20 INTRODUCTION TO DYNAMICS. [39. 



of the smaller disc, M% that of the larger, we must have 

 J/ x = 



Fig. 9. 



The equation of the smaller circle is r=# cos#. Taking as 

 element of the mass of the smaller disc the mass contained 

 between two arcs of radii r and r+ dr, we have for this element : 



or since p=&r, r=acos0, 



l = 2 ka*B cosW (cos 6). 



Hence M^kBd (cos 3 (9) 



cos 3 (9 - 



= f ka* f f cos 3 /9^ = | ka* - f = 



The centroid of the element dfJ/j lies, according to Art. 29, 

 at the distance r sm from O. We have therefore 



sin (9 cosW0 r 



