F. E. Wright— Bi-qiiartz Wedge Plate. 397 



sin' 2 (-- — 8 J = -9 cos' 2 a sin 2 f " + 8 J 



or 



• a _ a . » /-— .a ~ /— a 



Sin 



. a 

 sin — cos o 



1 — V 9C0Sa 

 tq 8 = • fo - 



_ cos8— cos— sin8= V"9 cos a SU1 — cos S+V'9 cos a cos — sin 8 

 ( 1 — V"^ cos a) — cos °- sin 8 (1 + V'9 cos a) = 



— V 9C0Sa 



+ V'9 cosa 



or 



1 '05409 — cos a a 



tq 8 = • tq - 



J 1-05409 + cos a ,J 2 



The formula of Bates expressed in this notation reads 



1 — COS a a , a 



to 8 = .tq-—tg z - 



J 1 + COS a (/ 2 J 2 



and differs from the above only in the constant in the fraction. 

 For the sake of comparison the angles 8 have been figured 

 for a = 1° to 15° by both formulas and included in the follow- 

 ing table : 



a 



S (new formula) 6 (Bates formula) 



o° .__. o' o' 



1° 2' 0' 



2° 3' 0' 



3° 4 7 r 



4° 7' 1' 



5° 10' 2' 



6° 14' 4' 



7° IS' 6' 



8° 22' 10' 



9° 28' 14' 



10° 35' 19' 



ll c 43' 25' 



12° 52' 33' 



13° 1°03' 42' 



14° 1°16' 53' 



15° 1°30' 1°06' 



This table as well as a discussion of the two formulae shows 

 that the angle 8 is increased in every instance by reason of the 

 loss of light by reflection in the small nicol prism. 



These differences can be allowed for upon the scale of the 

 quartz compensator. The operation for any angle a consists 

 in first adjusting the zero of the quartz compensator scale 

 with respect to the analyzer without intervening sugar solution 



Am. Jour. Sci. — Fourth Series, Vol. XXVI, No. 154. — October, 1908. 



28 



