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

BRENNAN'S MONORAIL

75

"If, on the other hand, with the disc spinning very fast,
the pressure maintained at A is not vertical but horizontal,
in the direction of the precessional rotation just described, then
there will be no apparent revolution about ED, but there will
be a rotation of the frame BAC about BC, and A will rise,
the angle through which OA rises being in this case a measure
of the time-integral of the moment of the pressure about ED.
"If now, while we maintain a constant downward pressure
at A, we also apply a constant horizontal pressure as if to
accelerate the horizontal precession of the spindle, then the
precession will not indeed be permanently appreciably accelerated,
but A will rise at a rate proportional to the horizontal force, and
work will be done by the horizontal and against the vertical
force.
"These are the chief relevant physical facts which lay at
Mr. Brennan's disposal and of which he has availed himself with
such remarkable skill and success. We will endeavour to
explain his arrangement by pointing out its relation to the
Foucault gyrostat just described. In the first place the frame
EBCD is pivoted on the body of the car at E and D, so that
when the car is erect DE is vertical. Mr. Brennan then makes
the spindle of his disc into the armature of an electro-motor,
whose field-magnets are carried by the pivoted and still balanced
frame BAG. When everything is in equilibrium and the car
is running erect, the spindle OA is horizontal and at right angles
to the rail. We will suppose the car to be running in the
direction BC and will refer to A as the right-hand end of
the spindle.
"Now let a wind-pressure be applied to the left side of the
car. The car begins to turn over relatively to the gyrostat,
and thus at once brings down a guide plate G, (see Fig. 36)
fixed to the car, and bent into a circular arc as shown, so as
to press on a small roller R1, turning loosely about the end F
of the spindle OAF, which now projects beyond the frame
BAC. The pressure on this roller causes the spindle to precess
from A towards B with an angular velocity proportional to the
pressure, and the turning-over of the car is arrested, but at
the same moment the friction between the rotating spindle and the
roller makes the latter roll along the under side of the guideplate and thus evokes a horizontal frictional force on the spindle
tending to accelerate precession. This causes the end F of the
spindle to rise and push back the car against the wind-pressure.
Thus the car turns over to meet the wind and is carried over
beyond the vertical (perhaps considerably beyond) to a new
inclined neutral position at which the moment due to gravity
just balances the moment of the wind-pressure. This tilted
position is reached, however, with a certain momentum which
carries the car beyond it. Up to the instant of reaching this
position the moment of the wind-pressure has been in excess of