16 THE MICROSCOPICAL NEWS. 
so that if we had an objective of 1-8th in, and an eye-piece of 2 in. 
the focal length of the Microscope 
UE aaa ~ 40 
A Microscope of a focal length of 1-4oth in. would magnify 400 
times, so that if this method of arriving at the focal length of the 
Microscope were correct, we should only have to multiply the 
power of the (1-8th in.) objective (80) by that of the (2 in.) eye-piece 
(5) to have the total magnifying power (400), the brass tube being 
assumed to be constant at ro in. 
The fallacy of this method lies in the fact that the true formula 
is not : . 
te Ta 
A 
are but jj = 
A being the distance between the posterior principal focal plane of the 
objective, and the anterior principal focal plane of the eye-piece, Or, as 
Prof. Abbe terms it, the rational or offical tube-length, in contradis- 
tinction to the mechanical or physical length.* 
As Ais the divisor of the fraction which represents the focal 
length, the latter is of course larger or smaller according as A is 
smaller or larger, that is, it varies inversely as A; and as the mag- 
nifying power is inversely to the focal length, the magnifying power 
varies directly as A, which is therefore seen to be a fundamental 
factor of microscopic amplification. 
We can now see how it is that two objectives of the same focal 
length may yet give differing magnifying powers with the same tube 
and eye-piece. “By the different methods of construction adopted 
by their makers, the focal plane of the one objective may be further 
off the back lens than is the case with the other. The distance 
A between the focal planes of the objective and eye-piece will be 
correspondingly diminished, and the focal length of the whole 
Microscope increased. The magnifying power will, therefore, be 
diminished. 
Again, take the case of two objectives of say 1-8th in. and 1 in. 
focal length used with the same eye-piece (2 in.) and tube. If the 
distance A remained constant, say to in., the total focal length 
would vary with that of the objectives, 
* The principal focal planes are the planes passing through the point on the 
axis in which parallel rays coming from the opposite side of the lens are brought 
toa focus. “ Anterior” and “ posterior ” are used in reference to the direction 
in which the rays come to the observer. 
