OP GRAVITY. 



Iii the same manner we may shew that 



where y' is the limiting value <>f tlio ordinnte of the centre 

 J of the element 7\M/A when its breadth is indi-li- 

 nitely diminished; y is therefore = Jy; hence 



\Y, liavr now only to substitute in (1) and (2) for y its 

 value in terms of x, and then to effect the integration by the 

 ordinary methods. 



112. It will not be necessary for the student in solving 

 an example to repeat the whole of the preceding process. 

 11 he understands how the necessary exactness may !>< 

 given, if required, he may proceed shortly thus. The li 

 PQML**yaX ultimately, and the co-ordinates of its c ntre 

 of gravity are x and \y ultimately. Hence 



the integrations being taken between proper limits. 



Unless the contrary be specified, we shall h<Teaft< T sup- 



pose the bodies we consider to be of uniform <&??><>//, and 



shall therefore not introduce any factor to represent the 



density, because, as in the preceding Article, the factor will 



ippear. 



113. Ex. 1. Let the curve be a parabola whose equation is 



