Prof. Challis on the Dispersion of Light. 501 



The values of X, in brackets were those used in determining the 

 constants. The adopted unit of X, which is arbitrary, was chosen 

 for convenience in calculating. 



The following results were obtained by a like comparison for 

 oil of cassia, which was selected on account of its great disper- 

 sive power. The numbers are taken from Professor Baden 

 Powell's paper in the Transactions of the Royal Society for 1837, 

 Part I. p. 22. 



Rav Val e of ^ ^v ^ hy Excess of 



^' u o /*. k serva tion. calculation. calculation. 



B. . . . 1-5885 2-541 (2-541) O000 



C. . . . 1-5918 2-422 2-428 +0-006 



D. . . . 1-6017 2-175 2-174 -0001 

 E . . . . 1-6155 1-945 (1-945) 0-000 

 F . . . . 1-6295 1-794 1-791 -0-003 

 G. . . . 1-6607 1-587 1-583 -0-004 

 H. . . . 1-7002 1-464 (1-464) 0-000 



The equations for determining the constants gave 



A = 4-55574, B = 0-64905, C=4-46624. 



In the first example, the difference between the first and last 

 values of fju is 0-0433, and that between the first and last values 

 of X is 1-077. Hence a difference of 0*001 in X corresponds on 

 the average to a difference of 0-00004 in (jl. In the same man- 

 ner it will be found that in the second example a difference of 

 0*001 in X corresponds to 0*00010 in fi. Taking these propor- 

 tions into account, it will be seen that the accordance between 

 theory and observation is much more exact in the above com- 

 parisons than in the corresponding ones made by Professor 

 Powell in the Transactions of the Royal Society for 1835, 

 Part I. p. 252, and in the paper above cited. The accordance 



h k 

 might be made still closer by assuming a to be equal to ^ + ^ 



but as another constant would then have to be determined, the 

 resulting equation would amount to little more than a formula 

 of interpolation. The above comparisons, however, by showing 

 that the equation [6), derived entirely from antecedent physical 

 principles, is capable of giving results in accordance with expe- 

 riment, afford evidence both of the truth of the theoretical expla- 

 nation of dispersion, and also of the principles on which it rests. 

 I had previously obtained other equations, none of which were 

 found on trial to admit of satisfactory comparison with experi- 

 ment; but at the same time, as the present more complete in- 

 vestigation has shown, they were not strictly deduced from the 

 a priori principles. 



