Ml 



limits depend on the nature of the curve. But if y be 

 the centre of gravity of the perimeter, 



v--' 



y- id, ' 



e limits being the same as before. 



efore the whole surface y&fd* " the are described 

 centre of gravity, multiplied by the length of the 





 r ir</ by the revolution of a circle round a straight line in its 



the distance of the centre of the circle from the axis of 

 volution be . !*e the radius of the circl 



ngth of the path of the centre of gravity of the area of the 

 jure is 2irn, and the area of the figure is ir6* ; 



refore the content of the solid 



Also the length of the path of the centre of gravity of the 

 perimeter is Siro, and the length of the perimeter is 2ir& ; 



efore the surface of the solid = \ifal. 



2. To find the centre of gravity of the area and also of 

 ihe arc of a temici 



A semicircle by revolving about its diameter 



re ; the content of the sphere is - ira 1 , and the surface 



', the radius being a; the area of the semicircle is - rra 1 , 



d tin* perimeter ira; -v f the distance of the centre 



gravity of the area from the diameter 



content of sphere 

 2ir. area of semicircle a ' 



ft distance of the centre of gravity of the arc from the diameter 



. arc of semicircle 



