Indices of Doubly-refracting Crystals. 829 



The angle of incidence of the beam is changed by rotating 

 the plate in definite steps and the amount of: rotation read 

 off on the attached fixed graduated circle c, with its plane 

 parallel to the beam and its axis normal to it. Angles of 0°, 

 10°, 20°, 30°, 40°, and even 50°, were usually available on 

 either side of the normal position. The crystal, mounted in 

 a cork plate, was at first conveniently held by a spring clip ; 

 but later *, more elaborate means for mounting the plate 

 parallel to the axis of rotation were adopted. The normal 

 position is found with certainly by slightly rotating the 

 crystal around the horizontal axis in either direction, until 

 the interference rings in the field of view change their 

 direction of motion. This, for the ordinary ray, determines 

 the minimum thickness e. The same operation is then per- 

 formed around the vertical axis, both adjustments being 

 usually easy and the result satisfactory. 



With the angle i given, the corresponding angle of refrac- 

 tion, r, i. e., the angle of the ray with the optic axis of the 

 crystal, may be computed when the index of refraction for 

 the given case is known. Hence the refractions in different 

 directions, r, both for the ordinary and extraordinary ray, 

 follow, as far as about r = 30° from the optic axis, in the 

 above apparatus. Plates are not usually large enough for a 

 larger internal angle on the one hand, while the errors of 

 measurement multiply on the other; but by selecting a plate 

 cut parallel to the axis, the final 30° of the quadrant may be 

 found. To obtain the intermediate 30° a plate cut obliquely 

 to the axis or else a plate of large area would be necessary. 



When the plate is cut parallel to the axis and the difference 

 of the refractive indices (as in quartz) not too large, the two 

 interferometer ellipses, corresponding to the ordinary and 

 extraordinary rays, are in the field at once, making an ex- 

 ceedingly beautiful design. Their distance apart may then 

 be found micrometrically in terms of the refraction of the 

 ordinary ray, giving an acceptable datum even in case of an 

 imperfect, i. e., slightly wedge-shaped plate. In other words, 

 the ordinary and extraordinary rays encounter the same 

 conditions, and their difference of path remains practically 

 unimpaired. 



To distinguish between the two families of intersecting 

 ellipses, it is necessary to polarize the incident beam in the 

 vertical and horizontal plane, respectively, seeing that the 

 crystal is revolvable about the horizontal or vertical axis. 

 When the plate is true and the mounting trustworthy there 



* It will be shown below that the eccentric mounting of the crystal, 

 as in fig. 1, is not, as a rule, advisable. 



PHI. Mag. S. 6. Vol. 24. No. 144. Dec. 1912. 3 I 



