180 REPORT—1885. 
while, on the hypothesis suggested above, we should find 
Po= — Bay {Al + pm+yn}. ; - (22) 
The theory as here modified would, it appears to me, agree in its results 
with all the experimental facts ; the main difficulty lies in the assumption 
of equations of the form i oe 
d a2 dt Bdz 
strictly incompressible. The value of p is generally A(z a 
x 
+ 7 2u for the medium when it is not 
dv , dw 
dy da ): 
and the introduction of p is based on the supposition that et ad + ne 
dx dy dz 
is zero, and A infinite; it is questionable if the substitution ought to be 
made, except in this case. 
§ 15. Kirchhoff’s paper on double refraction’ was read before the 
Royal Academy of Berlin, and is contained in their ‘ Transactions ;’ its 
more important part deals with the problem of reflexion and refraction. 
So far as the double refraction is concerned, it does not differ in any 
important points from Neumann’s theory. The medium is supposed to be 
incompressible, so that id ae -} ae vanishes, but the coefficient of this 
de dy dz 
expression is treated as finite, and the terms involving it in the ex- 
pression for the energy are omitted. The criticisms on Neumann’s theory, 
contained in Professor Stokes’s report, apply again here. 
Chapter IJ.—Disprrrsion or Licur. 
In 1870 Ketteler? published a paper on dispersion, which forms the 
first of his important series on that subject. He commences with an 
account of Cauchy’s theory and the various modifications which have 
been proposed. 
§ 1. Redtenbacker * had considered the problem under the supposition 
that each matter molecule is surrounded by an ether shell, and obtained 
the formula 
aR ML eh hcl ee 
\ being the wave length in the medium, and p» the refractive index. 
§ 2. Christoffel,* discussing Cauchy’s formula, already mentioned,® viz. 
had shown that, while a and & may be considerable in value, the 
other constants decrease rapidly. This two-constant formula may be 
written— 
2 pie eee |" "a 
DY Acer Neva 
1 Kirchhoff, Abhandl. der Konigl. Akad. zw Berlin, 1876. 
2 Ketteler, ‘On the Influence of Ponderable Molecules on the Dispersion of Light, 
and the Signification of the Constants of the Dispersion Formule,’ Pogg. Ann. 
t. cx). pile 
3 Redtenbacker, Dynamiden-System, Mannheim, 1857. 
4 Christoffel, Pogg. Ann. t. cxvii. 5 See p. 165. 
