I'ISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 287 



But in the case of the results of Table II. a hyperbola was fitted to the observations, 



its equation being 



X-(3460)'/X = (6-2489) W. 



The differences between X as calculated from the above formula and X observed nre 

 given in Table II. under the heading X (A .. X hyp . The mean value of the residuals 

 taken without regard to sign is between 13 and 14, or nearly three times the value 

 of the mean residual from the straight line. 



Even, this mean residual hardly exceeds the probable error of observation, so that 

 this would not be conclusive against the hyperbola. But an examination of the 

 individual numbers in the last column of Table II. shows strong systematic positive 

 residuals in the middle and negative residuals at the ends, and these systematic 

 divergences certainly suggest that the hyperbola is not the most suitable curve. 



The index of refraction of this particular glass is tolerably represented for the 

 visible spectrum by the formula 



-39125/{l-(2159-6/XY'}. 

 Thus 



X, = 2159-6, /t' = 1-5107, A', = 0'39125. 



From this X',, of formula (20) comes out to be 19247. This differs entirely from the 

 value obtained from the experiments, namely 3460. We are thus led to the 

 interesting conclusion that in this glass at least the free periods which produce the 

 ordinary dispersion are probably not active in producing the dispersion of artificial 

 double refraction. 



This removes theoretical justification in this case for the formula 



c = cy{i-(xyx)'}, 



even if it had not been shown inferior as a purely empirical fit. 

 We may then provisionally accept the law 



C = C /(1-X /X), 



and the results in what follows will be reduced with reference to it. 



At the same time it must be remembered that the physically significant formula 

 is prol>ably of type (16). It will be shown in 21 that even in the visible spectrum 

 there are local divergences from the linear law. 



17. Methods of Reduction. 



In lilting :i linear law 



X = A. + i-'W 



to a set of observations, the corrections due to the sinking and permauent stress had 



ti> In- taken inti> 



