500 Prof. Challis on the Dispersion of Light. 



their axes be parallel, may be denoted by such an expression as 



^ TAV 2 B'r 4 Or 6 „ "1 



r, the distance from an axis, being different for every different 

 axis. As, on account of the small ratio of the radius of the atom 

 to X, we are concerned here only with values of r extremely 

 small compared to X, it may be presumed that the first term of 

 the series is much more considerable than the remainder. 

 Guided by these considerations, I shall now assume that the 



factor a is equal to r-^, h being an unknown constant, but neces- 

 sarily positive, because cos 6 is negative. This quantity being 

 substituted for a. in the equation (rj), the relation between fi and X 

 may be put under the form 



(^_l)8_(^_l)A+£=iB+C=0, . . . {0) 

 in which 



These expressions show that A, B, and C are positive quantities; 

 but theory alone is incapable of determining their numerical 

 values. I proceed now to test the equation (0) by experimental 

 data. 



For this purpose I have adopted Fraunhofer's values of X, and, 

 for a first instance, have selected his values of fi for Flint Glass, 

 No. 13. (See arts. 437 and 751 of the "Treatise on Light" 

 in the Encyclopaedia Metropolitana.) To determine the constants 

 of (0), three equations were formed by means of the values of 

 /j, and X for the rays B, E, and H, the solution of which gave 

 the results 



A = 9-12778, B = 1-39857, = 11-97853. 



The values of X for the other rays were then calculated by the 

 formula (0) from the corresponding values of /ul, and compared 

 as follows with observation : — 



lay. 







Value of fj.. 



Xby 



observation. 



A by 



calculation. 



Excess of 

 calculation. 



B . . . 1-6.2775 



2-541 



(2-541) 



o-ooo 



C 







1-62968 



2-422 



2 425 



+ 0003 



D 







1-63504 



2-175 



2-174 



-0-001 



E 







1-64202 



1-945 



(1-945) 



0-000 



F 







1-64826 



1-794 



1-796 



+ 0-002 



G 







1-66029 



1-587 



1-592 



+ 0005 



H 







1-67106 



1-464 



(1-464) 



0-000 



