ON OPTICAL THEORIES. 235 
These results are all in close agreement with experiment. 
In another paper! this formula is carried to a higher degree of ap- 
a(N?—1)? 
a. 
proximation, and reduces to Q= This agrees well with the 
measurements of Soret and Sarasin, between the wave lengths 7604 and 
2143. 
§ 2. Ketteler’s contributions to the theory of double refraction have 
been very numerous. Most of the papers already mentioned,? contain 
something on the subject. The theory given in the first of the papers 
mentioned is in its fundamental principles in close accordance with that 
developed by Lord Rayleigh in 1871, though the equations given on p. 95, 
following Von Lang, as representing the motion in a crystalline elastic 
solid are incorrect. In it a distinction is drawn between the displace- 
ment normal to the ray, which leads, it is said, to equations of the form— 
2 1 - 
(m+ mae + P= ay . ‘ . (63) 
and those in the wave front, for which the equations are— 
q 
(pio) (Ss a #) Zt gig 8B) oe Lea 
The arguments by which the second equation is deduced from the first 
are somewhat obscure ; they are, however, further developed in a later 
paper.* The ray direction is defined as that in which the energy of the 
vibration is propagated, and the direction of vibration is normal to this. 
The fundamental equations of this theory have already been given.‘ 
They are, in their final form,° 
d?u , aU rues yp 
m3 RRA CT Eo =e V7 2u+ Bm’'U | 
» (65) 
d*u aU dU 
Ot acs ay th gre Bb ery: dhe 
ached lana aiid @ slic 
where the constants Co, 3, « and y may all be functions of the direction. 
It is shown in the paper (‘ Optische Controversen ”) now before us that the 
conditions of incompressibility require that Cy, « and y should be constant, 
so that the theory turns entirely on the variability with the direction of }, 
or rather of C’, which is connected with Cy by the equation— 
Cites cos oe ales aaa 
C= po as 
An? 
; This is fatal to the groundwork of the theory, for in its form in the 
Optische Controversen’ it is assumed that C’ and Cy are unconnected. 
The paper ‘ Zur Dispersionstheorie’ starts without the term in /, 
arriving at the equation C’ + C)=0, and then (p. 203) inserts the B ‘in 
: ‘Lommel, ‘ Das Gesetz der Rotationsdispersion,’ Wied. Ann. t. xx. p. 578. 
See p. 179 ; and also Ketteler, ‘ Zur Theorie der Doppelbrechung,’ Wied. Ann. 
t. vii. p. 94; ‘Theorie der absorbirenden Anisotropen-Mittel,’ Monatsber. der Kénigl. 
Akad. der Wiss. zu Berlin, November 13, 1879. 
* Ketteler, ‘Optische Controversen II.’ Wied. Ann. t. xviii. p- 631. 
4 See p. 228. 
* Ketteler, ‘ Zur Dispersionstheorie des Lichtes,’ Wied. Ann. t. xxi. p. 199. 
