152 On the Focal Length ee 
The first form of apparatus consists of a stand with a vertical 
block pierced with two holes, in one of which is placed the objective 
to be measured with its optical axis horizontal. Through the other 
hole (the lower one) slides a horizontal bar, at one end of which is 
the micrometer used as the object, at the other end the paper scale 
on which the size of the image is measured, reading with an eye- 
piece detached from the instrument. This bar is moved in either 
direction until the image is thrown directly on the paper scale, the 
motion being accomplished by a screw giving a fine adjustment, 
while the nut in which the screw plays is moved by the hand for 
the coarse adjustment. The length, /, between the two scales was 
measured once for all. 
The results given by this arrangement were very satisfactory, 
but owing to its horizontal position and a difficulty im centring 
the lenses, I afterwards adopted a somewhat different apparatus, 
with which most of the recorded observations were made. Here I 
employ a microscope stand, using simply the tube and stage, placing 
the objective in its usual position, and throwing the image of the 
micrometer upon the paper scale. The latter is now gummed to 
the end of the tube usually occupied by the eye-piece, which is 
replaced by a convex lens detached from the instrument as before. 
The distance, 7, now a variable, has to be measured with each 
objective. This arrangement can evidently be applied to all micro- 
scopes, rendering it possible for anyone to determine the focal length 
of his own objectives with the greatest ease. 
The following measurements will show the accuracy of the 
method :— 
Tolles, Second Quality, 3. Smith and Beck, 3. 
Apparatus No. 1. Apparatus No, 2. Apparatus No. 1. Apparatus No. 2. 
f= sdiionm: 7 = 246 mm. 7= 311mm. ? = 253 mm. 
M. = +2411 M. = :2418 *2107 30 M. = -2099 
P. E. = -00029 | P. E. = -00011 | °2107 30 Pp. = "0001 
p. e. = *00058 p. e. = *00022 | +2104 25 p. e. = *00019 
2086 20 
2086 20 
2079 20 
- = *2095 
Pp. HE. = 300025 
p. e. = *00083 
The preceding measurements were made with both forms of 
