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XIII . — On the Errors to be Corrected in Photographic Lenses . 
By E. M. Nelson, Pres. R.M.S. 
( Read 18 th May , 1898.) 
As there was no other paper on the Agenda, I thought it would be a 
good opportunity to put before you a brief and popular account of the 
errors which need correcting in a photographic lens. This will in 
no wise clash with the paper we have just heard, as that dealt with 
corrections that had already been effected in certain lenses. One so 
often hears and sees in print such erroneous and wild theories regard- 
ing photographic lenses, that it may not be amiss to lay before you 
one or two of the fundamental optical principles, such as are dealt 
with in the ABC books and primers on the subject. This is now 
all the more necessary because low-power photomicrography and 
ordinary camera photography overlap, the same lens being used for 
both purposes. 
The first and principal error to be met with in all dioptric lenses, 
photographic or otherwise, is that of chromatism ; this need not be 
enlarged upon, as all microscopists are acquainted with it, and its 
method of correction, by combining a high-power positive lens having 
low dispersion with a low-power negative lens having high dispersion, 
the power of the combination being the difference between the powers 
of its components. 
The second error may, like the first, and for the same reason, be 
dismissed in a word or two. It is of course the spherical aberration 
of the direct pencil, which in this instance we will restrict to axial 
parallel rays. This error is due to the spherical form of lenses causing 
axial parallel rays, passing through a part of a lens remote from the 
axis, to have a different focus from those passing through the axial 
portion of the lens. In some lenses the aberration is negative, which 
means that the marginal rays have a shorter focus than the central ; 
in other lenses it is positive, or the axial rays have a shorter focus 
than the marginal. Spherical errors are corrected by combining 
lenses which have equal amounts of positive and negative aberration. 
The third error is curvature of image ; this means that a real 
image formed by a lens having a positive focus is curved, presenting 
its concave aspect to the lens, and the radius of curvature is (approxi- 
mately) equal to the focal length multiplied by the refractive index. 
Thus, for example, if we take the refractive index as 1 * 5, the diameter 
of the curvature of the image may be estimated as three times the 
focal length of the lens which formed it ; so the image from a 6-in. 
focus lens would have a diameter of curvature of 18 in,, or a radius 
of curvature of 9 in. 
This error is, as far as possible, corrected by reducing the aper- 
ture, and by giving to the lens a suitable form. Thus, in a single 
