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

 Dividing (10) by (9) we find 



cot 2 tan^tan- = tan/3. .... (11) 



Hence /? is found, and from formula (B) we get the index of 

 refraction 



«,(<±*)l 



"= ; g \ \ (B) as) 



If we perform the calculation for the three data at 0° after they 

 have been adjusted to the extent of 10", then 



</ Na =22° 55' 5",, S Li =10'0", S Th =-8'20", * = 58° 38' 31". 



We accordingly find^ 



/3 Li =+3'16", /3 Th =-2'42». 

 This introduced into (12) gives 



n Li = 1-33154, n Th = 1-33566; 

 while by the ordinary methods these values are also found : — 



n Li = 1-33154, n Th = 1-33566. 



The differences are still inappreciable in the fifth decimal 

 place; hence we are perfectly justified in reckoning throughout 

 by means of the more simple formula (A). 



The results of observation are collected in the Tables I., II., III. 

 The arrangement had to be altered once, whereby the distances 

 were altered. The measurements made with the first arrange- 

 ment are marked by an asterisk (*). The column "corrected 

 temperature" contains the temperatures corrected (from —55°, 

 the atmospheric temperature being 8°) for the projection of the 

 scale and the correction of the thermometer compared with the 

 normal thermometer. The columns " angle of least deviation " 

 contain under <f> the readings of the universal circle, under ^ the 

 corrections on account of the excen trie position of the prism, and 

 under 8 the proper deviation of the ray. The atmospheric tem- 

 perature varied, during the whole of the observations (only a few 

 tenths of degrees Reaumur excepted), through 7° R. The atmo- 

 spheric pressure varied between 337 and 330 Paris lines, co- 

 lumn of mercury. The observations at 0° C. were made by filling 

 the hollow of the prism Pi with pure melting ice and waiting 

 until no further alteration was observed in the index of refraction. 



