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XLI. The Law of Dispersion. 

 By Edward Wilson, M.A* 



LORD RAYLEIGH, in his address to the British Asso- 

 ciation at Montreal, took occasion to observe that 

 Professor S. P. Langley's demonstration of the inaccuracy of 

 Cauchy's formula for the law of dispersion would have an 

 important bearing on optical theory. 



An abstract of this important demonstration is to be found 

 in the Philosophical Magazine, March 1884, It thus appears 

 that the true form of the function <f> in the equation fjb=cf)(X) 

 remains to be discovered ; and yet it is scarcely possible to 

 overrate the importance of its determination, for without it 

 not a single step can be taken in tracing a connexion between 

 the chemical constitution of a substance and its refractive 

 powers. 



The author holds with a somewhat deep conviction the 

 followiug propositions : — 



(1) That before the refractive and dispersive properties of 

 a liquid or solid substance can be made use of to determine 

 its chemical constitution or molecular structure, it is abso- 

 lutely imperative to determine the form of the function $ 

 in the equation fi = cj){X), 



(2) That it is the constants of this function which will have 

 to be correlated with chemical constitution and molecular 

 structure. 



The present paper is an attempt to supply the first of these 

 desiderata ; the second desideratum, though more difficult, 

 may possibly be attempted at a future time. 



An incontestable form of (f> could only be furnished by a 

 true Theory of Light, which it is to be feared is not likely to 

 be obtained for some time to come. Meanwhile we must 

 perforce be content to attempt the discovery of an empirical 

 formula, the probability of which being true must chiefly 

 depend upon the close agreement of its calculated results with 

 those of observation. 



Of such possible formulae the following, which, as analogy 

 would lead us to expect, assumes the exponential form, is 

 submitted for consideration. 



If v be the velocity in a refracting substance of a ray of 

 fight of wave-length \, and V the velocity in vacuo ; then 



c\ -± 



-« 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 26. No. 161. Oct. 1888. 2 C 



