224 REPORT—1885. 
correspond nearly to the maxima of absorption. Thus, as we go up the 
spectrum, the refractive power is a maximum for the value of n, given by 
=v? —Qve,and a minimum for *?=v?+2vea. There is, therefore, — 
abnormal dispersion in the neighbourhood of the absorption band, but | 
elsewhere the refractive index increases with n. Again, for large values 
of n we have N?=C?m/a?. Now, if the density and the rigidity of the 
ether be the same inall bodies, we should have C? = a?/m, and therefore in 
this case N=1. Thus the light of shortest wave lengths would be trans- 
mitted without refraction, contrary to experimental results. Sellmeyer, 
however, pointed out a method of explaining this difficulty which would 
be consistent with the supposition that C? is equal to a?/m. According 
to him, we must suppose that there is a strong absorption band some- 
where just above the visible limits of the spectrum—that is to say, that 
the value of 1? —2va is just beyond the limits of the visible spectrum, 
and that owing to this the refraction below the band is abnormally 
increased. 
The paper closes with a method for constructing the form of the 
refraction and absorption curves. 
Lommel’s equations can be solved in a similar manner, and lead to 
similar formule. The two theories can best be compared with each 
other and with experiment by changing the notation slightly, and 
adopting that used by Ketteler' in his criticism of the same. Let us put, 
therefore, 
3? = Bp ie | 
y? = pr, K fo : . (30) 
i ni(I — *) 
He 
Then Helmholtz’s equations (23) and (24) become 
1S bel as B v,? B?y,4 (19? — 0?) | 3] 
oe mn a k mn? — mn? { (19? — n*)? + nv 27K} ae 
and 
2k _m BAK (32) 
n 
en a2 pomn{ (vg? — 22) + n?v\2K?} 
and if we suppose A, \,, Ap to be the wave lengths corresponding to the 
periods n, v,, and vo, we find 
fr B2 4 fd? 1) 
| BAR! nm Xi (a 
N 
Fro) es re poet A a 2 
a? ie ae he wy 
' Comes muibier res 
B2 Kw ~ ¥ (33) 
qa™ pm 5 
Te Ke 2 2 
eal Kass 
Xo? ) af AP | 
1 Ketteler, ‘Optische Controversen,’ Wied. Ann. t. xviii. p. 387. 
