ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
781 
to combine a strongly chromatically over-compensated upper system 
with a strongly chromatically under-compensated front system. 
As regards the choice of refractive indices for the individual lenses, 
fluor spar (n = 1 • 434) is best for the convex lenses of the upper 
system, and for the concave, refractive indices (e. g. 1*57) which belong 
to a series of glasses of very varied high dispersions. For the middle 
lens, on the contrary, glasses with slight difference of dispersion, and as 
large as possible difference of the refractive indices, arc to be chosen ; 
and, finally, for the front lens a glass with strong colour aberration is 
to be used. The spherical correction of the system is made in the usual 
way. For the chromatic correction it is necessary to choose from a 
series of glasses with the determined indices those by which the colour 
aberration of the blue marginal and middle zone ray is removed, and at 
the same time the secondary aberration reduced as much as possible. 
Fig. 85. 
A Microscope System of 3 9 mm. focal length of Jena glass.* — 
Dr. Arthur Kerber has calculated the system he describes after the model 
of a 1/6 in., made by a well-known firm, with the 
idea of either establishing or altering the rules 
hitherto laid down for Microscope systems. 
The marginal and central zone rays are of the 
wave-length 0*55 ju, and of height of emergence 
K — 2^ and 1J mm., and the yellow and clear-blue 
rays are brought into union on the other side at the 
distance 
Ji* = 1 • 9 mm. approximately. 
The elements of the system, represented in 
fig. 85, are given in the following table, in which r 
denotes the radius, d the thickness, y the air-space, 
and h' the half-aperture of the glass lenses, while 
No. 8, No. 39, and No. 38 indicate the kind of glass used in the lenses, 
and refer to the lists of the laboratory at Jena : — 
r. 
d. 
y ■ 
h'. 
Cover-glass (No. 8) 

0*2455 

_ 
Front lens (No. 8) 
Middle lens : — 
1-9 
1-85 
0-5383 
— 
Flint lens fNo. 39) 
GO, — 4 
0-8 
0-1 

Crown lens (No. 8) . . 
Upper lens : — 
+ 4, + 4 
11 
0 
— 
Flint lens (No. 38) 
32-5, - 5-5 
0 8 
4 
2-5 
Crown lens (No. 8) 
5-5, + 7 • 5 
1-45 
0 
2-5 
The focal length of the system is 3 * 9 mm., the numerical aperture 
0-65. 
I. — The distance of union (z) and height of emergence ( h = z tan u) 
of the yellow rays, whose angle of inclination is determined by sin 2 a 
* Ccntral-Ztg. f. Optik u. Mech., xi. (1890) pp. 73-5, 86. 
3 i 
1890. 
