274 Proceedings of the Poyal Society of Edinburgh. [Sess. 
4. It must not be sensibly disturbed by azimuthal turning of the 
vehicle, or by the accelerating forces which result from such turning. 
5. It must not be disturbed by the accelerations which result from 
side-slipping of the vehicle. 
6. It should provide a non-revolving platform on which may be 
mounted instruments of precision, such as sextants, compasses, bomb- 
sights, and cameras. 
7. For use on an aeroplane the construction should be such as to 
allow of the aeroplane banking up to 90°. 
3. There must be no error due to the rotation of the earth. 
Principle of the Gray Stabilisers. 
It has been shown that long-period gyroscopic pendulums, provided 
with viscous damping, cannot give reliable results when set up on aircraft. 
As already explained, such devices leave the vertical quickly under the 
action of the forces which accompany turning movements of such craft, 
and return to the vertical only very slowly in the absence of such forces. 
In the Gray stabilisers, about to be described, this defect is entirely 
removed. 
The Gray stabiliser consists of a gyroscopic system, pivoted as in 
figs. 1 and 2, and having the following properties. Should the pivoted 
system be inclined to the vertical, during normal flight of the aeroplane 
or airship, a stabilising couple is applied to the gyroscope and the device 
is restored to the vertical. The stabilising couple is obtained by means 
of a special erecting device, and depends in no way on precession of the 
gyroscope, in the ordinary sense of the term. Daring curved flight of the 
aeroplane the erecting device goes automatically out of action. Thus the 
pivoted system leaves the true vertical very slowly, if at all, in the presence 
of curved flight, and approaches the vertical relatively quickly during 
normal flight. 
Consider a gyroscope freely mounted as in figs. 1 and 2. The arrange- 
ment is shown diagrammatically in plan in fig. 10. A gyroscope g is 
attached by means of pivots to a frame /, and / is in turn attached 
by pivots uprights u, u. The gyroscope is supposed mounted so 
that its centre of gravity lies at the intersection of the pivot axes. In 
order to make clear the action of the Gray stabiliser it is necessary to 
describe further some of the properties possessed by the arrangement. 
In the first place, suppose that the axis of the gyroscope is vertical. 
When this is the case the pivots PiPi are horizontal. Let now a couple of 
moment I be applied to the gyroscope in a vertical plane passing through 
