The Photometry of a Bull's-Eye Lens. 
395 
are 58 mm. diameter, but only beams 8 mm. diameter will pass 
through the substage condenser into the object glass; therefore, the 
bull’s-eye is only employing an aperture of 8 mm., and the useful 
light received by the bull’s-eye will be 
KS 2 L' 2 
The whole of this light is passed through the object spread out 
over an area which is the size of the image of the source of light. 
S 2 x 2 
The area of this image is — — , and the intensity of unit area will 
x 
be as before 
KS 2 L' 2 SV 2 _ KL' 2 __ K 50-26 _ K 
x 2 * x 2 x' 2 8 2 1*27’ 
The effect of using a bull’s-eye with a substage condenser is 
quite inconsiderable, and has thus only increased the intensity 
from (8) 2 to (8*16) 2 in the ratio of the slight alteration in the focus 
of the substage condenser caused by using parallel light instead of 
light coming from a distance of 392 mm. 
What has actually taken place due to the use of a bull’s-eye 
is that the size of the area of the object which is illuminated is 
larger without loss of illumination. The relative diameters of 
the image of the source of light in the two cases with and 
without the use of a bull’s-eye are approximately in the ratio of 
the focal length of the bull’s-eye to the distance of the light from 
the condenser, in this case 75 to 392. The use of the bull’-eye 
increases the diameter of the illuminated area approximately five 
times, but does not increase the intensity. 
An experiment with a photometric eye-piece shows a small 
but noticeable decrease in the light due to the loss by reflection 
at the surfaces, and to the absorption of the bull’s-eye, which loss 
has been neglected in this discussion. 
But on applying the theory to the modern form of dark-ground 
high-power illuminator it does not appear to agree with practice. 
The dark-ground illuminator referred to is of the type with two 
reflecting concentric surfaces. It forms a thoroughly good image 
of the illuminant, it has a focal length of about 3 mm., and is 
almost free from aberration, and there is no theoretical reason why 
it should not behave as any other well-corrected condenser. The 
following experiments show that it gives a far more intense light 
with a bull’s-eye than when it is used alone : — 
Experiment 1. — A piece of paper placed in immersion contact 
with a 3 by 1 slip with cedar-wood oil — 
