126 Mr GREEN, ON THE PROPAGATION OF LIGHT 



, dv dw du du dv dv dw dw 

 " dz dy dy dz dy dz dy ' dz 



1 _ du dw du du dv dv dw dw 

 ~ dz dx dx dz dx dz dx dz 



, _ du dv du du dv dv dw dw 

 ' ~ dy dx dx dy dx dy dx dy 



we thus see that s„ # 2 , s 3 , a, /3', y, are very small quantities of the 

 first order, and that the general formula (1) by substituting the pre- 

 ceding values would take the form 



cj> = Function («„ s 2 , s 3 , a, /3', 7') 

 which may be expanded in a very convergent series of the form 



<p = <p + <£, + 3 + <p 3 + &c. 



<p (f) { (p z &c. being homogeneous functions of s { , # a , * 3 , a, ft, y of the 

 degrees 0.1.2.3 &c. each of which is very great compared with the 

 next following one. 



But (p , being constant, if p= the primitive density of the element, the 

 general formula of Dynamics will give 



fffp dx dy dz \~ |« + ~ %v + ~ lw\ = fffdx dy dz (fy, + ty, + &c.) 



If there were no extraneous pressures, the supposition that the primitive 

 state was one of equilibrium would require (p x — 0, as was observed in a 

 former paper ; but this is not the case if we introduce the consideration of 

 extraneous pressures. However, as in the first case, the terms (p 3 (p„ &c, will 

 be insensible, and the preceding formula may be written 



fffp d* dy dz j — he + -^ It + -^ Sw J = fffdx dy dz (ty, + %) 



