296 PROCEEDINGS OF THE AMERICAN ACADEMY. 



was amateur or professional. Amateur records are indicated in column 

 II by the letter A. The last eight events are taken from records of the 

 Olympian Games, as published in the Boston " Transcript " for May 12, 

 1906. These international contests have been held in 1896, 1900, 1904, 

 and 1906. The best of these four records has been taken for each 

 event. 



In Figure 8, log T (see column VI, Table IV) is plotted as ordinates 

 against log L (column V) as abscissas. The circles mark the world's 

 records and the crosses the Olympian records. In order to keep the 

 chart within reasonably small dimensions, retaining a fairly extended 

 scale, the observations are made to cross the chart twice, by employing 

 dual scales of ordinates and abscissas. The straight line is drawn 

 through the 500-yard record to meet the remaining observations. It 

 runs off the sheet the first time at log T = 2.71 and log L = 3.5. It 

 then recommences at the left hand of the upper line and finally leaves 

 the sheet at log T= 4.9 and log L = 5.45. These parts of what would 

 be a single straight line on a larger sheet make an angle of 48° 22' or 

 tan" ■'I with the axis of abscissas. The record points conform closely 

 to this line, swinging slightly from one side of it to the other. They 

 lie above it as far as log L = 2.0. They lie beneath from log L = 2.0^ 

 to log L = 2.66, and again from log L = 4.0 to 4.5. In the remaining 

 parts they lie above. In other words, the straight line hits the record 

 path at log L = 2.1, 2.7, 3.75, and 4.5. 



Table IV gives in column VIII the values of the record times cor- 

 responding to the straight line in Figure 8. Column IX gives the 

 deviation from the world's record for each event and column X the per- 

 centage deviation. The percentage deviation commences at —44.5 for 

 the shortest run (19.5 meters). It dwindles to at about 110 me- 

 ters. It reaches a maximum of 8.5 near 200 meters, returns to at 500 

 meters, swings over to —8.5 at 2800 meters, returns to near 10 

 kilometers, swings to 4.9 at 18 kilometers, crosses the zero point near 30 

 kilometers, and then steadily increases numerically and in the negative 

 direction until it is —34.8 at 900 kilometers. 



The large discrepancies below 100 yards may be attributed to inertia. 

 This is indicated in Figure 9, where the speeds of the events are plotted 

 up to 201 meters. It is evident from the dotted line following the rec- 

 ords that runners attain their maximum apparent speed in the neigh- 

 borhood of 1 10 meters (120 yards). At shorter distances the retarding 

 effect of inertia prevents a higher average speed in the run from being 

 developed. At longer distances, the starting retardation is reduced in 

 effect, but fatigue acts in its place. The simple logarithmic law, repre- 

 sented by the heavy line, takes no account of inertia and assumes a 



