1880.] and Refraction of light. 835 



same expressions can be deduced without his assumption that 

 B = B'. 



Let us first take the case in which the vibrations lie in the 

 plane of incidence, then 



v = v' = 0, 



and w and u are independent of y. 

 The equations of motion are 



d^u _ -n d fdu dw\ 

 ^ df~ dz\dz~dx)' 



d?w __ -n d tdw du\ 

 df dw\dx dzj ' 



with similar equations for the other medium. 



The conditions at the surface become 



u = u, lU = iv. 



Assume with Green 



d-dr d-Jr 



u =—r- , w = — r- . 

 dz dx 



Then, for the equation of motion, we have 



df \dz^^ dx^j' 



if F===-. 

 P 



And for the second medium 



df U^' rfa^V' 



The equations are satisfied by 



J. (Ix^r nz \ . (Ix + n.z 



r J., (I'x + n'z \ 



with the condition 



n _ n^ _ n 



V~T~T' 



therefore n = —r^ , 



Vol. III. Pt. Viii. 



