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

 Eo + (Ap cos a + ^i) J- + (Ap COS /3 + ^2) ^ + (Ap cos y + A^)-^ 

 + (Bpcos a + S,)^ + {Bpcos ^+B,)p + {Bp cos 7 + ^3) ^ 



+ (C/>cos a + C,) ^ + {Cp COS /3 + C.) ^ + ( C/, cos 7 + C3) ^. 



Resolving this force as before along the three axes, and proceeding as in p. 186, 

 we find an expression for L similar to (H). There is, however, one important 

 difference. In the value of X, which is derived from the principle of indepen- 

 dent action, the quantities 



d^ (U^ d$ dl^ 



dz dy ' dy dz ^ 



have the same coefficient ; and the same is true of the quantities 



Now it is easy to see that in general this restriction has no effect in h- 

 miting the generality of the equations of motion of a homogeneous body. For 

 whether the coefficients be equal or not, each of the foregoing pairs of quan- 



