1921-22.] Gyroscope and “ Vertical” Problem on Aircraft. 275 
TiVi , or in a parallel plane. The mode of applying this couple is of great 
importance, and will be described immediately. At present suppose the 
couple produced, no matter how. This couple tends to turn the gyroscope 
about P 2 P 2 ’ a^^d would in fact do so if the flywheel of the gyroscope 
were not spinning; but in point of fact the gyroscope turns about the 
pivots PiPi at the appropriate angular speed. The couple being applied 
wholly about the pivots P 2 P 2 ^^d the system being freely mounted, the 
gyroscope turns wholly about the pivots PiPi . After time t has elapsed 
let the inclination of the gyro- 
scope to the vertical be 0. The 
horizontal component of angular 
momentum is Cn sin 0, and the 
rate at which this is increasing 
is Cn cos 60. Hence 
dO I 
dt Cn cos 6 
If I remains constant in 
amount and acts always in a 
vertical plane — that is, if the 
couple does not depend on the 
magnitude of 0 — then 0, or 
do 
, is given by the above equation. The couple acts so as to increase 0. 
A couple so applied we call a deflecting couple. 
Let now the gyroscope be inclined at an angle 0 to the true vertical 
about the pivots p-^p^ . If there is applied to the gyroscope a couple in a 
vertical plane passing through p^Pi , or in a parallel plane, the gyroscope 
will, of course, turn about PiPi . For one direction of the applied couple, 0 
will be increased ; for the other, 0 will be diminished. If the couple tends 
to diminish 0, it is called an erecting couple ; and if its moment I is inde- 
pendent of the tilt, the axis of the gyroscope moves towards the true 
vertical in accordance with the equation 
This equation gives 
d0_ I 
dt Cn cos 6 
sin ^ + const. ; 
Cn 
and if we denote the value of 0 when ^ = 0 by we have 
