ACCOUNTING FOR THE ABSORPTION OF LIGHT. 29 



connection which apply to the case of reflexion and refraction, the motion of the material parti- 

 cles being taken into account. It is evidently not allowable to simplify these equations by 

 putting E = E' and D = D', as we did in the previous paper. Moreover, instead of having 

 C = C, we have C = C + C . 



Our present purpose requires us to apply these equations only to the case of rays incident 

 directly on a refracting surface ; we shall therefore suppose that the quantities a, y, a^, y , a, y', 

 are each zero, and that /3, /3,, /3', are functions of x only : then the nine equations of connec- 

 tion reduce to three, viz. 



where h ■ 



dz dz dz 



C'+ D' 

 C + D' 



We shall assume v to be the velocity of propagation in the lower medium, and v, v" the two 

 velocities in the upper, namely, the two roots of the equation (l). We shall suppose that the waves 

 in the upper medium are an incident and a reflected, and in the lower, two refracted waves, one 

 propagated with the velocity v', and the other with the velocity v'', for it will be impossible to 

 satisfy the three equations (7), (8), (9), with only one refracted wave. Hence, using the same 

 notation as in the previous paper, we have from (7), (8), and (9), 



V+ V = V'+ F" (10), 



1 F' V" 



{V-V,)- = !-y + ~ (11). 



V V V 



V V" 



-r + -77=o (12). 



V V 



When V V" belong to the two refracted waves, and F' T/' to the corresponding waves of the 

 particles of matter, observing that the two latter waves are propagated respectively with the same 

 velocities as the two former (See Vol. vii. p. 421). 

 Hence, if we assume in general that 



V=ae''('-i>^ F, = a^e"H)^~', F' = a'e"('-^V^ &c., &c. 



We have from (10) (U) and (12), putting z=0, 



a + a^ = a + a" (13). 



a-a = - o' + _^ a (14) 



V V 



a, = ■ 



V 



7<. (15). 



Also by the two equations in the middle of page 423, Vol. vii.* we have (a and a ' or a" and a" 

 here, correspond to a and a^ there) 



,_ m v" -mB , „ m v"" - mB „ 



> / 



Hence by (15) we have 



/ / 



v''-mB v'" - m,B, v" 



a'=--^ 5 • -,r„ ^ — a (16). 



In the second of theae o - o, is written by niistaltc instead of o,- a. 



