232 THE NORTHERN MICROSCOPIST. 

visual angle of not less than 2’ nor more than 4’ for a dimension of 
0.5 » means that the aperture of 0.6 (73°.6) may be applied to {th 
objective or to a },th to discover the same details in the image, or, 
arguing conversely, that the limit for a one-twelfth may be between 
I.15 aperture as laid down incolumn 4, page 463*, and 0°6 as set forth 
in the fifth column in the same page. And so if we take the half-inch 
objective, which gives us, upon the English tube, an amplification of 
roo diameters, we shall see that the aperture may vary according to 
the needs of “ different individuals”’+ from 0°20 (23”) if 2’ of visual 
angle only are required, to 0.10 (11°.5 in air) if 4’ are necessary. 
Now the limits, as laid down in the table—of 23° on the one hand 
and 11°.5 on the other—for a half-inch objective when used upon 
an English tube, will no doubt be regarded by all microscopists as 
far too low. If, however, they have a leaning towards these figures 
let them get an objective constructed, a half-inch of 23°, and with 
it follow us in our remarks. 
Prof. Abbe tells us in his first paper (NORTHERN MICROSCOPIST, 
p- 207, line 19) that abundance of aperture is prima facie of no 
detriment except so far as it affects penetration and ease of working; 
too large an aperture for the amplifying power of an objective is 
called “waste,” and too small a one “empty amplification.” 
Now if there be two faults in an objective, it is easy to 
conceive that the “waste of aperture” or “lack of useful 
power ” is the least serious. Prof. Abbe tells us that in this case, 
details may be actually present in the image, but would not be 
visible to the eye for want of sufficient amplification. This is really 
the case; but as the necessary amplification can easily be obtained 
by using a deeper ocular, this objection must break down if we are 
able to prove that as good an image is thus obtainable as by using 
a higher power and a shallower eyepiece. The fault of “empty 
amplification” (the aperture too low in proportion to the magnify- 
ing power) cannot be remedied by the application of any appliance, 
the amount of light admitted will always be feeble, the defini- 
tion poor, and such objectives will never stand deep eyepieces 
for the simple reason that they only increase the size of an imper- 
fectimage. If abundance of aperture is primé facie of no detriment, 
the opposition to wider apertures, than those Prof. Abbe has laid 
down, must cease, if we are able to prove that any advantages are 
obtained by their use, independently of those appertaining to 
resolution. ‘The defining power of an objective is perhaps its most 
important feature; is it not the quality par excellence which dis- 
tinguishes it, and which has an important bearing upon all its other 
qualities? Prof. Abbe tells us (NoRTHERN Microscopist, p. 208, 
line 18), “ Provided the objectives are properly corrected and the 

*J.R.M.S. — +J.R.M.S., p. 462, line 25, 
