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LXVIII. Researches in the Undulatory Theory of Light con- 

 tinned: On the Absorption of Light. By John Toyey, Esq. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



AT the conclusion of my last paper (L. & E. Phil. Mag. vol. 

 xivf p. 323.) I said that I expected to be able to show 

 that our formulae were adequate to explain the cause of the 

 absorption of light. This expectation was founded on the cir- 

 cumstance that the quantity which we have denoted by h, has, 

 without any reason, been tacitly assumed to be entirely real ; 

 while it is obvious that, if /f be partly imaginary, the formulae 

 require to be transformed into others which will indicate an 

 absorption depending on k and x. The values of k depend 

 on the nature of the medium ; and it is well known that every 

 medium absorbs more or less of the light which falls on it. 

 Hence we infer that these values cannot be entirely real. In- 

 deed, if they were so, the formulas which we have previously 

 deduced would show that no absorption could take place. 



To effect the required transformation of our formulae, I 

 have had recourse to a method of investigation more general, 

 and, I think, more easy, than any which we have previously 

 used. This method I now proceed to develop ; setting out 

 from the differential equations, given at page 11. vol. xii. 

 of your Journal, viz. 



~^ = mS |(^(r) A), + ^^(r) (A^ A r, + A s A ?) Aj/|, 



~| = mS |^4^{r) A^ + 4/(r) (Ay Arj + A z A?) A^'^ . 



In deducing these equations the masses of the molecules 

 were supposed to be all equal*. When this is not the case, 

 m, which denotes any one of these masses, must be placed 

 under the sign, 2, of summation. If for the sake of abridge- 

 ment, we put 



w^{(f)(r)+^^(r) A/} = p, 

 m {<|)(r) + ^^(r) As;^} = p', (2.) 



m ^ (r) Aj/ A s = 5', 

 the equations (1.) will become 



^, = 2(;;A„ + (7A?), 



^, = S(/A? + ^A„); 



which are true whether the masses are equal or unequal. 

 ♦ See L. & E. Phil. Mag. vol. viii. p. 7—9. 



