298 ON THE PROPAGATION OF LIGHT 



, du dv du du dv dv dw dw 

 dy dx dx dy dx dy dx dy ' 



we thus see that s t , s 2 , s s , a', 0', 7', are very small quantities of 

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

 the preceding values would take the form 



<j) = function fo, s 2 , s a , a', &, 7'), 

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



< , fa, fa, &c. being homogeneous functions of s lf s 2 , s s a.', {?, 7', 

 of the degrees 0, 1, 2, 3, &c. each of which is very great com- 

 pared with the next following one. 



But fa being constant, if p = the primitive density of the 

 element, the general formula of Dynamics will give 



If there were no extraneous pressures, the supposition that 

 the primitive state was one of equilibrium would require fa = 0, 

 as was observed in a former paper; but this is not the case if 

 we introduce the consideration of extraneous pressures. How- 

 ever, as in the first case, the terms fa, <j!> 4 , &c. will be insensible, 

 and the preceding formula may be written 



jjjpdxdy* J 



Supposing p the primitive density constant, the most general 

 form of fa will be 



1 



2 A 2 3 



A, B, C, D, E, and F being constant quantities. 



In like manner the most general form of fa will contain 

 twenty-one coefficients. But if we first employ the more parti- 



