102 The Rev. S. Haughton on a Classification of Elastic Media, 



The equation of virtual velocities thus modified will become, considering 

 (x, y, z) as the positions of rest of the molecules, 



e I J! 5? + J In + 5 Ff ) ch'dydz = \llh Vdxdydz. (3) 



As V is a function of the quantities {a„ a,, a,, &c.) of a given form, we shall 



have 



,, dV dV^ dV^ 



hV=-r- cai + -j—^a, + -j— gas 

 aui cicu flos 



Substituting this value in equation (3), and integrating by parts, we obtain 

 g 8? + J' Iv + J zA d,dydz = IP Fdrc^2/rf^ 





■11 



/(ZF dZF, dF^ \ , , ,,, 



-III 

 -II) 



d dV d dV d dV\^^.., 



-— ■ — — \- -rr- • -T- + 1- • -1- i£.dxdydz 

 ax dai dy da^ dz das J 



d dV d dV d dV\^ J , , 



Tx-w^ry-w.-'Tz-wJ'"^"'^^'^' 



d dV d dV d dV\^, , , 

 T.-7R^d;j-7h^Tz--d^J'^'^'"^y'^'- 



The double integrals, as usual, denote the conditions at the bounding surface, 

 and the triple integrals give the general equations of motion in the interior. 

 The laws of propagation depend upon the triple integrals, and the laws of re- 

 flexion and refraction depend upon the double integrals. 



