404 
NATURE 
[AucusT 24, 1899 
MAGNETO-OPTIC ROTATION AND ITS 
EXPLANATION BY A GYROSTATIC SYSTEM} 
II. 
I MUST now endeavour to give some slight account of the 
theories that have been put forward in explanation of 
magneto-optic rotation. There is an essential distinction between 
it and what is sometimes called the natural rotation, the plane 
of polarised light produced by substances, such as solutions of 
sugar, tartaric acid, quartz, &c., some of which rotate the plane 
to the right, some to the left. When light is sent once along 
a column of any of those substances without any magnetic field, 
its plane of rotation is rotated just as it is in heavy glass or bisul- 
phide of carbon in a magnetic field. But if the ray, after pass- 
ing through the column of sugar or quartz, is received on a 
silvered reflector and sent back again through the column to the 
starting point, its plane of polarisation is found to be in the 
same direction as at first. Quite the contrary happens when 
the rotation is due to the action of a magnetic field. Then the 
rotation is found to be doubled by the forward and backward 
passage, and it can be increased to any required degree by send- 
ing the ray backward and forward through the substance, as 
shown in this other diagram (Fig. 8). 
Thus the rotations in the two cases are essentially different, 
and must be brought about by different causes. In fact, as was 
first, I believe, shown by Lord Kelvin, the annulment of the 
turning in quartz, and the reinforcement of the turning in a 
magnetic field, produced by sending the ray back again after 
reflection at the surface of an optically denser medium, points to 
a peculiarity of structure of the medium as the cause of the 
turning of the plane of polarisation in sugar solutions and quartz, 
and to the existence of rotation in the medium as the cause of 
the turning in a magnetic 
field. Think of an elastic 
solid, highly incompressible 
and endowed with great 
elasticity of shape and of 
the same quality in different 
directions—a stiff jelly may 
be taken as an example to 
fix the ideas, Now let one 
portion of the jelly have 
bored into it a very large 
number of extremely small 
corkscrew-shaped cavities, having their axes all turned in the same 
direction. Let another portion have imbedded in it a very large 
number of extremely small rotating bodies, spinning-tops or 
gyrostats in fact, and let these be uniformly distributed through 
the substance, and have their axes all turned in the same 
direction. 
Both portions would transmit a plane-polarised wave of trans- 
verse vibration travelling in the direction of the axes of the 
cavities or of the tops with rotation of the plane of polarisation ; 
but in the former case the wave, if reflected and made to 
travel back, would have the original plane of polarisation re- 
stored ; in the latter the turning would be doubled by the 
backward passage. 
To understand this it is necessary to enter a little in detail 
into the analysis of the nature of plane-polarised light. As I have 
already said, the elastic solid theory may not express the facts of 
light propagation, but only a certain correspondence with the 
facts. But its use puts this matter in a very clear way. Ina 
ray of plane polarised light each portion of the ether has a 
motion of vibration in a line at right angles to the ray, and the 
direction of this line is the same for each moving particle. The 
lines of motion and the relative positions of the particles in a 
wave are shown in the first diagram (Fig. 1 p. 379). As the 
motion is kept up at the place of excitation, it is propagated out 
by the elastic resistance of the medium to displacement, and the 
configuration of particles travels outwards with the speed of 
light, traversing a wave-length (represented in the diagram by 
the distance between two particles of the row in the same phase 
of motion) in the period of complete to-and-fro motion of a 
particle in its rectilineal path. 
Now, a to-and-fro motion such as this can be conceived as 
made up of two opposite uniform and equal circular motions. 
Think of two distinct particles moving in the two equal circles 
als 
Fig, 8. 
1 A discourse delivered at the Royal Institution by Prof. Andrew Gray, 
F.R.S. (Continued from p. 381.) 
NO. 1556, VOL. 60] 
AB in this diagram (Fig. 9), with equal uniform speeds in 
opposite directions. Let each particle be at the top of its 
circle at the same instant; then at any other instant they will 
be in similar positions, but one on the right, the other on the 
left of the vertical diameter of the circle. Thus at that instant 
each particle is moving downward or upward at the same speed, 
while with whatever speed one is moving to the left, the other 
is moving with precisely that speed towards the right. Imagine 
now these two motions to be united in a single particle. The 
vertical motions will be added together, the right and left 
motions will cancel one another, and the particle will have a 
motion of vibration in the vertical 
direction of range equal to twice the — — 
diameter of the circles, and in the 
period of the circular motions. 
The rate of increase of velocity : 
of the particle at each instant is the : 
resultant obtained by properly add- 
ing together the accelerations of the Fic. 9. 
particles in the circular motions, 
and therefore the force which must act on the particle to cause 
it to describe the vibratory motion just described is the resultant 
of the forces required to give to the two particles the circular 
motions which have just been considered. 
Now, what we have done for any one particle may be con- 
ceived of as done for all the particles in a wave. To understand 
the nature of a wave in this scheme, we must think of a series of 
particles originally in a straight line in the direction of pro- 
pagation of the ray, as displaced to positions on a helix surround- 
ing that direction. Fig. A of this diagram (Fig. 10), regarded 
from the lower end, and the black spots on the model before 
| you, show a left-handed helical arrangement. Let these particles. 
be projected with equal speeds in the circular paths represented 
by the circle at the bottom of Fig. A. On this circle are seen 
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the apparent positions of different particles in the helical arrange- 
ment when it is viewed by an eye looking upwards along its 
axis. This motion is shown by that of the black spots on the 
surface of the model (Fig. 11), when I set it into rotation about 
its axis. Let the particles be constrained to continue in motion 
exactly in this manner. As the model shows, the helical ar- 
rangement of the particles is displaced along the cylinder. This 
is the mode of propagation of a cevczdarly polarised wave, which 
is made up of helical arrangements of particles which were 
formerly in straight lines parallel to the axis. 
The direction of propagation of the wave is clearly from the 
