On Bull's-eyes for the Microscope. By E. M. Nelson. 313 
Q will therefore equal the distance A B or P' + the distance 
between the menisci + the thickness of the second meniscus. Then 
s will be drawn from centre B to the point where E meets r 
(fig. 32). 
The formula Q' = ya Q gives Q' which is the point to he used in 
determining f for the third lens in the same way as the point B or P' 
was used in finding the focus of the piano or crossed lens for the 
double. 
The reason why the aberration is decreased by the insertion of a 
second meniscus is because of the decrease of the factor b by the 
y 2 
increase of the denominator in the fraction ~ by the removal of the 
focus from P' to Q'. The total spherical aberration a b is therefore 
reduced. 
In the triple the light meets the surfaces at no great obliquity, 
consequently there is not much loss by reflection. 
With regard to the diameter and focal length of a combination 
suitable for a Microscope bull’s-eye, if it is required to fill the back 
lens of any substage condenser 1J in. would be more than sufficient, 
but for the illumination of opaque objects by means of lieberkuhns, 
parabolic reflectors, Ac., perhaps 2 inches would be better. Naturally, 
with a given back focus, the larger the diameter the larger will be the 
angle of light that is parallelized, but unless the whole of the paral- 
lelized beam is utilized there will be a corresponding loss. Taking 
all things into consideration I think a 2-in. will probably be the 
most useful size. As to focus, or rather working distance, with one of 
my metal chimneys having a 3 x 1 slip I find that 1 in. will be 
sufficient. 
Allowance will have to be made for the horns of the meniscus as 
well as for the brass mount. I have therefore made 
P = 1 • 6". 
Fig. 33 shows the proper mode of mounting a condenser. 
Fig. 33 . 
"nJ 
Fig. 34 is a drawing of a doublet of plate glass, p = 1*516; 
2 in. clear aperture; angle 70°; working distance 1*0". 
