362 



NA TURE 



[August 17, 1905 



as in the French Navy, may reduce the number of 

 English readers of the book. But, happily, we 

 possess many naval officers fully competent to take 

 their place in scientific discussions of naval strategy 

 and tactics. They will find much that is suggestive 

 in Captain Vidal's book, and may be trusted to 

 appreciate its investigations properly as well as to de- 

 duce therefrom rules for guidance, which will assist 

 brother officers not so well instructed as themselves 

 in the practical application of the theorems which 

 Captain Vidal has collected. Shortly stated, the 

 volume is better suited for the student than for the 

 average naval officer, but it deserves a place in the 

 professional libraries of all modern fleets. 



W. H. White. 



THE CORRESPONDENCE OF HUYGENS. 

 CEuvres completes de Christiaan Huygens. Publi^es 

 par la Soci^t^ HoUandaise des Sciences. Tome 

 dixi^nie. Correspondance 1691-1695. Pp. 816. 

 (Nijhoff : La Haye, 1905.) 



THIS volume completes the publication of the scien- 

 tific and miscellaneous letters of Huygens, the 

 ten volumes comprising in all twenty-nine hundred 

 letters and memoranda. There is, perhaps, not so 

 much variety in the contents of the present volume as 

 in those of previous ones, and the great majority of 

 the letters of interest written during the last five years 

 of Huvgens's life have been published before, but they 

 have now in many cases been further illustrated by 

 the addition of rough notes from the books of 

 adversaria of the author. 



The correspondence with Leibnitz, which had been 

 resumed in 1688 after a long interruption, went on 

 regularly during the years 1691-5, dealing partly with 

 pure mathematics, partly with the theory of universal 

 gravitation. It shows that Huygens never became 

 reconciled to the use of the differential calculus, but 

 continued to prefer geometrical methods. In 169 1 

 he acknowledges the utility of the calculus, and says 

 that he has made some progress in it ; yet in the 

 very last letter to Leibnitz (of December 27, 1694) 

 Huygens remarks that the new method " ne me 

 demeure pas pr^sente k 1 'esprit quand j'ai discontinue 

 longtemps k m'y exercer." But the numerous letters 

 and notes on the quadrature of curves, especially of 

 the folium of Descartes, exchanged between Marquis 

 de I'Hospital and Huygens show that the latter's 

 power of dealing with geometrical problems was as 

 vigorous as ever. He also continued to correspond 

 with Fatio de Duillier, whose letters foreshadow the 

 accusation of plagiarism which he launched against 

 Leibnitz in 1699, as he from 1691 repeatedly assured 

 Huygens that Newton was the discoverer of the 

 differential calculus, and that it would not be pleasant 

 for Leibnitz if Newton's letters to him were pub- 

 lished. Huygens, who continued to think the new 

 calculus unnecessary, did not omit to tell Leibnitz 

 that, according to Fatio, Newton knew more of the 

 inverse problem of tangents than Fatio and Leibnitz 

 did; to which Leibnitz quietly replied that everybody 

 had his own ways of proceeding, and perhaps he 

 NO. 1868, VOL. 72] 



knew of some which Newton had not yet perceived. 

 Fatio several times mentioned in his letters that he 

 intended to publish a new edition of the " Principia," 

 as Newton had declined to do it himself, and pro- 

 posed to expand it into a folio volume, which he 

 flattered himself would be more easily understood than 

 Newton's quarto. 



With Leibnitz, Huygens also exchanged ideas about 

 the nature and cause of gravitation. In 1692 Leibnitz 

 remarked that a vortex like that assumed by 

 Descartes is necessary to explain why the earth's 

 axis remains parallel to itself, while the fact 

 that all planets and satellites move in the 

 same direction also points to their being carried 

 along by some fluid matter. He rejects the 

 idea of Cassini, that the orbit of a planet 

 is not an ellipse, but a Cassinian oval, since no 

 physical reason had been given for this hypothesis. 

 The spherical shape of a drop of water, the fall of a 

 body to the earth, and the motion of the planets are 

 all, according to Leibnitz, caused by the " materia 

 ambiens." Huygens, on the other hand, thinks that 

 the sphericity of a drop is more likely caused by the 

 rapid motion of some matter which circulates inside, 

 and as to the planets he fails to see why we should 

 assume the existence of vortices when Newton had 

 proved that the law of inverse squares " with the 

 centrifugal force " produces the ellipses of Kepler. 

 He also makes other objections to the theory of 

 Descartes, particularly to the small spheres of the 

 second element which revolve round the accumulated 

 first element (the sun), and are supposed to have been 

 formed by the corners of the original matter being 

 rubbed off ; for if this matter offered any resistance 

 to this rubbing, what should limit the resistance, and 

 if there were none, what should prevent the total 

 destruction of the particles? The vorte.x which should 

 preserve the parallelism of the earth's axis is in- 

 compatible with the motion of the same matter in 

 all directions which should produce gravitation ; an 

 objection to which Leibnitz could only reply that we 

 have two such independent circulations here on the 

 earth, causing gravity and magnetism. Huygens 

 acknowledges that vortices are a convenient means 

 of explaining the common direction of planetary 

 motions, but the constant eccentricity of a planet and 

 the variable velocity in the orbit cannot be accounted 

 for by the theory. 



In this connection it is most interesting to 

 read some notes written by Huygens to the 

 well known "Vie de Monsieur Descartes," pub- 

 lished anonymously by .'\. Baillet in 1691. Accord- 

 ing to Huygens, Descartes was very successful in 

 getting his conjectures and fictions accepted as trutli, 

 just as novels may be taken for real history; but, on 

 the other hand, he dealt with tangible things, and 

 not with mere words as earlier philosophers had done. 

 Bacon did not understand mathematics and was want- 

 ing in penetration as regards physics, being unable 

 even to conceive the possibility of the earth's motion, 

 which he mocked as an absurdity. Galileo had enough 

 of mental power and mathematical knowledge to make 

 progress in physical science, and he was the first to 

 make discoveries as to the nature of motion, although 



