394 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
many reasons would be much more advantageous. That mineral there- 
fore affords greater convenience in the choice of the kinds of glass to be 
used in obtaining perfect compensating effects for the removal of the 
spherical aberration in lens-systems. 
Besides this advantage, which gains special importance in the con- 
struction of Microscope objectives of large aperture, fluorite possesses 
the further useful optical properties of an abnormally low colour- 
dispersion, and a relation to the partial dispersions for the different parts 
of the spectrum which is very serviceable for the removal of the 
secondary spectrum. For the three hydrogen lines H^, the 
differences of the refractive index are — 
Material. 
- Na 
N^. 
An 
Ny - 
n - 1 
- Na 
Fluorite 
0-00455 
0-00255 
1-43.38 
1 
95 • 4 
0-561 
Ordinary cale-silioate 
glass 
crownj 
0-00860 
0-00487 
1-5179 
1 
60-2 
0-566 
Aluminium - phosphate 
glass 
crovvnj 
0-00737 
0-00407 
1-5159 
1 
7(T() 
0-552 
Borate flint glass 
0-01026 
0-00582 
1-5521 
1 
0-567 
If the interval from Ha to (C to F) be taken as a measure of the 
mean dispersion (A n), the above table shows that the fluorite, not only 
taken absolutely, but also relatively to the value of (n — 1), possesses a 
considerably lower colour-dispersion than the most advantageous glass 
hitherto produced ; for while with the latter the so-called relative dis- 
persion does not sink below 1/70, with fluor-spar it is diminished to 
1/95. But tbe curvature which a compound lens of this medium must 
have in order to give an achromatic system of determined focal length 
when combined with a lens of greater relative dispersion, depends essen- 
tially on the amount of the relative dispersion of a medium. The 
smaller the An j (n — 1) the less curvature suffices for achromatism 
under otherwise similar circumstances for a given focal length. 
While thus a simple non-a chromatic lens of fluor-spar, on account of 
its low refractive power, necessitates a much greater curvature for a 
determined focal length than one of crown glass, on the other hand, an 
achromatic lens with this material requires less curvature than one made 
of crown glass, supposing that the same flint glass is used for the 
compensation of the colour-dispersion. 
Finally, the numbers in the last column of the above table show that 
tbe ratio of tbe partial dispersions in the two parts of the spectrum 
Ha to H |3 and H^ to H^ has for fluorite, in spite of its very low dis- 
persion, almost the same value as for an ordinary silicate crown glass 
with dispersion 1/60. On the other hand, for tbe aluminium phosphate- 
crown, the most advantageous glass so far as the relative dispersion is 
concerned, the blue end of the spectrum is seen to be relatively 
