Prof. Challis on a Theory of the Dispersion of Light. 269 



vestigation (in pages 421-426) I obtained a new formula for 

 dispersion. The numerical results from the two investigations 

 (exhibited in page 427) show that the second formula accords 

 with the experiments in a slight degree better than the first. 



Since the publication of that volume I have become acquainted 

 with Ditscheiner's measures of a large number of wave-lengths 

 for dark rays of the solar spectrum, and of corresponding refrac- 

 tive indices ; and my present object is to compare these data with 

 the theory modified as above stated. Ditscheiner's measures, 

 accompanied by investigations of appropriate formulae, are given 

 in a memoir in the Sitzungsberichte of the Mathematico-physical 

 Class of the Imperial Academy of Sciences at Vienna (vol. 1. 

 part 2 (1864), p. 296). The values of X were determined, 

 according to Fraunhofer's method, by the diffraction- spectrum. 

 The mean interval between the lines of the grating, in default 

 of means of measuring it directly, was, at first, inferred, by ob- 

 servation and calculation combined, from Fraunhofer's determi- 

 nation of the value of A for that component of the double line D 

 which is nearest the violet end of the spectrum ; and the wave- 

 lengths obtained for the other lines were thus made dependent 



o 



on that determination. Subsequently, having learnt that Ang- 

 strom had employed a value of the interval between the lines of 

 his grating obtained by direct mechanical means, Ditscheiner 

 succeeded in effecting a like determination with respect to his 

 own grating, and was thus enabled to calculate independent 

 values of all the wave-lengths. The results of this calculation, 

 which differ but little from those previously obtained, are given 

 in the above-cited publication (vol. lii. part 2 (1865), p. 289). 

 Those of these values to which there are corresponding determi- 

 nations of refractive indices, the number of which is seventy- 

 three, are used in the subjoined comparison with theory. 



Before entering upon this comparison, I propose to give some 

 account of the principles of the theory, and of the above-men- 

 tioned modification of it. The diminished rate of propagation 

 of waves in transparent substances is ascribed to the obstacle to 

 the free motions of the particles of the sether caused by reflec- 

 tions due to the incidence of the waves upon the atoms. These 

 reflections are supposed to take place as if the fluid were incom- 

 pressible ; and as they would thus be transmitted instantane- 

 ously, the mean effect, at a given position, of the simultaneous 

 reflections from a vast number of atoms may be conceived to 

 bear a finite ratio to the incident velocity, even though the space 

 occupied by atoms should be extremely small compared to the 

 intervening space. It is presumed that that ratio may be the 

 same at different parts of the same wave, and, consequently, that 

 the retarding force due to the atoms has a constant ratio to the 



