104 
A simple consideration shows immediately, that one system of 
lines is formed by the rays, in which the phase difference in the 
wedge is 2k (k= integer), the other by those with a phase dif- 
ference (2k-+1) a. The properties mentioned in c and d follow 
immediately from this. 
4. When all the rays of the broad incident beam are supposed 
to pass over an equally long path in the wedge, an idea of the 
state of polarisation behind the wedge is obtained in the following 
way. Let the angle between polarizer and principal plane of the 
quartz plate be a, between analyzer and principal plane w. From 
the wedge issues elliptically polarized light. Let one of the axes 
form an angle @ with the principal plane. Let cos ut be the light 
vector in the incident light and A cos (ut—y), B sin (ut—y) that 
according to the axes of the elliptically polarized light, issuing from 
the wedge. Let d denote the difference of phase between the ordinary 
and the extraordinary ray in the wedge. Then: 
cos & == A cos ¥ cos 0. F Bustin ass et BE tn) 
cos dsin a — Acosysin@O— Bsinycos@ . . . . « (2) 
0 == Asin ¥ cos’ — Bicony sun? ee eee a) 
sin dsina= Asinysin0 J- Beosycos@ . . .. . (4) 
From this set of equations follows: 
AN oll cos’ 20 (A = Beos ZONNE AB sin Basin, 
Ill. tg 20 = tg 2acosd, IV. sin2y = tg asin d sin 26. 
[ is a consequence of the supposition, that nowhere light is absorbed. 
The light issuing from the wedge is polarized rectilinearly, when 
A =O. Hence there appear black lines, if: 
==), therefore B = Lin for, e= kr 0 d= 2k a 
or a=ka—ô Jd = (2k + 1) a. 
A special solution is A—0, a = 4} a, d indefinite. 
In this way the properties in a—d have been found back. 
5. From the analyzer issue two rays of light with amplitudes 
cosacost and sinasinw, with difference of phase d, so that the 
intensity is 
Lf =3(1 + cos Za cos 2w + sin Za sin Ap cos d). 
This expression shows again, that there are two systems of dark 
lines for d= ka and d=(2k+ 1). The transition of one system 
to the other is such, that one system of lines becomes brighter, the 
other darker. A shifting, as described in e, does not take place 
