at a mark, involve the 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 friction, 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 carried on the ends of revolving arms, which themselves were carried by arms rotating more slowly, these latter arms again being carried 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 vertical 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, therefore, the opportunity for an almost endless variety of permutations 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 principle of never reading a book before he reviewed it, for fear of becoming prejudiced, we can speak of them in an unprejudiced 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 automatically, tiring itself and its master, producing even in sleep restlessness and dreams. Such a man obtains rest more easily,
