320 ON THE MOTION OF 



rotation can always be reduced by regarding as accelerating 

 forces tbe unknown reaction of the point or surface of sup- 

 port. Newton, whose name it is necessary to mention in the 

 history of almost every interesting or important speculation 

 in Mechanical Philosophy, is the first who attempted to deduce 

 from mathematical principles the laws of these peculiar mo- 

 tions as they exhibit themselves in that most remarkable ex- 

 emplification of them, the Precession of the Equinoxes 11 . 

 The singular sagacity of this extraordinary man seems to have 

 protected him from an erroneous result, amidst a number of 

 precarious and sometimes inaccurate assumptions to which 

 the tediousness and barrenness of the geometric method pro- 

 bably forced him to resort. An amended solution of this 

 problem was given by D'Alembert in 1749, with all the de- 

 velopments and verifications which the possession of a pow- 

 erful analysis had brought within his reach 14 . The treatise 

 in which this subject is discussed contains at the same time 

 every thing that is necessary for reducing in all other cases 

 the general problem of the free motion of a rigid body to its 

 six differential equations. This reduction was in fact ac- 

 complished by the same author in a memoir which he an- 

 nounced in 1758 as prepared for the press, but which was 

 not actually published until 1761, in the first volume of his 

 Opuscules Mathematiqucs' 5 . The results here obtained, and 

 to a certain extent the manner of obtaining them, differ from 

 the methods and formulas of more recent authors in little 

 else than the improved selection and arrangement of the sym- 

 bols now employed. In this respect D'Alembert was in no 

 degree superior to his cotemporaries, and indeed nothing is 

 more striking than the contrast which exists between the 

 profound and original views of this illustrious writer and the 

 negligent and inelegant notation in which they are expressed. 

 It is a little surprising that an author who has so often in his 



I' Principia, Lib. III. Prop. XXXIX. 



1 * Rccherclics sur la Precession des Equinoxes ct sur la Nutation de I' Axe de 

 la Terre clans le SysU'mc Ncwtonicn. Paris, 1719. 



15 Du Mouvement d'un Corps de Figure quelconque, animd par des forces 

 quelconques. Opusc. Math. Vol. i. 1761, p. 7 1. 



