10 Mr GREEN, ON THE REFLEXION 



/ttj j 7 i 4 d (du dv dw\ n rd 2 u d 2 u d fdv dw\-\] . 



/ a d (du dv dw\ jfTd^v d 2 v d /du div\~]\ . 

 \ «ty ' Wa? dy dz J L rfir das 2 dy \dx dz) -1 f 



\ a d_ [du rfv dw \ rd 2 w d 2 w d (du dv\~\ 1 . 



1 dz'Kdx dy dz) L dx 2 dy 2 dz' \dx dy) J J "*' 



seeing that we may neglect the double integrals at the limits x = — ee , 

 /y = +co, s = + oo; as the conditions imposed at these limits cannot 

 affect the motion of the system at any finite distance from the origin ; 

 and thus the double integrals belong only to the surface of junction, of 

 which the equation, in a state of equilibrium, is 



* x. 



In like manner we get 



fffdxdydzW? 



+ the triple integral; 



since it is the least value of x which belongs to the surface of junction 

 in the lower medium, and therefore the double integrals belonging to 

 the limiting surface, must have their signs changed. 



If, now, we substitute the preceding expression in (3), equate sepa- 

 rately to zero the coefficients of the independent variation 8u, §v, Sw, 

 under the triple sign of integration, there results for the upper medium 



