468 PROFESSOR MOSELEY, OX THE THEORY OF , 



The relation of the forces which compose the equilibrium of the 

 whole Prism, will then be the same with that of the forces impressed 

 on any one of its sections perpendicular to the axis. 



Let CBD, (Fig. 1,) represent any one of these sections. Suppose 

 the mass to be intersected in any direction parallel to its axis by a plane, 

 and let iV, A'', be the intersection of this plane with the section CB 

 of the mass. 



And first, let this intersecting plane in altering its position be sup- 

 posed to remain always parallel to itself. 



Take Az, the axis of », perpendicular to A" A^„ and let it make 

 an angle Q with the vertical. 



Let MN, = y„ MN, = y., AM = c, AK = k. 



M, = 0, 



M.. = SP sin (1) - sin 9 /(y, -y^) dC, 

 Jtfa = 2P cos <I) + cos e f(yi - y-i) d C, 

 N, = ^ cos ef{y{'-yi)dC + sin 9 fCiy,-y,)dC -t :E±F/( cos*, 



This hypothesis with regard to the position of the axis of », and these 

 .substitutions being made, all the equations of condition vanish except 

 equation I, the second of equations III, and the second of equations lY- 

 These resolve themselves into the following: — 



. = c 0)' 



{SPsin<l >-sine/(j^i-j^.)dC}2+^cosej(^i'-j^/)rfC+8me/C(j^,-j^,)rfC+2:=fcP^co3<D ^ 

 ■V= 2P cos *+ cos e fiy.-y-i) dC '"^ '' 



^d^P^jC^d^k COS0 aC-{y,-y.) {{z- C) sin e - ^ (^, .^.) cos 9} 

 j^ dC + {yi - y^) cos 



