The Arizona sentinel., 1888-02-18

evidently grows smaller and smaller
 Now. if they thus continue to swallow
 each other, aobTE o0iU eventually become
 Of tbe S1adEeS?
 Of course, it is clear that either the
 swallowing process must stop some
 down each others's throats. At whGt
 point, then, will the swallowing cease?
 If the reader finds himself ready on
 the spot with clear and precise an-
 swer to this question he will have
 proved himself of readier wit than
 the guest of the aforementioned
 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-
 animation of the ingenious.
 (Which, of any given moment, is
 moving forward fastest, the top of a
 coach wheel or the bottom?" To this
 apparently 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 ,thestop and bottom of the wheel must of=necessity be moving forward at the same rate, namely, the speed at which the carriage is travelling But little thought will show that this is far from
 being the case. A point on the bot tom-of the wheel is. in fact, by the di- rection of iis motion round the axis. moving backward, in an opposite di- rection 10 that in which the carriage is progressing, and is consequently stationary in space; while a point on the top of the wheel is moving for ward, with the double velocity 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 akln to the preceding: How can ship sail faster thar the wind?"
 Every yachtsman knows that a ship cal1 sail faster than the wind; that is 10 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 it can not, 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, as 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 well acquainted by experience with the fact. have found themselves able to explain.
 Let us consider the difficulty in the light of the following experiment: Place a ball at one side of a billiard table. and with the long cue held lengthwise, fl )m end to end of inc table, push the ball across the cloth. The cue here represents the wind, and the ball the ship sailing directly before ii; 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 can not possibly travel faster Now, suppose groove to be cut diagenally across the table, from one corner pocket to the other, in which the ball may roll. If 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 fast CT than the cue which impels it. sin ce it covers more than double the dis tance in the same time. It is in precise ly 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 i'm possible. "A body" thus argues the ingenious philoso- pher, must move either in the place where it is, or in the place where it is not. Now, a body in the place where it is is stationary, and can not be in motion; nor, obviously, can it be in motion in the place where it is not. it can not move at all" It was of this paradox it was said. solvitur ambulando-'1t is solved by walk ing" A more practical solution could hardly be required.
 Another paradox familiar to the Greeks-that of Achilles and the tor toise-is we'll 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 a hun lred yards the tortoise has run ten yards, and is, therefore. still that dis 5ance ahead. When Achilles has run hese ten yards, the tortoise has run one yard. When Achilles has run the pne yard; the tortoise has run one- ,enth of a yard. And when Achilles las run the one-tenth of yard the tortoise has run -hundredth. It is only necessary to continue the same process of reasoning to prove that can never overtake the tor +OiSa