CENTRE OP GRAY 



ilarly. if tlic curve BPQE L a surface 1\ 



round the axis of ?/. \vr have 



r and 7* denote as before the abscissse of the extremities 

 of the cir. 



1 f we use polar co-ordinates, we have x = r cos Q^y r sin 0, 



and 



thus if the curve revolves round the axis of x, we have 



and if the curve revolves round the axis of y, we have 



The limits of the integrations arc the values of 6 which 

 correspond to the extremities of the curve. 



Ex. 1. A cylindrical surface. 



Take the axis of the cylinder as the axis of #; then y = the 

 radius of the cylinder, and is constant ; hence 



- Kxdx i(^-0 h + c 



= #<te*-h^- TT- 



Ex. 2. A spherical surface. 



