A PARTICULAR METHOD IN CENTROIDS 



225 



solid wedge, transferred over to the position giving the section 

 BOB', and carrying its Center of Mass from ^ to g' \ we have then 



G G ' wedge 



gg ' hemisphere 



which becomes when a is indefinitely diminished 



#/'Xa a 



20^ 



Og: 





(11) 



From this the Center of Mass of a wedge of any angle 20, 

 cut out of a solid sphere hy the intersection of two diametral 

 planes, is easily found. Being the Center of Mass of an arc Z 2^ 



and radius—— its distance from the center is by (1) 



16 



37rr sin 



(12) 



The result in (11), like that in (8), might have been found by 

 considering the hemisphere made up of an infinity of wedges of in- 

 finitely small angle. Also the Center of Mass of a wedge Z 2^, re- 

 sult (12), might have been found by the method of this article. 



7. To find the Center of Mass of a segment of a solid sphere, 

 Let ACB (Fig. 4) be a section of the segment through its highest 

 point, and through O the center of the sphere. G, the Center 

 of Mass, is in this plane, and OG is perpendicular to AB. 



