The Arkansaw traveler., 1888-01-07


 If the reader finds himself ready on the spot with a clear and precise an- swer to this question he will have proved himself of readier wit than the guests of the above mentioned wine party. A little consideration, however, will probably be sufficient to clear up the mystery, and, like the preceding enigma of the railway, the problem may safely be left to the ex- amination of the ingenious.
 "Which, at any given moment, Is moving forward fastest, the top of coach- wheel or the bottom?" To this very simple question nine persons out of ten, asked at random, will give an incorrect reply. For at first sight it appears evident that both the top and bottom of the wheel must of nececessity be moving forward at the same rate, namely, the speed at which the carriage is travelling. But a little thought will show that this is far from being the case. A point on the bottom of the wheel is, in fact, by the direction of its motion round the axis, moving backwards, in an oppo- site direction to that in which the car riage is progressing, and is conse- quently stationary in space; while a point on the top of the wheel is nov ing forwards, with double the veloc- ity of its own motion round the axis and the speed at which the carriage moves.
 The following paradox, which has given rise to much discussion, is some- what akin to the preceding: "How can ship sail faster than the wind?"
 Every yachtsman knows that a ship can sail faster than the wind; that is to say, if the wind is blowing ten knots an hour, a ship may be making twelve or fifteen knots an hour. Now, it is obvious that if the ship is sailing straight before the wind 1t cannot, at the utmost, travel faster than the wind itself is blowing-as matter of fact, it will travel much more slowly. If, on the other hand, the ship is sail ing at an angle with the wind, it seems at first sight that the wind must act with less effect than before, and the ship in consequence sail more slowly still. But ss matter of fact the ship not only sails more quickly than be- fore, but more quickly, than the wind itself is blowing. This is a paradox which few, even of those who are we'll acquainted by experience with the fact, have found themselves unable to explain.
 Let us consider the difficulty in the light of the following experiment. Place ball at one side of a billiard table, and with the long cue held lengthwise, from end to end of the table, push the ball across the cloth. The cue here represents the wind and the ball the ship sailing directly be- fore it. only as there is here no waste of energy, which in the case of the wind and ship is very great, the ball of course travels at the same rate as the cue--evidently it cannot possibly travel .faster. Now, suppose groove te be cut diagonally across the table, from one corner pocket to the other, in which the ball may roll. Ii the ball be now placed at one end of the groove, and the cue held horizontally and moved forward as before, the ball will travel along the groove (and along the cue) in the same time as the cue takes to move across the table. This is the case of the ship sailing at an angle with the direction of the wind. The groove is considerably longer than the width of the table, more than double as long, in fact. The ball therefore travels much faster than the cue which impels it, since it covers more than double the distance in the same time. It is in precisely the same manner that tacking ship is enabled to sail faster than the wind.
 The foregoing mysteries of motion bring to mind the famous paradox of Zeno, by which he sought to prove that all motion is impossible. "A body" thus argued the ingenious philosopher, must move either in :ho place where is, or in the place where it is not. Now body in the place where 1t is is stationary, and cannot be in motion; nor, obviously, can 1t be in motion in the place where it is not. Therefore, it cannot move at al. :" It was of this paradox it was said, sotritur ombuldndo-"it is solved by walking. A more practical solution could hardly be required.
 Another paradox familiar to the Greeks-that of Achilles and the tor toise-is well known. Achilles (the swift footed), allows the tortoise a hundred yards start, and runs ten yards while the tortoise runs one. Now, when Achilles has run 6 hun- dred yards the tortoise has run ten yards, and is therefore still that dis tance ahead. When Achilles has run these ten yards, the tortoise has run one yard. When Achilles has run the one yard, the tortoise has run one-