THE OPTICAL, ELEMENTS OF THE MICROSCOPE LENS SYSTEM. 
55 
eter; after rotating the analyzer to its second position the distance between 
the same two points measured 48.9 divisions, which means an increase in 
magnification of 2.4 per cent. From Table 2 it is evident that the distor- 
tion increases (i) with the distance from the center of the field; (2) with 
the size of the analyzer, and (3) with the focal length of the objective used, 
low-power objectives suffering most from this defect. With large analyzers, 
the general disturbance of the optical correction of the lens system is so 
serious that only a small part of the field can be brought to sharp focus at 
a time. It is advisable, therefore, to use small, accurately adjusted analyz- 
ing prisms in the microscope. Some distortion is always present, but under 
these conditions it is reduced to a minimum. 
TABLE 2. 
Objective. 
Distance of 
object point 
from center 
in image in 
terms of 
Iman 
divisions. 
Distance betw 
object point a 
micrometei 
Principal plane 
of analyzer 
parallel with 
micrometer 1 ine. 
een center and 
measured by 
r eye-piece. 
Principal plane 
of analyzer 
normal to mi- 
crometer line. 
Percentage 
increase to 
magnification. 
Large analyzer: 
Fuess O 
I 1 
6 
4 
2 
I 
50.4 
2 7 .6 
47-75 
23.9 
47- 
52. 
28.3 
48.9 
24-45 
47-75 
3-18 
2-44 
2.40 
2.30 
1. 60 
Zeiss Apochromat 16 
Zeiss Apochromat 4 
Small analyzer: 
Fuess O ..... 
1 I 
6 
4 
2 
S:, 
48.75 
24-37 
48.25 
53- 
28.8 
49.65 
24-75 
48.9 
.92 
77 
.85 
.56 
35 
Zeiss Apochromat 16 
Zeiss Apochromat 4 
The distortion is evidently due to two factors: (i) Extraordinary light 
waves contained in the plane normal to the principal section of the nicol 
(in the Thompson type of prism the optic axis is parallel with the line of 
intersection of the end surface with the oblique plane along which the prism 
is cut) have the same refractive index e for all angles of inclination ; while 
for extraordinary waves transmitted in the principal section of the analyzer, 
the refractive index increases with the angle of incidence. For small angles 
of incidence, the difference in angles of refraction for waves incident at the 
same angle i, but in azimuths 90 apart, is not great (for i = 5, r = 32 1 '42". 6 
(azimuth 90 from principal analyzer plane), r' = 32i / 38".5 (azimuth o from 
principal analyzer plane) ; similarly, for i= io,r = 642'34 // .4, r' = 642 / i // .8, 
for *= 15, r= ioi'53".5 ( r' = 959 / 55".i) but it is perceptible, and increas- 
ingly so as the margin of the field is approached (* increases) and as the 
length of the prism increases. The second factor is the cementing film 
in the prism which has not precisely the same refractive index t or e' as the 
calcite, and produces, therefore, in the transmitted light beams, a slight 
displacement which becomes more serious the larger the angle of incidence. 
