272 Prof. Challis on a Theory of the Dispersion of Light. 



pressible fluid, and that for a compressible fluid it is different for 

 different values of X. According to the adopted hydrodynamical 

 principles, this quantity becomes a function of X only in conse- 

 quence of the effect produced on the distribution of condensation 

 about the surface of the atom by lateral spreading due to trans- 

 verse vibrations, these vibrations being brought into action by 

 the disturbance of the waves caused by their incidence on the 

 atom. I have not succeeded in obtaining by a priori investiga- 

 tion an exact expression for the condensation thus modified ; 

 but from the general expression for the condensation in trans- 

 verse vibrations I have inferred that the distribution of conden- 

 sation in this case must be a function of r-^ 3 X' being the effec- 

 tive breadth of the waves. (See Phil. Mag. (Supplement) for 

 December 1864, p. 500, and ' Principles of Mathematics,'p.370.) 

 Accordingly it has been assumed that, to a first approximation, 



k and k 1 being unknown physical constants. Consequently, 

 since X = pX' and k = /jlk' } the formula for dispersion in a simple 

 medium becomes 



m Vdt~ /cV(l+2A)-2A<V' 



The same form of expression applies to a compound medium, as 

 is shown in ' The Principles of Physics/ pp. 4.29 & 430. In the 

 existing state of physics it does not appear possible to obtain, 

 either by theoretical calculation or by experiment, the values of 

 the constants H, k, k' } A, and e 2 . But since the equation may 

 be put under the form 



A' B' r , 



the values of A', B', and C may be found by means of three sets 

 of corresponding values of /n and X given by observation. The 

 formula may then be employed to calculate values of X from 

 other given values of jn ; and a comparison of the results with 

 the corresponding observed values of X will, in proportion to the 

 degree of accordance, be evidence of the truth of the theory. 



Having gone through such calculations by making use of the 

 before-mentioned values of fi and X obtained by Ditscheiner, I 

 have collected the results in the annexed Table, in which also 

 KirchhofFs measures are inserted for the sake of identification 

 of the lines. Instead of calculating the constants A', B', C 



