234 Mr. Atry on Achromatic Eye-pieces of Telescopes, 
Professor Robison, in the books already mentioned, has 
given for the simpler forms of the eye-piece, a geometrical 
construction. That an optician should be able to apply an 
algebraical formula is not improbable; but that he should make 
a geometrical construction, and deduce a theorem, is almost 
impossible. In the more complicated cases, he has assumed a 
particular condition, namely, that the axes of the pencils shall 
meet on the field-glass. This puts a stop at once to all im- 
provements: and even for the completion of this solution a 
geometrical construction is required, not less difficult than the 
former. The extracts which have been made from this work by 
other writers, it is not necessary to notice. 
When engaged in some investigations respecting a peculiar 
construction of telescopes, the principles of which were laid 
before the Society about a year and half ago, I found it 
necessary to obtain a general formula for making it achromatic. 
At that time I was not acquainted with any of the works that 
I have described: and the difficulties of the case compelled me 
to. use a method, which appears to me to be free from most of 
the objections that can be laid to them. In principle it consists 
in finding an expression for the visual angle by tracing the 
axis of a pencil of rays through the eye-piece, and, by a kind 
of differential process, making its variation, depending on the 
alteration of the index of refraction, = 0. I have here applied 
it to eye-pieces of two, three, and four lenses, and have pointed 
out some of the uses and peculiarities of each construction. 
The latter part, I hope, may not be without its value: it is 
upon the achromatism of Microscopes. This, I believe, has 
not been treated of by any author: and as it is not less im- 
portant, as far as it extends, than the achromatism of Telescopes, 
and as its theory is singular, and (I think) not inelegant, I have 
introduced it in this paper. 
