THE DRIFT OF SERVICE PROJECTILES. 
463 
of gravity 0 of the shot. The vertical line P P' in Fig. 3 will be the line 
P P' in-Fig. 2. If the trajectory were perfectly straight it would simply 
describe a circle round P. If there were anything to bring it to sleep 
instead of a circle it would be a decreasing spiral, but at every instant 
this point is descending, as it does in Fig. 2 and the only condition is 
that the point of the projectile which forms this curve should be 
always moving at right angles to the radius vector from the point to 
the position of P for the time being, P moving from P to P. Fig. 3 
then is the sort of a curve that the point of the shot makes as it is 
going on in flight; Fig. 4 is the same curve, only showing the motion 
of the point relative to the trajectory and is made by keeping P fixed 
and superposing the radii vectores, both as regards length and direc¬ 
tion, of Fig. 3, on this fixed point, and this then is the motion of the 
point with reference to the line of flight round the line of flight; and 
you will see by actual measurement that the radius vector increases 
during the first quarter and the point goes wider and wider until the 
radius vector is horizontal (Fig. 3). From there the radius vector is 
shortening until you get the point under the line of motion; from then 
till the radius vector is horizontal on the left side it is still shortening 
and that is the shortest length of the radius vector in the whole revo¬ 
lution, after which it lengthens out again to the end of the fourth 
quarter. 
Now I wish just to show you how the radius vector lengthens and 
shortens. One end of the radius vector is moving at right angles to 
that radius vector, the other in the first quarter is moving in a direc¬ 
tion which, resolved along the radius vector, is increasing its length. 
This can be easily seen by inspection of Fig. 3 In the second and 
third quarters this latter end of the radius vector which really is moving 
down the line P P' is, when resolved along the radius vector, shorten¬ 
ing its length and this continues throughout the second and third 
quarters. This is why the point lies wider on the right than on the 
