﻿Rectification of the Spectrum, 945 



liquid are read off. Thus if 



N<=l/sin0t 



be the index * of the liquid at t°, 



N ao =:N t (l + «(*-20)) = Cl + *(*-20))/sin* < 



is the index at 20°. For carbon disulphide, at mean tempe- 

 ratures, a = '0008, nearly. 



Again, if the glass plate is now introduced and similar 

 measurements $*,, t' be made at #, the index of the plate 

 will be 



n = N^sin^' = N 2 o8in^./(l+«(* / -20)), 

 or 



n = sin <f>?(l + a{t — t')/sin(j} t \ 



Two symmetrical sets of values are thus obtained, one for 

 each of the two first orders of spectra, at x x and # 2 , on opposed 

 sides of the undeviated white ray, w. This method does not 

 usually succeed very well ; for it presupposes that in case of 

 the air plate and glass plate, which are successively inserted, 

 the total reflexion occurs at identical parts of the spectrum, 

 for identical positions x along the scale s. But supposing 

 the adjustment trustworthy, the wave-length corresponding 

 to any given n is found from the two positions x L and x 2 at 

 which the same n occurs, from the equation 



In general it is preferable to use the air plate first to find 

 the indices of refraction of the liquid, if these are not known 

 throughout the spectrum. There will thus be given two 

 symmetrical curves for the two first orders of spectra, 

 separately. Their distance apart x 2 — x 1 for the given values 

 of N determines the wave-length, X, sought; i. <?., if N is 

 plotted in terms of #, the horizontal distance apart of the 

 two curves is the x 2 — X\ which determines the wave-length 

 for the index N selected. Hence N is given in terms of A, 

 and should be reduced to 20°. In case of many liquids, in 

 particular carbon disulphide, N is well known in terms of 

 wave-length at the outset, so that the air plate is superfluous. 



The observations with the glass plate are made in the same 

 way. The symmetrical curves for sin <j)t' at t\ reduced to 

 sin cj)' at 20°, as found from the two first orders of spectra, are 

 plotted in terms of x. Hence their distance apart for two 



* In conformity with Kohlrausch's notation N and n are here used as 

 symbols for index of refraction. 



Phil Mag. S. 6. Vol. 23. No. 138. June 1012. 3 Q 



