12 
Transactions of the Society. 
We will now pay our sole attention to the curves. They are 
drawn so as to represent the alteration in screen distance with light 
of different wave-lengths. The lenses are all focused with light E, 
the length of this vertical line to where the curve cuts it is supposed 
to he 10 in.* The curve for a non-achromatized lens would con- 
tinuously slope downwards from left to right. The curve of an 
objective perfectly corrected for all colours would therefore be repre- 
sented by a horizontal line, because the screen would remain at the 
same distance from the lens, viz. 10 in., with the other colours as 
with the green. This result is, you will observe, obtained with some 
of the apochromatics. 
The ideal curve for an achromatic lens corrected for two colours, 
say D and F, and focused with light E, would slope downwards from 
B to D, it would then slope less from D to E, it would then rise a 
similar amount to F, so that F and D would have the same focus, 
and then finally it would slope away at Gr. The reason for a small 
dip at E is owing to the irrationality of the spectrum. Except for 
a slight over-correction, No. 4 represents an ideal achromatic. 
The column marked O.I. indicates the ratio of aperture to power ; 
it is the N.A. of the objective multiplied by 1000 and divided by the 
initial magnifying power of the objective.! This shows the efficiency 
of the objective from solely an optical standpoint : it can therefore 
appropriately be called “ The Optical Index/’ or O.I. 
If a Microscope is required to show all that a keen eye is able to 
appreciate then *20 N.A. must be given to it for every 100 diameters 
of magnification.! If we limit the power of the eye-piece of such a 
Microscope to 10 then the objective must have *26 N.A. for each 10 
diameters of initial magnifying power. The optical index therefore 
for a theoretically perfect Microscope objective will be 26 • 0. 
This gives a very convenient rule ; for dropping the odd decimal 
we get the following : — The limit of combined power for best definition 
with any objective of any given aperture may be found by multiplying 
its N.A. by 400. Example : — The limit of power for best definition 
with a 2/3 in. of ’3 N.A. is 120 diameters. The converse rule may 
be stated thus : — The ideal N.A. for any objective whose initial power 
is known can be found by multiplying *025 by that power. Ex- 
ample: — The ideal N.A. for a 1/2 of power 20 is *025 x 20 = # 5N.A. 
This ratio has not only been attained, but is surpassed by that most 
* Note particularly not 'proportional. Thus in curve 2, line E, though actually 
1 in., represents 10 in.; the line F, actually 1£ in., represents 1()£ in., not 12 in. 
which it would do if it were proportional. This remark applies to the whole diagram. 
f In discussions with regard to the Microscope it is better to consider this ratio 
as one of aperture to power , instead of the usual ratio of aperture to focus , which is 
employed when speaking of telescopes and photographic lenses. The reason for this 
is, that the foci both of telescopes and photographic lenses can be easily and accu- 
rately determined, whereas it is the power and not the focus which can be easily and 
accurately measured in a Microscope objective. 
% ‘Ratio of Aperture to Power,* by E. M. Nelson. English Mechanic, xxxviii. 
(1883) No. 979. 
