ON OPTICAL THEORIES. 243 
herical lining, which is in rigid connection with the ether outside. 
Then the equation of motion is— 
2 2 
Be gett AAC) (a, eT SENG 
da? 
Let the solution of this represent a train of waves of period 7 and 
length A, and let V be the wave velocity for the medium. Then 
maa eye (1-4) } 
a 2 J 
pa af C7? (== Ko?Ry 90 
=< [P C7? 4 1+ “my, KT tient: “E: : ] sa. 
and if , be the refractive index, since the velocity in free space is /e/p 
we have, if we put C,«,"?R,=q,m, etc. 
pars {acta 
a 
, 8 ; 
+ qk? (Ss dé z “Ha, 84s .) — terms in qo, 1s} ° PAN EL 
: It follows from this that, g, must be very little less than unity if the 
| formula, neglecting the terms in qp, etc., is to apply to a transparent sub- 
stance such as rock salt, which gives a value for » between 1 and 2 for 
| a range of the spectrum from the visible light to the longest waves emitted 
by a Leslie cube. The formula, we note, is the same in form as that 
given by Ketteler and Briot (see above, page 181), and Ketteler has 
shown that in some fairly transparent substances the coefficient 1—gq, is 
appreciable. qg, is essentially less than unity, so that the term in 7? comes 
in with a negative coefficient. The formula, then, will explain ordinary 
dispersion fairly if we put qo, 73, etc., all zero and take r greater than x. 
The critical cases are then discussed from the form 
cy C,7? (- qr” ry: qor” ze \ 
ee aa ee ee as we - (92) 
In this, 7 is greater than x, and less than «, for ordinary refraction. 
As r decreases down to «,, »? passes through the value infinity and then 
becomes negative, we have greater and greater refraction, and then the 
waves cease to be transmitted and absorption takes place. 
And here we are met with the question—What becomes of the energy 
thus absorbed ? According to our equation the ratio x, /£ becomes infinite, 
and the solution as it stands fails to meet this difficulty. Helmholtz 
introduced the term —y?dU/dt into the motion of the first shell, and this, 
representing as it does a viscous consumption of energy by the matter 
molecules, is objected to by Sir Wm. Thomson. Helmholtz’s solution 
given on p. 221 becomes identical with that at present under discussion if 
we put y=0; it is to meet this case in which r=x, that the term in y? is 
introduced, for if & represent the co-efficient of absorption on Helmholtz’s 
theory, and we suppose y to be small, then, with Thomson’s notation, 
204 
Ea Ae ae 
(? —«,2)2 
very approximately, K being a constant, and & may be very small except 
when 7 is nearly equal to x}. 
R2 
