KEN NELLY. — AN APPROXIMATE LAW OF FATIGUE. 281 



computed record time T' seconds and the published record time T 

 seconds, while column XII expresses this discrepancy in percentage of 

 the record time T. Thus, the 4-mile event should have been trotted 

 in 568.6 seconds by the formula, as against the published record of 598 

 seconds, a discrepancy of 29.4 seconds or 4.9 per cent of the published 

 record. It is seen that between the limits of 1 mile and 20 miles (1.61 

 and 32.2 kilometers) the average discrepancy between the recorded 

 time and the time taken from the equation (1) or the ascending lines 

 in Figures 2 and 3 is 1.8 per cent. The discrepancy is much greater in 

 the three longest events and reaches 34 per cent in the lOO-mile trot. 

 Owing to the age of these three records, however, it is submitted that 

 they may properly be set aside. At all events, between the limits of 

 1 mile and 20 miles the straight logarithmic line of times agrees with 

 the published records to an average of 1.8 per cent. If the suspected 

 4-mile record were set aside, the average discrepancy without regard to 

 sign would come down to l.l per cent. 



In Figure 4, drawn to uniform scale, the average speeds are continued 

 to 100 miles of course-length, or beyond the limits of Figure 1. The 

 curve of speeds corresponds to equation (2) or to 



33.9 

 V = — Y meters per second. (3) 



The figure shows the discontinuity which exists between the speeds 

 over the three longest courses and those over courses up to 20 miles, as 

 taken from column V, Table I. 



Horses Running. 



The records for running- horse races appear in columns I and II of 

 Table II. They are taken from page 258 of " The World Almanac " for 

 1905, which gives the records for 33 courses between \ mile (402.3 

 meters) and 4 miles (6437 meters) on American turf, revised to Decem- 

 ber 1, 1904. Column III gives the distances in meters and column IV 

 the average speed of each run. The times and the speeds are plotted 

 against distance to uniform scale in Figure 5 and to logarithmic scale 

 in Figure 6. In the latter case the entries in columns V, VI, and VII 

 are used. It is to be noticed that in Figure 5, with uniform ruling, 

 the observations follow curves, whereas in Figure 6, with logarithmic 

 ruhng (or logarithms of the quantities on uniform ruling), the obser- 

 vations fall substantially on straight lines. The two curves drawn 

 in Figure 5 respectively correspond mathematically to the two straight 

 lines drawn to meet the observations in Figure 6. 



