IN CRYSTALLIZED MEDIA. 127 



Supposing p the primitive density constant, the most general form of 0, 

 will be 



0i = - £ {As, + Bs> + Cs 3 + 2Da + 2E(X + 2Fy'), 



ABCDE and F being constant quantities. 



In like manner the most general form of 2 will contain twenty-one co- 

 efficients. But if we first employ the more particular value, (2) we shall get 



- 2 0! = As, + Bs 2 + Cs 3 

 - 2 2 = Gs\ + Hs\ + Is\ + 2P* 2 6' 3 + 2Q*,s 3 + 2Rs l s i 



+ La* + M(P+ ivy*. 



Or by substituting for s 1} s 2 , s 3 , a, /3', y their values, given by system 

 (3), continuing to neglect quantities of the third order, we get 



- 2 = - 2 0, - 2 2 



~ jdu n -r>dv nr . dw 



= 2Aj- + 2B- r - + 2C- r - 

 ax ay a% 



+ A 

 + B 



+ 



die) + [da;) + \dx) J 

 UduV (dv\ 2 (dwy\ 



(4.) 



„ (du\* „ (d#\ n jtdwV 9 T>dv dw Q du dw 

 \dx) \dy) \d%) dy d% dx dx 



ndudv , idv dw\ z M fdu dw\ 2 „ (du dvy 

 dxdy \dz lly) \d* dx) \dy dx) 



Having thus the form of the function due to the internal actions of 

 the particles, we have merely to substitute it in the general formula of 

 Dynamics, and to effect the integrations by parts, agreeably to the method 

 of Lagrange. Thus, 



