230 REPORT— 1885. 
seems to consider it an objection to his theory that it gives a value dif- 
fering from unity to the refractive index for infinite waves, but the objec- 
tion is not, I think, serious. As has been stated before, the dispersion 
equation given by his theory has been repeatedly tested by Ketteler,! 
and the agreement between theory and experiment is very satisfactory.. 
Thus we may probably look upon this equation as one established em- 
pirically by his experiments, and while not agreeing with the reasoning 
employed by Ketteler in forming his equations of motion, may see in 
those equations the expression of a possible law of action between matter 
and the ether. 
§ 9. Let us now turn to Voigt’s work, which is of more recent date. 
He has been a severe critic of his predecessors, and objects strongly to 
various points in their work. 
In his first paper? on the subject Voigt, following Boussinesq,> 
remarks that md?u/dt? and pd?U /di? being quantities of the same order, 
U will be very small compared with u because p is very large compared 
with m; it is therefore not necessary to introduce terms involving U 
into the differential equations for v. To this we may reply, (1) that it is 
quite possible that the coefficients of U and its differential coefficients. 
involve » the matter density, and that in consequence the terms in ques- 
tion are comparable with md?u/dt®, and (2) that in the critical case 
near the absorption band the value of U becomes large, and may be 
quite comparable with w. 
Voigt also objects to the form adopted for = in all the previous 
theories, viz. — (kU + ydU/dt), pointing out that Helmholtz introduced 
the «U ‘zur Vereinfachung der Rechnung,’ and the ydU/dt to explain 
the transformation of light-energy into heat. If the ponderable matter 
is to be looked on as an elastic solid, then, according to Voigt, we ought 
to put for = terms like a?V?U + b?dé/dz. To this Lommel replies“ 
that the matter molecules each as a whole are not affected by the pas- 
sage of the wave of light, but that intra-molecular or atomic motions are 
set up, and that the forces arising from these are represented by his 
terms, how he does not explain. 
Of course, since it is assumed that U = Ae*t+m™@-alc” 
V?U= —(k + in/c)?U, the difference between the two will only show 
itself in a change in the refraction formula. 
The main criticism ° of Ketteler’s work relates to the method in which 
the equations are obtained. To this we have already referred. 
§ 10. After these criticisms we turn to the consideration of Voigt’s © 
own theory. His fundamental equations are, as we have seen, 
1 Ketteler, ‘Constructionen zur anomalen Dispersion,’ Wied. Ann. t. xi. p. 2105: 
‘Einige Anwendungen des Dispersionsgesetzes auf durchsichtige, halbdurchsichtige 
und undurchsichtige Mittel,’ Wied. Ann. t. xii. p. 363 ; ‘ Experimentale Untersuchung 
liber den Zusammenhang zwischen Refraction und Absorption des Lichtes,’ Wied.. 
Ann. t. xii. p. 481 ; ‘ Photometrische Untersuchungen,’ Wied. Ann. t. xv. p. 336. 
2 *Bemerkungen zu Herrn Lommel’s Theorie des Lichtes,’ Wied. Ann. t. xvii. p. 468.. 
8 See p. 213. 
4 Lommel, ‘ Zur Theorie des Lichtes,’ Wied. Ann. t. xix. p. 908. 
5 Voigt, ‘Ueber die Grundgleichungen der optischen Theorie des Herrn E.. 
Ketteler,’ Wied. Ann. t. xix. p.691; ‘ Duplik gegen Herrn Ketteler,’ Wied. Ann. t. xxi.. 
p. 534; Ketteler, ‘Erwiederung auf Herrn Voigt’s Kritik, Wied. Ann. t xxi. p. 178;: 
‘Duplik gegen Herrn Voigt,’ Wied. Ann. t. xxii. p. 217. 
® Voigt, ‘Theorie des Lichtes fiir vollkommen durchsichtige Medien,’ Wied. Ann.. 
t. xix. p. 873. 
