530 THE POPULAR SCIENCE MONTHLY. 



at a mark, involve tlie addition of two other famous mathematical 

 principles ; namely, the epicycloids of Hipparchus, and Galileo's 

 law of gravity. Billiards bring in the insoluble mystery of fric- 

 tion, which creates a breach of continuity in the path of the ball. 

 Cards, backgammon, and various games for the evening at home, 

 involve the doctrines of permutations and of chances. 



In the ancient astronomy the planets were imagined to be car- 

 ried on the ends of revolving arms, which themselves were carried 

 by arms rotating more slowly, these latter arms again being car- 

 ried by arms of still slower rotation. This epicycloidal motion of 

 Hipparchus is evidently closely analogous to the motion of the 

 human hand, which rotates upon the wrist- joint, while the wrist 

 is carried in a circle about the elbow- joint, the elbow in a circle 

 about the shoulder, and so on. The ingenuity of Hipparchus had, 

 as it were, contrived a huge imaginary man, carrying the planet 

 between his thumb and finger. The friction of the billiard-table 

 diminishes the rotation of the ball upon the instantaneous ver- 

 tical axis at such a rate as to bring it presently to an end, leaving 

 only the rotation upon a horizontal axis. At this moment the 

 curved path of the ball becomes instantly a straight line. Cards 

 involve the smallest prime number, and that in two ways, there 

 being two colors, red and black, and also two suites of each color. 

 Cards also involve the relatively high prime thirteen, and, less 

 conspicuously, the intermediate numbers. They furnish, there- 

 fore, the opportunity for an almost endless variety of permuta- 

 tions and combinations ; and if these are produced by shuffling, 

 they involve also the doctrine of chances. We ourselves do not 

 know how to play a single game of cards ; therefore, on Sydney 

 Smith's jDrinciple of never reading a book before he reviewed it, 

 for fear of becoming prejudiced, we can speak of them in an un- 

 prejudiced manner. Their universal popularity we have just 

 explained. But it is a nearly invariable rule that the best things 

 are also the worst. Fire is a good servant but a bad master ; and 

 strychnine, one of the most valuable of tonics, will kill a man as 

 promptly as it will a wolf. Cards are capable of great abuse, and 

 they have been so greatly abused that many persons interdict 

 their use also. Yet they have a use ; and their sanitary value as 

 a recreation and diversion of the mind is, in certain cases and for 

 certain persons, very high. The invalid needs rest, and often finds 

 the best form of rest in the exercise of different powers from those 

 which have become fatigued. This is as true concerning mental 

 as concerning bodily exercise. When a man is tired, weighed 

 down with anxiety and care, or with a continuous application of 

 the mind to one set of questions, his brain is apt to go on auto- 

 matically, tiring itself and its master, producing even in sleep 

 restlessness and dreams. Such a man obtains rest more easily, 



