156 
Transactions of the Society. 
Therefore the raison d'etre for the “ extra thin ” slip has gone, hut 
the mischief that it does with the wide-angled cone of axial illumina- 
tion remains, which is, that it prevents an aplanatic wide-angled cone 
being obtained. I have always been of opinion that there should be 
a gauge for the thickness of slips as well as for their size. One- 
fifteenth of an inch is a very common size for ordinary slips, and would 
make an excellent standard. The “ extra thins ” are about half that 
amount, and must he regarded as quite useless ; for if an object, such as 
a diatom^ which possessed interesting fine secondary structure, were 
mounted on such a slip, the probability is that the secondary structure 
would for ever remain invisible. 
On the Construction of Achromatic Doublets and Triples. 
The above is the title of my own paper, which I am about to 
present for your kind acceptance to-night. As you have already been 
listening to me long enough, you will be glad to hear that a large 
part of the paper is mathematical, and consequently unreadable ; 
therefore I propose merely to go over a few points dealt with in the 
paper, and leave the mathematics for the Journal. The subject is a 
large one, far too large for any single address, consequently only a 
portion of the ground can be traversed ; the portion chosen for to- 
night may with propriety be called the middle portion ; for dispersion, 
which necessarily is the beginning of the matter, will be dismissed 
in a few words, and the end of the subject will not be reached by a 
long way. 
By the term “ achromatic lens ” a lens is meant that is capable of 
bringing two separated portions of the spectrum to the same focus, 
while an apochromatic lens brings three separated portions to the 
same focus. To-night, however, we shall deal with the achromatic 
lens. 
If we take any equiconvex lens, we shall find that it possesses an 
amount of a certain kind of chromatism, and that this amount of 
chromatism depends on the focal length of the lens, its diameter, and 
the substance of which it is composed. Now, if we take an equi- 
concave lens made of similar substance and of the same diameter and 
focal length, we shall find that it possesses an opposite kind of chro- 
matism, but of the same amount as that in the first lens. If, there- 
fore, we place these two lenses together, we shall have an achromatic 
doublet of the simplest construction, the chromatism of the one lens 
being destroyed by an equal amount of an opposite kind of chromatism 
in the other. The achromatism of this doublet will be of a very 
perfect kind, because all the portions of the spectrum are united 
at the focus. But the combination is of no practical value, owing to 
the great length of its focus, which is infinite, because the whole of 
the convergence obtained with the convex lens has been exactly 
neutralised by the diverging power of the concave. 
