28 
On the Limits of the Optical 
of the amplified image, and 1 J mm. as radius of pupil for bright 
illumination, the normal amplification is represented by the figures 
166-7, and the brightness of image follows the following rates : 
For an amplification of 333 "3 | brightness. 
which shows how rapidly the brightness must necessarily decrease 
with increasing amplifications. 
Were it possible to conduct a hemispherical cone of light from 
an object lying in water into an immersion lens, and form therewith 
a correct image, all these amplifications might be raised in the pro- 
portion 1 • 335 to 1 whilst the brightness of image remained the 
same. But, as already remarked, every instrument hitherto con- 
structed admits in air only, and not in water, a cone of incident light 
at all approaching to the hemispherical (180°). 
The sectional area of the pencil of light entering the pupil may 
be determined empirically with ease. Focus the instrument on a 
bright field, and withdraw the eye from the ocular (keeping the 
direction of the axis of the microscope) and look at the ocular 
itself. Just in front of it will be seen a small bright circle against 
a dark ground. This is the optical image of the objective lens 
which the ocular (i. e. chiefly its field glass) forms. All light 
which comes through the objective and has passed the ocular must 
be collected in this image of the objective. It corresponds, there- 
fore, to the area in which the several cones of light, transmitted 
from the bright points of the object, are collected at this spot. 
To gather all this light and thus get the largest and clearest field 
of vision, the pupil of the eye must be brought to this spot. 
The relation between the area of the image and that of the pupil 
gives at once the ratio by which the brightness of the image 
is less than that of the object when looked at with the unarmed 
eye. The same brightness of image as of object exists only 
when the size of the image is equal to or larger than that of the 
pupil. 
In the instance of the telescope. La Grange had already stated 
that the relation of size between the diameter of the objective and 
that of the picture of the objective formed by the ocular, is directly 
as the amplification, and he proposed to employ this ratio as a 
means of determining the amplification. With the telescope, how- 
ever, such a decrease of brightness is not a necessary accompaniment 
of increased amplification, because the amount of incident light may 
be augmented indefinitely by enlarging the object-glass or reflector. 
The aperture of the cone of light entering the microscope is, on the 
contrary, definitely restricted by the limits of the angle measuring 
that aperture. 
