166 : SECTIONAL ADDRESSES. 
be induced by his rider to go as hard as he ought. A man may be able 
to force himself to a greater degree of exhaustion than his rider can force 
a horse. An amusing incidental point brought out by fig. 5 is the fact that 
Fic. 5.—Records for horse-races. Small circles=old English records, 1721-1832. 
Large circles=later English records, 1880-1905. D=Derby, O=Oaks, L=St. Leger. 
Average speed, metres per second, against distance in kilometres. 
the small circles and the large ones are intermingled. The horses of 150 
years ago could run just as fast as their modern successors—a fair comment 
on the doctrine that the improvement of the breed of horses is the chief 
and a sufficient reason for encouraging the continuance of horse-racing— 
even in time of war. 
The Logarithmic Graph. 
Let us pass now to a consideration of the last diagram, fig. 6. There 
average speed in a race is plotted against the logarithm of the time occupied 
in it, the logarithm being employed, as stated above, for the purpose of 
including all records from 75 yards to 100 miles in the same picture. That 
people think, to some degree, in logarithms, although unconsciously, is — 
shown by the fact that the records which men have thought it worthwhile 
to make are distributed approximately uniformly over the picture from 
left to right. Fig. 6 presents the data of athletics perhaps more clearly 
than any other. The initial rise of the curve for men running, which is 
due to starting inertia, is very obvious. The rapid fall beyond 220 yards 
is clearly seen. It is obvious that the 100 and the 220 yards (3 mile) records 
are better than those lying in their neighbourhood, that the quarter-mile 
record is extremely good, the 500 yards record very bad, by comparison 
with its neighbours. This diagram should enable any enterprising and 
scientific athlete to select the records most easy to break: let him try 
those for 120 yards, for 500 yards, for three-quarter-mile, for three miles, 
but not for 220 yards, quarter-mile, one mile, and six miles. 
; 
: 
i 
; 
£ 
