90 C. J. MERFIELD. 



The following is a short summary of the values of u 

 determined by laboratory experiments: 



1. 



Mascart 1877 



u 

 ... 1*0002927 



2. 



Lorentz 1880 



2911 



3. 



Benoit 1888 



2923 



4. 



Ohappuis and Riviere 1888 



2919 



5. 



Kayser and Runge 1893 ... 

 u = 1*0002920 



2922 



On examination of the normals, giving the values of 

 d log r, it is quite evident that these quantities vary with 

 the zenith distance. This would seem to denote that the 

 so called constant of refraction, adopted in forming the 

 tables, not only needs correction but also a correction for 

 every zenith distance. 1 



Now denoting by Z the zenith distance for d log r equals 

 nought, we may form equations of condition of the follow- 

 ing type, 



Log <x - log a e = d log v — \Z-z\x 



or y — zx — d log r = 



in which y = Zx 6 



and log a c is the value used in the tables. The suffixes 

 denote observation and calculation respectively. In this 

 way the following condition equations are formed after 

 multiplying each by the square root of the weight of the 

 absolute term. 



2*7 y - 79*5 *- 0*01004 = 

 3*0 - 92*0 - 0*00525 = 

 1*5 - 52*1 - 0*00255 = 

 7*6 - 338*1 + 0*01490 = 



1 A similar conclusion has been arrived at by Mr. K,. Tracy Crawford. 

 To his thesis on the " Determination of the Constant of Eefraction " I am 

 much indebted. See Proceedings of the California Academy of Sciences, 

 Vol. i. 



