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



+ Bfi, + B,^, + Aft 

 + C'lY, + CaYo + C373 • 



0, = (a,-) Oj- + (a,") 02'^ + &c. 

 + (flii.) • "ift + &c., + (csflo) • 73"2 + "Sic. ; 



the expressions within the brackets denoting the corresponding coefficients. 



0j will contain nine coefficients, which will be constant, or functions of 

 {x,y,z), according as there are no external forces, or vice versa; and <p2 will 

 contain forty-five distinct coefficients. I shall consider these functions separatelj". 

 Introducing ^^ for T^in equation (4), we obtain, 



+ l\{AM-VB,h]-\-C,l^)dxdz, (12) 

 + \\{AM + B,hi + C3?f ) dxdy 



fdB, dB. dB\^ (dC, da dC\,J,,, 

 d'^ dA, dA, dA, 



[ifdA^ dA. dA 

 whence we obtain 



l^l^-^+^)^^ + (-^+ 



dt"^ dx dy dz 



— € 



dhj^_dB, dB^ clB, 

 dt- dx dy dz ' 



df dx dy dz 



(13) 



The terms on the right hand side of equation (13) must be added to the 

 dynamical equations arising from 0,. even in cases where (X, Y, Z) may be 

 neglected on account of the intensity of the molecular forces. If we wish to 

 take account of the external forces, we should use, instead of ( 13), the fol- 

 lowine ; 



