18 



Charges produced by Reflexions or Refractions, Ordinary or 



Extraordinary. 



6. Let us now consider the sudden changes in these partial diffe- 

 rential coefficients of the characteristic functions of the system, pro- 

 duced by reflexion or refraction, ordinary or extraordinary. The 

 general formula for such changes, is, from the nature of the inte- 

 gral F, 



aF(= F, -K.) = 0, (S) 



A being here the symbol of a finite difference, and F, , F^ , being the 

 two successive forms of the function F, before and after reflexion or 

 refraction. The condition {_S) may be considered as a form of the 

 equation of the reflecting or refracting surface ; and if m = o, be any 

 other form for the equation of this surface, we may, by introducing 

 a multiplier X, differentiate the following formula : 



Ar(= r,- F,) = A«, (T) 



as if the coordinates x, y, z, were three independent variables. Dif- 

 ferentiating in this manner the equation (T), and making, after the 

 differentiations, » = o, we find 



(t) 



