316 Proceedings of the Koyal Society of Edinburgh. [Sess. 
The devices which have been described are admirably adapted for 
use on an aeroplane. A device set up in the cockpit of an aeroplane is 
situated on, or very near to, the axis of rolling, with the result that the 
moving parts of the erector experience very little, if any, disturbing force 
due to rolling. Experiments carried out hy means of the sun- shadow 
methods described above have shown conclusively that these stabilisers 
remain absolutely undisturbed by the pitching and rolling motions of an 
aeroplane. As already pointed out, even were such motions to result in 
the establishment of horizontal accelerations the integral effects would be 
very small. 
The writers have repeatedly observed the performances of pioneer 
instruments during ordinary flights with compass steering, in weather 
of the most bumpy description. Under these conditions these early 
instruments maintained the vertical within an accurac}^ measured by a 
few minutes of arc. 
Desirability of using Powerful Gyroscopes. 
Let a gyroscope whose angular momentum is Cn be turning on its 
pivots towards the true vertical at angular speed 0 under the action of a 
stabilising couple. For the amount I of the couple we have l = Cn6. 
Now, for successful working I should be great, but 8 small ; hence On 
should be great. Obviously the stabilising couple should be very great 
in comparison with any frictional couple applied at the pivots. If it is 
assumed that the frictional couples are proportional to the load carried 
by the pivots, the advantage gained by employing large swiftly rotating 
gyroscopes will be at once apparent. The weight of a wheel is proportional 
to the third power of a linear dimension ; its angular momentum, for a 
given speed of rotation, to the flfth power of the same dimension. Hence, 
as the diameter of the flywheel of a gyroscope increases, the ratio of the 
stabilising forces which can be employed, for a given value of 6, to the 
frictional forces applied at the pivots increases rapidly. With very 
powerful gyroscopes the frictional forces do not count ; with small gyro- 
scopes the frictional forces may be comparable with the stabilising forces. 
For use on aeroplanes with their stabilisers the authors recommend 
the employment of a gyroscope having an angular momentum of 2000, 
in foot, pound, second units. This is the angular momentum possessed by 
a wheel of mass 20 pounds, radius of gyration 3 inches, when performing 
250 revolutions per second. Complete with its casing and bearings, such 
a gyroscope would have a mass of about 25 pounds, and the diameter of 
its casing would lie between 7 and 8 inches. 
