On the Errors to he Corrected in Photographic Lenses. 403 
a plane refracting surface has a diacaustic, but a plane reflecting 
surface has no catacaustic. 
The sixth and last error is a smaller one, viz. the chromatic error 
of the secondary spectrum. This is due to irrationality in the disper- 
sion of the media of which a compound achromatic lens is composed. 
This error is removed in two ways, viz. (<z) by the manufacture 
of glasses having proportional dispersions ; and (&) by combining 
three different media instead of two ; in other words, by making an 
achromatic triplet of three different media, instead of a doublet of 
two different media. Of these two methods the first is the better, 
and great strides have been made in this direction during the past 
10 or 15 years. 
To sum up, we find that there are no less than six errors to be 
corrected in a photographic lens, viz. : — 
(1) Chromatic aberration, primary spectrum. 
(2) Spherical aberration of direct pencil. 
(3) Curvature of field. 
(4) Spherical aberration of oblique pencil. 
(5) Astigmatism arising from focal lines of oblique pencils 
(caustics). 
(6) Chromatic aberration, secondary spectrum. 
By these considerations the following question is suggested, viz., 
what is meant by the term aplanatism ? * 
There can be no doubt that formerly it was applied to a single 
lens which had only been corrected spherically for a direct pencil, 
e.g. the aplanatic meniscus. Subsequently it implied the correction 
of the spherical aberration for parallel axial rays, and at the same 
time the correction of the chromatic aberration of these rays for 
the primary spectrum. Now, however, the term has been used more 
loosely, and it is often applied to a combination in which spherical 
aberration for axial parallel rays has been intentionally introduced 
for the purpose of flattening the field. 
From what has been said above, we can see the reason of the test 
applied to photographic lenses mentioned by Mr. Jourdain. The 
artificial star, one of the most sensitive tests for both spherical 
aberration and centreing, when the pencils are direct, is also one of 
the best for searching out focal lines, when the pencils pass through 
it obliquely, the lens being turned on its axis for that purpose. 
We are all, I am sure, greatly indebted to Mr. Jourdain for bringing 
this interesting subject before us by his account of the correction by 
lens distance, and also of the method of testing photographic lenses. 
In the above note no notice has been taken of this alteration of lens 
distance, because it is of the nature of a secondary correction of a 
higher order of error than any we have been considering. This brief 
article has only been written in order that the “ brass and glass ” sec- 
tion of our Fellows may have before them a few elementary optical 
principles connected with photographic lenses and their corrections. 
