334 ON THE MOTION OF 



subjoined to Dr Adrain's in the same number of the Diary, 

 to dispense with the conditions of a symmetrical density or a 

 vertical natural axis of rotation. In the hypothesis of perfect 

 rolling (the first instance I believe in which it has been con- 

 sidered in reference to an axis varying ad libitum) the formu- 

 las I have there given lead to a complete solution of the prob- 

 lem 40 considered in all the generality of which it is suscepti- 

 ble. It still remained to apply to oscillating bodies of any 

 form whatever what is there remarked of bodies with a sphe- 

 rical areola of contact, and at the same time to have regard to 

 the figure of the surface of support. This I have attempted 

 in the following dissertation ; with what success I leave to 

 those who are better practised than myself in speculations of 

 this nature, to examine and decide. 



Before entering upon this subject, I beg leave simply to re- 

 mark that the new words or new combinations of words occa- 

 sionally employed in the following paper, have not been intro- 

 duced from any idle love of innovation, but from the absolute 

 necessity of the case. The tedious circumlocutions and the 

 incessant repetitions to which I should have been forced with- 

 out the proposed abridgments, would have extended this com- 

 munication far beyond its proper limits, and would not I 

 think have added either to its interest or perspicuity. In 

 short, I have employed these terms precisely for the same 

 reasons that I employ the symbols of analysis, and attach 

 no sort of value to them after they have served my purpose, 

 but leave them to be accepted or rejected, as those who choose 

 to pursue this subject may happen to find it most convenient. 



50 In consequence of an error in developing the variation of the living forces 

 Hue to the progression of the system, a correction (to be made by substituting 

 c — h in place of e) becomes necessary in some of the expressions at the close oi 

 the paper above referred to. 



