ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
547 
principal planes. It is a well-known optical principle that when an image 
of an object as shown on the screen is found to be the same size as 
the object, the distance between the two will be four times the focal 
length of the lens. In the present instance let F represent the anterior 
principal focus, and F 2 the posterior principal focus, obtained as above, 
S 1 tbe anterior conjugate focus where one micrometer was placed, and S 2 
the posterior conjugate focus where the second micrometer was placed. 
Then the distance S 1 S 2 is equal to four times the focal length, plus the 
distance between the two principal planes, because an objective is not 
equivalent to a bi-convex lens. To get the differ- p rG> 59 
ence betwet n the principal planes it is only neces- 
sary to subtract the distance S 1 S 2 from twice the 
distance between the anterior and posterior prin- 
cipal foci. 
Now, to find where these planes are, take the 
distance from the front focus or anterior principal 
focus to the micrometer, this is the true focus, 
and measure it backwards towards or along the 
objective, it will fall in the tube, perhaps a quarter 
of an inch from the front end ; this is the first 
principal plane. Then measure from the back 
focus or posterior principal focus to the other 
micrometer, and that will be the distance to lay 
off on the tube from the back focus toward the 
front end of the objective ; mark it on the tube, as 
it is the much-desired posterior principal plane 
from which the 10 in. is to be measured. To 
ascertain all this practically perhaps seems hard, 
but it is not very difficult to get very close mea- 
surements. A low-power objective should be 
chosen, and laid on a piece of cork along the 
edge of a board or table. For micrometers, take 
a stiff piece of writing-paper, and rule a series of 
lines 1/50 in. apart, using a Brown and Sharp’s 
steel rule as a guide ; cut this paper across the 
lines so as to make two micrometers, thus secur- 
ing uniformity in the lines, as if each micrometer 
was ruled separately the lines might not agree. 
Dip these papers in oil or hot paraffin to make 
them transparent, and mount in a slit in a piece of 
cork at such a height as to be able to see them 
through the objective. Take all measurements 
with a pair of callipers, and lay them off on a rule. 
One ought to be able to get the principal planes 
within 1/50 in., and five times this would only 
make an error of 1 per cent, in the tube-length.” 
New Arrangement for the Quick Change of 
Microscope Objectives.* — Herr H. Boas describes a simple form of 
adapter which can be applied to any Microscope model, even to small 
* Zeitschr. f. Instrumentenk., xii. (1892) 1G2-4. 
2 p 2 
