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Transactions of the Society. 
theoretical explanation, is why the penetration as determined practically 
does not agree with the results obtained theoretically by Abbe’s method. 
For instance, we ought theoretically to get 5 mm. of penetration, but 
practically we only get 1 /2 mm. Again, a myopic person, who theo- 
retically should have less penetrating power than an emmetropic 
person, practically has more. To meet this the paralysis theory is 
suggested, but why there should be this paralysis, if it exists, I am 
unable to say. 
Taking accommodation depth first, all microscopists know that for 
every different screen distance, there is a different focus for the lens. 
Similarly for every different distance of virtual image there is a 
different focus for the lens. Accommodation depth is merely the 
difference in lens focus for different virtual image distances. The 
calculation of these different foci is very simple. 
Let us, in order to make it perfectly clear, take a real or screen 
image with a single biconvex lens first (fig. 41). It is well known 
that on either side of a lens there is a principal focal point. Now if 
we call the distance between the image on the screen and the principal 
focal point on that side of the lens w, and the distance between the 
object and the principal focal point on the other side of the lens v, 
and the focus of the lens / (see figs. 41 and 42), then 
/ 2 * 
v — — . (For proof see infra.) 
If we have another screen distance which we will call w, we 
4 2 
shall have another focus v , and v =- r The difference of focus is 
w 
therefore v — v, which is equal to _ — , and which may be more 
w w 
conveniently written ( - _ f 1 . If therefore, we put in for w the 
distance of least accommodation, and for w' that of greatest accommo- 
dation, the difference between these fractions will be the accommoda- 
tion depth we require. In the case of a simple lens / is the focus of 
the lens, but in a compound Microscope / is the focus of the entire 
Microscope. This may be very easily determined if M the magnifying 
power and D the distance of vision are known, because / = — . 
(In the absence of all knowledge of the well-known formula, 
/ = ^ the proof is given infra.) 
If, however, the object is in any other medium but air, y, the 
refractive index of that medium must be taken into account. The 
accommodation depth is therefore u / 2 (- When the sight is 
\w w J 
