ANIMAL MECHANICS. 303 

 OS = a Oa - I 



Y08 - 0 Oa' = /' 



a6>A r = 0 



Fig. 82. 



Let the point a be moved to the point b, by a rotation (w) 

 round the axis aSZ. Then, if 



/Sa = J. ^-Sa' = 3/ 



6V = ^' a£Z = a 



a/Sa' = ^ 



we have, since A and ^4/ are constant, 



p = act 



A' % - 2 A A' cos x ; 



If we describe a sphere 

 round 5 as centre, we shall 

 have (Fig. 83), 



2 A A' cos y. 



Sa = £/> = 

 aa' = a* 



bSa = w. 



Fig. 83. 



