56 L. B. Tuckerman 



the formal equality of the sensibilities shown above can not be 

 expected to be realized in practice. A careful comparison of the 

 Lippich halfnicol with the Laurent saccharimeter halfshade, in- 

 volving a partial discussion of the value oi f (f m ,a,f3,y, . . . ) 

 has been made by F. Lippich. 1 The relative sensibilities of vari- 

 ous systems actually realized in practice have been discussed bv 

 Brace. 2 



11. Errors in the Use of a Compensator 



Since elliptically polarized light is always measured by the use 

 of a compensator, an estimate of the accuracy of its determina- 

 tion can only be made by a discussion of the errors involved in 

 the use of a compensator. If light of ellipticity e o and azimuth 

 6 is changed by a compensator of order A^ and azimuth \p into 

 light of ellipticity e 1 and azimuth 0,, the coefficients determining 

 the errors in the determination of e o and o are the partial differ- 



_ . de dt de de n A d0 30 30 3 



ential coefficients: ^-% ^> =-f> ^tf' and-^— °. ^-°> -=-f» ^ry • 

 de x 30 x d\p 3Aj 3<?j 30, dip 3A^ 



By means of these the accuracy of the determination of c o and o 



may be found if the errors 8e v 80 r Si//, and 8A\ are known. 



If all azimuths are referred to the same axes of reference, the 



second form of the general theorem is the more convenient. 



Then in equations (13) letting ^(o, 1 )=</': 



P =+P 1 



Q o =-j- Qj ( 1 ^2 sin 2 2 i//sin 2 7r A 7 ; ) 



-\-K x sin 4 \p sin 2 7r N x 



+5i sin 2 \p sin 2 it N x 

 K= + Qj sin 4 ip sinV N Y 



-f/dCi — 2cos 2 2i/' sin 2 ?r A^) 



— S x cos 2 \p sin 2 7r A\ 



S = — Qi sin 2 <// sin 2 -k A\ 

 J rK l cos2\ps\r\2irN l 



-\-Si • • • COS2ttA^ 



'Lippich, F. Wicn. Ber., vol. 99, p. 695, 1890; Ztschr. f. Instk., vol. 12, 

 pp. 333-42, 1892. 



2 Brace, D. B. P/iyj. Rev., vol. 18, pp. 70-88, 1904. 



212 



