. Discovery. Science. 68 DISCOVERY the square of the speed. In the figure are shown the world's records, taken from Whitaker's Alman'ack, of flat races from loo yds. to i mile. Horizontally are plotted the times occupied in the race, vertically the squares of the average speeds at which the record was made. The curve joining the points is a fairly smooth one, though it is noticeable that the principal records (100 yds., 220 yds., J, |, and i mile) lie rather above the curve as a whole. More effort has been expended 100 gives approximately the relation between the rate of oxygen consumption [no
. Discovery. Science. 68 DISCOVERY the square of the speed. In the figure are shown the world's records, taken from Whitaker's Alman'ack, of flat races from loo yds. to i mile. Horizontally are plotted the times occupied in the race, vertically the squares of the average speeds at which the record was made. The curve joining the points is a fairly smooth one, though it is noticeable that the principal records (100 yds., 220 yds., J, |, and i mile) lie rather above the curve as a whole. More effort has been expended 100 gives approximately the relation between the rate of oxygen consumption [not supply) and the time occupied in the race. Now if the maximum oxygen " income " of a world's-record-holder be 5 litres per minute, and his maximum oxygen " credit " be 12 litres, then in various times he can take exercise equivalent to the following qtiantities of oxygen: Time: minutes . i Total oxygen available; litres 17 Oxygen per minute : litres . 17 3 27 Q 4 32 5 37 7-4 62 6-2 50. We see that the oxygen available per minute is much less in a long race than in a short one; hence the speed must be less too. Indeed, if the oxygen per minute in the above table be plotted against the time, it gives a curve of just the same type as that shown in the figure. This curve can be given a simple mathematical equation. Let x be the time occupied in the race and y the average rate of oxygen consumption per minute. Let A be the maximum oxygen " debt," and B the maximum oxygen "; Then assuming for simplicity that respiration can start at its highest Ll-I 00 oe U-l D_ CO en <: Dotted curve from equation â y= m + lioojx world's records, ioovzzo yos.,1/4,'/z %â imile O ditto , OTHER DISTANCES. 20 40 60 80 SECS. 200 on these records, and it is harder to beat one of them than one of the others ; indeed, simple inspection of the curve shows that the easiest records now avail- able, for any enterprising and scientific would-be record holder,
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