226 REPORT—1885. 
original form it is not open to this criticism, and accounts for the facts, 
but its fundamental equations are hopelessly at variance with Newton’s 
third law, so long, at least, as we suppose the mutual reaction limited to 
that between the matter and ether in the element of volume considered 
—that is,so long as we may suppose that there are many molecules in an 
element of volume. The original formula for dispersion leads to results 
which, as Lommel’ has shown, agree fairly with experiment ; and by carry- 
ing the approximation a step further the agreement becomes closer still, 
so that his fundamental equations might be taken as an empirical repre- 
sentation of the facts with some approach to the truth. 
Voigt’s theory differs from these mainly in the values assigned to A 
and A and the methods by which those values are obtained; and before 
treating at length of it, it will conduce to clearness if we consider 
Ketteler’s theory, the results of which have considerable resemblance to 
the two already mentioned, while the work itself is earlier than Voigt’s. 
§ 7. Ketteler? is the author of a large number of papers on this 
subject, and the form in which he has presented his theory has varied 
somewhat, though the central idea which he has endeavoured to express 
has remained the same throughout. The idea seems to be as follows. 
The exact expression of the action between matter and ether, the A and A 
of the fundamental equations, is unknown to us, and we must therefore 
endeavour to eliminate it from the equations. This we can effect by con- 
sidering the work done per unit time on the whole system, into which, of 
course, the mutual reactions will not come, and equating it to the rate of 
change of the kinetic energy. This alone, of course, will only lead to one 
equation, and though in some of his work Ketteler appears to obtain two 
out of it, this, as we shall see shortly, is done by the aid of an additional 
hypothesis. 
It is, however, not till some of the later papers that these views are 
completely developed. In his first paper* he assumes that the action of 
the matter on the ether is to increase its rigidity by the quantity ea, and 
to introduce a resistance axp, where « is constant for the medium and a is 
some unknown function of its dynamical condition, while the forces on the 
matter are a(e’V7p'+x’p’), p’ being the matter displacement, so that, 
considering the motion parallel to z, we have for the ether 
2 2 
m = (e 4+ ea) em + akp } 
and for the matter (36) 
d2 / d2 ! 
m! waa + xp’ 
Arguments similar to those employed by Sellmeyer lead to the equation 
PXP 
aN hy (200 
fait soa (37) 
and on multiplying the first of the equations of motion by p, the second 
1 Lommel, ‘ Ueber das Dispersionsgesetz,’ Wied. Ann. t. xiii. p. 353. 
? Since the above was sent to press, Ketteler has published his optical theories in 
the form of a book, Theoretische Optik : Braunschweig, F. Vieweg und Sohn, 1885. The 
fundamental equations are formed as indicated below (Equation 43), and the remarks 
made in connection with that section apply. 
’ Ketteler, ‘Versuch einer Theorie der (anomalen) Dispersion des Lichtes in 
einfach- und doppelt-brechenden Medien,’ Carl Repertorium, t. xii. p. 322. 
