406 
alignment along the direction of the magnetic force, and with 
a preponderance of one of the two directions of rotation over the 
other. Each rotating molecule is an infinitesimal electro- 
magnet, of which the current distribution is furnished by the 
system of convection currents constituted by the moving charges. 
The subject of magneto-optic rotation has also been con- 
sidered by Larmor, and two types of theory of these effects 
have been indicated by him in his report on the ‘‘ Action of 
Magnetism on Light.” One is represented by Lord Kelvin’s 
theory, which is illustrated by Maxwell’s chapter on molecular 
vortices in his ‘‘ Electricity and Magnetism.” FitzGerald’s 
paper ‘‘On the Electromagnetic Theory of the Reflection and 
Refraction of Light,” in the P/zlosophical Transactions for 
1880, is related to Maxwell’s theory, and explains the rotation 
produced by reflection from the pole of a magnet by means of 
the addition of a term to the energy of the system. The other 
theory is also a purely electromagnetic one, and supposes that 
the effects are due to a kind of zolotropy of the medium set up 
by the magnetisation, and so attributes them to a change of 
structure which introduces rotational terms into the equations 
connecting e/ectréc displacements and electric forces. This 
latter theory therefore regards the magneto-optic rotation as 
only a secondary effect of the magnetisation, which is not sup- 
posed to exert any direct dynamical influence on the transmission 
of the light-waves. 
It is not possible here to enter into the subject of these 
theories, but I should like to direct attention to a paper by 
Mr. J. G. Leathem, published in the Phzlosophical Trans- 
acttons, in which the type of theory just referred to has been 
worked out and compared in its results with the experiments 
of Sissingh and Zeeman in refiection. These investigators 
made measurements of the phase and amplitude of the magneto- 
optic component of the reflected light for various angles of 
incidence. For both these quantities the theoretical results of 
Leathem agree very well with the observed values. 
Returning now to the gyrostatic medium, between which and 
the electromagnetic theory, it is to be remembered, there is a 
correspondence, we may inquire in what way the gyrostats, 
when moved by the vibrations of the medium, react upon it, 
and so affect the velocity of propagation. The motion of a 
gyrostat is often regarded as mysterious, and it can hardly be fully 
explained except by mathematical investigation. But the general 
nature of its action may be made out without much difficulty, 
First of all, a gyrostat consists of a massive fly-wheel running 
on bearings attached to a case which more or less completely 
encloses the wheel. The mass of the wheel consists in the 
main of a massive rim, which renders as great as possible 
what is called the moment of momentum of the wheel when 
rotating about its axis. 
The diagram (Fig. 13) 
represents a partial sec- 
tion of the case and fly- 
wheel of a _ gyrostat, 
showing the arrangement 
of fly-wheels and bear- 
ings. 
Now let the fly-wheel 
of such a gyrostat be 
rapidly rotated, and the 
gyrostat be hung up as 
shown in this other dia- 
gram (Fig. 14), with the 
plane of the fly-wheel 
vertical, and a weight 
attached to one extremity 
of the axis. The gyro- 
stat is not tilted over, 
but begins to turn round 
the cord by which it is 
suspended with a slow 
angular motion which is 
in the direction of the horizontal arrow, if the direction of rota- 
tion is that of the circular arrow shown on the case. The same 
thing is shown by the experiment I now make. I spin this 
gyrostat and hang it with the axis of rotation horizontal by 
passing a loop of cord round one end of the axis so that 
the weight of the gyrostat itself forms the weight tending 
to tilt it over about the point of suspension. The axis of 
rotation here again remains nearly horizontal, but turns slowly 
round in a horizontal plane as before. 
NO. 1556, VOL. 60] 
Fic. 13. 
NATURE 
AUGUST 24, 1899 
The explanation in general terms is this. The weight gives 
a couple tending to turn the gyrostat about a horizontal axis 
at right angles to that of rotation. This couple in any short 
interval of time produces moment of momentum about the axis 
specified, the amount of which is the moment of the couple 
multiplied by the time, and may be represented in direction 
and magnitude by the line op. This must be compounded 
with the moment of momentum OA already existing about the 
axis of rotation, and gives for the resultant moment of mo- 
mentum the line oC, which is the direction of the axis of 
rotation after the lapse of the 
short interval of time. The axis 
of rotation thus turns slowly round 
in the horizontal plane, and the 
more slowly the more rapidly the 
fly-wheel rotates. 
The gyrostat in fact must have 
this precessional motion, as it is 
sometimes called, in order that 
the moment of momentum of the 
gyrostat about a vertical axis may 
remain zero. Thatit must remain 
zero follows from the fact that 
there is no couple in a horizontal 
plane acting on the gyrostat. 
Thus any couple tending to 
change the direction of the axis 
in any plane produces a turning 
in a perpendicular plane. For 
example, if a horizontal couple, 
that is about a vertical axis, were 
applied to the axis of the gyrostat 
in the last figure it would turn 
about a horizontal axis, that is, 
would tilt over. 
Again, consider a massive fly- 
wheel mounted on board ship 
on a horizontal axis in the di- 
rection across the ship. The 
rolling of the ship changes the direction of the axis, and pro- 
duces a couple applied by the fly-wheel to the bearings and 
an equal and opposite couple applied by the bearings to the 
fly-wheel. This couple is in the plane of the deck, and is re- 
versed with the direction of rolling, and has its greatest value 
when the rate of turning of the shipis greatest. Thus the force 
on one bearing is towards the bow of the ship, the force on the 
other towards the stern, during a roll from one side to the other ; 
and these forces are reversed during the roll back again. This 
is the gyrostatic couple exerted on its bearings by the armature 
of a dynamo on shipboard. 
In the same way, when a gyrostat is embedded in a medium 
and the medium is moving so as to change the direction of 
the axis of rotation, a couple acting on the medium in a plane 
at right angles to the plane of the direction of motion is brought 
into play. To fix the ideas, think of a row of small embedded 
gyrostats along this table with their axes in the direction of the 
row, and their fly-wheels all rotating in the same direction. 
Now let a wave of transverse displacement of the medium in the 
vertical direction pass along the medium in the direction of the 
chain. The vibratory motion of each part of the medium will 
turn the gyrostatic axis fromthe horizontal, and thereby in- 
troduce horizontal reactions on the medium. Again, a wave of 
horizontal vibratory motion will introduce vertical reactions in 
the medium from the gyrostats. 
Now, a wave of circular vibrations, like those we have already 
considered, passing through the medium in the direction of the 
chain, could be resolved into two waves of rectilinear vibration, 
one in which the vibration is horizontal, and another in which 
the vibration is vertical, giving respectively vertical and hori- 
zontal reactions in the medium. The magnetisation of the 
medium is regarded as due to the distribution throughout it of 
a multitude of rotating molecules, so small that the medium, 
notwithstanding their presence, seems of uniform quality. The 
molecules have, on the whole, an alignment of their axes in the 
direction of magnetisation. These reactions on the medium 
when worked out give terms in the equations of wave propa- 
gation of the proper kind to represent magneto-optic rotation. 
It is worthy of mention that the addition of such terms tothe 
equation was made by McCullagh, the well-known Irish mathe- 
matician, who, however, was unable to account for them by any 
Fic. 14 
a 
