AucustT 24, 1899] 
IMA TU RL 
405 
bottom of the diagram to the top, and from the end of the 
model towards your left to the other, when the particles have a 
right-handed motion, and is in the contrary direction when the 
direction of rotation is reversed. For a right-handed helical 
arrangement the direction of propagation for the same direction 
of motion of the particles is the opposite of that just specified. 
The direction of propagation remains, therefore, the same when 
the direction of motion and the helical arrangement of the 
particles are both reversed. All this can be made out from the 
Fig. B shows part of a right-handed arrangement of 
diagram. 
polarisation produced in the forward passage is undone in the 
backward. 
It is easy to see that the same thing will take place if the 
reflection is at the surface of an optically rarer medium, so that 
the direction of motion of the particles is the same in the 
| reflected as in the direct wave. The helical arrangements, 
| however, are reversed by the reflection, and hence the wave 
| which travelled the more quickly forward travels the more 
slowly back, and again the turning of the plane of polarisation 
is annulled by the backward passage. Thus Lord Kelvin’s 
hypothesis of difference of structure com- 
pletely explains the phenomena. 
| 
| 
| 
| 
| 
We fass now to the other case, that of 
magneto-oplic rotation. Let us suppose, 
to fix the ideas, that the right-handed 
Fic. 11. 
particles corresponding to the opposite arrangement of Fig. A ; | 
and if the particles have the motions shown at the bottom of the 
diagram the propagation will be for both in the same direction, 
from the bottom to the top. 
In Fig. 10 we suppose the periods equal and also the wave- 
lengths, the distance along the axis from particle 1 to particle 9. 
The combination of the circular motions A and B gives recti- 
linear motion; the combination of the wave motions of Figs. 
A and B gives a plane polarised wave the plane of polarisation 
of which does not change in position. If, however, while the 
periods were equal, the wave-lengths were unequal as shown in 
this other diagram (Fig. 12), the plane of polarisation would 
rotate, as shown by the lines drawn across the paths in the 
figure on the right, for the circular motions of particles in the 
longer wave would gain on those in the shorter. 
A little consideration will show that the direction of the re- 
sultant rectilinear motion will, in consequence of the unequal 
speeds of propagation, turn round as the wave advances, and 
will do so in the direction of motion of the particles in the more 
quickly travelling wave, generating the screw surface shown in 
the model I have already exhibited. 
We must now consider the forces. The particles moving in 
the circular paths have accelerations towards the centres of these 
paths, and forces must be applied to them to produce these 
accelerations. These forces are applied in the present theory 
by the action of the medium, and it is the reactions of the par- 
ticles on the medium that are properly called the centrifugal 
forces of the particles. The requisite centreward forces then are 
supplied by the state of strain into which the medium is thrown 
by the displacement of parts of it, which form in the undisturbed 
position a series of straight arrays in the direction of propa- 
gation, into these helical arrangements round that direction. 
The greater these elastic forces the greater the velocity of | 
propagation of the wave. 
In an elastic medium these forces depend on the amount of 
the relative displacements of the particles, and will be greater 
for displacements in the right-hand helical arrangement than for 
displacements in the opposite direction if the medium has a 
greater rigidity for right-handed distortion than for left, and the 
right-handed wave of distortion will be transmitted with greater 
speed, and wice verst. This is the case of solutions of sugar 
and tartaric acid, quartz, &c., for which a helical structure has 
been supposed to exist in the medium. 
Taking this case refer to Figs. A and B of our large diagram 
(Fig. 10), and let the right-handed wave travel the faster. Let 
the waves travel up, be reflected at the upper ends, as at the 
surface of a denser medium, and then travel down again. The 
reflected waves are those shown in Figs. A’, B’ of the diagram. 
By the reflection, the helical arrangement will be unaltered. 
But the plane of polarisation, as we have seen, turns round in 
space in the direction of the motion of the particles in the more 
quickly moving wave ; it therefore turns round in the direction 
of the hands of a watch as the wave moves in the upward direc- 
tion in the diagram, and in the opposite direction when the | 
wave is travelling back. Thus the rotation of the plane of 
NO. 1556, VOL. 60] 
circular ray travels faster than the other, 
and that whether direct or reversed. Here, 
as in the other case, the elastic reaction of 
the medium on the displaced particles 
depends only on the distortion, and if 
there be no structural peculiarity in the 
medium there must be the same reaction 
in the particles in both the circular waves 
which combine to make up the plane- 
polarised one. 
Thus the actions on the particles being the same for both 
waves, and the velocities of propagation being different, the 
motions concerned in the light propagation cannot be the same. 
There must in fact be a motion already existing in the medium 
which, compounded with the motions concerned in light 
propagation, give two motions which give equal reactions in 
the medium against the equal elastic forces, applied to the 
particles in the case of equal helical displacements. 
Thus Lord Kelvin supposes that in the medium in the mag- 
| netic field there exists a motion capable of being compounded 
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Fic. 12. 
with the luminiferous motion of either circularly polarised beam. 
The latter is thus only a component of the whole motion. 
In the very important paper in which he has set forth his 
theory Lord Kelvin expresses his strong conviction that his 
dynamical explanation is the only possible one. _ If this view be 
correct, Faraday’s magneto-optic discovery affords a demon- 
stration of the reality of Ampére’s theory of the ultimate nature 
of magnetism. For we have only to consider the particles of a 
magnetised body as electrons or groups of charges of electricity, 
ultimate as to smallness, rotating about axes on the whole in 
