The Penetrating Power of the Microscope. Eg E. M. Nelson. 333 
The method of obtaining these quantities is shown, and a table of the 
penetration of an objective of ’5 N.A. for objects in air under various 
amplifications and with a myopic accommodation is given. It will 
he noticed that with low powers the accommodation depth accounts for 
the greater part of the depth of vision, but as the powers become 
higher, its effect rapidly diminishes. 
We have here the means of applying a crucial test. If we take 
the lowest power in Abbe’s table we find that the depth of vision is 
twenty-nine times as great as the focal depth. If, however, Abbe’s 
table had been calculated for normal accommodation, the depth of 
vision would be thirty- five times greater than the focal depth. Now, 
as a photographic plate can have no accommodation, a photograph 
taken under similar circumstances ought to exhibit 1/28 or 1/35 of 
the penetration of the visual image, according as the eye is myopic or 
normal. I have performed these experiments and have failed to find 
any marked difference between the photographic and visual ap- 
pearances of the image with normal vision, the same aperture, the 
same cone of illumination, the same amplification, and the same object 
being employed in both cases. 
Prof. Abbe’s table would, however, lead one to expect a great 
difference between the visual image and the photograph in the case 
of low powers. 
With a 4-in. objective of •' 08 N.A. eye-pieced to give ten diameters, 
and with two objects in balsam having a difference of level amounting 
to • 5 mm., if the upper object is perfectly focused the lower will be 
out of focus. 
With a 2-in. objective of ’13 N.A. eye-pieced to give an amplifi- 
cation of 20 diams., a difference of level of *2 mm. is sufficient to 
throw the lower object quite out of focus. These observations were 
moreover confirmed by one wholly unaccustomed to use either the 
Microscope or any optical instrument ; this is worthy of note, because 
the appreciation of minute differences of focus and sharpness of images 
is, to a large extent, a matter of practice. I therefore conclude that 
the depth of vision with normal sight, and an aperture of ‘08 N.A. 
and a power of 10 diameters, is '02 in. in a medium of 1 - 5 refractive 
index. This is nearly 1 /7 of the result obtained according to Abbe’s 
formula, when his accommodation distance and circle of confusion are 
used, and nearly 1/9, when calculated with my accommodation distance 
and circle of confusion. 
We will now pass on to the photographic tests with low powers. 
I photographed with a 3-in. objective of '08 N.A., and with a 
power of 10 diams., two foraminifera mounted in balsam, which were 
separated by • 008 in. I also photographed the same object with an 
apochromatic 1 in. of • 3 N.A. and a power of 20 diams. The 
results in both cases were practically identical with those obtained 
visually. For the higher powers an object peculiarly sensitive to 
focal adjustment was selected, and at the same time one not requiring 
