RYLANDS, ON THE MICROSCOPE. 29 
definite meaning, and that the amount of this power possessed 
by a telescope can be obtained by calculation. This must be 
true of a microscope also. This power must not be confused 
with angular aperture, which has reference to the objective 
alone; neither has it any connexion with either definition or 
thickness of field. In one word, as magnifying power 
expresses the angle subtended by an object or image at the 
eye of the observer, so penetrating power is the measure of 
the angle subtended by the eye at the object, or the equivalent 
of that angle in the case of telescopic or microscopic vision. 
The one is the measure of size, the other of brightness. This 
latter, however, must not be confused with “illumination.” 
The one power is neither less important nor less essential to 
distinct vision than the other. There required little magni- 
fying power, and there was no illumination, in the case of the 
church-steeple, still the hour could be read on the dial. It is 
the power by which this was accomplished that we have to 
consider.* 
Referring those who wish to investigate this matter fully 
to the paper in the ‘ Phil. Trans.,’ I shall content myself with 
making use of such portions of Sir W. Herschel’s formula as 
is sufficient for our present purpose. This may be given as 
follows : 
Putting P for the penetrating power of a refracting tele- 
scope, 
« for the proportion of light which remains for 
purposes of vision after passing through a 
single lens, 
nm for the number of lenses in the instrument, 
A for the available diameter of the object-glass, 
and a for the diameter of the pupil of the eye; we 
have— 
pa Vor 
a 
— 

By applying this to the microscope, we shall obtain that 
which alone can be correctly called “ penetrating power.” 
We shall see clearly in what the value of increased angular 
aperture really consists, and I think we shall come to the 
conclusion that the term under consideration represents some- 
thing sufficiently important to prevent its being laid aside on 
account of any foregone carelessness or confusion. 
The great distinction between the telescope and the micro- 
* We are not told what magnifying power was employed in viewing the 
church-steeple, but I gathered from something in the paper that the pene- 
trating power of the telescope was about forty times that of natural vision. 
