Mar. 19, 1874J 



NATURE 



379 



the Transformation of Multiple Integrals, the theory of 

 the Potential, and the functions of Laplace. A know- 

 ledge of the figure and dimensions of the earth forms the 

 basis of all the numerical results of Astronomy. In 

 § 25 he carefully defines the several terms made use 

 of in the two subjects, equating in a useful way the 

 varying terms employed by different writers. 



The foundation of our subject, as all our readers know, 

 is " great Newton's own ethereal self," Newton, " the 

 crown and glory of his race." " The propositions on 

 Attraction are numerous, exact, and beautiful ; they re- 

 veal his ample mathematical power. The treatment of 

 the figure of the earth is, however, still more striking, 

 inasmuch as the successful solution of a difficult problem 

 in natural philosophy is much rarer than profound re- 

 searches in abstract mathematics. Newton's solution 

 was not perfect ; but it was a bold outline, in the main 

 correct, which succeeding investigators have filled up but 

 have not cancelled. Newton did not demonstrate that 

 an oblatum is a possible form of relative equilibrium ; 

 but, assuming it to be such, he calculated the ratio of the 

 axes. This assumption may be called Newton's postu- 

 late with respect to the figure of the earth ; the defect 

 thus existing in his process was supplied about 50 years 

 later by Stirling and Clairaut " (§ 44). Newton appears 

 to have arrived at his theorems in attraction in 16S5 ; the 

 first edition of the " Principia " made its appearance in 

 1687. (De Morgan, in his " Budget of Paradoxes," p. 81, 

 discusses some of the sources of the apple story.) 



Mr. Todhunler nowhere takes account of theories main- 

 tained before the time of Sir Isaac Newton ; these were, 

 for the most part, if not entirely, «on-mathematical. A 

 sketch is given in Book 111. of Maclaurin's "Account of 

 Sir Isaac Newton's Philosophical Discoveries, in Four 

 Books." * We draw attention to this work because no 

 reference is made to it in the History, whereas great part 

 of Books III. and IV. is devoted to the subject of gravi- 

 tation. 



The same reason (for we cannot suppose Mr. Tod- 

 hunter not to have consulted the work) has possibly 

 induced him to pass over in silence the " Theorica; 

 Mediceorum Planetarum ex causis Physicis Deducta:"f 

 of Borelli, though Libri, in his Catalogue, states that this 

 writer " uses the principles of the law of Attraction as 

 afterwards promulgated by Sir Isaac Newton." 



Hardly a subsequent chapter but contains from one or 

 another writer an acknowledgment of Newton's high 

 powers ; we shall here content ourselves with citing only 

 Laplace's warm eulogy: — "Cct admirable ouvrage contient 

 les germes de toutes Its grandes decouvertes qui ont ct(5 

 faites depuis sur le systC:me du monde ;" and further, he 

 says, that the first step thus made by Newton in the 

 theory must appear immense. 



Huygens next appears on the scene. Our author 

 (§§ 64, 65) clears up one or two points, more especially 

 the rightful claim to priority of Newton over Huygens ; 

 an error which crops up in Barlow's " Matheinatical Dic- 

 tionary" and Svanberg's work on the Lapland Opera- 

 tions. 



From § 48 we gather that Mr. Todhunter has not seen 

 the Opera reliqua. S'Gravesandc, in the preface to vol. ii. 

 (we quote from the edition Amstel, 1728, 4to.), says, " Trac- 



* London, 1775. I'd edit. 8vo. 

 t Florenlia, 1666. 410. 



tatus de lumine et dissertatio de gravitate qua ambo 

 scripta gallice dedit auctor, quamvis primum ut ipse 

 in hujus prasfatione monet, in linguam latinam vertere 

 sibi proposuerat : " the second is turned into Latin with 

 title " De causa gravitatis." 'X\ve.prafatio occupies pp. 95, 

 C)6, disseriatto pp. 97-116 with an additamentum down 

 to p. 136, and there is a plate : the De vi centrifugd occu- 

 pies pp. 107-134. 



In the Opiiscula postuma (Lugd. Bat. 1703, 4to.) the 

 treatise De vi centrifugd (pp. 401-428) is founded, if we 

 mistake not, on a different view of gravitation from that 

 assigned to him by Mr. Todhunter in § 50. 



Miscellaneous investigations, up to the year 1720, are 

 then considered : Burnet's " Theory of the Earth " is 

 glanced at, Keill's examination of the same, David 

 Gregory's writings (which contribute nothing new), 

 Hermann, Mairan (" Misapplied Mathematics and Mis- 

 placed Ingenuity") and the Cassinis, under whose power- 

 ful influence doubts arise as to the real shape of the 

 earth, are more fully discussed. 



We proceed to Maupertuis, a memoir * by whom is said 

 (§ 128) to be the first example of the adoption of the 

 principle of attraction by French mathematicians. We 

 offer here a collation of the first editions of two of his 

 works with the second editions which Mr. Todhunter 

 discusses (§ 143). 



The avertissement of 3 pp. in the 1738 edition of the 

 Examcn dhititeresse is not reproduced in the 1 741 edi- 

 tion : the 82 pp. of text, as also the 3 pp. of contents, at 

 end, and the one page of errata, appear to be identical 

 with the matter in the later edition. For the Examett des 

 ttois, &c., the bookseller's nvertissenient {/^^ip.) is common 

 to both : the 42 pp. of text appear to be the same ; there 

 is no list of errata ; the foot-notes of the later edition 

 appear as side-notes in the 1738 copy. The copy we 

 consulted had the two essays bound up together, and is a 

 duodecimo volume. 



In the " Philosophical Dissertations on the Uncertainty 

 of Human Knowledge" by the Marquis d'Argens, author 

 of the " Jewish Spy," to which is added M. Maupertuis' 

 "Dissertation upon Gravity ,"&c.,translatedfrom the French 

 edition, in 2 vols. 1753, with the running title "The 

 Impartial Philosopher," we have the following : — "After 

 M. Maupertuis had examined the Newtonian system and 

 after he had undergone infinite dangers and difficulties 

 in the frozen regions of the North, in verifying a particular 

 part of it, he concludes that we may look upon gravity as 

 a power diffused through all parts of matter by which all 

 its particles attract each other. The concurrence of all 

 the force of matter which composes the earth, attracts and 

 causes bodies to fall towards its surface, keeps the moon 

 in her orb, and produces with regard to the other planets, 

 and with respect to the sun, the like phenomena, always 

 in proportion to the quantity of their force, their direction, 

 and their distance" (pp. 255-263). 



Whilst treating of Maupertuis, we think we have seen in 

 the Graves' hbrary the English translation of his " La 

 figure de la terra . . . au cercle polaire," 1738: possibly 

 the extract cited above is taken from it. In § 149 Mr. 

 Todhunter says " Childrey seems" &c. : Joshua Childrey, 

 1623- 1670, was of Magdalen College, Oxford, Arch- 

 deacon of Salisbury, 1663. He wrote " Britannia 



» ' ' Sur les loi.x de I'attraction : " cf. Bailly. 



