356 Prof. D. B. Brace on Achromatic Polarization 



observations. Two observations, however, were made giving 

 coincidence for the twenty-fourth order of Iceland spar and 

 twenty-fifth order of quartz. A third observation under 

 more favourable conditions gave good coincidence for the 

 orders forty-four Iceland spar and forty-six quartz. The 

 ratio of twenty-two Iceland spar to twenty-three left-handed 

 quartz was selected as the best for achromatism, but further 

 experiments will be necessary to confirm this result. 



Comparison of Aragonite and Left-handed Quartz. 



Small wedges were made of aragonite, but the bands were 

 too indistinct to determine their ratios. However, with a 

 wedge whose edge bisected the greater angle between, and 

 whose face was normal to, the plane of the optic axes good 

 coincidence was obtained in the region of the thirtieth to the 

 fifty-eighth order of quartz throughout the spectrum. With 

 a similar wedge, but with its face parallel to this plane, no 

 definite comparisons could be obtained. The determinations 

 for Iceland spar and aragonite have been reserved for future 

 observation. 



If we wish to use a combination of two crystals which have 

 not been directly compared their ratio can be easily deter- 

 mined provided coincidences have been obtained over the 

 same portion of the spectrum. Thus the ratio of the orders 

 of mica to selenite is 8:7, and of mica to quartz 9 : 8. 

 Hence the ratio of selenite to quartz would be 9 : 8 :: 8 : 7 

 or 63 : 64; which would be possible in a part of the spectrum, 

 as stated above. 



Tbe results of these observations show that with the more 

 available crystals achromatism cannot be obtained over the 

 entire visible spectrum, but that certain pairs of crystals will 

 achromatize more perfectly than others. For example, better 

 coincidences were obtained with selenite and mica than with 

 quartz and mica. These two pairs are particularly suitable 

 over the others in making compound retardation plates, such 

 as achromatic quarter-wave plates, and the orders used are 

 comparatively low. 



Having found the linear relation between N 1; N 2 , . . . and 

 satisfied equation (2 a) for a part or the whole of the spectrum, 

 as the case may be, we can solve equation (1 a) for any given 

 resultant retardation N of several crystals. For example, if 

 N = \ for mica and selenite we have 



N M -N 8 =X, j^-f, N^Nm^X, 

 /. N M =8\ and Ns=7X. 



