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L. On Differential Double Refraction. By E. J. IIendtorff, 

 M.S.> Fellow in Physics, University of Nebraska*. 



IF a train of waves, polarized at a definite angle to the 

 principal axis of a crystalline plate, pass perpendicularly 

 through the same, the retardation of the component light- 

 waves is a function of the thickness of the crystal, the dif- 

 ferential dispersion, and the absolute wave-length of the 

 light. 



The object of the present investigation was to determine 

 this relative retardation in different crystals for the different 

 wave-lengths in the visible spectrum. The method was 

 similar to that first used by Prof. D. B. Brace f. This 

 method greatly simplifies the work inasmuch as the order 

 can be at once determined by means of the plate itself, the 

 only requisite being that the thickness of the plate vary. 



If a crystalline wedge or plate be placed under a polari- 

 scope so that the principal axis of a crystal makes an angle 

 of 45° with the plane of polarization of incident white light, 

 the nicols being crossed, and examined with a spectroscope, 

 a series of sharply defined black interference-bands will be 

 seen to cross the spectrum, as first discovered by Miiller. 

 These black bands occur where 



V(n e —n ) N 



\ 



is a whole number, n e and n being the principal indices, X 



the wave-length, and D the thickness and N the order of 



the plate. The disposition of these lines in the spectrum is 



dependent upon the actual differential dispersion of the 



crystal for different periods. As the crystal is changed in 



thickness the interference-bands move across the spectrum. 



If the differential dispersion be normal and the crystal be 



increased in thickness, the bands move toward the red; if 



diminished, toward the violet end of the spectrum. If now 



the number of bands m passing say the D line be counted — 



m being reckoned positive when the bands move toward the 



red — and if n is the ratio of the initial to the final number of 



bands between any two wave-lengths, we have 



N 

 n= t7-t , 



whence 



„_ mn 



1 — n 



* Communicated by Prof. D. B. Brace. 

 t Phil. Mag. Oct. 1899, p. 345. 



2N2 



