4<54 Mr. Tovey on the Absorption of Light. 



Since >j and ^ are entirely real, it appears, by (26.) and 

 (27})} that ay and «2 must be of the forms 



«y = Cy + C2 >/:zT, ^2 = C/ — Cg ^:ri : (28.) 



therefore, by (27.) 



a sin b -^^Cj i a cos 6 = — 2 c 2 • (290 



Again, by (24.) and (27.), 



a! sin Z>' = /3 (cos y + v/^^ . sin y) u, 



+ /3 (cos y — V^ . sin y) ^2 J (30.) 



«' cos &' = /3 (cos y -f ^ _ 1 . sin y) «y -/ — 1 

 4- /S (cos y - ^31 . sin y) «2 ^ ZTi ; 



hence, by (28.), 



a' sin ^/ = 2 /3 {c^ cos y -C2 sin y) , . 



a' cos 6' = — 2 /3 (^2 cos y + c^ sin y) ; 



and hence, by (29.) 



«'sin6' = «^sin (Z> + y) , 



a' cos h' — a^ cos (^ + y) ; 



therefore a' = a (3 , b = b + y , (33.) 



or a' =— a^, b = b + y + tt . (34.) 



Since a^ and ag are arbitrary so also are c^and Cc, , by (28.); 

 and consequently a and b, by (25.). 

 By (23.) and (26.) we have 



13 = 2 {a e^* sin (W2^ -t- ^'^ + b)} , 



? = 2 {/3 « e^-^ sin (wif + ^ ^ + Z» + y)} . 

 In these expressions, which are equally general with the for- 

 mula? (10.), all the symbols denote real quantities. 



We have remarked that the equations (22.) determine the 

 values of//, ?', /3, y, for any given value of w. The values of 

 h, i, determine those of g. A', by (23.). Now the intensity of 

 the light depends on a e^^' and /3 a e*'*', so that if the vibra- 

 tions in the ray under consideration be represented by (35.), 

 its intensity will be expressed by 



(See Airy's Tract on Light, art. 23, and note.) Hence if we 

 suppose the origin of x to be at the surface of any medium on 

 which a ray of light falls, we perceive that, unless e be zero, 

 the intensity of the light will vary with x ; and since experience 

 shows, that whatever be the medium which a ray of light tra- 

 verses, its intensity is thereby diminished, we infer that e must 

 have sensible values, and that these values must be negative. 



