area P<. '1m knesi 



of the solid and p its density, kp (yAjr -f u) is the mass 



.<) abscissa of the centra of 

 gravity of the whole figure CHI .'// 66, 



1 X*p(jx+) A* + 



niforra. The summa- 

 idc all the figures like PQML, which are cora- 



v suppose n to increase without limit, and ea< 



mit ; then the term 1 

 vanishes; for it expresses the sum of 

 all the figures lik- icfore less than a rectangle 



H breadth Ax and for its height the greatest 

 .itc comprised between CD and UK. Also the term 



it is less than the product 



and as we have ju>: vanishes. 



the expression for x becomes, when thr number of 



v increased and each term indefii 

 diminished, 



i 



Moreover, j-' must lie 1" f A: suppose it 



equal to here v is less than A. ::.< nuincrator 



be written 



nn -I as the 1 umot be so great as A. 



ultin 



X" 8 



he above formula wi! -he correct value of j- 



when we nereo0 the number of divisions indefinitely and 

 dym'nisA each tort* v/ y , and extend the summation over 



yjoos CDKll. i his will be expressed according to the 

 ordinary notation of the Integral Calculus thus, 





