;J22 ON THE MOTION OF 



point 13 , and along with Maclanrin had resolved velocities and 

 forces in the direction of these coordinates 19 . 



Euler had ohserved hefore Maclaurin that all forces what- 

 ever soliciting a point might be resolved in three directions 

 parallel to three fixed rectangular coordinates. He merely 

 employed these however for the purposes of immediately re- 

 solving the forces again into three others also rectangular but 

 not fixed, the tcmgentialis, normalis premens, and the nor- 

 mally deflectens. Maclaurin appears to have been the first 

 who endeavoured to turn to account the advantages of having 

 the forces fixed in their directions, but the geometrical me- 

 thods to which he in common with all his countrymen were 

 unfortunately attached, made it impossible for him to realize 

 to any extent the benefits of this arrangement. 



It became an easy matter then to reduce to a regular form 

 the calculus of the motion of a point, but it was by no means 

 so obvious what were the three elements which were equally 

 concerned in defining the rotations about the centre of gra- 

 vity. The formulas which were first invented for this pur- 

 pose were given by Euler in 1750, and may safely be pro- 

 nounced among the expressions in the science most remark- 

 able for their simplicity and absolute generality 20 . In the 

 perfect form in which they came at once from the hands of 

 Euler, they have been extensively employed by later mathe- 

 maticians, and particularly by Lagrange in his Mecanique 

 Analytique. A year before the publication of this paper, Eu- 

 ler had given a solution of the problem of the compound ro- 

 tation of the earth 21 , which he acknowledges, in a memoir on 

 the same subject inserted in the Transactions of the Berlin 



18 Mechanica analytict exposita. Auct. Eulcro. 173G. Tom. [. p. 339. 

 11. 



19 Mechanica, Tom. II. 477. — Treatise of Fluxions, by Colin Maclaurin. 

 Edinburgh, 1742, p. 391, § 470. 



i0 De'couverte d'un nouveau principe de Mecanique. Memoires de 1' Aca- 

 demic Royale dcs Sciences de Berlin. Tome VI. 1750. 



21 Reclierches de la Precession des equinoxes, et sur la nutation de 1'axe de 

 la terrc. Memoires de l'Acad. de Berl. Tome V. 1749. 



