Marcu 4, 1915] 
VATURE 23 

the most general motion they are superimposed. This 
second curious effect was not referred to by Lord 
Kelvin, and I have not seen it noted before. The 
co-existence of long and short periods is, however, 
characteristic of rapidiy spinning gyrostatic systems. 
Now suppose that the wire so long and of so 
slight torsional rigidity that this rigidity cannot 
stabilise the gyrostat in the position of unstable 
equilibrium. ‘then the effect of the component of 
rotation of the earth about the vertical is to produce 
tilting of the axis of the flywheel from the horizontal 
position, since this turning gives a rate of production 
of angular momentum about a horizontal axis at 
right angles to that of rotation. A slight tilt suffices 
to give an equilibrating couple, and so we can have 
the gyrostatic axis in a north and south vertical 
plane, and nearly horizontal, whiie the wire is with- 
out twist. Into this position the gyrostat is guided 
by manipulation of the torsion-head. The effect of 
the horizontal component of the earth’s angular speed 
is now practically zero. 
If now by the use of the torsion-head the gyrostat 
axis be brought to rest in a nearly horizontal position 
at an angle » with the north and south horizontal 
direction, the component of turning about this posi- 
tion of the axis is wcoslcos@, and about a hori- 
zontal line at right angles to the new position of 
the axis is wcos!lsing. The former has no influence 
on the gyrostatic axis, the latter gives a rate of 
production of angular momentum about the vertical 
amounting to Cnwcoslsing. Hence a couple of 
moment equal to this must be applied by means of 
the torsion-head to produce equilibrium, and_ this 
as we see is proportional to sin 9. 
X.—General Dynamical Theory of Gyrostatic System 
with any Number of Freedoms. 
I cannot do more than mention the gyrostatic 
investigations contained in the second edition of 
“Natural Philosophy.’”’ These were written while 
the proofs of § 345 of the book were in his hands, and 
consist of additional sections (§§ 345'-345**vill) inter- 
polated at that stage. From many points of view 
this part of the book is exceedingly interesting. It 
continues a subject which was also expanded in the 
same way on the proof-sheets (in §§ 343a-343m), that 
of oscillatory motion. Oscillatory motion for systems 
of two, three, four, six, or more freedoms with gyro- 
static domination is enough to tax the skill of the 
most expert analyst, for questions arise regarding the 
roots of the determinantal equations and their inter- 
pretation, which require great care in handling. -I 
may only quote the general conclusions as to gyro- 
static domination. 
Let the number of the freedoms be even (that is, 
the freedoms exclusive of those by which the _ fly- 
wheels have angular momenta about their axes). Let 
the equilibrium of the system when at rest (without 
spin of the flywheels) be either stable, or unstable, 
for every freedom. If the wheels are so linked up to 
the system as to render gyrostatic domination pos- 
sible, then with sufficiently rapid spin the equilibrium 
becomes stable, with half the whole number, 2n say, 
of its periods of vibration exceedingly small, and the 
other half very large. Each set of periods is given 
by the roots of a determinantal equation of degree n. 
The latter periods are tc the first degree of approxima- 
tion independent of the applied forces, and were called 
“‘adynamic,’”’ the former periods were called ‘‘ preces- 
sional,’’ and do depend on the applied forces. 
The first approximations to the fast and slow 
azimuthal motion of a top are in point. The angular 
speed Cn/Acos@ does not depend on any applied 
forces, the other speed M gh/Cn does. 
NO. 2366, VoL. 95| 

XI.— Difficulties of Mechanical Hypotheses and 
Models. Conclusion. 
I have now dealt with most of Lord Kelvin’s 
investigations and theories. These were related in 
many ways to electricity and magnetism, and in all 
of them he ever sought some dynamical explanation 
that would work. This, indeed, was the distinguish- 
ing feature of all his researches, the bringing of 
everything down to dynamics, and the construction 
where possible of illustrative mechanical models. 
Electricity and magnetism are highly dynamical 
affairs; we send signals by wire or ‘ wireless,’’ we 
transmit power in a wonderful manner by an agency 
which we are still far from completely understanding, 
an agency which causes absorption of energy at one 
place on the earth’s surface, and evolution again of 
a large portion of that energy at another place. The 
vehicle is the ather, for, in spite of all that I have 
been able to learn regarding the new theory of rela- 
tivity, I still believe in the zther’s existence. In all 
this we are held fast by dynamical laws, no doubt 
not yet formulated in full detail, but to a consider- 
able extent already correctly comprehended. 
* * * * * * 
Lord Kelvin certainly had confidence in his own 
theories and clung firmly to his conclusions. He was 
tenax propositi, yet he could on occasion acknowledge 
that he had made a mistake. His genius ranged 
over the whole field of physical science; no problem 
was too great or too small to attract his attention. 
No obstacles, no complications, daunted his spirit of 
inquiry. The thunders of Jove, the birth of the 
world and the cold death prepared for it by dissipa- 
tion of energy, the harnessing of the energies of 
nature for the service of man, the guidance and safety 
of mariners, the genesis of waves and their breaking 
into spray and spindrift, all these questions, and many 
others, engaged his thoughts, to the lasting benefit 
of humanity and the increase of knowledge. Through- 
out all he was keen and calm and dispassionate, a 
truly unaggressive and kindly natural philosopher. 
The function of science is to enable man to pene- 
trate the secrets of nature, and to apply that know- 
ledge to the promotion of the welfare and happiness 
of all living beings. No one would have repudiated 
with more scorn than Lord Kelvin that emanation of 
the Pit, the modern doctrine that culture—scientific, 
philosophical, or artistic—entitles a self-appraised and 
self-chosen nation to wade through seas of blood to 
the domination of the world. 


UNIVERSITY AND EDUCATIONAL 
INTELLIGENCE. 
Lonpon.—The report of the Military Education 
Committee to the Senate of the University for the 
year 1914 shows that very valuable service has been 
rendered to the country by the University Contingent 
of the Officers Training Corps. The number of cadets 
and ex-cadets of the Contingent gazetted to commis- 
sions between August 5, 1914, and the end of the 
year was 773, and the number of graduates and 
students of the University (not being past or present 
cadets of the O.T.C.) gazetted to commissions during 
the same period was 156. Allowing for officers com- 
missioned from the O.T.C. before August 5, the 
total number of officers now serving, who are ex-cadets 
of the University of London O.T.C., or were recom- 
mended for their commissions by the University, is 
estimated at 1troo. In addition, a large number of 
graduates and students of the University have been 
granted commissions through other channels or are 
