CENTRE OF GRAY I TV. 



Ex. 3. An arc of a circle. 



Take the origin at 

 the centre of the ci: 

 and the axis of x bi- 

 secting the arc. Then 

 jj = ; and supposing 

 J a to be the angle sub- 

 led at by th- 

 . and a the radius of 

 the circle, we have, by 

 . 132, equation (4), 



_ _ a*/*, cos 6 dd __ a sin a 



Ex. 4. The arc of a semicycloid. 



Take the origin at the vertex, and the axis of y a tangent 

 there; then (J^\ = - ; hence 



therefore 

 therefore 



2 (2o) 



