461 



The function deduced from this supposition con tains //<eew 

 coefficients only. It may be thus written : 



20 = Jai' + Bji.,^ + Cys^ + Lu^ + Mv^ + Nw^ 1 



+ 2{Lf3.2y3+Maiy3+Nai(52)+KUivtv+V2Uw+Wsuv) I ^^^ 



+ 2m( t/iai +F1/3.2 + ^^173) + 2t?( Uiai + ¥2(^2 + fV^ys) 1 

 + 2w ( f/aai + ^3^2 + ^^373) ; J 



where 



d^ ^ dn dt, 



dr, dK _dt: d^ _ ^ , ^ 

 ''^Tz^'Ty'''' dx^ dz' "^ dy dx 



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, I 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 different con- 

 stants or coefficients of )3-273' 0173, ai/3.2» viv, 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 : 



