# A couple of calculations

A few years back, I ired the Usenet police yet again. I posted to the billiards news group what I thought was a simple countereaxmple to Coriolis's proposition that if we take a sphere rotating at a constant velcocity, a given great circle C on the sphere, and the projections of rotational velocity vectors at points on C onto the plane of C, then all such projections have the same magnitude. A few minutes later I made another post retracting the previous one.

Coriolis's proposition appears on page 3 of the present edition (and page 4 of the original edition). It is correct and, since it puzzled me once, I've sketched out a proof of Coriolis's great circle theorem.

Much later on (our page 65, or p. 93-94 in the French), there is an interesting calculation of how far off-center (given by a), one may cue without miscuing. The cue is assumed to weigh three times as much as the ball, and the cue velocity after impact is assumed to be less than the ball velocity after imapct (a necessary condition that they separate). I've also written up a derivation of the formula for the ratio of a/R, where R is the radius of the ball.