PLANE CUttVE. 



values must bo substituted in the preceding 

 ssions and the integrations then effected. 



If we use polar co-ordinates we hare x-rcos0, y-rsin 0, 

 Eeooe 



for r and ,*1 we must substitute their values in terms of 6 

 Itiation to the curve. 



V straight rod of uniform thickness and 



Tnk origin on the line we have y -#r, where is 



constant ; by equations (3) of Art. 132, supposing the 



origin to be at one end of the rod and h the abscissa of the 

 other 



- ff x <bs h _ ffffxdx fth 



That ix, the centre of gravity is the middle point of the rod. 



. 2. Suppose the transverse section of the rod to vary 

 as the ft* power of the distance from on the 



'.. and suppose the axis of x to coii 

 ixis of the rod; then y-0, and on (1) of 



we put /. where /i is constant Uciice, if h 



be the length of the rod, 



