in the Velocity of Propagation of Light in Water. 351 



We shall therefore be satisfied with determining A and B for a 

 subsequent purpose from the formulae for the lithium -ray (1) and 

 for the thallium- rav (3). 

 We find 



At = a 1 — aj^ + ctj 4 , 

 whence 



« 1= 1-32432 



log« 2 =0-436957- 6, 

 log* 8 = 0-709100— 11; 



whence 



log /3 l = 0-51 1831- 9, 

 log/3 2 =0-184866-13,' 

 /3 3 = 0-442606 -17. 



Making use of the formula 



A <+r 



(?) 



and inserting the corresponding values of X and t, we may find, 

 exactly to units of the fourth decimal place, the index of refrac- 

 tion for every Fraunhofer's line we please and for every tempe- 

 rature (between 0° and 80° R). 



In order to show that the dispersion -formula (7) is nearly suf- 

 ficient to give the relations of refraction for all temperatures, I 

 adduce here some values of the D line calculated by its means, 

 and place side by side with them the numbers taken directly out 

 of the Table. 



Index of Refraction for the D line. 



R. 



Reckoned from 

 (7). 



Observed and 

 compared. 



Difference. 



o 







1-33369 



1-33374 



-0-5 



8 



1-3334 



1-3335 



-1 



16 



1-3329 



1-3329 







24 



1-3319 



1-3320 



-1 



32 



1-3306 



1-3306 







40 



1-3290 



1-3290 







48 



1-3271 



1-3271 







56 



1-3250 



1-3250 







64 



1-3229 



1-3229 







72 



1-3207 



1-3207 







80 



1 3187 



1-3185 



+ 2 



As Cauchy's first approximation gives satisfactory results, and 

 the calculation of the coefficients in ChristoffePs otherwise far 



