and the Laws of Plane Waves propagated through them. Ill 



^^_dA, dA, dA^ 



df ~ dx dy dz ' 



_^d^_dB, dB, dB,_ 



dt' dx dy dz ' 



d^ dx dy dz 



If no external forces act, equations (13) disappear, in consequence of J,, A.2, 

 &c., becoming constants ; but the conditions at the limits (12) will still remain, 

 unless the coefficients be not only constant, but zero. 



The part of the differential equations of motion depending on 0o will be 

 found by introducing 60, in place of BF in equation (3), and integrating by 

 parts, according to the methods of the calculus of variations ; but it may be 

 found more readily by introducing c^, for T', in equation (4). Neglecting the 

 equations of condition at the limits, we obtain for the equations of motion, 



— e 



5^ = K)^+(«.-);^+K)-;^ 



.(aA)S.(«...)$.(.A)S 



+ (aA + aA) ^ + {aA + aA) ^ + {aA + aA) |^ 



+ («.<^.)54+(a.cO^ + (a3C3)^J 



+ 2(5A)||; + 2(5.y|^^+2(M.)^ 



(14) 



