OF THE MOTIONS OF A SOLID BODY. 263 



we shall have -s/Cp^-f-jf^+r*) for the angular velocity of 

 rotation. 



Scholium. It is obvious that the quantities jo, ^, and 

 r, of v^rhich the determination is extremely important in ail 

 inquiries respecting rotatory motion, are independent of 

 the situation of the plane of x' and /, and that they are 

 sufficient to express the relation of the momentary axis of 

 rotation to the principal axes of the body, being however 

 themselves susceptible of perpetual variation at succes- 

 sive times. 



§ 29. Eqiiations for determining the position of the 

 momentary axis, and of the principal axes, in terms of the 

 time . Case of rot at ion derived from an impulse no t pass ing 

 through the centre of gravity. Formula for determining 

 the direction of the primitive impulse. Example of the 

 rotation of the planets and of the earth in particular, 

 P. 80. 



355. Theorem. When the body revolves 

 freely, without any foreign disturbance, we 

 have, with respect to the plane of greatest ro- 

 tatory power, cos e = y, ta ^=y and d^zz 



~'abc^^I^^ ■' ^' being^r^ +3'^+'"S and H 

 being a constant quantity ; d^ being also in 

 general = 



ABCdp' 



V \ {ACk"^-H^-{-{AB-AC)p"') . {H^BCk^-{AB-BC)p'2^ 



The equations (D) ,(346), afiFord us, by making the 

 fluxions d^, dN\ and dN'\ which depend on the forces. 



