1LM 



IRE OF GRAVITY. 



of the eentre of gravity of PQqp. 

 agrees with that ; 



llcncc the above equation 



Tin* process and the figure in tin- y. tw<> An 



1 liave been unnecessary if_our only object liad been t<> 

 establish the formulae for x and ?/, since these formula- can be 

 obtained more simply as we have just shewn. But we .-hall 

 ire hereafter other formula 1 , involving double integration, 

 and have therefore directed the reader's attention to i 

 !er to accustom him to the subject. 



120. Ex. Let OPE be a parabola having f..r its 

 y* = 4oar, and OE a straight line ha vim: J'>r its equation 

 find the centre of gravity of the area OPE between the curve 

 and the straight line. 



Here ^ (x) = 2 *J(ax), ^ (x) = 

 from the equation 2 V(^) = kh > 



therefore h = ~ 



, c = 0; h is to be found 



Thus 5 



8a 



