1921-22.] Gyroscope and “Vertical” Problem on Aircraft. 287 
Returning to figs. 13 and 14, let the pivoted system be inclined to the 
vertical on the pivots P 2 P 25 with the erector displaced in the direction of 
the reader, and let the erector be rotating in the direction opposed to that 
in which the gyroscope is spinning. The action is precisely that already 
described, but the direction of the integral couple applied to the gyroscope 
by the erector has been reversed, with the result that the pivoted system 
moves away from the vertical with angular speed 2mg{T^ — r^l 7 rCn. Thus 
the upi-ight position of the pivoted system is one of stability when the 
erector is rotating in the direction of spin of the gyroscope, but is one of 
instability when the erector and gyroscope are rotating in opposite direc- 
tions. This property possessed by the system of gyroscope and rotating 
erector is of great import- 
ance in connection with what 
follows. 
Now let the stabiliser, as 
illustrated in fig. 12, be set 
up on an aeroplane with the 
pivots P 2 P 2 lyi^g foi"® ^iid 
aft. Let the direction of 
rotation of the erector be 
that in which the gyroscope 
is spinning. If the aeroplane 
moves in a straight path 
with uniform speed it is 
clear that the pivoted system 
will set itself in the true 
vertical. Pitching and rolling motions of the aeroplane produce no sensible 
effect in disturbing the pivoted system. This is not surprising. When 
fitted up within the cockpit of an aeroplane, the apparatus, it is to be 
remembered, is situated on, or at all events very near to, the axes about 
which the aeroplane rolls and pitches, and hence the horizontal accelerations 
which accompany these motions of the aeroplane are very small. Further, 
the horizontal accelerations, small in amount, are rhythmic in character ; and 
hence, even if their maximum values were large, the net effects produced 
on the pivoted system could only be very small. It is a proved fact that 
the simple apparatus, as described above, when placed on an aeroplane in 
ordinary flight moving side-on to half a gale of wind, is capable of finding 
and maintaining the true vertical within an accuracy of Ar ^ degree. 
During such flight the balls are observed to remain, on the whole, in their 
proper resting positions, with occasional excursions for correcting purposes. 
