172 SECTIONAL ADDRESSES. 
where ¢ is half the total time of flight, the distance through which the 
centre of gravity of the body was raised must have been about 2.5 feet. 
The men competing must have had an original height of their centre 
of gravity of about 2.7 feet. Thus, in the high-jump, their centres of 
gravity went about 5.2 feet high into the air. They cleared a height 
of five feet: they just managed to wriggle their centres over the bar. 
Now, paradoxical as it may seem, it is possible for an object to pass over 
a bar while its centre of gravity passes beneath; every particle in the 
object may go over the bar and yet the whole time its centre of gravity 
may be below. A rope running over a pulley and falling the other side 
is an obvious example. It is conceivable that by suitable contortions the 
more accomplished high-jumpers may clear the bar without getting their 
centres of gravity above or appreciably above it. Let us calculate, how- 
ever, on the assumption that the centre of gravity of a jumper just clears 
the bar. The world’s record high-jump is 6.61 feet, the centre of gravity 
of the performer being presumably about 3 feet high at rest. He raises 
it therefore 3.61 feet into the air, from which we may calculate that the 
whole time occupied in the jumpis about 0.96 second. Seeing the amazing 
complexity of and the skill involved in the rapid movements and 
adjustments involved in a record high-jump, it is striking that all those 
events can occur within a time of less than one second. All the character- 
istics of the proprioceptive system must be evoked in their highest degree 
in carrying out such a skilled, rapid, and yet violent movement, 
Long-Jumping. 
It is well known to athletes that success in long-jumping consists in 
learning to jump high. It is not, of course, the case that a record long- 
jumper performs at the same moment a record high-jump. He must, 
however, cover a very considerable height. The world’s record long-jump 
is 25.48 feet. With the check provided by the vertical impulse in the last 
step we cannot well imagine the horizontal velocity to be greater, at this 
moment, than that of 100 yards completed in 10 seconds; that is, than 
30 feet per second, Let us assume this value: then the performer re- 
mains in the air for 25.48 
; that is, 0.85 second: hence we may calculate 
that the vertical distance covered is about 2.9 feet. Assuming the centre 
of gravity of the subject to have been originally 3 feet high, this means 
that it must have reached a height 5.9 feet in the air, enough, in a high- 
jump, to enable its owner to clear’5.9 feet. It is interesting to find that the 
simple laws of mechanics emphasise so strongly the precepts of the athletic 
trainer. Not only must one jump high if one wishes to break a long-jump 
record, but one must bring one’s centre of gravity nearly six feet high into 
the air; for one must project oneself vertically, so that one may remain 
for 0.85 second above the ground. 
Conclusion. 
The practice of athletics is both a science and an art, and, just as art 
and science are the most potent ties tending to draw men together in a 
world of industrial competition, so sport and athletics, by urging men 
to friendly rivalry, may help to avert the bitterness resulting from less 
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