348 Prof. D. B. Brace on Achromatic Polarization 



testing various combinations for achromatism. Muller* first 

 studied interference in crystalline plates by means of spectrum 

 analysis. Fizeau and Foucault f and others have also studied 

 the same phenomena in crystals taken singly. The obser- 

 vations of Mouton $ on the differential double refraction in a 

 plate of selenite indicate anomalous disperfion at - 491/i, that 

 is, e — co is a minimum in this region. Later observations by 

 Dufet § indicate, on the contrary, that it is normal, and follows 

 the law of Briot in the visible spectrum, as do quartz and 

 Iceland spar. The observations of Mouton should agree with 

 the latter's observations if the retardation in the plate used by 

 Mouton were 9A, instead of 10X, according to his measurements. 

 Jn all such combinations then the plates must be placed 

 in subtractive order. How far the conditions of (6) are 

 fulfilled by crystals already examined is not readily deter- 

 mined from present available data. 



Since -^r- 1 , -sr^ are the number of bands in the spectrum 



between the wave-lengths X and A-fSX., it must be possible 

 by varying the length of the path to make this number the 

 same throughout the spectrum, in order to obtain perfect 

 achromatism. 



For this purpose direct comparisons of the interference- 

 bands in two crystals were made. The displacement of the 

 bands and the increase in their number, and also the de- 

 termination of the order at any point in the spectrum, may 

 be anticipated from the law for differential double refraction. 

 Assuming as the law for differential double refraction, Briot's 

 law for dispersion — 



where A, B, C, D are all positive quantities, we have 

 e-« d/ k . B .0 



N=rf- 



'«!(*+S + s?-*0- ■ • < T > 



Hence 



also 



= x4(3A + Af- + f)., . (9) 



8 5N 



-8\(-8\) 



* Pogg. Ann. vol. lxix. p. 98. 



t Ann. de Chim. et Phys. (3) t. xxvi. p. 145 ; t. xxx. p. 148. 



t Comptes Rendvs, t. lxxxviii. pp. 1087, 1189 (1879). 



§ Journal de Physique, 1888, pp. 305-306. 



