22 L. B. Tuckerman 



where the upper or lower sign is taken according as cosv is pos- 

 itive or negative, i.e. according as cos2wiV 1 is positive or negative. 

 None of the preceding equations involving the double rotation 

 of compensator and nicol determine the sign of c since they are 

 all affected by an ambiguity of sign. To determine the sign of 

 e o it is necessary to use the equation : 



tg 2 w=sin 2 6 o tg 2 ir yV,=sin 2 fitg 2irN l ( 40 ) 



1 — e* u 

 giving sin 2 o and tg 2 ir A\ their proper signs. 



The direction of the major axis of the ellipse is evidently given 



by either %(p+ P '), or y 2 {R+R') — ~. 



4 



8. Halfshadj-: Analyzing Systems 



These will be discussed under two types : Type A and Type 

 B. In Type A the two halves of the halfshade consist of ana- 

 lyzers whose principal azimuths make a slight angle with each 

 other. In Type B the two halves consist of doubly refracting 

 plates whose principal azimuths are the same but whose orders 

 are different. The light emerging from the plates is analyzed by 

 a nicol. 



Type A. 



Lippich Half Nicol. 1 

 Brace Sensitive Strip. 2 

 Jellett Split Prism. 3 

 Cornu-Jellett Split Nicol. 4 

 Lippich Split Nicol. 1 



lippich, F. Naturwiss. Jahrbuch "Lotos." vol. 2, 1SS0 ; Wien. Bcr., 

 vol. 85, pp. 268-326, 1SS2 ; Ztschr. f. Instlc, vol. 2. pp. 167-74. L882; Wien. 

 Bcr., vol. 91, pp. 1059-96, 1SS.5 : Ztschr. f. Instk., vol. 12, pp. 333-42, 1892; 

 Ztschr. f. Instk.. vol. 11, pp. 326-27. 1894; Wien. Bcr.. vol. 105, pp. 317-61, 

 1896. 



"Brace, D. B. Phil. Mag. (6), vol. 5, pp. 161-69. 1903. 



3 Jellett. J. H. Brit. Assoc. Report, vol. 2, p. 13. I860. 



*Cornu, Alfred. Bull, dc la Soc. Chim.. vol. 14, p. 140, 1870: 



178 



