from {120} lecturing. See some letters on the History of Perspective, which I wrote in the _Athenaeum_, 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, mathematicien, fort mal traite par Descartes, et a ce qu'il paroit avec justice."[234]

Beaulieu's quadrature amounts to a geometrical construction[235] which gives [pi] = [root]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 ecrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la force de ses Problemes, si sa trop grande presomption ne l'avoit porte a avancer en cette Science une proposition aussi absurde, qu'elle est contre la Foy et raison, en faisant la circonference d'un Cercle fixe, immobile, et le centre mobile, sur lequel principe Geometrique, il a avance en son Traitte 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 Brahe[237] to Beaulieu, there is but one expression of admiration for the genius of Copernicus. There is an exception, which, I {121} believe, has been quite misunderstood. Maurolycus,[238] in his _De Sphaera_, 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 Terram _in girum circumverti_ posuit: 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 of _tolerating_ a person _as being_ more 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 Scavans et specialement d'un General d'Armee ou Capitaine, pour promptement ranger une Armee 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 signifie _plus_ au commerce, et a l'Armee _Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons. [It is quite true that P and M were used for _plus_ and _minus_ in a great many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armee _rang_. Q signifie _quare_ en l'un et l'autre usage. C signifie _cube_ en la mesure, et _Cavallerie_ en la composition des bataillons et escadrons. Quant a l'operation de cette science, c'est {122} d'additionner un _plus_ d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait le moindre du _plus_, et la reste est la somme requise ou nombre trouve. Je dis seulement cecy en passant pour ceux qui n'en scavent rien du tout."[240]

This is the algebra of the Royal Household, seventy-three years after the death of Vieta. Quaere, 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 the _beaux_. 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 his _Geostatique_, 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.

{123}

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 Nugae" 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 of _Difficiles
Nugae_. London, 1677, 8vo.

This is another tract of Chief Justice Hale, published the year after his death. The reader will remember that _motion_, in old philosophy, meant any change from state to state: what we now describe as _motion_ was _local motion_. This is a very philosophical book, about _flux_ and _materia prima_, _virtus activa_ and _essentialis_, 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 famous _Pleas of the Crown_[245] and other law works did not appear until after his death. One of his {124} contemporaries was the astronomer Thomas Street, whose _Caroline 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 the _Caroline 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, the _most eminent man that ever advanced the progress of science_, and one of the [very moderate] best and most purely religious men that ever lived."

{125}

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 name _antimoine_, 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. {126}
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 yet _transmute_; but they may in time: they poke about most assiduously. It seems, then, that the conviction that alchemy _must_ be impossible was a delusion: but we do not mention it.

{127}

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]

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

Among the smaller paradoxes of the day is that of the _Times_ newspaper, which always spells it _chymistry_: 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 with [Greek: chemeia] or with [Greek: chumeia].

Lettre d'un gentil-homme de province a une dame de qualite, sur le
sujet de la Comete. 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 the _new 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."

{128}

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 been _on the dice_ with 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.

{129}

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.

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

1008449087377541679894282184894
3 --------------------------------
6997183637540819440035239271702

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

MATHEMATICAL THEOLOGY.

Theologiae Christianae 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. {130} 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 formulae, 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 the _Principia_ of 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 derived {131} from 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.