Marcu 4, 1915 | 
NATURE 21 

weight hung on the lower hook. The gyrostatic 
arrangement is very difficult to realise with ordinary 
gyrostats, but presents no difficulty with our motor 
instruments. You see what the arrangement is. A 
frame of four equal bars is constructed, by jointing 
the bars freely together at their extremities in the 
manner shown by the diagram. It is hung from a 
vertical swivelling pin at one corner, so that one 
diagonal of the frame is vertical, and another vertical 
swivelling pin at the lowest corner carries a hook. 
Four equal gyrostats are inserted, one in each bar, as 
shown, with its axis along the bar, and they have 
equal rotations in the directions shown by the circular 
arrows. Under the couples tending to change the 
directions of the axes of the flywheels, and applied 
by the weights of the gyrostats and bars, the system 
precesses round the two swivels, and so preserves a 
constant configuration. If now a weight is hung on 
the hook at the lower end, the frame is elongated a 
little, and a new precessional motion gives again a 
constant configuration of the frame, different, of 
course, from the former one. Two gyrostats, the 
upper or lower pair, would serve quite well to give 
the effect. 
Lord Kelvin suggested that if the frame were sur- 
rounded by a case, leaving only 
the swivel-pins at top and bottom 
protruding, it would be impos- 
sible, apart from special know- 
ledge of the construction of the 
interior, to discern the difference 
between the system and an en- 
closed spiral or coach spring, sur- 
rounded by a case and fitted with 
hooks for suspension and attach- 
| ment of weights. But unless the 
masses of the gyrostats are very 
small (while their angular 
momenta are exceedingly great), 
so that the change of kinetic 
enegy due to the change in pre- 
cessional motion may be put down 
A entirely, or nearly so, to the work 
mk = 
done by gravity on the weight 
carried by the hook, in its descent 
from one configuration of 
Fic. 6. steady motion to another, 
the distance through which 
the frame is lengthened is not simply proportional 
to the load applied. 
A fair idea of the action, and, indeed, an approxi- 
mate realisation of the property aimed at, is obtained 
by means of the arrangement shown in Fig. 6 above. 
We have had it before. A gyrostat is hung with its 
axis horizontal by a cord in the same vertical as the 
centroid. The flywheel spins, but as there is no 
couple there is no precession. A weight mg is 
applied in a vertical line at distance 1 from the cen- 
troid, as indicated by the diagram; a slight, very 
slight, tilting of the gyrostat is produced, and the 
gyrostat moves off with not quite steady precession, 
of average angular speed pp. Neglecting the slight 
deviation now set up of the suspension cord from 
the vertical, and putting A for the moment of inertia 
of the gyrostat about a vertical axis through its 
centre, we get for the kinetic energy of the azimuthal 
motion the value }Ayn*+i3ml?y?. The work done 
by the weight mg in its descent through the small 
distance h involved in the tilting is mgh. Hence 
we get $(A+m/) 2=m gh. 
As we have already seen, however, we have in this 
case n=mgl/Cn. Substituting in the equation just 
found this value for #4, and supposing that A is great 
in comparison with mlI?, so that the term 3m /? py? 
NO. 2366, VOL. 95 | 

may be neglected, we find after a little reduction the 
equation— 
h AFe 
Thus h is proportional to m. 
It will be evident that if on the right-hand side of 
the first equation there had been terms due to descent 
of the gyrostat through a distance of +h or £h, this 
equation of proportionality could not have been 
obtained. 
The idea, however, underlying the arrangement is 
very suggestive, and carries us a long way towards 
obtaining a definite notion as to how the elastic 
properties of bodies may be explained. 
(A gyrostatic pendulum was here shown. See for 
figure and description Nature, April 17, 1913.) 
VII.—Vibrations and Waves in Stretched Chain 
of Gyrostats. 
[An account of this paper was given in the lecture, 
and will be found (with details of the mathematical 
discussion appended) in the Journal of the Institution 
of Electrical Engineers. | 
VIII.—Gyrostatic Observation of Rotation of the 
Earth, 
The famous French experimentalist, Léon Foucault, 
suggested two ways of determining the rotation of 
the earth. One was observation of the apparent 
turning of the plane of vibration of a long pendulum, 
suspended so as to be as nearly as possible free from 
any constraint due to the attachment of the pendulum 
wire to its fixed support. This classical experiment 
was carried out with fair success at the Panthéon 
at Paris, and was repeated under the domes of the 
cathedrals of Amiens and Rheims. If the exponents 
of ‘Kultur’? in Northern France were aware of 
this fact, they seem to have attached to it just as 
little weight as they gave to the more sacred 
associations of the beautiful old church of the latter 
city. 
Foucault’s other method was based on the fact that 
a gyrostat, if mounted properly, retains unaltered the 
direction of the spin-axis when the supports are 
turned round. Here, for example, is our pedestal 
gyrostat, mounted freely in its enclosing frame 
which is carried by a vertical rod, swivelling in a- 
vertical socket carried by the supporting stand (see 
Fig. 7 above). I can set the spinning gyrostat with 
its axis in any direction I please, and, when I 
turn the supporting stand round, a friction couple of 
some little magnitude is applied to the vertical rod. 
You see that I do not alter the direction of the 
spin-axis perceptibly. Yet the friction couple is 
sufficient to carry the gyrostat round with the stand 
when there is no spin. The spin results in a great 
increase of virtual inertia for turning displacements, 
as we shall see quantitatively in the case of one of 
Lord Kelvin’s experiments, which I am about to 
describe. 
In practice it is found desirable to subject the 
gyrostatic apparatus to a constraint which is per- 
fectly definite; for example, the axis of spin may 
be kept horizontal. Solutions of the problem are to 
be found in the gyrostatic compasses now in use on 
the warships of various navies. 
At the British Association meetings at Southport 
and Montreal, in 1883 and 1884, Lord Kelvin sug- 
gested methods of demonstrating the earth’s rotation, 
and of constructing a gyrostatic compass. One of 
these had reference to the component of rotation 
about the vertical, the component, in fact, demon- 
strated by the Foucault pendulum experiment. If o 
be the resultant angular speed, the component about 
the vertical at any place in latitude | is wsin 7, while 
