KENNELLY. — AN APPROXIMATE LAW OF FATIGUE. 207 



maximum speed on an indefinitely short course. It is probably not 

 worth while going to the complication of correcting the formula by a 

 term or terms introducing a retardation at the start, since races below 

 100 yards are rare, and the deviation between the actual and computed 

 speeds disappears beyond loo yards. 



At the other end of the line in Figure 8 the deviations become large 

 after log L = a or beyond 100 kilometers. Beyond 150 miles the de- 

 viations exceed 20 per cent. It is possible that the discrepancy may 

 here be accounted for by reason of the fact that somewhere in this 

 neighborhood the runner stops at intervals to take food, or rest, and 

 there is no longer a continuous performance enacted. According to 

 the logarithmic straight line, the speeds on courses between 450 and 

 623 miles (724 and 1003 kilometers) are only two-thirds of what should 

 be expected. 



Summing up the entries in column X, without regard to sign, it is 

 found that if all the events are included from 19.5 meters to 1003 

 kilometers, the average deviation is 8.9 per cent. If, however, the 

 summation be limited to the range from 100 meters to 100 kilometers, 

 the average deviation is 4.3 per cent. This appears to be a satisfac- 

 tory result, considering that the range of distance is 1000 to 1, and the 

 range of record times 2500 to 1. 



From a practical standpoint it may be inferred from an inspection of 

 either Table IV or Figure 8, that it should be easier for trained ath- 

 letes to beat the world's records between 600 meters and 9 kilometers, 

 or between 30 and 1000 kilometers, than to beat the records between 

 100 meters and 600 meters, or between 10 kilometers and 30 kilo- 

 meters. Expressed in another way, we should expect the degree of 

 physical exhaustion in record runs over the short courses up to 600 

 meters to be more severe than on the courses from that distance up to 

 9 kilometers. The existing one-mile or three-mile record does not seem 

 to be so severe as the records from 100 yards to 500 yards. Whatever 

 mathematical conclusions may be drawn from the data, the belief seems 

 unavoidable that a study of Figure 8 will be useful to athletes training 

 for running with a view to breaking records. 



The crosses in Figure 8, representing Olympian records, while useful 

 as a check, do not serve the results in establishing the straight lines, 

 because these Olympian records are inferior to the corresponding world's 

 records, excepting that for the 100-meter race. 



The line of Figure 8 corresponds to the following formulas : 



log r = g log /. - 1 . 2307 (1 2) 



