300 PROCEEDINGS OF THE AMERICAN ACADEMY. 



or T= seconds. (13) 



17.01 ^ 



log V = 1.2307 - i log X (14) 



or V = — '-J— meters per second. (15) 



Men Walking. 



The data for walking races are given in columns I and III of Table 

 V. They are taken from page 244 of " The World Almanac " for 1 904, 

 and are world's records, amateur and professional. The best records 

 in walking, unlike other athletic sports, seem to have been made entirely 

 by professional walkers. 



Figure 10 indicates the points found by plotting log T from column 

 V against logL from column II. In order to economize space, the 

 series of points is carried twice across the sheet to two sets of scales. 

 The straight line, seen in two segments, is drawn through the 4 -mile 

 record point, and is drawn to meet the other points fairly. It makes 

 an angle of 48° 22' or tan~^ |, with the axis of distances. The entries 

 in column VIII correspond to points on the straight line. The com- 

 puted times T' of each event are thus obtained and set down in column 

 IX. The last column gives the percentages of deviation between the 

 actual and computed record. The observations commence above the 

 line, or the record times for the 1-mile and 2 -mile events are long, or 

 the speeds low, by comparison with the 4-mile and the 50-mile records. 

 This can hardly be accounted for by inertia, as in horse-racing; because 

 at the low speed of walking, the retardation, due to starting from 

 rest, must disappear in less than 100 meters. 



The points fall below the line between 4 miles and 30 miles, repre- 

 senting faster speeds than the computed to the extent of nearly fi per 

 cent. Between 40 and 70 miles the agreement between the observed 

 and computed times is close. Beyond 70 miles the speed falls below 

 that computed by the logarithmic line. The deviations do not exceed 

 5 per cent until beyond 1 20 miles. 



The mean percentage of deviation, without regard to sign, is 5.6 per 

 cent over the entire series of events, and 3.4 per cent between the 

 limits of 1 mile and 120 miles. 



There seems to have been scarcely any improvement in walking 

 records during the ten years preceding the date at which these have 

 been selected (1904). 



