An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

54

CELTS

pressure on the right-hand side causes the bullet to "drift" to
the left.
In the case of a boomerang the varying air pressure is due
to both of the above causes and to others of a more complicated
nature.
55. Celts. Referring to the Celts described in the Introductory Chapter, the explanation of their behaviour is to be
found in the direction of the normal reaction at the point of
contact with the smooth horizontal plane.
In Fig. XI. (Plate I.)* the surface near the point of contact is
approximately spherical, so that when the stone is tilted in
any direction the normal reaction passes through the line GC
and so has no moment about GC. Hence the stone will have
no tendency to turn about GC.
But in Figs. XII., xiII., this is not so, and phenomena (a) and (b)
are explained in the following way:
Phenomena (a). Each base is in these two cases roughly
ellipsoidal near the point of contact, but the ellipsoidal surface
is "slewed round" slightly, relatively to the main body of the
stone.
Accordingly, when the stone is slightly displaced from its
position of equilibrium, the vertical reaction, which is normal
to the ellipsoid at the point of contact, does not pass through
GC.
Hence it has a moment about GC tending to turn the stone
about GO.
In Fig. xII. the vertical taps at A and at B result in moments
of opposite sign about GC; in Fig. xiII. they result in
moments of the.same sign, i.e. from A to B.
Phenonmena (b). When the stone is spun about the vertical
GC, since the conditions are not absolutely perfect, small
oscillations will be set up, and the normal reactions already
described will be called into play.
These may or may not tend to stop the rotation, and so
they may either increase or diminish the oscillations.
The particular effect of the normal reaction will of course
depend on the special shape of each stone.
In any of the above cases, the motion, whether reversed or
not, will only cease when the original energy of spin has been
destroyed by friction or communicated by oscillation to the
horizontal surface on which the spinning takes place.
A complete analytical investigation of the above phenomena
is given by Mr. G. T. Walker in The Quarterly Journal,
No. 110, 1896.
* For Plates I. -II. see end of book.