290 M. Frauenhofer on the Refractive and Dispersive Power 
freely fall upon the prisms. Hence it was easy to measure 
in this manner, by the theodolite, the angle of incidence. Know- 
ing, therefore, this angle, and also the index of refraction, and the 
angles of the prisms, which can be obtained exactly by the same 
ruler of the theodolite, the ratio of dispersion could then be de- 
duced by a very exact expression*. 
The observations made with two similar prisms agreed so 
well, that in an object-glass calculated after these data, there was 
no injurious aberration of colour. But if, in determining the 
relative dispersion,, we employ different pairs of prisms, formed 
of the same kind of glass, and having their angles different, the 
results present differences which might leave an uncorrected 
aberration injurious to object-glasses of considerable dimensions. 
This result conducted me to the following experiments. 
If we look at an object across two prisms of flint and 
crown glass, with their refracting angles in opposite direc- 
tions, particularly with a telescope, it will never appear 
without colour. At a certain angle of the incident rays, the 
dispersion is a minimum, and, either by increasing or dimi- 
nishing this angle, the dispersion increases. The remaining dis- 
persion arises, as is well known, from the different prismatic co- 
lours having a different ratio of dispersion in the two kinds of 
glass. If, in crown-glass, for example, the dispersion of the 
red rays is to that of the same rays in flint-glass as 10 to 19, then 
the violet rays may be dispersed in the ratio of 10 to 21. Hence, 
the two dispersions can never entirely compensate one another. 
It would be of great importance to determine for every spe- 
cies of glass the dispersion of each separately coloured ray : But, 
since the different colours of the spectrum do not present any 
precise limits,, the spectrum cannot be used for this purpose. 
More precision would be obtained, if we possessed glasses or 
coloured fluids which permitted only light of the same colour to 
pass ; the one, for example, permitting only the blue light to 
pass, and the other only the red. I have not been fortunate 
enough, however, to procure either a glass or a fluid which pos- 
sessed this property. In every case, the white light which pass- 
* The method of examining the dispersion of two prisms through a telescope 
was first proposed and used by Dr Brewster in 1812. See Treatise on New Phi- 
losophical Instruments , p, 300 .— Transl. 
