461 



The function deduced from this supposition contains/yXeen 

 coefficients only. It may be thus written : 



2«I» = ^ai^ + i?i3./ + C732 + Lu^ + Mv^ + Nw^ 1 



+ 2u(U^a, + F,^, + W,y,) + M U,a, + V^. + ^^^73) | 

 + 2M;(f7:,ai+ ^3^2+ JV:,y3); J 



where 



dn dK dl d% ,..-^ + ^ 

 ''^dz^Ty'^^dx^dz' ""-dyUx 



In the case of a homogeneous solid, this function will give 

 Navier's equations containing only one constant. 



" On examining the equations of a system of attracting 

 and repelling molecules, obtained by a different process by 

 M. Cauchy, 1 found them to contain twenty-one coefficients, 

 and concluded from a hasty examination, that they could be 

 derived from the function (1), by introducing six differentcon- 

 stants or coefficients of ^,73, aiTa, «i/32, vw, uw, uv; which 

 would make function (1) identical with Mr. Green's function for 

 light. I supposed, therefore, that Mr. Green's equations were 

 the same as M. Cauchy's, and consequently, in my classifica- 

 tion of elastic media have called Mr. Green's function, the 

 function of a system of attracting and repelling molecules A 

 more attentive consideration of M. Cauchy's equations has 

 convinced me that this is an error, and that Mr. Green's equa- 

 tions do not represent the equations of a system of attract- 

 ing and repelling molecules. 



" It has now become necessary for me to show how 

 M Cauchy-s equations may be derived from the principles 

 laid down in my first memoir. This is easily done as fol- 

 lows : 



