Prof. Challis on a Theory of the Dispersion of Light. 277 



wave-lengths of both lines, viz. 58951 and 58891, the mean be- 

 tween which was used in the previous comparison. The results 

 from the two sets of data were as follows : — 



log A! = 1-235 1358, logB' = 0-646131.1, C' = 9-229205; 



log A'= 1 -1215922, log B' = 04245740, C' = 7-699399. 



Ray. 



Excess of calculated wave-length. 



By first 

 calculation. 



By second 

 calculation. 



Mean. 



B 





 -43 



r-94 



1-34 







+37 







-118 



+ 106 







-135 



- 75 



- 58 







+ 38 







+ 53 



- 21 



-1141 



- 54/ 



- 29 



+ 18 



+ 19 



- 59 



C 



D 



E 



F 



G 



H 





Here again the mean excesses for B and C are more accord- 

 ant than those deduced by the former calculation from Ditschei- 

 ner's values of fi and the same values of X. Also the law of the 

 mean excesses agrees generally with that of the means obtained 

 by the next preceding calculation, although their amounts are 

 somewhat larger. As the more refrangible of the lines D again 

 gives more consistent results than the other, the theory, I think, 

 may be considered to have decided that this line was bisected by 

 Fraunhofer. In future calculations I shall assume that this was 

 the case. 



It remains to discuss more particularly the consequences of 

 applying the dispersion-formula to substances of different densi- 

 ties and different refractive powers. With this object in view I 

 begin with comparing Ditscheiner's values of X for the seven 

 principal rays (that for D being 58989), with values calculated 

 by the formula from Fraunhofer' s refractive indices for flint-glass 

 No. 23 (prism of 60°) and flint-glass No. 3. The specific gravi- 

 ties of the two substances are respectively 3*724 and 3*512 (that 

 of No. 13 is 3*723). In these two instances the calculation of 

 A', B', C was made from one set of data, viz. the observed values 

 of fM and X for the rays B, E, G. The following results were 

 obtained, C x — A signifying the excess of the calculated above 

 the observed value of X : — 



For No. 23, 



log A' =1*0667953, 

 for No. 3, 



log A' = 1*0581414, 



log B'= 0-2920263, 



C' = 7-095094; 



log B' = 0*2846254, C'=7'061636. 



