1921-22.] Gyroscope and “ Vertical” Problem on Aircraft. 273 
angular speed of the earth. Thus for a pendulum of the type described 
set up at the equator, we have approximately 
or 
mgh sin 6 _ 2;r 
Qn cos 0 Uay ’ 
tan 6 ■■ 
27T Cn _ T 
Day mgh Day ’ 
where T is the precessional period of the pendulum for steady precessionai 
motion. If the pendulum is set up in latitude X, we have 
T 
tan 0 = — — cos A. . 
Day 
The following table shows the magnitude of this error for various 
periodic times. The pendulum is supposed set up at a place in latitude 50°. 
Table III. — Exhibiting Error due to Earth’s Rotation 
FOR the case of A GYROSCOPIC PENDULUM PROVIDED 
WITH Gravity Control and Viscous Damping. 
Periodic Time of 
Pendulum 
in minutes. 
Approximate Error, in 
Latitude 50°, due to 
Rotation of Earth. 
2 
0°045 
4 
0-09 
8 
0-18 
16 
0-36 
32 
0-72 
The above errors relate to a pendulum set up on a steady platform 
at rest. If the pendulum is carried on a moving vehicle, for example an 
aeroplane, the errors due to the motion of the vehicle are so large that 
it is unnecessary to consider those due to the earth’s rotation. 
Complete Solutions of the Problem. The Gray Stabiliser. 
The following are the requirements which must be fulfilled by a con- 
trivance which completely solves the problem of the true vertical : — 
1. It must find and maintain the true vertical with minute accuracy. 
2. It must provide for the stabilising of instruments against both 
rolling and pitching motions of the vehicle on which it is mounted. 
3. It must not be sensibly disturbed by such rolling and pitching 
motions. 
VOL. XLII. 
18 
