^ii Mr-. l^Ai^DZi^'s Invefrig.'?rf'on of 



that a cone, a conoid, a prifm^ or a pyramid, &c. of certain 

 tiimeiifions, will have the like property of continuhig, with- 

 out any refb-aint, t6 revolve about any axis paffing through its 

 center of gravity. 



When the axis, about wliich a body may be made to 

 r-evolve, is not a permanent one, the centrifugal force of its 

 particles will difturb its rotatory motion, fo as to caufe it to 

 change its axis of rotation (and confequently its poles) every 

 inflant, and endeavour to revolve about a new one : and I can- 

 not think it will be deemed an uninterefting proportion to de- 

 termine in what track, and at wliat rate, the poles of fuch 

 momentary , axis will be varied in any body whatever; as, 

 without the knowledge to be obtained from the folution of 

 fuch problemx, we cannot be certain whether the earth, or any 

 other planet, may not, from the inertia of its own par- 

 ticles, fo change its m.omentary axis, that the poles thereof 

 fliall approach nearer ancl nearer to the prefent equator, or 

 whether the evngation of the momentary poles, arifing from 

 that caufe, will not be limited by fome known lefler circle. 

 Which certainly is an important confideratioii in aftronomy ; 

 efpecially now that branch of fcience is carried to great per- 

 fection, and the acute aftronomer endeavours to determine the 

 motions of the heav-enly bodies with the greateft exadnefs 

 poffjble. 



I do not know that the problem has before been folved by 

 any mathematician in thefe kingdoms; but I am aware that it 

 has been coniidered by fome gentlemen, very eminent for their 

 mathematical knowledge, in other nations. The folutions of 

 it, given by the celebrated M. LeoiNhard Euler and M» 

 D'Alembert, 1 have feen : and we learn from what the laft 

 mentioned gentleman has faid, in his Opujcules Mathematiques^ 



that 



