228 REPORT—1885. 
reaction of the matter on the ether produces a force —m/C’ oat while 
the action of the ether on the matter is expressed by a force —mO ap | 
. . ; ie dt?” 
and, indeed, in his most recent work on the subject! he realises clearly 
that the energy principle only leads him to one equation, viz. :— 
d?p d?p! 
m ry dp + m’ aie dp’ = eV *pdp — xp'dp’ : . (41) 
e being the rigidity of the ether in free space—and then combines with 
this a ‘second equation relating to the special mode of action of the 
matter particles, which can be no other than the renowned fundamental 
equation of Bessel’s theory of the pendulum’; this may be written 
. d2p - d?o! ae 
m ae” + m! a kp! . ; , . (42) 
It is then further assumed that the matter particles exert a force Am'p’ 
on the ether, and the equations finally become— 
2 2,/ 
m ee —m'Cy 2 =eV7p + Bmp! 
43) 
2 27 , ( ) 
70} d*p / dp! Bis (ee dp 
m 0 7p +m aa = ¢ + ey 
leading to the equation 
N- NE = = ay dre boa 
where K is a quantity depending on y. When K is small, as is always 
the case in transparent media, this becomes the formula already men- 
tioned, which has been tested over so wide a range by Ketteler. It is 
clear from these last equations that the action of the matter on the ether 
ray 
is represented by m! Coe + Pm'p’, and of the ether on the matter by 
072" It is difficult to conceive of the mechanical principles which 
would lead to these terms as they stand, and the occurrence of the 
imaginary quantity in the expression for the refractive index, to which 
they lead, is a blot on the theory. 
§ 8. In fact, the form of the equations given in his earlier papers a 
leads to results which are more directly intelligible, while the equations 
themselves can, it seems to me, be established by the aid of a suggestion 
due to Ketteler himself (‘ Hine dritte Annahme,’ p. 397). 
For, taking the notation employed when considering Helmholtz and 
* In Ketteler’s paper &, é’ are used for the displacements. I have retained p, p’, in 
accordance with the notation already employed. 
1 ‘Zur Dispersionstheorie des Lichtes,’ Wied. Ann. t. xxi. p. 199. See also 
Ketteler, Theoretische Optik, p. 85, et seq. 
2 Ketteler, ‘ Optische Controversen,’ Wied. Ann. t. xviii. p. 387. 
