KENNELLY. — AN APPROXIMATE LAW OV FATIGUE. 289 



Referring to Figure 6, it is to be observed that the record speeds are 

 low, or the times high, with respect to the straight lines up to 1000 

 meters (0.G2 mile). It is possible that this discrepancy on the 

 short courses may be due to the inertia of the horses ; that is to 

 say, the horses may be supposed to lose time, or to miss attain- 

 ment of speed, over the short runs below a kilometer, owing to the 

 effort required to start their bodies into motion from rest. This 

 time lost in acceleration is ignored in the straight-line logarithmic law, 

 which assumes that the animal starts with full speed. For courses 

 of over 1 kilometer, the discrepancy disappears. 



Moreover, horse-races are stated to be rarely run over distances less 

 than 5 furlongs (1006 meters) ; so that the question of the discrep- 

 ancy over short courses is of but little practical importance. 



The ascending straight line in Figure 6, drawn to meet the points as 

 fairly as may be, is carried through the 1-mile record, and makes an 

 angle with the axis of distance of 48° 22', whose tangent is |. The 

 falling line is also carried through the 1-mile record and makes an 

 angle with the same axis of — 7° 7' 30", whose tangent is — i. 



The straight lines of Figure 5 correspond to, or determine, the fol- 

 lowing equations : 



log r= llogZ— 1.6274 (4) 



and log r= 1.6274-^ log Z. (5) 



These are also respectively equivalent to : 



Z§ 

 7'=--— seconds (6) 



42.4 

 and V = -j-y meters per second. (7) 



By comparing equations (7) and (3) it appears from them that the record 

 speeds of trotting horses is less than the record speeds of running 

 horses over a given distance in the ratio of 33.9 to 42.4, or by 20 per 

 cent of the latter. 



On courses longer than 1 kilometer, the straight lines of Figure 6 

 fit the observations of Table II with satisfactory precision, some ob- 

 servations lying on one side and others on the other. The greatest 

 discrepancies are at 2\ miles and at 4 miles. Figure 5 shows in its 

 upper line that both of these performances were remarkable. The 

 speed over the 2^- mile course appears from the data to have been 

 greater than the speed in the 2-mile event. Again, the speed in the 

 4-mile race was actually higher than the speed in the 3-mile race. 



VOL. XLII. 19 



