
334 THE NORTHERN MICROSCOPIST. 
nee Ean 
as in the numerical aperture table of the R. M. S., and the wave- 
length computed at .5269 p, then the theoretical resolving power 
of an air-angle of 60° will be represented by 48,200 lines to an 
inch; and this power will increase in the direct ratio of the numerical 
aperture until the widest balsam-angle has been attained. 
The penetrating power or stereoscopic capacity will, however, 
decrease with each increase of the numerical aperture. Professor 
Abbe has shown that, with any given aperture and amplification of 
the image, the power of penetration depends upon two factors, viz. : 
the depth of focus of the objective, i<., its capacity for showing 
portions of the object within and beyond the principal focal plane, 
and the depth of accommodation of the eye, or the range of its 
power to bring rays of different degrees of parallelism to a focus on 
the retina. The depth of focus is in the inverse ratio of the ampli- 
fication, but the depth of accommodation is in the inverse ratio of 
its square; the former also varies inversely with the numerical 
aperture. So that, whereas in low powers the depth of accommo- 
dation is the chief factor, in the medium powers these two factors 
become equal, and in the higher powers the depth of accommoda- 
tion becomes unimportant, and the depth of focus the principal or 
only factor in the entire depth of vision. According to Professor 
Abbe’s table, if, with a numerical aperture of .50 and an amplifica- 
tion of 10 diameters, the total depth of vision be = 2.153 mm., 
with roo diameters it will be reduced to .0273, or 7th, and with 
1000 diam, to .00094 mm., or gyyqth. The numerical equivalents 
for penetrating power in the table of the R. M.S. represent only one 
of these factors, that of focal depth, the other being unimportant, 
except with low amplifications. 
It is beyond the scope of this paper to treat of the practical 
advantages and disadvantages of the use of wide apertures as 
affected by manipulation, working distance and other considera- 
tions, or of the relationship between the aperture and the power 
employed. But as an attempt to convey the views of the leading 
microscopists of the day on the definition and value of aperture as 
an abstract quantity in the optics of the microscope, I trust it will 
not be without a useful purpose, 
