546 Mr. E.J. Rendtorff on 



To test for achromatism in a crossed pair of plates, let us 



assume that two crystals of the orders N x and N 2 present a 



maximum achromatism. If crystal plates of these, of the 



N N 



orders . /AT ! -> T N and ■ /XT 2 XT , , be crossed, an achromatic 

 4(Nj— N 2 ) 4(N X — N 2 )' 



quarter wave-plate results. The orders 2 of mica and If of 



selenite, for oSTa light, were used for one of these pairs of 



plates. A Fresnel rhomb was placed at an angle of 45° to 



the plane of polarization of the polarizer, and, with nicols 



crossed, the achromatic plate was placed above the rhomb in 



such a position as to give a minimum illumination. The 



light passing through the analyser was then examined with a 



spectroscope. Total darkness existed in the neighbourhood 



of the Na line, with a gradual increase of illumination toward 



the red and violet, showing that the colours had not been 



compensated for perfectly. When placed under a polariscope 



the achromatic plate showed very little change of tint on 



revolving the analyser. It consequently approximated to the 



ideal achromatic condition. 



Let us assume that we have two crystals, such as Iceland 

 spar and quartz, of the 212" and 222" order for Na light, 

 respectively. Let us furthermore assume that the inter- 

 ference-bands produced by them coincide at the Na lines, 

 and that the last visible red band in the quartz extends j^j 

 of a band beyond the corresponding one in selenite, while a 

 certain violet band in the selenite spectrum extends a similar 

 distance beyond the corresponding quartz band. Orders of 

 5*55 for quartz and 5*30 for selenite will then make a plate 

 whose phase-retardations will be 90° 25' for the extreme red, 

 90° for the yellow, and 89° 35 / for the violet rays. 



In conclusion, the author desires to thank Professor Brace 

 for many valuable suggestions that enabled him to carry out 

 this work. 



[Note. — In determining the order of crystal-plates ob- 

 servers, as well as cutters, generally have committed serious 

 errors, at least for the higher orders ; and the tabulated 

 indices must consequently be erroneous to some extent. In 

 this method of determining the order no error is possible 

 ordinarily, it being merely a matter of counting. The method 

 most generally used is to determine the order by comparison 

 with a plate or wedge of another crystal, usually of quartz. 

 As already shown, this method cannot be used directly without 

 knowing the relative orders for achromatism of the two 

 crystals, and correcting accordingly. Heretofore the number 



