RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 209 
because it is realized when the objective is used without an eye- 
piece, as a ‘‘simple microscope.” 
We have now 
N = [N]v 
and conversely 
N 
v= —. 
[N] 
A 
The value of v, which was defined above by the quotient —, and 
which indicates the enlargement of the dissipation-circles by the 
ocular, is therefore also the quotient of the total amplification of 
the microscope by the normal amplification of the objective, and 
thus expresses the zzcrease of power, beyond the normal power of 
the objective, which is obtained in the compound microscope by the 
tube and ocular combined. I shall, therefore, call the quantity uv 
the saper-amplification which is applied to a system, or which it 
has to bear when it is the objective of a compound microscope 
with a given length of the tube and a given ocular. 
We arrive now at the proposition:—When an objective (for 
which the constant visual angle of the inherent dissipation of light 
is given) is used with any length of tube and with any power of the 
ocular, the angular dissipation is always increased in the ultimate 
image in proportion to the super-amplification which the objective 
has to bear, z.e., according to the quotient of the total amplification 
of the microscope by the normal amplification of the objective. 
The foregoing considerations lead to a comprehensive expression 
and measure of the combined effect of tube and ocular in the 
compound microscope, which holds good (as may be shown) in 
regard to a// functions of the instrument. If, for example, we 
know that the objective of a microscope has a focal length f = 
4 inch—which gives the normal amplification [N] = 20, for a dis- 
tance of vision 7 = 10 inches—and that this objective is used for a 
power of N = 200, we have a super-amplification v = 10. We have 
thereby analysed the composition of the total power of the instru- 
ment as between objective and ocular, or the manner of co-opera- 
tion of these two elements of the composite system, in quite a 
general manner ; and we know that all essential conditions of the 
optical performance remain the same as long as the same value of 
vis maintained, whatever may be the particular conditions as to 
length of tube and depth of ocular. At the same time we have 
established a numerical test of the s¢vazz to which an objective 
must be submitted in order to obtain a certain total power of the 
microscope. We know that if an amplification of 200 is required 
with a 1-inch instead of a 1-2 inch as in the preceding example, 
