186 REPORT—1885. 
to N, or if V be the velocity of light, v that of the source towards the 
receptacle, in the ratio V+v to V. 
This principle has been considered by other writers, among them 
Petzval, Von Ettingshausen, Klinkerfuess,| Van der Willigen,? and 
Seccbi,? and an interesting discussion of their work has been lately 
given by H. H. Turner, in a dissertation for a fellowship at Trinity 
College, Cambridge. 
Chapter IV.—Reriexion anp RErrRActIon. 
§ 1. The various theories of reflexion and refraction advanced by 
Fresnel, Green, MacCullagh, Neumann, and Cauchy have been discussed 
by several writers, and attempts have been made to reconcile them with 
the experiments of Jamin, Quincke, and others. Jamin was the first to: 
show that by reflexion at most transparent media plane polarised light 
becomes elliptically polarised, and that this elliptic polarisation is most 
marked when the angle of incidence does not differ much from tan —!y. 
Moreover, forsome substances for which the refractive index is greater 
than 1:4 the phase of the component in the plane of incidence is re- 
tarded relatively to that at right angles to the plane, while if the index be 
less than 1°4 the reverse is the case. 
The original theories of Fresnel and MacCullagh do not in any way 
explain this phenomenon, and are therefore incomplete. 
§ 2. Cornu‘ has discussed the application of Fresnel’s theory 
to crystals, and has suggested a means of explaining the apparent 
discontinuity of the displacement normal to the surface to which that 
theory leads. The explanation—which Professor Stokes has been in 
the habit of giving, independently of Cornu, in his lectures at Cambridge— 
rests on the fact that the density of the ether is different in the two media. 
If, then, we take two planes in the two media parallel to the interface 
and at a small distance apart, the quantity of ether between the two 
planes remains the same; hence, if u, w’ be the displacements normal to the 
planes, and p, p’ the densities, the equation of continuity gives pu=p'w', 
and this is the condition assumed by Cornu in his papers. This con- 
dition, combined with those of the continuity of the displacement parallel 
to the surface, is consistent with the equation expressing the conservation 
of energy. 
The correctness of this condition depends on the view we take of the 
ether in the two contiguous media. If the two portions of ether be 
treated as two separate elastic solids in contact over a common surface, 
then over that surface the displacement must be the same in the two 
media; but the equality of the displacement normal to the surface cannot 
extend beyond a very small distance within the medium, and in the dis- 
placement is included that which comes from the pressural wave, as well 
as that which produces light. During the motion, of course, the bounding 
surface of the two media does not remain plane, but is a curved surface, 
the co-ordinates of any point on which at time ¢ are u,v+y, w+ 4. 
1 Klinkerfuess, Astronomische Nachrichten, t. xv. p. 17, t. lxvi. p. 337. 
? Van der Willigen, Archives du Musée Teyler, t. iii. p. 306. 
3 Secchi, C. #. t. Ixxxii. p. 761, t. lxxxiii. p. 117. 
* Cornu, ‘ Recherches sur la réflexion crystalline,’ Ann. de Chim. (4), t. xi. 
p. 283. 
