336 Mr Olazehrook, On the Reflexion [Feb. 9, 



and if V is > F, n may be greater than unity, and therefore I' 

 becomes imaginary. 



In this case, assuming the functions /, f^ to be harmonic in 

 form, the equation is satisfied by 



_ /' 

 i|r = Ke v''^' sin {hz — t + e'), 



where 



1 _ n _ n 



r = n" - 1 



v -1 



= (/^V-l) (17). 



And for the first medium we have 



-y^r — K sin f -jT^ + /i^ — i j + «i sin f i^- + hz — t + e^ 



It is necessary to introduce the quantity e^, for as with Green 

 one of the conditions introduces cosines of hz — t on the right 

 hand, the other sines, so that it is impossible to satisfy both unless 

 we have both cosines and sines on the left, put hz — t = ^„, then 

 the surface conditions give, since 



?=_Z^ = cos^, V^^V, 



KCosXo + 'c^co&{xo + e,)=KCOs(Xo+e) (18), 



cos (b r , .. kI . . ,. _ -. 



— p^l'*=cosxo-/ficos(x„+ej} =- -psm(;)^o + e) (19). 



V 

 From (19), since ^r =/-t, 



/* cos (/) [k cos X, - /^i cos (x„ + ej} 



= -k' \/{fj? sin^ <^ - 1) sin {x^ + e). 

 Hence, expanding and equating coefficients of cos Xo and sin Xoi 

 K -\- K^ cos e^ = K cos e', 

 K^ sin e^ = K sin e, 

 fi cos 4>{fc — K^ cos ej = — K /^(/j? sin^ <^ — 1) sin e', 

 fjb cos ^K^ sin e^ — — K /^{/j,^ sin^ ^ — 1) cos e\ 

 Substitute for k sin e. k cos e' in form. 



