the Rotatf/ry Motion of Bodies, 33! 



I do not find that the refolving the forces H, I, K, in any other 

 manner will conduce to the attainment of any uieful conclufion. 

 It appears, by what is done above, that the force 



His = -^^xCDW/3^/3', 



3<23RT 



I is = — "-^ X BC . Cfir - Bm~ . -y^, 

 3«niT 



K = "-^ X BD V^^i ; 

 3^'RT 



R being = B>^o"^+D^iGT+e/3y. 

 And it is obvious, that each of the three lafl: mentioned forces 

 will be = o, if any two of the quantities b, c, d, be equal ; 

 two of the values of thofe forces then vanifhing, by reafon of 

 that equality; and the third value alfo vanifhing by either 



/3, y, or (5", being at the fame timerro. Therefore, in that" 

 cafe it happens, that M. Euler's computation agrees with 

 mine: in every other cafe, I am clearly of opinion, his con- 

 clufions are, not true. The fame may be faid of M. D'Alem- 

 bert's conclufions refpe£ling the fame propofition. 



The evagation of the pole, of a revolving, body confidered 

 above, does not arife from gravity, the attra6lion of any other 

 body, or any external impulfe whatever ; but is only the con- 

 fequence of the inertia of matter^ and muft neceflarily enfue, . 

 according to the theory here explained, in every body in the 

 "univerfe, after having been made to revolve, without reftraint,' 

 about any line pafling through its center of gravity, that is not^. 

 permanent axis of rotation. 



The Earth being neither uniformly denfe nor a perfect 

 fpheroid mufl, in ftridnefs, be confidered as having only three' 

 permanent axes of rotation, agreeably to what I have proved 

 in my" Mathematical Memoirs ; and, as it is difturbed in its 

 rotatory motion by the attrad:ion of the fun and moon (and 



other 



