Prof. Cballis on a Theory of the Dispersion of Light. 279 



Hence the following results were obtained, C^ — M signifying 

 the excess of the calculated above the observed value of //, : — 



■ 



Ray. 



<"• 



X. 



(V-(V 



B 



152431 

 1-52530 

 1-52798 

 1-53137 

 1-53434 

 1-53991 

 1-54468 



6-8833 

 6-5711 

 5-8989 

 5*2783 

 4-8687 

 4-3170 

 3-9742 



000000 

 -0-00288 

 -0-00142 



0-00000 

 -fO-00080 

 +0-00100 



0-00000 



C 



D 



E 



F 



G 



H 





The values of C^— O^ for the rays C, D, F, G, inasmuch as they 

 correspond to large values of C A — A , show that it is necessary 

 to take into account a greater number of terms of the series. It 

 was, in fact, to be expected, from what was said above, that an 

 approximation could not be obtained by determining only three 

 constants. 



The above data for the rays B, D, F, H having been employed 

 for calculating the constants of four terms of the series, the 

 results were 



A = 2-290385, A, = [0-2260364], -A 2 = [0-8234811], 

 A 3 = [1-7942593]. 



Hence on calculating the values of fi for the rays C, E, G by 

 means of these constants and the above values of \ for the same 

 rays, the excesses C^ — O fl to five places of decimals were found 

 to be respectively +0-00001, 0-00000, —0-00006. These re- 

 sults prove that the relation between fju and X for this substance 

 is very closely expressed by taking account of only four terms of 

 the series. 



Lastly, I employed the same series to four terms to calculate 

 Cfx — Ofj. for the rays C, E, G for water, the means (to five places 

 of decimals) of two determinations of the refractive indices by 

 Fraunhofer being adopted, viz. 



Bfju = 1-33096, 0/^ = 1-33171, Dp= 1-33358, E/*= 1*33585, 



F/* = 1'33780, G/*=l-34128, 11^ = 1-34417. 



Calculations made with the data for B, D, F, and H gave 



A = 1-748267, A, = [0-1049879] , -A 2 = [0-9854382], 



A 3 = [1-8172302]; 



and the values of C M — O^ found for the rays C, E, G were re- 

 spectively -0-00002, +0-00002,-0-00005. These differences, 



