power of the speed within the limits of racing speeds; so that a recordmaker, if he were able to double his speed, would become exhausted 512 times more quickly. Of course, the straight line can only be regarded as an approximation to the actual conditions, and we are not justified in asserting that the law of the inverse ninth power applies strictly. The exhaustion time as the inverse ninth power of the average speed is an average law, derived from the world's records, as made by a number of different individuals at different times. It is, however, certain that whether the time of exhaustion for any particular racer is as the inverse ninth, eighth or other power of his speed, it is a relatively high inverse power. We may safely conclude from the records that a recordmaking runner can not increase his speed within racing limits without bringing down his time of exhaustion very rapidly. Otherwise, the record times over different lengths of course would surely follow a different series.

It further follows from this deduction that a record-making runner can not afford to run at an unduly high speed for any appreciable time during his race; because, if he were to do so, he would thereby exhaust himself at a yet more unduly great rate. It would seem that in order to make his best time he must keep to a uniform pace, at least to a first approximation. It is evident that on the last lap he will put forth all his remaining effort, and spurt if he can; because he should arrive at the goal run out if he has done his utmost. If, however, he is able to spurt to a marked extent on his last lap, he has held too much energy in reserve, which he consumes unduly rapidly at the higher speed. According to the logic here set forth, he should have been able to reach the goal more quickly by a slight uniform increase in speed over the whole course.

According, then, to the deductions that the straight line of the illustration leads up to, an athlete of record-making quality should be enabled to make his best time over his best course or courses, by being paced at a uniform rate, say with an automobile. This, however, assumes that the runner would exert himself as fully behind an automobile as when running shoulder to shoulder with an antagonist. This is, perhaps, treating an athlete like a mere automaton, instead of like a human being. It seems more reasonable to suppose that an athlete's best performance can only be elicited under the spur and incentive of individual competition. Besides, the interest of a race to the onlookers would probably be greatly diminished if instead of the struggle of a number of racers were substituted the effort of a racer to keep up with a motor.

Nevertheless, the opposite proposition will be likely to meet with general approval; namely, that the worst way to elicit a good performance from a record-making type of runner is to incite him to an unduly high

speed at some part of the course before the end. The average speed of a record-making Olympic runner on a 100-meter course is given in the table as 9.26 meters per second. In the 1,500-meter race, Sheppard averaged, as we have already seen, 6.16 meters-per-second. Suppose that he commenced, say, by running at 9.26 meters-per-second. This would have been only 50 per cent. more than his average speed. It is clear that, had he done so, he would have been run out in 10 seconds. Again, if he had commenced by running at 7.09 meters-per-second, his average speed over the 800-meter course, and not quite 15 per cent. above his average speed over the 1,500-meter course, he would have been run out after 112.8 seconds, or only about half way.

It seems possible, however, to combine the incentive of shoulder-toshoulder competition with uniform pace-making, and without loss of interest to the spectators, by running a light flag or pennant by the side. of the track, on a slender wire of steel or phosphor-bronze. It would only be necessary to set short posts beside the track, each supporting a light metallic guide-pulley. Over all these pulleys would run the wire alongside the track, making a complete loop or endless chain. The wire would be propelled at some point in the course by a small electric motor, driven by a portable storage battery, as in the outfit of an electric automobile. An attendant at the motor would be charged with the duty of keeping the speed of the motor and wire uniform at that corresponding to the record for the particular event. By means of a stroboscopic fork, i. e., a tuning-fork carrying slotted wings on its prongs, through which a rotating target carried by the motor appears to stand still, it is readily possible to keep the speed of such a motor and wire constant to within a small fraction of one per cent.

When the runners were placed and ready to start, a small flag would be gripped on the running wire a few paces behind the men. As this flag reached the starting line, the starter would fire his pistol. Owing to the starting inertia of the men, the flag would gain a few feet at the first, and the runners would get under way with the flag slightly ahead. Since the flag would reach the winning post in record time, it would be the object of the men to outdistance it at that point. According to the reasoning above presented, they should best be able to do this by keeping close to the flag, which would serve as pacemaker. They should certainly be advised thereby if they started off at too high a speed. The spectators would have the advantage of seeing not only the contest. of the actual runners; but also a contest with the " ghost" of the best runner that heretofore had made the record of that event his own, as impersonated in the flag running beside the track.

In raising the ghost of the record runner as above, there might be a danger of hurting the race by the runners losing heart if they failed to keep up with the flag. There might also be a danger of the specta

tors' losing interest if the flag removed all temptation from the runners to jockey for first place, thus tending to sustain monotony at the expense of sport. Whether these dangers are serious could only be determined by actual trial.

It would, of course, be possible to reduce the speed of the flag, by preconcerted arrangement, to a more readily attainable local record, in place of a more ambitious world's record. One per cent. reduction in speed might make a very marked difference in this respect. There can be little doubt that the flag and motor-driven wire would be a useful device in the training of runners for the track at suitably graded speeds.

The same line of reasoning applies to other races. If the world's records in walking, swimming, skating, rowing, horse-running, horsetrotting and horse-pacing be similarly analyzed, and plotted on logarithm paper, the points will be found to fall very nearly upon a straight line in each case. Moreover, all of the straight lines have the same, or at least substantially the same, inclination, or represent and involve substantially the same law of fatigue. The only exception is found in bicycle-riding.

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2" An Approximate Law of Fatigue in the Speeds of Racing Animals," by A. E. Kennelly, Proceedings of the American Academy of Arts and Sciences, Vol. XLII., No. 15, December, 1906.

MONTE ALBAN AND MITLA AS THE TOURIST SEES THEM

BY PROFESSOR CHARLES JOSEPH CHAMBERLAIN

THE UNIVERSITY OF CHICAGO

N April, 1908, while investigating the Mexican cycads in the vicinity

IN

of Oaxaca, I took occasion to visit the ancient ruins on Monte Alban and at Mitla. A botanist could hardly be expected to speak with any authority upon archeological matters, but, having taken an excellent camera for photographing the cycads, I could not resist the temptation occasionally to point it at objects of mere human interest. Upon examining the photographs, a friend, who has made some reputation as an archeologist, suggested that an illustrated account, written from the standpoint of an ordinary tourist, would be of interest to the public, while the photographs might be useful to those better acquainted with the general subject.

Oaxaca is easily reached. Starting in the morning from Puebla over the Mexican Southern Railway, there is a pleasant ride of 228 miles through magnificent mountain scenery and prosperous plantations. From Tomellin to Las Sedas, forty miles, there is a grade so

steep that I was told one could coast all the way from Las Sedas to Tomellin. On the trip back I tried it and found it to be delightfully true. On a small square platform, resting upon two pairs of freight car wheels, the trip was like a long, breezy shoot the chutes, the speed sometimes reaching more than thirty miles an hour. The precipitous cliffs, lofty mountains and deep gorges, together with gigantic cacti, are some of the sights of the Republic.

The station stops of greatest interest are Tehuacan and Tomellin. Tehuacan is beginning to be called the Carlsbad of the New World, for its wonderful mineral waters are producing cures which rival those of some of the famous Mexican shrines. The water certainly has a pleasant taste to recommend it and throughout Mexico one constantly meets people who have been cured of various kinds of kidney, liver and stomach troubles. At Tomellin, the Chinaman, Dick-Kee, who con