of Chromatic Dispersion. 179 
found from the following formula, 
4(B+C+G+H)—3D+E+F) _ 
S = 
d 
and its logarithm is 24216417. 
With a view to a further generalization, it is needful to ex- 
amine the effects produced on the extrusions by raising the 
normal wave-lengths of the fixed lines to different powers, and 
dividing these by the indices of refraction. Selecting for this 
purpose the medium flint-glass No. 80 of Fraunhofer, the ob- 
served indices of which are pretty nearly accurate, it will be 
found that, while with the first powers of the normals the extru- 
sions are 
B —0-000419, C —0-000159, D-+0:000277, E +0-000468, F +0-000422, 
G —0-000047, H —0-000542, S +0-001167, 
with the squares of the normals they are 
B —0:000049, C —0:000025, D-+0'000031, E -+0-000063, F +0-000068, 
G —0-000026, H —0-000062, S +0:000162, 
and with the cubes they become 
B +0-000184, C-+0-000027, D —0-000148, E —0-000159, F —0-000096, 
G +0-000020, H-+0-000172, Ss +0-600403. 
It will be observed that in this last series the extrusions have 
changed their signs, and are greater in amount than with the 
squares. There must accordingly be an intermediate exponent 
of the normals between 2 and 3, at which the extrusions will be 
reduced to their lowest amount. This exponent of least extru- 
sion will be found to be, for flint-glass No. 30, as nearly as pos- 
sible 2:2, with which the extrusions become 
B +0-000007, € —0-000009, D —0-000010, E 4+0-000004, F +0-000024, 
G —0-000017, H-+0-000001, S +0-000036. 
These values are so insignificant that they may be regarded as 
arising from small errors of observation, and they may be entirely 
thrown out of view in the calculation of the indices. The follow- 
ing are the differences between the indices thus calculated and 
those given by observation :— 
B —0-000020, C —0-000026, D —0-000088, E +0-000035, F +-0-000138, 
G —0:000180, H +0-000007. 
These differences are so small as to lie quite within the limits of 
probable error in the observed indices. 
Now what is thus true of flint-glass No. 30, will be found to 
hold good with respect to all other media. ach has a specific 
exponent of least extrusion, which is constant for the medium 
and temperature. The question thus arises, How is this expo- 
