ON OPTICAL THEORIES. 247 
and from the observations which have been made on the value of the 
principal incidence, for which the retardation is }7, we can find a value 
for rv. For silver Sir J. Conroy’s observations give (rv)! = 3°65. 
And here we are met with a great difficulty. Hxperiments show that 
there is very little chromatic effect about metallic reflexion. Thus, since 
the value of the principal incidence depends mainly on rv, this quantity must 
be independent of the period. Now »?+ 1 is approximately proportional 
to 7? when r is small compared with «,, and so this result requires that r, 
which is proportional to the effective rigidity, should also vary in a certain 
definite manner, and it is difficult to see how the theory is to give this. 
The theory is then applied to the case of a thin metal plate, and leads 
to the fact that the phase of both components is accelerated by the 
transmission. The accelerations for the two cases are given by— 
é cos 6 + € -i) \, vibrations normal to the plane of incidence, 
Tv 
écos@ + (;- r) \, vibrations in the plane of incidence, 
qT 
when dis the thickness of the plate, and e and f are found in the same 
manner as above. 
This acceleration was discovered by Quincke, but the details of his 
results do not agree well with the formule. The formule are consistent 
with Kerr’s discovery of the rotation of the plane of polarisation by 
reflexion from an iron plate when magnetised, but not with Kundt’s 
result that transmission through a thin plate of iron in a magnetic field 
produces a very large rotation of the plane of polarisation. 
In a final appendix an account is given of a gyrostatic molecule, the 
properties of which would give to the medium the heliacal effects seen in 
sugar and other active solutions. The molecule consists of a spherical 
shell in which are imbedded two gyrostats having a common axis, which 
initially is a diameter of the shell. One end of each axis is connected 
with the shell by a ball-and-socket joint, while the second extremities of 
each are connected together at the centre of the shell by a second ball- 
and-socket joint. ~ 
§ 4. Having thus given an account of the various theories proposed 
based in some way on the mutual reaction between the ether and matter, 
it remains to compare and contrast them. 
The theories of Boussinesq and Voigt have much in common, and 
| neither of the two as they stand applies to the case of bodies showing 
strong absorption, for the matter motion is entirely neglected. The theo- 
ries of Sellmeyer, Helmholtz, and Thomson come under one head in 
that they all make the mutual reaction to depend on the relative dis- 
placement of the matter’and ether. 
Lommel’s theory seems to me untenable: in its original form it con- 
tradicts the third law of motion, and if modified so as to be consistent 
with that, it leads to impossible laws for the relation between refraction 
and absorption ; besides this, his theory of double refraction does not 
lead to Fresnel’s wave surface, and there seems no reason why the co- 
efficient a”, which occurs only in the equation of motion of the matter, 
should be the one to be treated asa function of the direction. The laws of 
circular polarisation and of the double refraction in quartz, to which the 
theory leads, and which seem to agree with experiment, may be obtained 
