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Proceedings of the Koyal Society of Edinburgh. [Sess. 
the axis of g' is perpendicular to the pivots P 2 .P 2 ’ which lie fore and aft 
with respect to the aeroplane. Thus the axis g' lies athwart the aeroplane. 
Consider the action of this device when mounted on an aeroplane 
which is moving in the direction indicated by the arrow a. Let the 
pivoted system be mounted so that its centre of gravity lies below the 
plane of the pivots P 2 P 2 ’ ^^d let the direction of rotation of the 
gyroscope g' be that indicated by the curved arrow. Suppose the device 
initially upright, and let the aeroplane move in a curved path. 
The couple experienced by the pivoted system as a result of the 
cent rewards acceleration of the aeroplane is Mviph, where M is the total 
mass of the pivoted system, li the distance of its centre of gravity below 
the plane of the pivots, v the linear speed of the aeroplane, and its 
angular speed in azimuth. This couple is applied about the pivots P 2 P 2 • 
But the gyroscope g' is being turned forcibly in azimuth at angular speed 
ijj ; and if Ico is the angular momentum of g', the pivoted system experiences 
a couple due to this cause of amount Icoip. With the direction of spin of 
g' shown this couple is applied about the pivots y> 22^2 fhe direction 
opposed to that of the couple This holds for both directions of 
turning in azimuth. The resultant couple is thus (Mvh — Ico)i/f, and is zero 
when Mvh = lo). Since the periodic time of the pivoted system is given 
hy T = 27rCnlMgh, the condition that the resultant couple should be zero 
becomes 
U?^ = iw, or 
Cn 
27TV 
7 ^' 
Thus if ^? = 100 feet per second and T = 6 minutes, we must have 
I(jO _ 27T X 100 _ 1 
Cw“32 x 600 ""l9 
(about). 
If the condition is not exactly fulfilled, we have (Mt’/i — Ico )ifj for the 
resultant couple, and for the angular speed at which the system turns 
about the pivots — Let there be, say, a 5 per cent, error 
in lo), so that, say, Iw = 19MfA/20, then the angular speed at which the 
pivoted system turns about p^2^i is M'^A0/2OC?i. In other words, when the 
aeroplane is in curved flight the virtual precessional period of the system 
is 20T, T being the actual precessional period. Thus if the period is 
6 minutes, the system behaves during the curved motion of the aeroplane 
as if the periodic time of the gyroscopic system was 2 hours. 
The actual mode of construction is illustrated diagrammatically in 
fig. 35. Two large gyroscopes are employed, one of which is tilted with 
respect to the vertical, as shown. The system is attached to the frame / 
