KENNELLY. — AN APPROXIMATE LAW OF FATIGUE. 331 



eighth root of the distance. Doubling the distance means increasing 

 the time 118 per cent (Table XIII). 



(b) The time occupied in a record-making race varies approxi- 

 mately inversely as the ninth power of the speed over the course. 

 Doubling the speed cuts down the racing time 512 times (Table XIV). 



(c) The distance covered increases approximately as the eighth 

 power of the ninth root of the time. Doubling the time of the race 

 allows of increasing the course length by 85 per cent ( Table XV ). 



(d) The distance covered increases approximately as the inverse 

 eighth power of the speed over the course. Doubling the speed cuts 

 down the distance that can be covered 256 times ( Table XVI ). 



(e) The speed over the course varies approximately as the in- 

 verse eighth root of the distance. Doubling the distance brings down 

 the speed about 9.3 per cent ( Table XVII ). 



(f) The speed over the course varies approximately as the inverse 

 ninth root of the racing time. 



It may be noted that all of the statements (a) to (f) are different 

 aspects of one and the same fact. 



(g) If any of the three quantities Z, T, and F = -=, be plotted on 



logarithm paper as ordinates to either of the other quantities as ab- 

 scissas, the record points will fall on, or near to, a straight line 

 (Figures 2, 3, 6, 7, 8, 10, 11, 12, 13, and 15). 



(h) Athletes aspiring to break racing records might succeed better 

 in attacking those whose points fall below the straight lines of speed 

 against distance, or above the straight lines of time against distance, 

 rather than those whose points fall on the opposite sides of those lines. 



(i) The records presented on bicycling do not determine the 

 proper highest speed of cycling below 30 miles (48 kilometers), since 

 there is apparently no reduction in speed by fatigue up to that 

 distance. 



(j) With the exception of bicycling, as above noted, the law of 

 fatigue in racing is the same, or very nearly the same, with horses as 

 with men, in air or in water, as indicated by the records analyzed 

 in this paper. 



