ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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shortened, although the value of the A n / (w — 1) is only diminished to 
1/70. Consequently fluorite may be said to offer special advantages for 
the simultaneous union of three rays of the spectrum, i. e. for the 
removal of the secondary colour-dispersion. 
The above-mentioned phosphate crown glass, it is true, in combina- 
tion with the above or a similar borate flint glass, also allows a direct 
achromatism for three different colours (not the three rays Ha, Hy, 
yet three rays within the less refrangible part of the spectrum). It 
therefore serves for the construction of a double lens with only tertiary 
colours remaining ; but in this combination the curvatures are some- 
w'hat disadvantageous. This is due to the fact that the numbers for the 
relative dispersion An / (n — 1) in these two media — 1/70 and 1/54 — 
show only a slight difference. If, however, fluorite be substituted for 
the above crown glass, then a combination is obtained which satisfies the 
condition of the union of three different colours, and at the same time 
gives a very considerable difference of the relative dispersions of the 
two constituents (1/95 and 1/54). This difference still remains 
sufiiciently large if the calc-silicate crown be substituted for the 
borate flint. The dispersion of this glass is, moreover, almost rigidly 
proportional to that of the fluorite through the whole visible dispersion. 
Accordingly, with these two media, a double achromatic lens of almost 
absolutely complete colour-union could be made ; for there would be no 
tertiary spectrum remaining over. Having regard then to all the con- 
ditions which regulate the construction of a perfect lens-combination — 
the spherical aberration in systems of large aperture, as well as the 
chromatic aberration of first and second orders — fluor-spar affords more 
profitable relations than any material at present at our disposal in 
optics. The data on which the present conclusions are based, were 
made known long ago by the spectroscopic measurements on fluor-spar 
which Stefan published in the year 1871. The numbers given above 
are from the measurements of Dr. Riedel, of Jena, made in the year 
1880 and later at the author’s instigation, with the use of hydrogen 
lilies, on different varieties of the mineral. They agree with the values 
found by Stefan within the limits of errors of measurement, so far as 
they concern the same parts of the spectrum. The characteristic optical 
properties of fluor-spar shown by these spectroscopic measurements are 
doubtless due to the specific effect of the fluorine which makes up fifty- 
six per cent, of the calcium fluoride. It might therefore be reasonably 
expected that if it were possible to introduce this element in consider- 
able quantity into artificial fusions, kinds of glass would be obtained 
which, partially at least, would exhibit the valuable peculiarities of 
fluor-spar. 
Experiments made in this direction by Dr. Schott in 1881 and the 
following year in the course of his work on the improvement of optical 
glass have to a certain extent realized that idea. By the use of fluorides 
in small quantity glasses were produced which, with lower refractive 
index, exhibited also a very diminished dispersion. These experiments, 
however, showed clearly at the same time (as Dr. Schott has already 
indicated) the extraordinary technical difficulties which stand in the way 
of the production of sufficiently homogeneous glass of such a composi- 
tion. These difficulties at first appeared to be so great that it seemed 
