The Tracks of Tops’ Pegs on the Floor

1. The initial transient state. One can get useful information of the behaviour of a top by observing the track of its peg on the floor. This may be obtained by making the top move on tracing paper such as is used in typewriting. Eleven years ago I could see that after letting down a top there was a transient initial adjustment leading to a steady state of rolling and precession 1). During this steady rolling there is no sliding. This can be seen by the sharpness of the traces left by a mark on the peg. In the track of the transient state these are diffuse, showing an oblique slip. In the steady rolling state the inclination of the top’s axis, 8, defines the radius r and hence the circumference of a circle on the peg consisting of the successive points of contact. with the floor. Given the spinning angular velocity w the velocity ‘YW must be the translatory velocity of the top, and this should be perpendicular to the vertical meridian plane of the top. It would be a haphazard coincidence if on letting down the top these relations would .obtain; hence the top has to slip until the adjustment has been made. The initial transient state is well visible in figures 1 and 2. Figure 1 refers to a blunt spherical peg. It shows a narrowing spiral in the steady part. Here the top rises gradually. Figure. 2 refers to a rather. sharp peg, this top having dimensions, inertia coefficients andspin-. ning velocity practically the same as the other one. The diameter of.