TItE DRIFT OF SERVICE PROJECTILES. 
of rotation in tlie same way as in the theorem of the parallelogram of 
forces), we get a resultant axis of rotation for that instant, the direc¬ 
tion of which, passing through the centre of gravity, lies between the 
component axes of rotation and will be close to the axis of the spin 
caused by the string as this is very much faster than the second com¬ 
ponent rotation. The first component rotation has for its axis the 
long axis of the top; the second has an axis through the centre of 
gravity at right angles to the plane of the paper. So that, the resul¬ 
tant axis being in the plane of these two axes, the effect of this instan¬ 
taneous motion is to move the resultant axis out of the plane of the 
figure in a direction at right angles to that plane; and that is the point 
I want to get out—that the initial motion of this axis is round an axis 
eccentric to the top and in a plane at right angles to the plane of the 
board. And this occurs at every instant; the next instant it will move 
at right angles to the plane it was in at the previous instant and so on. 
So that eventually this series of instantaneous motions resolves itself 
into a circular movement of the upper end of the top right round the 
vertical. Now an ordinary top has the property of going to sleep, a 
gyrostat top, such as children play with, has no property of going to 
sleep and the reason is that the gyrostat top will keep its point in the 
same spot as it is spinning; an ordinary top will not, it will go run¬ 
ning round the table and therefore there is a certain amount of friction 
set up as that point moves over the ground that causes a rotation round 
an axis 0 D. Combining this third axis with the resultant instan¬ 
taneous axis which we have just got you get a final resultant axis 
which approximates very slightly to the vertical; the result being that 
the circular movement of the upper end of the top will alter into a de¬ 
creasing spiral and every instant, by reason of the friction of the 
ground, an ordinary top will come nearer and nearer in to the vertical 
and finally go to sleep; but with a gyrostat top there is no motion of 
this kind and in the case of a projectile in flight I cannot find any reason 
why there should be any motion of going to sleep at all; there may be, 
but I cannot find it; and at all events that does not interfere with 
what I am about to say. Now, in applying this principle to the motion 
of a shot, the effect of the two rotations on a projectile—viz., the spin 
of rifling and a force that is tending to turn the point away from the 
line of motion is that its axis must move in a direction at right angles, 
or very nearly at right angles, to the plane containing the long axis and 
the line of motion at that instant. I do not see that anything can stop 
this motion. If the long axis finds itself at any instant non-coincident 
with the line of flight, it is an absolute impossibility for the point to 
go down in the same plane into conjunction with the line of flight; it 
can only move out of the plane, and when it is out it is still going at 
right angles to the instantaneous position of the plane until it com¬ 
pletes a regular spiral round that line. _ The only condition, apart from 
the fact that the shot may go to sleep eventually, is that the motion of 
the point must be always at right angles to the plane containing the 
long axis and the tangent to the line of flight. Now if the trajectory 
is a straight line there may be a possibility of its going to sleep, I 
