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od ON OPTICAL THEORIES. 239 
ballast, their motions do not come into the surface conditions. While, 
finally,' Ketteler adopts the principle enunciated by Kirchhoff,? and 
already discussed above,* viz. that no work is done by the action of the 
stresses in the media on the bounding surface. In applying this principle 
he equates to zero, as Kirchhoff has done, the terms involving the dilata- 
tion ; and this, as has been already shown, leads to MacCullagh’s formule 
on his assumption as to the equality of the density in the two media, and 
to Fresnel’s if the rigidity be assumed equal in the two. The theory is 
applied to metallic reflexion and total reflexion within crystals in another 
paper. Thus, while Ketteler’s first theory> was in reality Green’s 
erroneously altered, this second theory is that given by Kirchhoff in the 
paper already quoted. Neither of them really seems to me to involve the 
distinctive features of Ketteler’s theory of the propagation of light. 
§ 2. Voigt’s theory is contained in the paper already referred to.® 
The conditions assumed are :-— 
I. The displacement of the parallel to the surface ether is continuous 
in the two media. 
II. The displacement normal to the surface multiplied by the density 
is continuous.” 
III. Kirchhoff’s principle—viz. that the work done by the stresses on 
the interface of the two media vanishes. 
Tn evaluating the expression for this work Voigt takes into account 
correctly the terms arising from the action of the matter on the ether. 
The displacements which come into the equations expressing the first 
two conditions are strictly displacements of the ether relatively to the 
matter, but since it is assumed that the motion of the matter particles 
is very small compared with that of the ether, the absolute displacements 
of the ether particles are introduced. 
The results arrived at, however, are hardly satisfactory. In the first 
place, in evaluating the expression for the work done on the surface, the 
term involving the dilatation is omitted. Voigt has taken it into account 
in his equations of motion; his reason for omitting it here is not given. 
He thus avoids the question of the so-called longitudinal vibrations. 
He then considers the case of vibrations at right angles to the plane 
of incidence, and arrives at the formule— 
E, + R, =D, 
(m, +17, —,7?) (E, — R,) sin¢, cos¢, : . (74) 
= (m2 + 72 — Ng7”) D, sing. cos, 
_E, B, and D being the amplitudes of the incident reflected and refracted 
‘Waves. 
* ‘Ketteler, ‘Optische Controversen II.’ Wied. Ann. t. xviii. p. 632. 
* Kirchhoff, Abhandl. der Berl. Ahad. 1876, p. 57. 
5 See p. 193. 
* Ketteler, ‘Ueber Probleme welche die Neumann’sche Reflexionstheorie nicht 
‘lésen 24 kénnen scheint,’ Wied. Ann. t. xxii. p. 204. 
5 See p. 162. 
® Voigt, ‘ Theorie des Lichtes fiir vollkommen durchsichtige Medien,’ Wied. Ann. 
‘t. xix. p.873. See also Voigt, ‘ Ueber die Grundgleichungen der optischen Theorie des 
-Herrn E. Ketteler,’ Wied. Ann. t. xix. p. 691, especially p. 696 seq. 
| 7 See p. 186; also Cornu, Ann. de Chim. (4), t. xi. p. 283. 
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