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



^^ ,. dP,dF,dP, 



, dQi dQ., dQ^ 



(Z - W') = -— , ^ , ^^3 



" ^ ' ~ dx dy dz ' 



These equations are the same as those deduced by a totally different method 

 (which will be given presently), and involve no restriction as to the extent of 

 the deviation of (a;, y, z) from their original values (a, b, c). 



If we suppose x — a + $, 1/ = b + ^], z = c + ^, the expression for the mo- 

 ments of the molecular forces will become 



Qiq + Q'hq' + &c. = PMi + ^2812 + Ps^cL, 



+ Rfyi + E^iyi + -^3^3 ; 

 where 



_d^ _d^ _d^ 



"'-rf^' "'~S/' "'-Tz' 



^'-dx' ^'-Ty' ^'-Tz' 

 ^ _ ^f ^ -d^ ^ _ ^? 



^■-rf^' ^^-^' ^'-Tz- 



If we lestrict the molecular forces by the condition 

 Qlq+ QHq' + &c.=^hV, 

 we shall have the relations 



