(^different Specie^ qf GIclss. SI 
The preceding Table shews the difference of dispersion rela- 
tive to differently coloured rays for each conabination of refract- 
ing substances. For example, for Jimt-glass^ No. IS, and water ^ 
the ratio of dispersion of the rays in the space BC, is as 1 to- 
S.56, and of the space GH as 1 to S.73. As these differences, 
however, are very small in some substances,' as in flint-glass^ and 
oil of turpentine^ we may expect, with some confidence, that, in 
varying the ingredients, we may obtain a kind of glass, in which 
the differences will be smaller than in that which has hitherto 
been employed. The crown-glass M, for example, is of such 
a composition. ^ 
Calling 1 the aberration of an object-glass of croxvn-glass^ 
No. 9., ondi flint-glass^ No. 3., produced by the difference of dis- 
persion relative to the different colours, this aberration becomes 
about 0.57 for an object-glass of the same focus, and composed 
of crown-glass^ No. 9., 2 i\\di flint-glass^ No^ 13, It will be 0.52 
for an object-glass of crown-glass M, and flint-glass^ No. 13. 
and 1,74 with crown-glass^ No, 9, and crown-glass M. In 
calculating these aberrations, I have taken into account the 
relative intensities of the differently coloured rays, of which I 
have already spoken. 
The results given by two prisms of flint-glass, No. 23. shew 
the degree of confidence which may be placed in the measured 
angles. With the prism of 45° made of this glass, a change of 
an arc of 2^^ produces a change of 1 in the 5th decimal of the 
index of refraction. With a prism of 60°, it requires an angu- 
lar change of 3".5 to produce the same variation in the decimal. 
If in achromatic object-glasses, the aberration produced by 
the unequal refrangibility of the differently coloured rays ought 
to be destroyed, then, since the focal lengths of the lenses of 
flint and crown glass ought to be nearly in the ratio of the dis- 
persion of the two kinds of glass ; and since, on the other hand, 
the ratio of dispersion for the different colours is not the same, 
it is evident that some aberration must still remain ; and we 
must therefore determine this ratio, in order that this aber- 
ration may be a minimum for the distinct vision of objects. 
This cannot take place, if the difference between the focal 
lengths for the rays of different refrangibility in the same object- 
glass is a minimum, for the different colours have not the same 
intensity : the aberration of the yellow rays, for example, which 
