Suppose we illustrate. You put a ball on a billiard-table, and, holding the cue lengthwise from side to side of the table, push the ball across the cloth. Here, in a rough way, the ball represents the ship, the cue the wind, only, as there is no waste of energy, the ball travels at the same rate as the cue; evidently it cannot go any faster. Now, let us suppose that a groove is cut diagonally across the table, from one corner-pocket to the other, and that the ball rolls in the groove. Propelled in the same way as before, the ball will now travel along the groove (and along the cue) in the same time as the cue takes to move across the table. The groove is much longer than the width of the table, double as long, in fact. The ball, therefore, travels much faster than the cue which impels it, since it covers double the distance in the same time. Just so does the tacking ship sail faster than the wind.