ZOOLOGY AND BOTANY, MICROSCOPY, ETO. 
135 
a different name to one of them, and he thought you ought to give a 
different name to the thing which was not astigmatism. Mr. Whipple 
and the Kew authorities ought to invent a name,* and then every one 
would be obliged to adopt it. 
The Chairman, in proposing a vote of thanks to Prof. Thompson, 
6aid that this paper constituted a really important contribution to the 
knowledge of optical measurements. The instrument which had been 
shown and explained promised to he very useful indeed in the actual 
examination and specification of lenses. Hitherto there had been no 
accurate method which was easily applicable for finding the constant on 
which the action of any lens, and, still more, a combination of lenses, 
depended. In the ordinary treatment of the properties of lenses in this 
country, even in scientific text-hooks, one got no further than dealing 
, with lenses which were not infinitely thin, but which were dealt with as 
though they were, and he hoped the paper would have a great effect in 
widening the ordinary optical discussions, and bringing the ordinary 
theory more nearly into accord with actual practical experience. As yet 
they had hardly got beyond Newton’s optics. What Gauss introduced 
long ago, the idea of the virtual thickness of the lens, had scarcely been 
recognized in all its importance in this country, though it was of the 
utmost value in facilitating the statement of the properties of lenses. 
One small point in the paper which he thought of some importance, was 
the introduction of a term for what he believed had no name before, 
which was often referred to in foreign writings as the vertex, and which 
was here called the pole. Prof. Thompson had already made important 
contributions to optical theory ; and he would refer especially to some 
papers of his whicli appeared two years ago in the ‘ Philosophical Maga- 
zine,’ where he showed how very simply the properties of lenses could be 
expressed by the method he had hinted at in the beginning of this paper 
— by speaking of the curvature they impressed on the wave front of a 
beam of light passing through them. In those papers he had treated all 
the ordinary cases from that point of view with extreme simplicity and 
beauty, and he hoped this method would be adopted generally in the 
ordinary treatment of optics. 
The Dioptrical Principles of the Microscope-t — Prof. G. Macloskie 
considers that the formulae for calculating tho path of light through a 
centered system of lenses is unnecessarily complex. He has tried a 
simple formula in Matthiessen’s ‘ Dioptrik,’ and finds that it can be 
extended to all cases, so that a single formula can be used to determine 
the focal lengths of lenses, doublets, objectives, eye-pieces, and of the 
entire optical system of a Microscope or telescope. For the refraction 
of a ray through a surface from a medium with index n 0 to another with 
index n x we have the two focal lengths 
n i 
* Tho author has since suggested the term aplanatism as a suitable name to 
denote this quantity. t The Microscope, xi. (1801) pp. 200-15. 
( Ji = 
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