324 ON THE 310TION OF 



tion in the second volume of his Mecanique 29 . It is remark- 

 able that in considering this variety of the problem, Landen, 

 an English mathematician of excellent abilities, found him- 

 self unable to comprehend its principles, after fourteen years 

 of earnest and almost unremitted efforts to overcome its dif- 

 ficulties, and that too with the solutions of Wildbore. Frisi. 

 Euler and D'Alembert before him. In opposition to these 

 writers he contended to the very day of his death that a cor- 

 rect analysis would give a constant angular rotation about the 

 instantaneous axis. 



The latter part of DAlembert's memoir is occupied with 

 the general equations when any accelerating forces are pro- 

 posed, and contains some valuable extensions and simplifica- 

 tions of the formulas he had given before. It was now 

 Euler's turn, however, to take the lead. In 1765. he had 

 brought the general equations of rotatory motion into the 

 form in which they are presented by Laplace in the first vo- 

 lume of the Mecamque Celeste 30 , and there is an acknowledg- 

 ment in the fifth volume of the same work 31 , that the equations 

 of Euler appear to him to be the very simplest which it is 

 possible for the science to obtain. The work in which these 

 formulas are given 32 contains two interesting applications, hav- 

 ing some connexion with the subject of the present essay ; 

 the determination of the motion of a heterogeneous sphere on 

 a horizontal plane, and a similar inquiry with respect to the 

 motion of certain bodies, a given point in which remains in 

 contact with the plane. Of these I shall speak more particu- 

 larly hereafter. 



The general results of Euler are obtained by the aid of the 

 discovery of Segner. As the motions of a system, however, 

 flow necessarily from its state at a given time and the forces 

 by which it is solicited, it seems fair to demand a solution of 

 the problem in which recourse shall not be had to the pro- 



29 Mecanique Annlytique, Tome II. 1815. p. 261 — 263. 



10 Mtc. (VI. Tome 1. p. 74. 



3 ' Mtc. Cel. Tome V. p. 255. 



52 Theoria motus corporum solidorum seu rigidorum. Rostoch. 1765. 



