248 REPORT—1885. 
with sufficient approximation to fit the experiments from other theories ; 
and, indeed, the fact that the wave surface in quartz does not become a 
sphere and a spheroid when the heliacal terms are neglected is fatal. 
With regard to Ketteler’s theory in the form finally given to it by its 
author,! it seems to me to have no possible mechanical basis. With the 
interpretation which he gives of the constants involved, his equations 
appear to contradict Newton’s third law as effectually as do Lommel’s, 
while, so far as the problem of reflexion and refraction is concerned, I 
cannot recognise the validity of Kirchhoff’s principle as it is applied by 
Ketteler. At the same time I think that the suggestion of Ketteler—to 
which, however, he himself takes objection—already mentioned, leads 
to results which, so far as dispersion is concerned, agree closely with 
experiment, 
We may with advantage compare the dispersion formula which it 
gives with that which comes from the theories of Helmholtz and Thomson. 
If we neglect the terms depending on viscous action, we have, accord- 
ing to Helmholtz, for p, the refractive index, 
v4 
_BYy BY} xf 
2— a ——— 
B — 1 pr,” pm, xe" iy 1) . . . (100) 
while, according to the modified form of Ketteler, 
fea 
eo 1+2 4A? i } - (101) 
oo (x3 pee 
| Xo 
Ketteler’s equations come from Thomson’s or Helmholtz’s by writing 
for C, the quantity — 4?C, /r?, or for 3? in Helmholtz’s notation — n?/3?, 
We may write Ketteler’s equation in the form of a series thus— 
a ~ ee DE el 
nis 1 =D Ag? Ao! 102 
=p [ + 2 2 nasal, ip aty ] . ( ) 
two terms of which will give us Canchy’s series with three constants. 
This modification leads also to an escape from one of the difficulties 
suggested by Sir William as to the explanation of double refraction. 
For his general expression for p? will become, if we write for C, the 
value —4r?C, /7?, 
a eae ea | SeEianinm saao8 } . (103) 
p 
Mm, \kK\2— 7? 
If we neglect for a moment the terms on which the dispersion depends, 
as being small compared with the term 47?C,/p, which gives rise in the 
first instance to refraction, we get that 
2 12 _ 47? (C, — C,') 
Pertti aa so ee 
p 
and there will be double refraction independently of the period. 
’ Ketteler, ‘ Zur Dispersionstheorie des Lichtes,’ Wied. Ann. t. xxi. p. 199. 
. (104) 
