we have no means of discovering from these records what the highest speed of a bicycle rider may be. It is inconceivable that there should be no fatigue for 50 or 30 miles. If the record speed over 30 miles be 23.77 meters per second, the speed over 2 miles should be much greater. If the same law of fatigue held for bicycle riders as for runners, walkers, swimmers, and skaters, the speed at 2 miles should be approximately 15 or 1.40 times greater; viz., 33.3 meters per second, or 74.4 miles per hour. There is no proof, however, that the same law of fatigue applies, and the air resistance at such high speeds might influence the results. It is, however, evident that the speed at 2 miles, or similar distances, is kept down abnormally to that at 30 miles. The explanation suggests itself that the records are all made on a circular track of considerable lateral inclination. The cyclist, on short runs, perhaps attains the highest speed that he dares and not the highest speed that his muscles could develop. When travelling at 23.75 meters per second (53 miles per hour), careful steering must be needed to keep on the track, and perhaps the records indicate the limit of steering nerve rather than the limits of speed and endurance below 30 or 50 miles. The case is somewhat similar to that of automobiles in this respect. The track records of heavy-weight gasolene automobiles, as given in "The World Almanac " for 1906, indicate speeds of 30 meters per second (67 miles per hour) at 1 mile, and hardly any reduction up to 10 miles, or no sensible fatigue within those limits. At 1000 miles (1609 kilometers) the speed is 20.35 meters per second (45.5 miles per hour). But on the straightaway courses, as distinguished from track courses, the speed averaged 46.77 meters per second (104.5 miles per hour) at 1 mile, and fell off distinctly with distance at a rate very similar to the fatigue rate of racing animals. Until, therefore, we have a wide straightaway course, say 5 kilometers long, provided for cyclists, of as good quality throughout as is presented in circular tracks, the cyclist's maximum speed will remain a matter of doubt. SUMMARY OF RESULTS. A summary of the results of the various analyses in regard to accuracy is presented in Table XI. Column I refers to the table considered. Column II, the character of the race. The total number of records in each table appears in column III. The range of distances covered is given in column IV, both in miles and in kilometers. The sum total of the percentage deviations, without regard to their sign, as found for each table, including every record, is given in column V. The quotient of the sum in column V, by the number of records in column III, gives the mean percentage deviation for each table in column VI, or the mean difference between the computed record time and the actual record time in percentage of the latter. Reasons have been given in connection with each table why certain records should be left out of consideration. The remainder are discussed in columns VII, VIII, IX, and X. These contain what may be called the net results, while columns III, IV, V, and VI contain the gross results. In the net results, horses come out the best, and nearly equally well for trotting, running, or pacing, viz., 1.9 per cent mean deviation. The horses come out much better than the men in this comparison. It should be observed, however, that the ranges of distances covered by the horse-races are relatively small, 20, 6.4, and 4, whereas with men the ranges are successively 1320, 120, 6, 185, 300,- much greater. Perhaps if the ranges covered in the horses' performances had been similar to those covered in the men's performances, the disparity in precision would disappear. In the men's performances the net average deviation is about 4 per cent, except in skating, where it is 7.5 per cent. The net average deviation of all the 207 records is 3.9 per cent. Considering the gross results of columns III, IV, V, and VI, the lowest deviation is found in trotting horses (2.43 per cent) followed by men swimming (3.52 per cent). The greatest deviation is in skating (13.26 per cent). The mean deviation of the whole series of 257 records, rejecting none, is 7.05 per cent. It is submitted that the summary in Table XI demonstrates the proposition that the records in races of men and of horses approximately follow straight lines when plotted on logarithm paper; because the average percentage deviation of all the records is only 7 per cent from the line, and excluding 50 of the records as unreliable for reasons assigned, this average deviation falls to 4 per cent. The record time that should belong to any given distance within the usual limits, and for any of the events considered, except bicycling, can thus be assigned with these probable degrees of accuracy. It is not so remarkable that the records of any one event, such as men running, should approximately conform to a logarithmic straight line; but it is remarkable that the straight lines should be parallel, or substantially parallel, in all of these eight classes of events, including three gaits in quadrupeds and three gaits in bipeds, besides motion in the water and over ice. Figure 15 collects all of the logarithmic straight lines on one sheet to a reduced scale. The ascending parallel straight lines are time-distance lines. The descending parallel straight EXPLANATION. At the right of the Figure the numerals 1.0 to 5.0 are loga rithms of time (seconds). VOL. XLII.-21 FIGURE 15. Speed-distance and Time-distance Lines. Ascending lines, time-distance; descending lines, speed-distance. 50 miles 100 kiloms. 100 miles 120 miles 100 Seconds. 4.0 10,000 1,000 5.0 100,000 |