184 





<;i:AYITV. 



And p being supposed a known function of x and ?/, the 

 integrations present no theoretical difficulty. 



Similarly the polar formulae may be modified. For example, 

 instead of the formula given above for x we now obtain 

 - ffpr* sin 6 cos 6 dOdr 



In this case p must be expressible as a function of r and 

 6, in order that the integrations may be practicable. The 

 most common cases are two ; in one the density depends only 

 on the distance from a fixed point in the axis of revolution, 

 so that by taking this point as origin p is a function of r ; in 

 the other case the density depends only on the distance from 

 the axis of revolution, so that p is a function of r sin 6. 



\ _S. To find the centre of gravity of a solid we divide it 

 into elements as follows: draw a series of planes perpen- 



