42 
focal length, this process is unexceptionable; but does not 
succeed so well with those of high power and aperture; the 
boundary is very faint, and sometimes difficult to observe. 
This is especially the case if the light be not uniformly dif- 
fused, or if the boundary be irregular; and if there be any 
false light, it is impossible to distinguish it from that which 
really contributes to vision. 
«‘This was strikingly the case with an objective which 
lately came under my examination ; it was a sixteenth, said 
by its maker to be 160°, and in which light actually was 
visible to that extent, though not satisfactorily. When, how- 
ever, it was tried on the Pleurosigma Fasciola, it could not 
(even with the most oblique illumination that Amici’s prism 
can give) be made to show this test better than a twelfth from 
the same artist, whose aperture is only 129°. This unex- 
pected result made me seek some mode of measurement which 
would not only give the angle of aperture, but also show 
how the light was distributed; and the following seems to 
fulfil both these requirements. 
“* As a lucid point in the focus of the objective sends out 
from the eye-piece rays nearly parallel, so light sent in the op- 
posite direction through the microscope will converge at that 
focus, and then diverge in a cone whose angle equals the 
aperture of the objective. If this cone be intercepted at 
right angles to its axis by a screen, and the diameter of its 
section, together with the distance of the screen from the 
surface of the objective, be carefully measured, they give the 
aperture. If S be the diameter of the section, D the distance, 
O the diameter of the objective, and J that of the image of 
the luminary used which is formed in its focus: 
A S§+0O O 
2), al Dalene O ze 
2 tan 
the upper sign being used if the section is measured within 
the penumbra, and vice versd. In my practice J was so small 
