The Re V. J. H. Jellett on th e Equilibrium and Motion of an Elastic Solid. 187 



J- d^ dl^ d^ dh^ d^ dl^ 



dx dx '^ dy dy " ' dz dz 



IdUl^ c^. dc^\ fd^ dc^ d^ rf?A fd^ dl^ d^ dH 



'-■\dydz+dzdy)+^'^^^\Tzl^+d-vd7) + '^'^^-[d^d^ + TyTx 

 p f/)/ dc^ di] dc^ , „ dri rfB| 



, ('}!i'^i,<^<^,-r. fchldi£dydh^\ fdy di^ drjdl^ 



'^-' \dy dz ^ dzdy)^ ^"•■■' \dz dx +d^li) + ^'^^ [dT^l^+d^d^ 



Similar expressions are found for the moments of the forces Y and Z. 



5. Let X', y, Z' be the external forces necessary to keep the particle at rest. 

 Then, the equation of virtual velocities being in general 



Iff (X'5? + r'?,; + Z'll) dm + jTf {L+M + N) dxdydz = ; 



if we substitute for Z, M. N their values found as above, we shall have the 

 equation 



. = [[j {X'lk + F'E,; + Z'l^) edxdydz 



Where t is the density, and 



P-A ^^4-^1 '^^^A '^^ 



+ ^-'°'^ + ^°'""% + ^-';7^5 (K) 



VOL. XXII. 2 c 



