Indices of Doubly-refracting Crystals. 833 



therefore be known, i. e., the glass plate need not be 

 scrupulously plane parallel, as it is merely necessary to get 

 the glass difference and the air difference for two successive 

 lines, however far apart the air and glass positions may be 

 for either line. Equation (8) also follows at once from (3j 

 by inserting the equivalent of fi for the two spectrum lines. 



Granting the approximate form of Cauchy's equation, the 

 error of b thus obtained should be well within 1 per cent. 

 Its influence on /jl should not exceed one unit in the fourth 

 place. Unfortunately, however, the equation in question is not 

 warranted to this extent when the lines of the spectrum are 

 as far apart as D and E, for instance. The question relative 

 to b will be resumed in § 5. Meanwhile I may observe that 

 the dispersion equation with three constants would need 

 three spectrum lines for the determination of the two essential 

 constants. This is a cumbersome procedure^ but from the 

 nature of the problem is nevertheless probably the only 

 resort; particularly in the case where a long column of 

 glass, crystal, or liquid is to be investigated, for exceptionally 

 accurate indices of refraction. 



'In conclusion it is worth while to determine the value of 

 fie in terms of /x found from the normal position, when the 

 difference of these indices (as in quartz) is not large. In 

 fact, since d(A~N)=edx, 



dfx _ /jl cos 2 r ,q 



d(AN) — e/ub cos r/fjia — AN sin 2 r + e sin r sin (i — r) ' 



If i = r = 0, this reduces to 



d/M _IXa 



rf(AN) ~~ e 



(10) 



If in equation (9) the value of yu, is introduced, the corre- 

 sponding value of fie may be computed from the AN and 

 AN', which put the two ellipses, respectively, on the fiducial 

 sodium line. The result gives a fair value for /Lt e , even when 

 /jl varies with the incidence * due to errors of adjustment, 

 seeing that jjl must be constant and is found from the normal 

 position. 



4. Oblique Incidence. — The incident light was polarized in 

 the vertical plane before reaching the slit, the D line being 

 as usual fiducial. When viewed through an analyser, the 

 light reaching the telescope in case of the more oblique 

 positions of the plate on its horizontal axis was elliptically 

 polarized in one of the superimposed spectra, the latter 

 showing the usual channeled structure with more dark bands 



