1921 - 22 .] Gyroscope and “Vertical” Problem on Aircraft. 259 
of the gyroscope turning about the pivots . The frame / is pivoted 
at P2P2 uprights u, u carried on a base b. 
Provided that the lines of the pivots PiP^ , P2V2 I'be same plane 
and perpendicular to one another, that the frame / is in neutral equilibrium 
with respect to the pivots p^p^ , and that the intersection of p>^p^ and P2P2 
coincides with the centre of gravity of the gyroscope and its casing, the 
gyroscope is said to be “ freely mounted.” 
In connection with what follows it is necessary to point out some of the 
properties possessed by a freely mounted gyroscope. If, for example, the 
gyroscope is turned about the pivots ppp^ so that its axis of spin is inclined 
to the vertical at an angle d, and the base is then turned in a horizontal 
plane through 90 °, the gyroscope is now inclined at an angle d to the 
CL 
^ 4 - 
Fig. 1. 
vertical, but about the pivots ppp ^ ; the inclination of the axis does not 
move round as the base turns in azimuth. If the apparatus is set up on 
an aeroplane with the pivots p^p^ ''fore and aft,” turning of the plane in 
azimuth does not result in the carrying round with the machine of any 
deviation of the apparatus from the vertical which may exist ; the deflec- 
tion from the vertical remains in the same plane as before. Thus, suppose 
that at an instant the axis of spin is inclined to the vertical about the 
pivots P2P2 • bet the aeroplane now turn in a circle, going once round in 
time T'. At time Ty 4 the inclination is about pppp, at time T72 it is 
about_p2^2 5 time ST'/I it is about pppp^ and at time T' it is about pppp, 
and so on. If at time t — ^ the apparatus is inclined to the vertical in such 
manner that the error in range (about the pivots ppp^ is Or and the error 
in line (about the pivots P22^2) b ’ then at time T74 the amounts of the 
errors in range and in line are d^ and Or respectively. 
The arrangement described is of little use on an aeroplane, inasmuch 
as it has not itself what may be called a sense of the vertical. It must be 
