1921-22.] Gryroscope and '‘Vertical” Problem on Aircraft. 297 
integral couple is reversed. When 0 is less than sin ~ the ball- 
system b goes out of action and the pivoted system approaches the vertical 
at a speed determined solely by a. Further, if the ball-systems are not 
identical, then when 0 is greater than the critical angle the pivoted system 
experiences a differential couple ; and if the system a is more powerful 
than b, it approaches the vertical at an angular speed which depends 
on the magnitude of the differential couple and the angular momentum of 
the gyroscope. 
This form of stabiliser, when mounted on an aeroplane, has the property 
that it is blind to the apparent vertical for azimuthal rates of turning of the 
aeroplane greater than where v is the speed of the aeroplane, since 
each ball is being accelerated towards the centre of the path in which the 
aeroplane moves at the instant. Hence radial motion of the balls takes 
place when During normal flight the ball-system {a) alone 
functions ; and if any small error has been introduced during the curved 
flight, correction takes place relatively quickly. 
The compound erector described above is peculiarly well suited for use 
on an aeroplane (or an airship), since the speed v is great, and i/j is usually 
great. There is no difficulty in constructing the compound system so that 
