126 
Transactions of the Society . 
Now, a spectrum may be produced by diffraction or refraction, 
but there is an important difference between those spectra ; for in the 
diffraction spectrum the angular displacement of any particular por- 
tion of the diffracted beam is always proportional to the wave-length ; 
but this is not the case with that obtained by refraction. For example, 
if we take two beams of light, one consisting of waves measuring from 
7000 to 6000 tenth-metres, the other of waves measuring* from 5000 
to 4000, and cast diffraction spectra of them upon a suitable screen, 
then if w r o suppose that the spectrum arising from the light consisting 
of the longer waves is 1 in. long, the spectrum of the light having 
the shorter waves will also measure 1 in. 
But under similar circumstances a refraction spectrum from a 
glass prism would be of very different proportions ; for if the spectrum 
arising from the light of the longer waves was still 1 in. long, that 
from the shorter waves would measure more than 1 in., and further, 
different kinds of glass would yield different proportions. In brief, 
the character of the dispersion in a refraction spectrum varies with 
the nature of the substance from w r hich that dispersion is obtained, 
and this is the point that is of such importance in lens construction. 
Dispersion is measured by the difference of the refractive indices 
of the various Fraunhofer lines. In order to illustrate this, and 
other points to be dealt with later, an extract is appended from 
Messrs. Schott and Co.’s Jena catalogue of optical glasses, which is 
the most comprehensive and best arranged table as yet published. 
The next table is that of wave-lengths for the various Fraunhofer 
lines in inches and tenth-metres with reciprocals. A' is the potassium 
line near the Fraunhofer line A, and Gr' a hydrogen line near Gf. 
The following is an explanation of Table I. In order to find v, 
the reciprocal of the dispersive power, you divide the figures in the 
first column, less one, by those in the second column. The method 
of finding the refractive indices for lines other than D is obvious : 
thus, to find that for A', subtract the upper figures in column 3 from 
those in column 1 ; to find that for F, add the upper figures in 
column 4 to those in column 1 ; to find that for C, subtract those in 
column 2 from the sum just obtained; Gf' is found by adding the 
upper figures in the 5th column to the refractive index of F. 
The small figures below the others in the 3rd, 4th, and 5th 
columns are obtained by dividing those immediately above them by 
the figures in the 2nd column. It was pointed out in my previous 
address that v, the figures in the last column, represented the foci of 
positive and negative lenses which when combined would make an 
achromatic combination ; it is obvious therefore that in selecting two 
glasses suitable for this purpose, we must take care to have a sufficient 
amount of difference between them ; thus, for example, if we were to 
use the first two glasses in the list, we should only have a dispersive 
ratio of 1 • 02 = ~ = V ; the focus of the combination would there- 
v 
