Dr. Ketteler on the Dispersion of Light in Gases. 343 



Whether and to what extent a special correspondence is dis- 

 coverable between the several coefficients of this series and those 

 of Cauchy need not now be considered. 



It can be shown that the formula (III) does in reality com- 

 prehend with great exactness the whole of the phenomena of dis- 

 persion that have yet been investigated. 



That this equation applies very accurately to the results of 

 observation on the dispersive properties of gases has been already 

 shown above. 



The best measurements which we possess of the indices of re- 

 fraction of Fraunhofer's lines (those, namely, which we owe to 

 Fraunhofer, Rudberg, and Landolt) have been compared with it, 

 and a very good agreement has been found*. In general the 

 differences are identical with those which result from the appli- 

 cation of Cauchy's primary series, as reduced to their first two 

 terms by Christoffelf. 



I have myself employed the spectra of lithium, sodium, and 

 thallium in order to measure, as accurately as possible, the in- 

 dices of refraction of the corresponding lines for a prism of heavy 

 glass. With the aid of a SteinheiPs spectroscope, belonging to 

 the physical cabinet of the University of Heidelberg, which was 

 most kindly placed at my disposal by Professor Kirchhoff, I ob- 

 tained the following indices of refraction : — 



n u =1-683879, n Na = 1-691361, n Tl =1*698535, 



numbers which I consider all the more accurate since, in con- 

 sequence of the small intensity of the sources of light and the 

 short duration of the experiments, all variations of temperature 

 were avoided, as well as because, in the method that was em- 

 ployed of having the prism fixed, the error of the minimum de- 

 viation was avoided. 



On the other hand, we may calculate from the first and last 

 of these numbers the following value for the second : — 



By formula (III). By Christoffel's formula. 



n' Na = 1-691351. n" Na = l'691356. 



So that, in units of the fifth decimal place, the difference n—n' 

 amounts to 1, and the difference n — n" to 0*5. In view of the 

 sources of experimental error, these differences may obviously be 

 regarded as inconsiderable. 



Lastly, as to the quantity /3 = X , it is of the same order 

 for gases, liquids, and solids; thus, for example, calculation 

 gives : — 



* Much better than when the earlier formula was used, 

 t Poggendorff's Annalen, vol. cxvii. p. 27. 



