460 
THE DRIFT OF SERVICE PROJECTILES. 
admit; I cannot see it, but it may be so; but the condition of a top 
going to sleep is that the vertical always remains in one given direc¬ 
tion and condition of sleep is that the axis of the top be coincident 
with the vertical. Supposing that the vertical were capable of 
altering its direction you could not have the top going to sleep with 
a variable direction for it to go to sleep in; and if the trajectory is 
curved I do not see the possibility of the shot going to sleep, because 
the direction of the line in which it is trying to go to sleep is always 
changing, so that it cannot attain the position of sleep. 
Now if the trajectory were straight the curve that this point will 
describe round, and with reference to, the line of flight, will be either 
circular or spiral. It will be circular if there is sufficient spin and if 
there is no reason for its going to sleep. If there is a reason 
for its going to sleep, it will form a decreasing spiral until it goes 
to sleep. If the spin is not sufficient to keep it there against 
the turning power of the resistance of the air then it will de¬ 
scribe an increasing spiral, but that spiral will be perfectly regular, 
simply from symmetry; there is nothing to take it out of regularity and 
the result will be that the curve will lie as much at one side as the 
other, there cannot be any reason why the resistance of the air should 
take it bodily to one side or the other and there cannot be any drift. 
But the case must be very different when the trajectory is curved, as I 
will now show, but one more thing I want to say in connection with 
this spiral motion or precession, and that is, that so long as the point 
is above and to the right of the line of motion or the resistance of the 
air and until the axis of the shot gets down on to a level with the line 
of motion, it must be going to the right and down. Directly it gets 
below the line of motion then it will be still going down, but it will be 
coming in to the left, simply because the point must move at right 
angles to the perpendicular from the point on to the line of motion, so 
that when it has got right underneath it will move to the left and up 
and in the last quarter it is coming up, but to the right again. What 
I want you to remember is that, as long as the point is to the right and 
above the line of motion, it must be going down and it also must be 
going out to the right, simply from the nature of the instantaneous 
motion which causes the axis to precess. 
Big. 2. 
