The President's Address. By E. M. Nelson. 
157 
Now, if we can obtain a different substance for the concave that 
will yield a greater quantity of opposite chromatism for a given focus, 
then we need not make its focus so short. In other w T ords, a concave 
of a longer focus will supply the requisite quantity of opposite 
chromatism to neutralise the chromatism in the convex. 
A useful achromatic combination can therefore be constructed by 
uniting a short focus converging lens made of a less dispersive sub- 
stance with a long focus diverging lens made of a higher dispersive 
substance. The object, therefore, of this paper is to show how useful 
achromatic combinations of any given focal length can be made. 
In the first place, we must have two glasses possessing different 
optical qualities, called dispersive powers. Tn order to determine the 
dispersive power of any glass, we must know the refractive indices of 
that glass for three different portions of the spectrum. For our pur- 
poses, the three portions indicated by the three Frauenhofer lines C, 
D, and F will suit. C and F are called the extremes and D the 
mean. When these data are known the dispersive power can be found 
by dividing the difference of the refractive indices of the extremes by 
that of the mean, less one. This is written — — ~ ; its reciprocal 
/x D - l 
or — is known by the symbol v. 
H'-p ~~ H'g 
Method I . — Let v be the reciprocal of the dispersive power of the 
less dispersive medium, and v that of the higher dispersive medium. 
(In the Jena glass catalogue the values of v are printed in heavy 
type.) Then v' is the focus of the positive lens, and v that of the 
negative lens ; these when combined will make an achromatic doublet. 
(It will be noted that the v of the crown glass denotes the focus 
of the flint lens, and vice versa ; in other words, they are crossed 
over.) 
Example * J. — Taking the glasses in the Jena catalogue marked 
No. 23 and 39, we find v =32-0 = the focus of the positive lens, 
and v = — 51*2 = the focus of the negative lens. We have now to 
find F the focus of this combination ; it will be 
v'v _ 32-0 x - 51-2 _ - 1638*4 _ OQ 
v' + v 32-0-51-2 -19-2 
It will be of material assistance if we reduce this to a combination 
whose focus = 1*0; we must therefore divide the foci of the lenses 
forming the combination by the focus of the combination. 
Thus : 
/ = Si - •*»> /' - iftl - - •» ; and F = 1*0. 
* A Fellow of tlie Royal Astronomical Society (also a Fellow of this Society) 
who, by publishing for so many years a fortnightly article in the ‘ English Mechanic,’ 
has done so much to enkindle the scientific spirit in this country, has expressed a 
strong opinion that all formulae should be accompanied by examples worked out. 
This recommendation of his will be adopted throughout this paper. 
