412 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
(5) Microscopical Optics and Manipulation. 
Microscope Magnification.* — Mr. W. Le Conte Stevens, in spite of 
the distinction drawn by some authors between “magnification” and 
“ amplification,” j sees no good reason for discarding the usual acceptation 
of the term magnification, as denoting the ratio of the diameters of the 
retinal images produced with and without the magnifying instrument 
respectively. To obtain the magnification of a Microscope it is necessary 
to know the equivalent focal length of the eye-piece and objective, and 
also the tube-length. Unfortunately all of these data are seldom supplied 
by the makers. The equivalent focal length of the eye-piece is rarely 
given, and great diversity exists as to the points to be taken as the limits 
of tube-length. The tables of magnification given by certain firms are 
only applicable when “ standard tube-length ” is used, and such a 
standard exists only in name. Examination of such a table supplied by 
one maker showed that the magnification was calculated by dividing 
100 by the product of the focal lengths of objective and eye-piece. This 
rough approximation is deduced as follows : — 
Fig. 49. 
Let a'b' (fig. 49) denote the image of the object ab given by the 
objective 0. 0 c is taken as the focal length of the objective, and 0 c' 
as the tube-length, 10 in. The magnification of the objective m is then 
given by 
a' b' 10 
m 
a b 
f ‘ 
The eye-piece increases the visual angle from a to a producing a virtual 
image assumed to be 10 in. away. For the magnification m' of the eye- 
piece whose focal length is F we have 
. tan \ a' 10 
m = — — — • 
tan J a F 
The total magnification M is then 
M — m m' = 
100 
7 *' 
A more exact formula is obtained as follows : — For the objective we 
have 
m 
°rv _ t_ 
ab O c ’ 
where T is the tube-length defined as the distance from the focal plane 
to the point which behaves as an optical centre. 
Amer. Journ. Sci., xl. (1890) pp. 50-62. f See this Journal, 1889, p. 818. 
