304 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
foot, pound, second units. Let the device be supposed initially upright, 
and suppose that the aeroplane turns at an angular speed of 9° per second. 
If the speed of the plane is 100 feet per second, the acceleration athwart 
the aeroplane due to the turning motion amounts to 188 inches per second 
per second. As a consequence of this acceleration being great, (3 is 
small, amounting to less than 5° for an erector speed of 8 revolutions per 
minute. Taking /3 as 5°, we obtain ^^ = 1-46, and d.^ = 0‘12, in minutes 
of angle per second. 
If we attach a mass m' to the pivoted system, as described above, 6^ 
becomes zero, and during the turning motion there is no appreciable dis- 
turbance. The value of mh is 2mgacos filirvip, and hence, inserting the 
assumed values of the quantities, we obtain 
2 X 32 X 0-97 X 57-3 
mh=z . 
16 X 12 X 100x6 
= 0-0205. 
The pivoted system ceases to be neutral for straight flying. Its pro- 
cessional period T, for steady processional motion, is given by 
rp 27T X 250 
^ 32 X 0-0205 
= 41, (in minutes, approximately). 
No disadvantage is brought about by introducing gravity control in 
the manner here described. In turning rapidly the effect of the mass m' 
is to counteract the action of the erector. When the aeroplane turns, the 
pivoted system behaves as a neutral gyroscope — that is, one for which the 
periodic time is infinite. 
The value of m having been chosen so that is zero for a particular 
value of ifs, there will come into existence, for other speeds, a differential 
couple causing the pivoted system to turn, at any instant, about the pivots 
PiPi • Ib in the example above, there is a change in iff amounting to 
10 per cent., 9^ will amount to 0-146 minutes of angle per second. There 
will be no change in the value of 6 ^ . 
The couple required to cut off the erector, during rapid turns of the 
aeroplane, may also be brought into existence by causing a small weight, 
carried by the pivoted system, to move over laterally, to one side or the 
other, according to the direction of iff. The lateral distance through which 
this weight must be moved does not depend on ifj, and hence is constant. 
The weight may be conveniently operated by means of electro-magnets 
controlled by a commutator the component parts of which are mounted on 
the frame / (fig. 26) and one of the uprights u. 
