200 Prof. Moseley's Reply to Mr. Earnshaw's 



.-. DG = |(AC-|A B) 

 .-. AG = |AC-iAB + i A B 

 .-. 3 A G = A C + A B. 

 Let A G = a 



A B = b M = weight of mass 

 AC = c 

 Let also X be the point about which the moments of the 

 pressures upon A, B, C are equal. Let these pressures be re- 

 presented by A, B, C ; also let a represent a constant quantity, 

 and let A X = x : 



... A = £ 



x 



x — b 



c = 



X — c 



The two equations of equilibrium are, therefore, 



^ +-*.'+ -ii « M 1 



x x—b x—c I 



ab etc , T 



1 + =M« 



x — b x—c J 



(x—b) (x—c) + x(x—c) + x(x—b) _ -jyj") 

 x(x— b) (x—c) 



a ?>(x -c) +c(x-b) = Ma 



(x—b) (x — c) J 



3x' i -'2x(b + c) + be _ M 1 

 x (x — b) (x—c) 



a xJb+^-2bc = Ma j 



3.T 2 — 2.r(6 + c) + 6c __ 1 

 x{x (b + c) — 2 be} ~ a 



,\ 3ax 3 —2ax(b + c) + abc= x q (b + c) — 2 he x 

 '. x\3a — b—c) — 2x(ab + ac—bc) = —abc 



> 



ab+ac—bc I /ab + ac — bc\ 3 abc 



2>a—b—c ~V \ Sa — b—c ) ~ Sa—b—c 



