208 THE MICROSCOPICAL NEWS. 
The angular diameter of the same dissipation-circles in the 
visual image is therefore 
Ew 
U= ——-Z 
Oe 
which shows that the enlargement, by the action of an ocular, of 
the dissipation-circles which are inherent in a given objective, is 
numerically expressed by the quotient of the optical length of the 
microscope-tube by the focal length of the ocular. 
If, for example, an objective of any kind be used with an ocular 
of say 1 inch, the length of the tube being such that the anterior 
principal focus of the ocular is 10 inches above the posterior 
principal focus of the objective, we shall have the of/zcal-length of 
the tube A = 10, ¢ = 1, and the quotient will yield the number 
ro; and this will express the fact that under these conditions the 
dissipation of the light in the ultimate image of the entire micro- 
scope has a visual angle ten times as large as any image which is 
projected by the same objective without an eye-piece. ‘This result, 
obviously, does not depend on the supposition of any definite: 
distance of projection (/). The same will hold good for every 
position of the image, be it a virtual image (as in the ordinary use 
of the microscope) or a real one, as is the case when the image is 
projected by objective and ocular conjointly on a screen or photo- 
graphic plate. 
The foregoing proposition admits, however, of a simpler and 
more expressive enunciation still, which is shown by the above 
formula for the amplification of the entire microscope : 
AS 
N =—, 
; So 
which may be written :— 
ZA 
NSS: 
S¢ 
A 
In this equation the quotient — (which may be denoted by the 
letter v) is one factor of the total amplification N ; and the other 
l 
factor - indicates that amplification which the objective alone will 
fi 
; Z 
yield for the same distance of projection (2). The value of - which 
I shall denote by the sign [N] may be conveniently called the 
normal amplification (the own proper amplification) of th2 objective, 
