350 M. R. Riihlmann on the Alteration produced by Heat 



of refraction for each 1° R. increases from 0-00005 to 0-00028, 

 and is greatest at the highest temperatures. 



(2) The relative dispersion between the sodium and lithium- 

 lines is expressed by 



D 1= ?z Na -w Li =0-00220-0-0000000751^ 



+ 0-0000000000082^ 



} • • (*) 



and attains a minimum when -. — =0, i. e. at 67 0, 6 R. 



at 



The relative dispersion between sodium and thallium is ex- 

 pressed by 



(5) 



D 2 =rc Th -rc Na =0-000194-0'000000120*n 

 + 0-Q0000Q0000271/ 4 , .... J 



and becomes a minimum when — — 2 = 0, i. e. at 47°'l 11. 



The relative dispersion between the lithium- and thallium-lines, 

 D 3 =0-00414-0-000000195/ 2 + 0-0000000000353^ (6) 



is least (between 0° and 80° R.) at 52°'6 R. These last results 

 relating to the dispersion in water may certainly cause surprise, 

 since they are partly in contradiction to Gladstone and Dale's 

 results. The values, however, here concerned are very small ; 

 and the small difference in undular length between the rays 

 chosen by us is not calculated to decide conclusively whether we 

 have to do with the results of an interpolation-formula which 

 does not quite suit, or really with a natural phenomenon. 



By the help of these formulae for the indices of refraction we 

 are in a position to state the three relations, 



A i A i 



3 3 



from which A, B, and C may be derived as functions of the 

 temperature. 



As water shows very little dispersion, we may, in Cauchy's 

 dispersion -formula 



T> 



put rc= A + r-g without much error for the first approximation. 



