ON OPTICAL THEORIES. 227 
by p’, we find that the condition (37) requires the coefficient of a to 
vanish separately, and we are led to the two equations 
jap Bp! dp 
Up Ma 
ogee aa os 
dp), Habtalat 0.6! soul 
(Sew) #0 (ei ve) 
and these are the two fundamental equations of the theory, from which an 
expression is found for the refractive index in terms of the wave lengths 
‘and constants, viz. :— 
TOs Madhotega ass Yor aout »iseoll 4 noe 
A? 
See sea 
where the = must be taken to include the different kinds of matter 
particles in the medium. So far, at any rate, the theoretical bases of 
these expressions are no more secure than those of Lommel and Helm- 
holtz. The dispersion equation, however, is much more simple than that 
given by Helmholtz, and agrees well, as Ketteler! has himself shown, with 
experiment. 
A second paper ? develops some farther consequences and traces the 
form of the dispersion curve in various circumstances. 
In a third paper * the principles of the theory are stated and applied 
to doubly refracting media, but the equations from which he starts—the 
Same as those given above, only written with three co-ordinates—do not 
express the physical facts which they are intended to do, and the theory 
‘deduced can only be considered as empirical. 
A further attempt, based on this principle of energy alone, is made in 
# more recent paper * to establish two independent equations. Thus, the 
ether mass in an element being displaced a distance ds, the matter mass 
ds’; then the equation 
m <P ds +m! Ode! = 9 V0 Ss P ; - (40) 
is supposed to express the law of the conservation of energy for the ether 
motion ; it neglects entirely the forces on m! from the action of neigh- 
bouring matter. The conservation of energy principle alone will give 
but one equation when applied to the system, though it will of course 
eliminate the unknown reactions between matter and ether. 
Similar remarks must be made with regard to other papers* dealing 
with the formation of the fundamental equations. The equations D of 
the last article referred to are only true on the assumption that the 
' See p. 181. 
* Ketteler, ‘Zum Zusammenhang zwischen Absorption und Dispersion,’ Po0qg. 
Ann. t. 160, p. 466. 
’ Ketteler, ‘Zur Theorie der Dispersion und Absorption des Lichtes in doppelt- 
brechenden Mitteln,’ Pogg. Ann. Ergiinzung, Band viii. p. 444, 
* Ketteler, ‘Das Dispersionsgesetz,’ Wied. Ann. t. vii. p. 658. 
> Ketteler, ‘ Theorie der absorbirenden Anisotropen-Mittel,’ Monatsber. der Konigl. 
Akad. der Wiss. zu Berlin, Nov. 13, 1879; < Optische Controversen,’ Wied. Ann. 
t, xviii. p. 387; < Erwiederung auf Herrn Voigt’s Kritik,’ Wied. Ann. Bd. xxi. p- 178. 
’ Q2 
