40.] DETERMINATION OF CENTROIDS. 



The mass of the larger disc is 



21 



Substituting these values into the equation of moments we 

 find' 



M^XI 6 



x= ^ * * = a = o.i6i6..a. 

 M % ^M l 5(3-^-2) 



40. Proceeding to the determination of the centroids of 

 curved surface-areas, we begin with 

 the special case of the homoge- 

 neous area of a surface of revolu- 

 tion. If the axis of x coincide 

 with the axis of revolution and 

 R = rsm6 be the distance of any 

 point P of the surface from this 

 axis (Fig. 10), the equation of the 

 surface, or of its meridian section, 

 is x=f(R} ; and the element of 

 area is 



Fig. 10. 



dS = 



= R V 



We have therefore for the centroid of the portion of the surface 

 contained between two sections at right angles to the axis and 

 two meridian planes (i.e. planes through the axis) including an 

 angle 0: 



