1921-22.] Gyroscope and “Vertical” Problem on Aircraft. 317 
Where instruments are to be employed on aircraft, consideration has 
to be paid to the weight of the apparatus. Such considerations do not 
appl}^ to the application of gyroscopes to problems of naval gunnery, and 
for stabilising precision instruments on board ships of war in connection 
with anti-aircraft devices. In such cases it is desirable that the angular 
momentum of the main gyroscope, or combination of gyroscopes, should 
be upwards of 5000 in foot, pound, second units. Such gyroscopes are 
available in America, but not in this country. Given such gyroscopes, 
it will be found that the authors are in a position to supply apparatus 
capable of finding and maintaining the vertical, at any part of the ship, 
within an accuracy of 1 minute of arc. 
The above remarks should not be misunderstood. The Gray stabiliser, 
if properly adjusted and used, is capable of furnishing excellent results 
when small gyroscopes are employed. But instruments intended for the 
National Defence should embody the very best practice. 
No Error in Gray Stabiliser due to Rotation of Earth. 
It has already been pointed out that the resting position of a gyroscopic 
pendulum, provided with gravity control and viscous damping, is one 
in which the axis of the pendulum is inclined to the true vertical at an 
angle T cos X/Day, where T is the periodic time of the pendulum for 
steady precession, and X the latitude (see Gray’s Gyrostatics, p. 342). There 
is, however, no error in the case of the Gray stabiliser. 
Consider a freely mounted gyroscope placed with its axis vertical. 
The axis of the gyroscope would leave the vertical in this latitude, in 
consequence of the rotation of the earth, at an angular speed of about 
1 minute of angle in 7 seconds of time. A Gray stabiliser, when deflected, 
seeks the vertical at angular speed IjCn, where I is the moment of 
the erecting couple. If IjCn is greater than I minute of angle in 7 
seconds of time, there is no error. Critics of the Gray stabiliser have 
persistently affirmed that the accuracy with which the resting position is 
attained is affected by the rotation of the earth. Such is not the case. 
The stabiliser, properly adjusted, stands erect even when the precessional 
period for steady motion is infinite ; and the reason is obvious. As soon 
as error begins to grow up, the erector sets to work to annul it, and the 
vertical is never more than infinitesimally left. The most persistent 
supporters of the notion that an error is produced by the rotation of the 
earth have, however, abandoned it. 
(Issued separately August 10, 1922.) 
