SEQUEL TO THE GENERALIZATION. 109 



instance of Professor Airy's calculation of an ine- 

 quality of Venus and the earth, of which the period 

 is 240 years. The approximation of the moon's 

 motions has been pushed to an almost incredible 

 extent by M. Damoiseau, and, finally, Plana has 

 once more attempted to present, in a single work 

 (three thick quarto volumes), all that has hitherto 

 been executed with regard to the theory of the 

 moon (E). 



I give only the leading points of the progress of 

 analytical dynamics. Hence I have not spoken in 

 detail of the theory of the satellites of Jupiter, a 

 subject on which Lagrange gained a prize for a 

 Memoir, in 1766, and in which Laplace discovered 

 some most curious properties in 1784. Still less 

 have I referred to the purely speculative question 

 of Tautochronous Curves in a resisting medium, 

 though it was a subject of the labours of Bernoulli, 

 Euler, Fontaine, D'Alembert, Lagrange, and La- 

 place. The reader will rightly suppose that many 

 other curious investigations are passed over in utter 

 silence. 



9. Precession. Motion of Rigid Bodies. The 

 series of investigations of which I have spoken, 

 extensive and complex as it is, treats the moving 

 bodies as points only, and takes no account of any 

 peculiarity of their form or motion of their parts. 

 The investigation of the motion of a body of any 

 magnitude and form, is another branch of analytical 

 mechanics, which well deserves notice. Like the 



