ON THE REFLEXlUff AND REFRACTION OF LIGHT. 253 



or, by merely changing the two constants and restoring the 

 values of a, /?, and y, 



A fu 



2*, = --4 (-7- 

 \dx 



du dv dw\* 



J 

 dx dy dz) 



-p((du dv\* fdu dw\* ,(d^ dw\* 

 ^+ + + + \dz + dy) 



(dv dw du d.w du dv\] . ~. 



\dy' dz dx' dz dx ' dy)) ' " * 



dy' dz dx' dz dx ' dy 



This is the most general form that < 2 can take for non-crys- 

 tallized bodies, in which it is perfectly indifferent in what direc- 

 tions the rectangular axes are placed. The same result might 

 be obtained from the most general value of < 8 , by the method 

 before used to make $ 2 symmetrical all round the axis of z, ap- 

 plied also to the other two axes. It was, indeed, thus I first 

 obtained it. The method given in the text, however, and which 

 is very similar to one used by M. Cauchy, is not only more sim- 

 ple, but has the advantage of furnishing two intermediate results, 

 which may possibly be of use on some future occasion. 



Let us now consider the particular case of two indefinitely 

 extended media, the surface of junction when in equilibrium 

 being a plane of infinite extent, horizontal (suppose), and which 

 we shall take as that of (yz) 9 and conceive the axis of x positive 

 directed downwards. Then if p be the constant density of the 

 upper, and p / that of the lower medium, < 2 and (/> 2 (1) the corre- 

 sponding functions due to the molecular actions; the equation 

 (2) adapted to the present case will become 



(3); 



w y , v /} w t belonging to the lower fluid, and the triple integrals 

 being extended over the whole volume of the fluids to which 

 they respectively belong, 



