KEXNELLY. 



AN APPROXIMATE LAW OF FATIGUE. 



325 



true of this ideal athlete also tends to be true of any normal athlete, 

 even though his range of speeds and distances be limited. 



As an example of this rapid rate of exhaustion, take the 20-mile 

 (32.19 kilometers) running event in Table IV. The speed at which 

 this race was run averaged 4.794 meters per second as shown in 

 column IV. At twice this speed or 9.588 meters per second, there is 

 no exact distance in the table ; but the nearest is 131.5 yards (120.2 

 meters) at 9.696 meters per second. The time of the 20-mile event 

 was 6714 seconds in column II. The time of the 131.5 yard event was 

 12.4 seconds, or 541 times less, as against 512 times in Table XIV. 



Again, consider the last event in Table VIII of swimming records. 

 The 4000-yard (3657-meter) event was finished in 3824 seconds at a 

 speed over the course of 0.9564 meters per second. If we take a speed 

 1.5 times greater than this, or 1.4346 meters per second, we find one 

 near to it in the table ; namely, 1.420 meters per second (column XI) 

 in the 150-yard (137 -meter) event. According to Table XIV, the time 

 of exhaustion at 1.5 times greater speed is 38.4 times less than the 

 original. The time should therefore be 3824 -^ 38.4 = 99.6 seconds. 

 The actual time of the event is given as 96.6 seconds. 



Distance 



Equation (28) leads to the following expression for L : 



L^c^ T^ meters. (30) 



That is, as more and more time is allowed for racers to occupy in an 

 event, the distances they will traverse will not be directly proportional 

 to the time, but will vary as the eighth power of the ninth root of the 

 time, approximately. A few numerical values are given in the accom- 

 panying table : 



TABLE XV. 



Distances traversed avitii Increasixg Racing Time. 



