power of the speed within the limits of racing speeds; so that a record-maker, 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 record-making 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