328 PROCEEDINGS OF THE AMERICAN ACADEMY. 



According to these results the speed has to be reduced 1.33 times to 

 race 10 times the distance, and 1.78 times to race 100 times the dis- 

 tance. Thus, taking the 100. 6-meter event (110 yards) in Table IV, 

 the speed over the course is 9.144 meters per second. At 96.56 kilo- 

 meters (60 miles), nearly 1000 times greater distance, the speed has 

 fallen to 3.572 meters per second, or to 39.1 per cent of the former. 

 According to Table XVII, the speed should fall to 42.2 per cent on 

 increasing the distance 1000-fold. 



Another consequence of formula (28) is expressed thus : 



8 



F^ c ' T~^ ^ — r meters per second (33) 



or the speed over the course approximately varies inversely as the 

 ninth root of the racing time. 



In Table XVIII the speeds of the various racers are set down as 

 computed for courses of 1 kilometer and of 1 mile. Thus over 1 -kilo- 

 meter courses the speed of the running horse is 17.88 meters per sec- 

 ond (column VI), and the time for the race 55.9 seconds. At the end 

 of the series come swimmers, with a speed of 1.108 meters per second 

 and an inferred kilometer-time of 902.4 seconds. Table VIII shows 

 that the time for 1.006 kilometers was 925.4 seconds. Turning to the 

 mile range, the speed of the running horse is 37.7 miles per hour over 

 the 1-mile range. His mile-time is 95.5 seconds, both computed and 

 recorded. The speed of the swimmer is 2.336 miles per hour, and the 

 mile-time 1544 seconds as computed, and 1476.2 seconds as observed. 

 The speed of a running man is almost precisely half that of the trotting 

 horse, for distances above 1 kilometer where starting retardation ceases 

 to affect the horse. The speed of a professional walker is very nearly 

 the speed of a professional rower (singles). 



It is to be noted that all these speeds are average speeds over the 

 courses. There is no evidence among the records to show what the 

 speed was at different points in the course. So far as concerns anything 

 appearing in the data, the speed of a runner, for example, which 

 averages 7.17 meters per second over a 1-kilometer course, might be 

 10 meters per second in the first part and 5 in the last part, or vice 

 versa. Evidence is lacking to show what the facts are, and they are 

 of great importance to the science of athletics. The speed of a world's- 

 record type of trained runner might be determined at any or all 

 points of a course, either by securing a light recording chronograph 

 on the back of his belt, with a thread payed out as he ran, or by 

 pacing the runner with a light motor-car carrying an automatic speed 



