186 The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 



Substituting for X its value from (E), we find the following expression for 

 the moment of that force : 



, / dc^ ^ dc^ , dii 



p- cos a I COS a — 1- COS j3 -j h COS 7 -j- 



Ti / d>] ,, dii , drj 



This expression denoting the moment of that part of the force acting on ??i, 

 which results from the relative displacement of m', it is evident that the com- 

 plete moment of the forces X, which act upon m, will be found by multiplying 

 (G) by the element of the mass, and integrating through the entire sphere of 

 molecular action. Let e be the density at the point x', y', z\ and a the radius 

 of the sphere of molecular activity. Then the element of the mass will be 



dfj, = ep- sin 6 dp dO d<p ; 



and the limits of integration with respect to p, 0, 4,, will be and a, and tt, U 

 and 27r, respectively. If then we assume, 



J,,„. = \\\ Ap" cos' a cos a dfi = ££"1° A ep* cos a sin' e cos' (/> dp de dxp, 

 A^pj = \\\ A^ cos a cos /3 cos a! d^i, 



A^ ^■ = \\[Ap^ cos a COS7 cos a dfX, 



&c. ; 



•5=«a' = fij Sp^ cos- a cos a' dfj., 

 &c. ; 



C„2„' =||J Cp^ COS^ a COS a dfx, 

 &C. ; 



we shall find for the complete moment of the forces X acting upon the particle 

 m, the expression 



