30 RYLANDS, ON THE MICROSCOPE. 
scope exists im the fact that while the former, practically 
speaking, is suited to receive parallel rays from a distant 
object, the latter has to deal with rays which are sensibly 
divergent from a closely approximate pot. On this account 
the formula will require some modification. 
In natural vision the rays emergent from any point of an 
object, which are employed for the purposes of vision, form a 
cone having the area of the pupil of the eye for its base. 
When the microscope is applied, the available aperture of its 
anterior lens takes the place of the pupil, and a cone of very 
different proportions is substituted. It is on the relative 
magnitude of the angles at the vertices of these cones— 
allowance being made in the latter case for the light lost im 
its passage through the instrument —that penetrating power 
depends. Thus the connexion with angular aperture is seen 
to be sufficiently close to form some excuse, perhaps, for one 
definition which has been given. 
It is only necessary to premise further that the formula 
may be stated in a rather more convenient form, thus : 
Ale, 
If A be now made to stand for half the angle of aperture 
of an objective, and a half the angle subtended by the pupil 
of the eye at ten inches, instead of the diameters of these 
apertures as before, the formula applicable to microscopes 
will be— 
tan A 
tan a 

1s 
Further, if we are content to adopt 0°2 inch as the mean 
or standard diameter of the pupil, which is sufficiently exact 
for general purposes, the equation becomes— 
P= 100 tan A 4/3" * 
* From two series of measurements of the diameter of the pupil I ob- 
tained the following results : 
In full daylight, near the window of a well-lighted room, 0:15 in. ; at the 
most convenient distance for distinct vision from a Highley’s argand gas 
lamp, 0°25 in.; the mean of the whole being 0°2 in. 
As simplicity is a great matter in such calculations as the one now under 
notice, it may be worth while to remark, that if the value of 2” for the in- 
struments of our best English makers should be found to be sufficiently con- 
stant, which is quite probable, the expression, so far as they are concerned, 
may be reduced to a single operation, and the value of P taken almost at 
sight from a table of tangents. 
The angle of aperture of an objective should be obtained by Mr. Lister’s 
method (‘ Phil. Trans.,’ vol. exxi; see also Quekett, p. 464), separately with 
each eye-piece and length of draw-tube. 
P= 
