IM 



plane* will 



' 



. <lra\v plain-* p ilar to the axis off, 



' ach strip is divided into parallelepipeds such as at in 



.; . 1 utcs of j and x + Aor, 



c of t\ Ay A* is the volume of ft, 



and as the co-ordinates of its centre of gravity are ultimately 



a?, jr, and *, we hare 



Mxdxdyds _ Mydxdyds 



* &* 



129. In applying the above formulae to examples, great 

 care is necessary in assL :--r limits to tne integra- 



tions ; this we snail illustrate by Example*. 



o centre of grarity of the eighth part of 

 an ellipsoid cut off by three principal planes. 



to the surface be 



equation to the curve in which the surface meets 

 lane of (2, y) is 



rate first with respect to *, and take for tlu limits i-O 

 and f-c*/fl - j-|i); w ^ thus include all the elements 

 like ft which form the strip fpqQ. Next integrate with re- 



toy, and take for the limits y-0 and y-&A/(l - T) ; 



us include all the stripe like PpqQ which form the slice 

 LplmqM. Lastly integrate with respect to x, and take for 



