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

BRENNAN'S MONORAIL

77

round past the end of the spindle F, and thus the middle position
will be lost. To remedy this Mr. Brennan employs a second
similar gyrostat with an equal disc, spinning at an equal rate
in the opposite direction, about a spindle which, when all is in
equilibrium, is parallel to or even in a line with the spindle of
the first disc. The pivoted frame BAC of the first is so linked
to the corresponding frame of the second that any lateral tilt of
the first is communicated to the second, but at the same time
each of the discs is free to precess. The precession of the second
disc is equal to that of the first, but in the opposite direction,
and any deviation from this equality and opposition is prevented
by toothed gearing which connects the axle ED of the first with
the corresponding parallel axle of the second. Such a system
offers no resistance to turning with the car on account of a curve
in the track, while to any upsetting moment it behaves like a
single gyrostat of double mass, and enables the car to meet the
upsetting moment of the so-called centrifugal forces by leaning
over towards the inner side of the curve, exactly as it leant over
to meet a wind-pressure.
"It should, however, be observed that this adjustment does
not get rid of the force tending to displace the rail laterally,
and that this can only be completely met by sloping the track
on which the rail is laid with exactly the same super-elevation
as is required in an ordinary railroad curve (a slope which
depends on the velocity prescribed). M r. Brennan gets rid of
the danger of upsetting, but not of the need of providing against
displacement of the rail.
"It remains to examine what will happen when we pass from
a model to a car of larger dimensions. Fortunately, the result
works out very favourably, since we find that if we make the
linear dimensions of everything n-times greater, we can afford
to spin the gyrostats n-times slower and yet secure the same
righting effect, with the same angular excursion and return of
the spindle along the guides.
"This result is of great importance, for it means also that the
centrifugal stresses in the real gyrostats need not be greater
than in the model, and that the rate of spin may be reduced
from 7000 per minute in the model to 875 per minute in a car
of eight times the size. A greater rate in a smaller gyrostat
is however a preferable option.
"In this explanatory outline we have been guided by the
patent specifications already published; but we understand that
Mr. Brennan has already made important improvements which
will not be published till further protection has been obtained."
74. Note on the change of dimensions in a larger car
compared with those of a model one. The efficiency of the
erecting power of the gyrostat on the car, may be conveniently
defined as the ratio of the impulse of the upsetting couple (due,