276 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Horses Trotting. 



Table I, the data of which are taken from page 259 of " The World 

 Almanac and Encyclopedia" for 1906, gives in column I the date of 

 the record, in column II the distance run, or length of the course, and 

 in column III the best record time. For these data " The World 

 Almanac " is made responsible. These data have been checked, how- 

 ever, by those given in the same publication for preceding years. No 

 event has been rejected. The best records for 1, 2, 3, 4, 5, 10, 20, 

 30, 50, and 100 miles of trotting are taken. They are stated to be 

 World's records, and at least one, — the 4-mile event — is stated to 

 have been made in England. 



Commencing with the above data, column IV shows the distances 

 expressed in meters. The meter and kilometer are so much simpler to 

 deal with numerically than the foot, yard, furlong, and mile, that it is 

 worth while to reduce all distances to meters. Column V gives the 

 average speed at which the record was made, expressed in meters per 

 second. Thus, taking the first event, the mile (1609.3 meters) was 

 trotted in 118.5 seconds. This represents an average speed of 1609.3 

 ~- 118.5 = 13.58 meters per second (30.4 miles per hour; or 44.5 feet 

 per second). 



Turning now to Figure 1, the abscissas are laid off both in miles and 

 in kilometers, as far as 20 miles (32.2 kilometers). The ordinates rep- 

 resent speeds both in meters per second and in miles per hour. An- 

 other scale of ordinates gives the record time of each run in seconds. 

 It is seen that the speeds, taken from column V, drop from 13.58 

 meters per second (30.4 miles per hour) at 1 mile (1609 meters) to 9.18 

 meters per second (20.6 miles per hour) at 20 miles. The average 

 speed of the trotting horse that made the 20-mile record was there- 

 fore 67.6 per cent, or about two-thirds of that of the trotting horse 

 which made the 1-mile record. 



Taking next the time ordinates, the rising line in Figure 1 closely 

 follows the first six successively increasing times. It is evident that 

 both the speed-distance line and the time-distance line are curves, 

 when thus plotted. The curvature of these curves is greatest near the 

 start, or over the short courses, and diminishes as the course increases. 



If, however, the speed and the time with respect to distance be 

 plotted on logarithm paper, as in Figure 2, instead of on ordinary 

 cross-section paper, as in Figure 1, the points fall approximately upon 

 straight lines. 



The above fact is the gist of this paper. That is to say, if we con- 

 sider the three quantities L, T, and V, or length of course, record 



