314 MESSRS. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND : 
refer the motion to axes moving with the tangent to the trajectory (see § 3.2). The 
effect is quite insignificant over the range covered by the present trial, but becomes 
of importance at later stages of the trajectory, where it is responsible for producing 
the drift.* 
It is convenient to illustrate this effect by considering a simple case of steady 
motion. 
1.34. An Illustration of the Gravity Effect. —Let the centre of gravity of a shell 
be constrained to move through air at a constant 
speed v, in a vertical circle (fig. 7), the inclination of 
the path to the horizontal being 6 at any instant. 
Thus v and dO/dt are constant. There is a possible, 
steady motion in which the axis OA always lies in 
the plane through OP perpendicular to the plane of 
j,. o „ the circle, the angle AOP (S) being constant. The 
couple M tending to increase S will also be constant, 
so that the contemplated motion is the same as the steady motion of a top making 
an angle |-7r + <i with the vertical which corresponds to the normal to the plane of the 
circle. The angular velocity of the axis about this normal is — 6'; the value of S as 
given by the ordinary formula for the steady motion of a top under these 
conditionsf is 
( 1.341) — ANff cos Bff 2 sin S cos $ = M = n sin S. 
If 6’ is not too large and // is not too small, a possible value of S is small; we may 
now regard /u. as independent of S, and the equation then reduces to 
(1.342) S = -AN O'/fi = -4 sO'/Q, 
the term neglected being of order S 3 . When a shell is moving freely the angular 
velocity 6' increases, and the linear velocity diminishes up to a point beyond the 
vertex of the trajectory. If the initial motion is identical with the above steady 
motion, this will cause the couple M to diminish, so that the axis of the shell will lag 
behind its position in the steady motion. This lag gives rise to a component angular 
velocity of the axis tending to increase the yaw S, until a state of relative equilibrium 
is reached, in which the yaw is slightly less than its equilibrium value, and the axis 
lags slightly behind (i.e., above) the tangent OP. When the velocity is high and 
the spin N not too large, M is large and the true position of the axis lies very near 
the equilibrium position. It will be shown in fact, in Part IV., that the assumption 
* For a shell whose spin and direction of motion are related like a right-handed screw the drift is to the 
right of the plane of fire. 
t See, e.g., Routh, ‘ Rigid Dynamics,’ vol. II., Art. 207. 
