CHAPTER VII. 



OF THE MOTIONS OF A SOLID BODY OF 

 ANY GIVEN DIMENSIONS. 



§ 25, 26. [Introduction.'] Equations which determine 

 the progressive and rotatory motion of the hodi/ in 

 question. 



1339> Theorem. " 349/' When a system 

 of bodies has a rotatory motion round any 

 centre, the effect of each body, in turning the 

 system round a given point, must be esti- 

 mated by the product of its momentum into 

 the distance of the body from that point ; and 

 the power of each body, with respect to the 

 original centre of rotation, will be expressed 

 by the product of the mass into the square of 

 the distance. 



Suppose the bodies A and B, fixed to the ends of two 

 equal levers, to meet each other, and simply to communi- 

 cate their motion, and let B be twice A, and moving with 

 half its velocity, then the motion of A will exactly de- 

 stroy the motion of B, and this effect is therefore the mea- 

 sure of the motion of A : but if tlie bodies A and B be con- 



