330 PROCEEDINGS OF THE AMERICAN ACADEMY. 



recorder, or by noting on a chronograph the times of the runner's 

 passage past a suitable number of fixed points along the track. 



Although nothing can be stated directly from the data in this 

 paper as to the degree of uniformity or of variation in the speed of 

 a record-making trained racer, yet if it is proper to apply the inference 

 drawn from a long series of complete races to the speed conditions 

 during the operations of any one taken singly, then it should follow 

 that the speed of a record-maker is very nearly uniform throughout 

 the whole course. If, as appears from the whole series, the time of 

 exhaustion varies inversely as the ninth power of the velocity, and this 

 condition applies within the limits of any single race, then it is easily 

 seen that the quickest way to reach the winning post is to take at 

 the outset that speed which will just produce exhaustion at the goal, 

 and keep to that speed throughout the course. The penalty for 

 raising the speed at any part would be a degree of untimely exhaus- 

 tion far outweighing the benefit gained. Trainers commonly direct 

 practising athletes to spurt, or accelerate, near the end of the run. 

 This advice must be sound on any theory, because to slacken speed 

 at the end, if there is any balance of running energy left, would be 

 absurd. The runner naturally expends all the available energy balance 

 on the last lap ; but if he is able to accelerate to any appreciable extent, 

 it must mean that he has kept too much energy in reserve, and he 

 would have done better to adopt a higher general speed. If, on the 

 contrary, his pace falls to any appreciable extent at the end, he would 

 have economized time by maintaining a lower general speed. Ex- 

 perimental evidence to test this theory would be of great interest. 

 If the theory is correct, athletes, in training for a given event, ought to 

 be motor-paced, the speed of the pacing motor being set uniform. 

 In the earlier practice, this motor-speed should be, say, 15 per cent 

 less than the desired record-speed, and the athlete should train to keep 

 close to the motor. As the training progressed, the uniform speed of 

 the motor over the course should be raised, say, 1 per cent at a time. 

 Of course these suggestions advance beyond the warrant of evidence 

 at this time. 



Conclusions. 



An analysis of the various national and international appended 

 racing records, as above detailed, leads to the following conclusions, for 

 trotting, pacing, and running horses, as well as for running, walking, 

 rowing, skating, and swimming men : 



(a) The time varies approximately as the ninth power of the 



