KENNELLY. — AN APPROXIMATE LAW OF FATIGUE. 293 



An inspection of column X, Table III, containing the computed 

 record times according to formulas (8) and (10), shows that the i-mile 

 record was 2 seconds longer than the computed time, the mile 2^ 

 seconds shorter, and the 3-mile, 4-mile, and 5-mile events considerably 

 longer. These deviations appear in column XI, and are given in 

 percentages of the respective actual records in column XII. The ^-mile 

 deviation of 3i percent maybe explained by inertia on short courses. 

 The deviations of 10^, 8, and 8 per cent on the long distances are not 

 explainable in such a manner. The 3-mile and 4-mile records date 

 from 1891, and the 5-mile record from 1874. Reference to the 

 records of 1892, as given on page 273 of "The World Almanac" for 

 1894, shows that at that time the pacing records were low by com- 

 parison with those at the present date. Thus the mile record 

 (1.6 kilometers) in pacing was 124 seconds, and the 2-mile record 

 (3.2 kilometers) was 287.75 seconds, which are in deviation from the 

 modern records of those events, according to Table III, by 7.6 and 

 11.9 per cent respectively. Consequently, it seems fair to say that 

 these records of 3, 4, and 5 miles, which are 8 to 10.5 per cent 

 off the straight lines in Figure 7, would have been close to similar 

 lines drawn for records in 1894. In other words, the 1-mile and 

 2-mile records have steadily improved since 1891, whereas the 3-mile, 

 4-mile, and 5-mile records remain as they were at that date. 



If we eliminate the 3-mile, 4-mile, and 5-mile records from considera- 

 tion, the average discrepancy between the computed and observed record 

 times is seen in column XII to be 1.9 per cent. If, however, we have 

 to consider all of the events, the average discrepancy is 5.4 per cent. 



Summing up the analysis of horse-racing as presented in Tables I, II, 

 and III with their accompanying curve-sheets, it is submitted that the 

 logarithmic straight lines meet the observations, within reasonable 

 limits of range, to 2 per cent of average discrepancy. Moreover, these 

 corresponding straight logarithmic lines are parallel to each other for 

 running, pacing, or trotting. This means that there is a similar law 

 of fatigue in each of these styles of progression. 



Men Running. 



The first two columns of Table IV give the world's records of running 

 races. The first four events, up to 45 yards inclusive, are taken from 

 the Amateur Athletic Union Records, as given on page 262 of " The 

 World Almanac " for 1906. The remaining events, up to 623 miles 

 inclusive, are taken from page 242 of " The World Almanac " for 1904. 

 For each event the best record has been selected, whether the holder 



