122 



CENTRE OF GRAVITY. 



Plane Area. Doubl 



118. There is another method of dividing a plane area 

 into elements, to which we now proceed. 



Let a series of straight lines be drawn parallel to the axis of 

 y, and another series of straight lines parallel to the axis of a;. 

 Let st represent one of the rectangles formed by these straight 

 lines; and suppose x and y to be the co-ordnattfl of *. and 

 x + A# and y+ Ay the co-ordinates of t. Then the area of 

 the rectangle st is Ax Ay, and the co-ordinates of its centre 

 of gravity are ultimately x and y. Hence, to find the abscissa 

 of the centre of gravity of any plane area, we can take the 

 sum of the values of o-AxA?/ for the numerator, and the sum 

 nf th- values of AxAy for the denominator, Aa; and \<j being 

 indefinitely diminished. Thi< ifl rxpn-ssed thus, 



_ffxdxdy 



~ 



larly, 



ffydxdy 



