288 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
and when the aeroplane yaws. It is to be observed that the device cannot 
leave the true vertical at an angular speed greater than 2mg{r^ — r^)l 7 rCn, 
and this speed can be arranged so that, under the conditions which prevail 
on an aeroplane, very high accuracy is obtained. The forces which accom- 
pany bumps are great in amount, but it is obvious that they have no 
appreciable effect on the instrument. 
Let now the aeroplane move in a curved path. The pivoted instru- 
ment, it must be clearly understood, is mounted and balanced up so as 
to be neutral with respect to both the pivot axes p^Pi a>ndp 2 P 2 , so that 
the disturbance produced by the curved motion will be due solely to 
the erector. At each instant the entire instrument is being accelerated 
towards the centre of the path in which the aeroplane is moving, and it 
will be clear on reflection that the balls function in such manner that the 
pivoted system moves, at each instant, from the true vertical towards the 
apparent vertical. The balls are situated in a field of force whose amount 
per unit of mass is ^ where v is the speed of the aeroplane and ifj 
is the azimuthal rate of turning of the aeroplane. The direction of this 
field is contained in a vertical plane lying athwart the aeroplane, and 
makes an angle tan ~ ^(i;j/r/g) with the true vertical. The direction of the 
field clearly goes round with the plane ; the field is in fact made up of 
two component fields, one vertical, the other horizontal and rotating with 
the plane. From what has been said already it will be clear that af tex- 
tile aeroplane has turned through an angle ip the inclination 9 of the 
pivoted system to the true vertical is given by 
TrCmfr 
Let m=l ounce, r^~r^ = l inch, = (in foot, pound, second units), 
?/f=9 degrees in 1 second of time (a usual value of ip for large bombing 
aeroplanes in 1917-18). Introducing these values into the equation, we 
obtain 
0— 18*6 sin ^ij/ (in minutes of angle). 
With the above values of m, r^ — r^, etc., the maximum disturbance 
amounts to less than one-third of a degree, and is introduced by a 
manoeuvre involving a half turn. As already pointed out, after a half 
turn of the aeroplane the pivoted system is inclined to the vertical wholly 
on the pivots p^Pi , so that the line bars of a bombsight are correct immedi- 
ately straight flying is resumed. 
After a yawed turn amounting to 10° the disturbance introduced is less 
than 2 minutes of angle. After a complete turn the disturbance is zero. 
