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





Flint-glass 





Flint-glass 





Ray. 



No. 23. 

 Value of p. 



Ca-Oa. 



No. 3. 



Value of \i. 



Ca-Oa. 



B 



1-62660 







1-60204 







C 



1-62847 



6 



1 -60380 



-128 



D 



1-63367 



-36 



1-60849 



-131 



E 



1-64050 







1-61453 







F 



1-64676 



+ 6 



1-62004 



+ 48 



G 



1-65885 







1 -63077 







H 



1-66969 



+23 



1-64037 



- 28 



Here it is observable that the values of Ca — O a for No. 23, 

 like those for the similar substance No. 13, are very small, and 

 considerably less than the values for No. 3. The law of the 

 excesses of calculation for the latter substance is nearly the same 

 as that of the excesses deduced with the same values of X from 

 Ditscheiner's values of jjl, but they are of larger amount, at the 

 same time that the refractive indices are less. It seems, therefore, 

 that the dispersion-formula becomes inexact in proportion as the 

 refractive power of the substance is less than that of No. 13 or 

 No. 23. I found, in fact, on applying it, just as in the last two 

 instances, to Fraunhofer's crown-glass No. 13, the specific gra- 

 vity of which is 2 # 535, and the refractive and dispersive powers 

 very low, that it altogether failed. Yet, since the results of the 

 other calculations seemed to indicate generally a systematic de- 

 viation of the calculated from the observed values of X, there 

 was a probability that the deviations were such as might be cor- 

 rected by a more approximate formula, and that the failure in 

 the instance of the crown-glass might be due to inadequate ap- 

 proximation, and not to error in the principles on which the 

 formula was founded. In order to obtain a nearer approxima- 

 tion I reasoned as follows. 



If the principles of the theoretical investigation be true, the 

 variations of fi 2 for a given substance depend wholly on varia- 

 tions of —r; that is, y? is a function of =-£ and constants. We 

 may therefore assume that* 



;/ 2_ a • -A-i 



fl — A + ^2 



_i_ lis i 113 , & 



To ascertain the degree of approximation attainable by this series, 

 I first applied it in the instance of the crown-glass No. 13, 

 taking only the first three terms. The values of A , A,, A s , cal- 

 culated from the subjoined values of yu, and \ for the rays E, E, IT, 

 were found to be 



A =2«254474, A 1= = [0-4926929], -A 2 = [1-21200.22]. 



