An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

BRENNAN'S MONORAIL 73
Professor H. A. Wilson and exhibited by him at a meeting of
the Physical Society of London in November 1907, as a method
of automatically hurrying the precession. It consists of a spiral
spring SH, one end of which, S, is fixed to the rectangular
frame ABCD, while the other end, H, is attached to the small
crank ZH, which turns about OZ as the wheel precesses, and
is rigidly fixed to the carrier EXF. It will be seen that so
long as the wheel, and consequently the crank, are in the plane
of the rectangular frame BD, the tension in the spring has no
moment about OZ; but immediately the wheel precesses and
the crank moves out of the plane of the frame, the tension of
the spring has a moment which tends to hurry the precession,
and consequently causes the wheel and frame to return to their
vertical position. But the momentum of the wheel and frame
will cause them to overshoot the vertical position,* so that
the wheel will again precess out of the plane of the frame, the
precession will again be hurried and the previous process will
be repeated. Thus oscillations are set up of increasing amplitude,
with the result that the frame and gyroscope eventually fall
over. Professor Wilson thus illustrates the necessity for
"damping" the oscillations set up by any automatic hurrying
of the precession. We understand that Mr. Brennan has several
means which he employs in order to damp these oscillations,
one of which is clearly explained in the following article from
the Times Engineering Supplement for June 5th, 1907,
which is here reproduced by the kind permission of the author,
Professor Worthington, late Headmaster of Devonport Naval
Engineering College, and that of the Times authorities.
Apart from its immediate bearing on the monorail, the article
serves as an excellent recapitulation of much that has already
preceded it in previous chapters.
"THE BRENNAN MONO-RAIL CAR."
"The interest excited by Mr. Brennan's mono-rail car, both
among the general public and among engineers, is due partly
to the obvious importance of the possible revolution in methods
of transport which his car suggests and partly to surprise at
the results he has obtained from what we believe is an entirely
new application of gyrostats in combination.
"The majority even of mechanical engineers, to say nothing
of the general public, have too little experience of the properties
of the gyrostat to have been able to realize what it is that
Mr. Brennan has done, or to appraise his inventions. We
say inventions, rather than invention, for the stability of his
car depends, as his patent specifications show, on at least three
* It will be found that owing to this tendency on the part of the gyroscope to
overshoot the central position, we can, by a succession of taps on one side of it,
cause it to fall over on that side.