ON OPTICAL THEORIES. 181 
Thus pp and dy are the refractive index and wave length for the shortest 
waves transmitted, and po/® the refractive index for the largest possible 
waves. 
§ 3. The various theories are then compared with experiment, by 
Ketteler, and it is shown that the formula 
1 B,C 
dead heioidh aati it . : ; » (25) 
represents the results of the comparison most accurately. This formula 
was obtained by Briot, working on the same lines as Redtenbacker, but he 
supposes the coefficient K, which he shows depends on the direct action 
between matter and ether, to vanish. Van der Willigen! also called 
attention to the importance of the term in A”, but could not account for 
its existence. Ketteler, following Briot, then analyses the manner in 
which these various terms arise, and shows that the force on any 
vibrating ether particle may be written 
An? Di F 
ae isplacement of particle 
2 
x {(g+WQ-L) - Sp M4 oth yh. 
This, of course, gives 
alsa by. CH eepeyais (4 tu wigan) 40, Hee MS 
The term in g + / arises from the mutual reactions of the ether particles, 
supposed to be uniformly distributed. If the action of the matter be 
simply to produce a periodic variation in the density of the ether, the 
terms in L and M are introduced, while the term involving g, + /, 
comes from a direct force expressed by mm,rf\(r) between the ether 
and matter particles m and m, respectively. If we put rf\(r) = p/r’, 
then the value of g; + h, is —4(m— 2)3myp/r"*". 
Briot supposes that the term KA?, to which this gives rise, is not 
required by the experimental results, and therefore puts n=2. Ketteler, 
however, shows that this term must be included. 
Holtzmann and C, Neumann had already insisted on the importance 
of retaining in the equations terms to express this direct action, and 
Neumann gives as the expression in an isotropic medium for the force 
arising from a displacement 1, 
Cea dz NC dat 
But the theory of dispersion in its complete form requires that the 
motion of the matter particles should also be included. ‘This is treated 
of in the next section of the Report.? 
A problem closely connected with dispersion is the relation between 
the refractive index and the density of a medium. This has been dealt 
with experimentally by various physicists, notably by Gladstone and Dale 
in England, and Ketteler in Germany. 
§ 4. L. Lorenz? has recently developed the theory of the transmission 
» Vander Willigen, Archives du Musée Teyler. 2 See p. 213, etc. 
8 L. Lorenz, ‘On the Refraction Constant,’ Wied. Ann. t. xi. 
