Ca^pacity of the Microscope. By Prof. Helmlioltz. 39 
As regards the final result, it makes no difference whether the 
aperture at the circumference of the pencil of rays be supposed to 
be situate a little more to the front or to the back. The image of 
this aperture formed by the ocular lenses will be very shghtly 
larger when it is situate at the back lens than when it lies in the 
front lens, but the difference is without any practical significance. 
In equation [8] h' is the breadth of fringe in the last image, 
a the divergence angle in the medium where the aperture lies, 
X the wave-length at the same place, N the amplification of the 
last image, as distinguished from that formed by the rays passing 
the aperture. 
If, on the other hand, we put for the amplification of the 
last image referring to the object Xj , and for the wave-length, 
and refraction index for the medium in which the object lies, we 
may according to equation [7J make, as a is, by assumption, small, 
w, . n 
a I is the divergence angle in the first medium. 
Putting the value of ^ in equation [8], it becomes 
Nj sin. aj 
or, as \n — \^ = \^ Uq, which last refers to air medium, we 
have 
= e. 
Ni 2 sin. Oj 2 sin. a^ 
This e is the true magnitude of those lengths in the object, which 
in the magnified image of the fringes appear equal, and will 
therefore be effaced. Therefore, e may be considered the measure 
of the smallest distinguishable distances in the object, e will be 
smallest when is largest, — that is to say, when amounting to a 
right angle. In that case 
^ = h\' [9] 
This determination of hmit is likewise, as maybe seen, independent 
of the construction of the optical instrument. It holds just as valid 
for a photographic apparatus as for the relation of the microscope 
to the eye of the observer. These are the formulae which were 
applied in the calculations previously given. — From the Proceedings 
of the Bristol Naturalists Society, New Series, vol. i. part 3. 
