KENNELLY. — AN APPROXIMATE LAW OF FATIGUE. 



323 



times increases the time 100 times. Since the equation (28) is not set 

 up as a rigid law, but as a statistical approximation, or approximative 

 law, we cannot expect to find the relations of Table XII accurately 

 presented by all the events. For instance, if we limit ourselves to the 

 first statement that twice the distance should be covered in 2.1.S times 

 the time, we can examine all the cases of pairs of such events in the 

 records already considered and find what the ratios of time are when 

 the distances are as 2 : 1. The answer to this question is contained in 

 the following table : 



TABLE XIII. 



Taking, for example, the case of running men with reference to Tables 

 IV and XIII, there are 57 pairs of records in which one distance is just 

 double the other, commencing at 20-40 yards and ending with 150-300 

 miles. The sums of all the time ratios for these 57 pairs of events is 

 123.754, representing an average value of 2.171, as against 2.181 re- 

 quired by Table XII from equation (28). The highest ratio in any of 

 these pairs is 2.593, and the lowest 1.818. 



It will be seen that men running and men swimming come nearest in 

 their averages to the ratio 2.181 ; while men skating deviate the most 

 (4 per cent). Taking all the 146 pairs of double distances presented 

 in the entire set of records, and without rejecting any, the average 



