220 REPORT— 1885, 
As 7 decreases still further the refractive power increases, but the | 
refractive index is less than unity. 
The presence of a second absorption band above the first will, of 
course, modify the conclusions. The change in refractive power is 
perhaps best illustrated by a curve, as is done in Sellmeyer’s paper. For 
the case above considered take values of the refractive power (n?—1) 
for ordinates, and the reciprocals of the periods for abscisse, then the 
equation in the case of one absorption band will be 
K 
a i ara) 
a—wv 
where a = 1/8?. 
Thus the curve is an hyperbola, with the axis of « and the linea = a 
as asymptotes. If there be two absorption bands we have 
eae L 
al a—« b—2x 
and in this case there would be two critical values for « (viz., aand b) for 
which the refractive power would become infinite, and near which the 
dispersion would be anomalous. 
In 1874 there appeared a paper by Ketteler! on the same subject. 
In an earlier paper he had enunciated as the Jaw of dispersion in a gas 
the formula 
1 being the wave length and a, § constants. 
Further comparison with experiments had led him to the formule 
Ig diem oe B 
as paar ?—C 
and he now shows that by a proper interpretation of the constants this 
will include the case of abnormal dispersion, 
§ 6. The theory of the mutual reaction between the matter and ether 
was next developed by Helmholtz, and his work was continued by 
Lommel, Ketteler, and Voigt. The method adopted by Ketteler differs 
somewhat from those of the other three. Helmholtz2 (in 1875), Lommel# 
(in 1878), and Voigt‘ (in 1883) start in the same manner to form the 
simultaneous equations satisfied by the displacements of the ether and 
matter particles in a given element of volume. Let u, v, w be the dis- 
placements of the ether particles of density im in an element of volume év, 
U, V, W those of the matter particles of density pu. 
The forces on m are, as in Boussinesq’s paper referred to aboye,> 
considering only the components parallel to the xaxis :— 
’ Ketteler, ‘Das specifische Gesetz der sogenannten anomalen Dispersion,’ Pogg. 
Ann. Jubelband, p. 166. See also p. 181. 
* Helmholtz, ‘ Zur Theorie der anomalen Dispersion,’ Pogg. Ann. t. 154, p. 582. 
* Lommel, ‘Theorie der normalen und anormalen Dispersion,’ Wied. Amn. t. iii. 
. BOO. 
: * Voigt, ‘ Theorie des Lichtes fiir vollkommen durchsichtige Medien,’ Wied. Ann. 
t, xix. p, 873. 
= Seep. Zila; 
