1921-22.] Gyroscope and “Vertical” Problem on Aircraft. 313 
so that the horizontal component of spin, due to the tilt of tlie upper 
gyroscope, lies athwart the aeroplane. Let the gyroscopes be identical, 
apd let the angular momentum of each be Cn. The condition required for 
complete compensation becomes 
Cn sin 0 __ ‘2-n-v 
Cn + Cn cos 0 gT ’ 
or tan ^0 
27TV 
?T 
In practice the two gyroscopes are mounted within a frame (fig. 36), 
one rigidly, the other so that the angle 6 may be set in accordance with 
the above equation. The value of v above is the air speed of the aeroplane, 
or airship. In the case of a ship the value of v is the speed of the ship 
relative to the water. 
The construction will be clear from the figure. The two gyroscopes 
and ^2 mounted on the frame F, g rigidly, g^ on pivots jp/p, as shown. 
One of the pivots is extended, and carries, at its extremity, a quadrant q. 
This quadrant may be turned by means of a worm, as shown in the lower 
figure. The pivots p, p lie fore and aft with respect to the vehicle on 
which the apparatus is mounted. The erector, or erectors, may con- 
veniently occupy the space between the gyroscopes. 
One advantage obtained by using the two gyroscopes in the manner 
described will be obvious. When the pivoted system is provided with 
bottom weight, any small change in the position of the centre of gravity 
of the system due to movement of the film does not appreciably alter the 
resting position of the system. 
