54 L. B. Tuckcrman 



(0,2 — 6 o )=90°, i.e. to set the analyzing nicol at right angles to 

 the plane of polarization of the original light. This gives : 



. T/ sin2(i,2)sin 2 7rAA~ 



Since sin 2 2(i,2)sin 2 2wAiV r is always small in practice, the equa- 

 tion for maximum sensibility (98), neglecting higher powers, may 

 be written : 



. ,sin2(T,2) (sin 2 7rAA T - — sin 4 ?rAA") r/ . _ N 



7 sin 2 ir AA' ■'.v 



For low values of AX, sin**AiV may be neglected in comparison 



with sitrVAA", and the sensibility in both cases is practically the 



same. 



For large values of AAT, however, as in the Bravais biplate, where 



AN= I /\, the ratio of the two sensibilities may be as great as two 



to one. 



Of the other factors, a,/3,y, . . . . on which the sensibility de- 

 pends, the sharpness of the dividing line, which is inherent in the 

 halfshade, is of the greatest importance 1 ; and in this respect the 

 Brace halfshade is far superior to the Bravais biplate. In join- 

 ing the two halves of the Bravais biplate, it is difficult, if not im- 

 possible, to avoid considerable diffuse reflection with its conse- 

 quent depolarizing action. In the Brace halfshade the thin edge 

 of the mica is mounted in balsam of nearly the same index of re- 

 fraction, so that this effect is reduced to a minimum, and the di- 

 viding edge is clear and sharp. 



Laurent Saccharimeter Halfsliadc. — The sensibility to azimuth 

 variations is of special interest when the incident light is plane 

 polarized. Then e o =o and from (95) 



4 j sin 2 (o, 1 — OJ) sin 2 ( 1 , 2 ) sin 2 it A t sin 2 it AN 



I m ! 1 -j- cos 2 (0,1 — 6j cos 2(1, 2) 



I — sin 2 (0,1 — o )sin2 (i,2)cos27rA r cos27r AA" 



'Lumnier, O.. and Brodhun, E. Ztschr. f. Instk., vol. 9, pp. 41-50, 1SS9. 



2IO 



