EXAMPLES. '.'.', 



plane have any position; and refer the 

 -ate sciiii-diainrtcrs if axes; let tbo plane 

 ) be j> i of the cutting plane, and 



>se the equation to the ellipsoid to be 



\- sunpoae the segment cut off by the plane to be divided 

 an it: :hin slices by 



es parallel to the plane of (y, :). By the a of 



ellipsoid these slices will be bounded by ellipses which 



trcs on the axis of x\ and thus we see th.v 

 e of grav: : ..tV will lx on the axis of 



Consider one of the slices bounded by ulanes which have 

 heir abscissa * an >' respect it will be 



that the volume of the slice is ultimately 



wVe (l -- ^J si 



sn <a sn 



.< angle between the axes of y and *, and a is 

 the angle which the axis of x makes with the plane of (y, ). 



constant volume, and Xa' the ab- 

 scissa of the plane cutting off the segment ; then 



F wb'c' sin a> sin a / ( I - -z ) dx 

 Ji*\ a / 



- wab'c sin sin a [1 - X- l (1 -X")J. 



Now by the properties of the ellipsoid 



ira'Uc sin a> siu a = irabc, 

 a, b, c are the semi-axes of the ellipsoid ; thus 



r-ic{i-x-i(i-x')) CO- 



An ' c the abscissa of the centre of gravity of the 



segment cut off, 



