RELATION OF APERTURE AND POWER IN THE MICROSCOPE, 207 
cipal focus (which focus is generally in composite systems not very 
far from the back surface). The linear dissipation of the light in 
that image will be 
e— Ay, 
whilst the amplification of the object is 
A 
i 
This objective-image being observed by means of an ocular of a 
focal length ¢, and a virtual image being projected to a distance Z 
from the eye-point (the distance of distinct vision) the linear 
amplification N” to which the objective-image is submitted will be 
Z 
N’ =-, 
and the total amplification of the ultimate image 
Al 
Ny SN 
which is the general and strict formula for the determination of the 
power of a compound microscope by means of the focal lengths of 
objective and ocular, and the distance A, which I shall call the 
optical length of the tube.* 
At the same time we obtain the /zear dissipation of the light at 
the ultimate (virtual) image, owing to the simple*enlargement of 
the circles e through the ocular, 
Z 
= Ne = e—. 
d 
or 
A 
aa 
d 
* as the focal length of a composite system is always the quotient of the 
linear amplification N of the image, by the distance of that image from the 
posterior principal focus of the sytem (which is in the case of the microscope 
the place of the Ramsden circle above the ocular, or the eye-point, very 
approximately), we have the focal length of the entire microscope. 
by NFP 
Fo Ee ae, 
N A 
where the length A may be defined now as the distance between the posterior 
principal focus of the objective and the avfertor principal focus of the ocular, 
because this latter focus must coincide with the objective-image (very approxi- 
mately at least) in order to obtain the ultimate ‘virtual image at a considerable 
distance. 
