Differential Double Refraction. 547 



of bands for homogeneous light between the zero order and 

 the position of the white band, resulting from the plate to be 

 compared and the plate of reference, has been taken directly 

 as the order of the unknown plate. 



An example of such an error probably occurs in Dufet's * 

 determination of the optical constants of selenite. Instead of 

 using a comparison wedge, as usually done, he used as reference- 

 plate Iceland spar cut normal to the optic axis and placed 

 between the polarizer and analyser of a polarizing-microscope 

 so as to obtain the characteristic rings and black cross. The 

 selenite plate being placed next to this and adjusted until the 

 rings are visible, the position of the black ring is noted, and 

 then the order of the ring determined by substituting sodium 

 light. His apparent orders vary for plates of different thick- 

 ness from 27*28 up to 83*37. Now from the results obtained 

 above, the order 33 of Iceland spar corresponds to the order 35 

 of selenite (parallel to the principal cleavage-plane) . Hence, 

 assuming the differential dispersion of Iceland spar to be the 

 same for different directions and neglecting the effect of oblique 

 transmission, the order 27 ought to be 28, or more probably 29, 

 and 83 should be 88 for selenite ; that is, the difference between 

 the greatest and least indices should be increased by approxi- 

 mately 6 per cent,, or from "00918 to -00973. Now the 

 observations of von Lang t by means of a prism give '009665 

 for selenite. Mouton J obtained by means of interference- 

 bands -00988. The order of his plate he determined by the 

 method of successive approximations, using the first two 

 terms in Cauchy's formula. Dufet, however, attributes an 

 error of one order too much in Mouton' s plate, and then finds 

 results concordant with his own. The astonishing agreement 

 between results of Dufet with a prism and with a plate should 

 be mentioned. However, that the orders of his plates are 

 seriously in error cannot be doubted, as he mentions no 

 correction. The apparent anomalous differential dispersion 

 obtained by Mouton is not confirmed by Dufet. The results 

 obtained above do not indicate any such state. Compare 

 figs. 3 and 4. It would be desirable to have the correction 

 referred to introduced into the various tabular results given 

 for crystals by different observers, or new data obtained with 

 these corrections. Work of this nature is now in progress 

 in this laboratory. This process of obtaining the order of 

 interference-bands has been extended to the determinations 

 of indices by interference methods, comparisons being made 



* Dufet, Journ. de Physique (2) vii. p. 297 (1888). 

 ± Wien. Ah. Ber. xxxvi. (2) p. 793 (1877). 

 % Compt. Rend, lxxxyiii. p. 987 (1879). 



