268 Proceedings of the Koyal Society of Edinburgh. [Sess. 
From the above formulae the following table has been constructed: — 
Table I. — Exhibiting the Performance of a Gyroscopic Pendulum, 
OF Precessional Period 6 Minutes, when situated on an Aero- 
plane EXECUTING A TURN. 
Angle turned 
through by 
Aeroplane (ij/). 
Total Deviation 
of Pendulum 
from Vertical (6). 
Error in Range 
(^ 1 ). 
Error in Line 
(%)• 
30° 
1-62° 
1-57° 
0-42° 
45 
2-36 
2-21 
091 
90 
4-41 
3T2 
3T2 
135 
5-72 
2-21 
5-3 
180 
6-25 
0 
6-25 
225 
5-72 
-2-21 
5-30 
270 
4*41 
-3-12 
3T2 
360 
0 
0 
0 
These results are exhibited graphically in hg. 8. If the spin of the 
gyroscope is clockwise, as seen from above, and the aeroplane moves round 
in the counter-clockwise direction, as seen from above, the curve (a) shows 
the growth of the deflection of the pivoted system with respect to the 
vertical. If the aeroplane turns in the clockwise direction the growth of 
the deflection is as in (b). 
After the aeroplane has turned through 90° there is an error in line 
and also an error in range (6^^) ; when it has turned through 180° the error 
is a maximum, and is wholly about the pivots P 2 P 2 j there is no error in 
range at this instant. After the aeroplane has turned through 270° there 
are errors in line and in range ; and when a complete turn has been 
executed there is no deflection. 
Again, suppose that the pendulum is upright and that the aeroplane 
yaws, the change in direction of motion amounting, say, to 5°. The result- 
ing deviation from the vertical amounts to 3T2 sin 5°, or 0*27 (in degrees). 
As a further example we may find the minimum precessional period, 
for steady precessional motion, which the pivoted system must have if the 
disturbance due to a half-turn is not to exceed ^th of a degree. We have, 
if T is the period, 
27TX 100x2 1 
32T ~5x57-3’ 
which gives 
T = 11,260 seconds, or 3 hours 8 minutes. 
The above results, it is to be observed, hold for the case of an aeroplane 
which turns at a rate such that a complete circle is executed in a time 
