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



nearly the same law as in the former comparison, and that the 

 differences between the results of the first and second calcula- 

 tions are, for these three rays, even greater than before. These 

 inferences make it probable that the discrepancies are not due to 

 error in Ditscheiner's wave-lengths for the rays B and C. 



I next performed the same calculations with Fraunhofer's 

 values of fi for flint-glass No. 13 and Ditscheiner's values of X, 

 and obtained the following results : — 



By first calculation, 



log A' = 1-1982448, log B'= 0-5816970, C' = 8-687700; 

 by second calculation, 

 1-1255825, 



log A': 



logB'=04350178, C' = 7746712. 



Ray. 



Value of ft. 



Value of A. 



Excess of calculated wave-length. 















By first 



Bv second 



Mean. 









calculation. 



calculation. 



B 



1-62775 



68833 







+ 32 



+ 16 



C 



1-62968 



65711 



+ 7 







+ 4 



D 



1-63504 



f 59053 

 \ 58989 



-88 

 -24 



-147 



- 83 



-1171 

 - 53/ 



E 



1-64202 



52783 







- 65 



- 32 



F 



1-64826 



48687 



+47 







+ 23 



G 



1-66029 



43170 







+ 10 



+ 5 



H 



1-67106 



39742 



-69 







- 35 



In this case there is not the same discrepancy between the 

 comparisons for the rays B and C as in the two former calcula- 

 tions, and the law of the mean excesses is in some degree altered. 

 It must not, however, be concluded that the previous discord- 

 ances arose from inaccuracy in either or both of Ditscheiner's 

 values of fi for those rays, because it is possible that differences 

 in the character of the results may be due to differences in the 

 qualities of the glasses employed, and that the dispersion-formula, 

 which can only be regarded as approximate, may apply more 

 accurately in proportion as the refractive and dispersive powers 

 are larger. This point will be adverted to again presently. 



It being uncertain to which of the two lines D Fraunhofer's 

 determination of ft applies, I have compared the calculated 

 value of \ with the observed value for each line. The excesses, 

 given above within brackets, show that the more refrangible line 

 is considerably more in accordance with the theory than the other. 



The calculations were then repeated with the same values of 



fi and with Angstrom's values of \ already cited, and the wave- 

 length obtained for D was compared, as above, with the observed 



