463 
THE DRIFT OF SERVICE PROJECTILES. 
the axis and as the trajectory curves down it prevents its coming in 
by tending to retard the angular velocity with which the spiral is 
described round the trajectory. When the point, however, has got 
actually underneath, it begins to show itself on the left of the trajec¬ 
tory and begins to rise. Now, supposing the trajectory were straight 
it would have to traverse this third quarter in much the same time that 
it would take to traverse the first quarter under similar conditions, 
but since the trajectory is curved, this quarter will take a shorter time 
to describe because the point is moving up, while the direction of the 
tangent to the trajectory is moving down. The change in the direc¬ 
tion of the tangent therefore helps the point in this quarter by meeting 
it half way and, therefore, in this and the fourth quarter the time 
occupied is comparatively short. That is why it takes a longer time 
to describe the curve on the right than to describe the curve on 
the left, because as the point is trying to get down on the right the 
direction of the tangent is going down too, and, as I say, until 
the point gets down on a level with it, it must still go to the right 
and down. On the other hand, when the point on the axis is coming 
up the change of direction of the tangent, so to speak, meets it 
half way, both going in opposite directions and that is the reason 
why that quarter is so quickly passed over. In the one case, when 
the point is above the trajectory it depends entirely upon whether 
is fast enough whether the point gets down to it at 
all and in that case we get the spin losing control of 
the projectile and the point goes wider and wider 
to the right. If the spin be sufficient to give it a 
sufficiently fast precession then it will catch it up, but 
it entirely depends on the difference in the rate of 
change of the direction of these two lines how long it 
takes to do it. And in the same way when the point 
is coming upon the left-hand side it will move over all 
the faster the faster the trajectory curves downwards. 
That is one of the points I wish to bring to your 
notice : that the point takes much longer to come down 
on to the trajectory on the right than to get up to it on 
the left and that the faster the trajectory curves the 
longer it takes on the right, because it has further to 
get down to it. On the other hand it takes a very 
much shorter time than it would if the trajectory were 
straight to come up on the left; the balance of the 
curve in point of time is therefore greatly on the right. 
I have tried in Fig. 3 to show the sort of curve 
described by the point as it is making its spirals. 
The only condition we have is that the point must 
move in a direction at right angles to the plane con¬ 
taining the long axis of the trajectory at the time. 
And here we have it. This is the path of the point 
P in Fig. 2 as it moves down from 0 P to 0 P' and to 
see it I must suppose the observer to be at the centre 
the precession 
Fig. 3. 
