with the load, with the heaviest loads there appeared definite indications of a decrease in efficiency. Since with practically all the heavy loads the rate of speed was high, the possible relationship between efficiency and load naturally becomes a relationship between efficiency and speed.

From the curves in fig. 5 it can be seen that to obtain 1.565 calories of effective muscular work at 70 revolutions per minute, it is necessary that the subject give off 7.61 calories of total heat, thus showing a gross efficiency of 20.6 per cent. Furthermore, in order to produce 2.425 calories of external muscular work at 130 revolutions, the subject must actually give off 15.04 calories of heat, corresponding to a gross efficiency of 16.1 per cent. The values for the gross efficiencies at the different speeds have been computed and are presented in table 124. Since in computing the net efficiency, the value used for the base-line, i. e., that obtained with the subject lying quietly on a couch, is constant and applicable to the whole curve irrespective of speed, it is obvious that the values for the net efficiency would be similarly affected by the speed.

TABLE 124.-Gross efficiency of subject M. A. M. at varying speeds with
a current of 1.5 amperes. (See Fig. 5.)

When we consider the variations in the output of work with increased speed, further relationships between the curve for the total heat output and that for the effective muscular work are found which indicate the influence of speed. From the upper curve it is seen that the output of heat is constant per 10 revolutions; on the other hand, the increase in the effective muscular work performed is not constant for each 10 revolutions, but there is a distinct falling off. If, therefore, we divide the increase in the external muscular work between any two points on the curve by the increase in the total heat output corresponding to the same two points, we get an efficiency based upon increasing speed, the degree of magnetization, i. e., the load, being the same. For instance, in changing from 70 to 80 revolutions per minute, there is an increase in the effective muscular work equivalent to 0.205 calories. Under these conditions there is an increase in the total heat output of 1.24 calories. Dividing the increase in the heat output due to the muscular work (0.205 calories) by the increase in the total heat output (1.24 calories), we find an efficiency for the increased amount of work performed of 16.53 per cent. Computations of a similar nature have been made for the various increases in speed and the results are given in table 125.

It is thus evident that at the higher speeds with the same degree of magnetization there is a much larger heat output for the same amount of external muscular work performed, and consequently the efficiency decreases greatly as the speed increases, the optimum efficiency being at the lowest rates of speed, namely, about 70 revolutions. In perhaps no other table in connection

with these experiments is this more strikingly brought out than here. Had it been possible to have this subject ride at a low rate of speed with this magnetization, an even greater efficiency than here noted might have been found, but as the rate of even 70 revolutions per minute was a little lower than he liked, since he usually preferred to ride at the rate of 80 or 90 revolutions per minute, the experimenting was not extended further in the direction of low speeds.

TABLE 125.-Efficiency of subject M. A. M. for increased amount of work due
to increase of 10 revolutions in speed, with current of 1.5 amperes.

It is a striking coincidence that the decrease in the heat given off by the ergometer per revolution compensates almost exactly for the decrease in the efficiency of the subject, so that the total heat output per revolution of the pedal is exactly constant irrespective of speed.

Thus far in considering the results, the greatest emphasis has been laid upon variations in speed per se. The unavoidable variations in the amperage and consequently in the actual amount of work performed incidental to alterations in the speed evidently might affect the efficiency and this factor should also receive special consideration. Had it been possible to conduct experiments at 50 revolutions per minute and again at 111 revolutions per minute, it will be seen from the calibration curves of ergometer II that we would have had exactly the same heat equivalent of effective muscular work, and it is perhaps unfortunate that such a series of experiments was not attempted. Our experience in having the subject ride at a slow rate was, however, discouraging as he found it almost impossible to control his muscles so as to rotate the pedals less than once per second.

In considering these relationships, it is of more than ordinary interest to study the influence of speed on the net efficiency when the amount of effective muscular work remained constant. For this purpose we have collected such experiments as were comparable, and tabulated in table 126 the results according to the heat equivalent of muscular work performed at the different speeds.

The results given in table 126 show that with approximately the same heat equivalent of muscular work per minute but with different speeds, the net efficiency of the body was very considerably less with the higher speeds. For instance, when the heat equivalent of the muscular work per minute was approximately 1.95 calories per minute, the average of 18 periods with a speed of 90 revolutions showed a net efficiency of 22.6 per cent, while 2 periods with an increased speed of 124 revolutions per minute gave a net efficiency of 15.7 per cent. Similarly, when the heat equivalent of the muscular work was approximately 1.80 calories per minute, the net efficiency with 80 revo

lutions was 22.1 per cent and with 105 revolutions 17.7 per cent. With an average beat equivalent of the effective work of approximately 1.58 calories, the average of 10 periods in which the speed was 71 revolutions per minute showed a net efficiency of 24.5 per cent, while 1 period with the considerably greater speed of 108 revolutions gave a net efficiency of 15.6 per cent. Groups of experiments with an approximate heat equivalent of 1.35 calories are also compared, three periods with a speed of 71 revolutions per minute showing an average efficiency of 23.1 per cent; 1 period with a speed of 94 revolutions an efficiency of 20.4 per cent; and 4 periods with a speed of 105 revolutions an efficiency of 17.0 per cent. In still another group with a heat equivalent

TABLE 126.-Efficiency of subject M. A. M. compared at different speeds when the amount of effective muscular work per minute remained constant. (Ergometer II.)

of approximately 1.20 to 1.25 calories, the average net efficiency with 72 revolutions was 21.5 per cent; with 83 revolutions, 20.4 per cent; and with 88 revolutions, 19.5 per cent.

From a consideration of these various methods of computing the energy efficiency of the body, it is obvious that there are grave difficulties in the way of securing a base-line which will embrace only the extraneous muscular motions incidental to riding with load upon which could be superimposed a definite amount of muscular exertion productive of external muscular work. Certain it is that the various base-lines we have considered-lying, sitting, and riding no load with and without the motor-fail to meet this requirement. The comparisons previously made of the experiments with currents of 0.5 ampere and 1.5 amperes, and of 0.95 ampere and 1.5 amperes, indicate that experiments used for a base-line should be accompanied by an even greater amount of muscular work than would be required to overcome ordinary friction. With the best conditions it is possible to have the work done to such advantage that the increase in the effective muscular work may be as high as 33 per cent of the increase in the total heat output. On the other hand, we have to consider in this connection the various influences of speed upon the efficiency, since it has been clearly brought out in the previous discussion that the greater the speed the less is the efficiency, the greatest efficiency with the subject M. A. M. being obtained when he rode at the rate of 70 to 80 revolutions per minute. The ideal comparison, therefore, is found

when experiments are made at the same speed, preferably from 70 to 80 revolutions per minute, and changing from moderately severe to severe muscular work.

COMPARISON OF THE EFFICIENCY IN THE EARLIER AND LATER

EXPERIMENTS WITH THE ERGOMETER.

b

Since this is the second research carried out by means of this type of ergometer, a comparison of our results with those obtained earlier are of unusual interest. As has already been pointed out, the friction of these ergometers is so low that in calibrating them it was extremely difficult to measure the heat produced by means of the apparatus employed. In general the friction per revolution is not far from 1 to 2 per cent of the total heat produced. Under these conditions, it seemed to be entirely unjustifiable to utilize this figure in any of the computations, and hence in no experiment does the question of friction enter.

At this point the gross errors resulting from the use by Benedict and Carpenter of an erroneous value for the friction of the machine should be again pointed out. Their entire discussion of the mechanical efficiency based on "coasting" or no-load experiments is vitiated by the fact that in deducting the "coasting" value from the total heat produced, they attempted to deduct the heat produced by friction from that produced by the external muscular work. Their values, which have been given in table 110, have been recomputed by us and are given in table 127, in which it can be seen that the percentage efficiency based upon the so-called coasting values averages not far from 26 per cent as against the 24 per cent found and reported by them. Furthermore, their discussion of the internal friction of the legs is entirely unwarranted owing to this erroneous value for the friction of the apparatus. Our observations do, however, furnish interesting comparisons since the general thesis that the gross efficiency for bicycle riding is approximately 12 to 13 per cent and the net efficiency not far from 20 per cent confirms fully the values given for the previous research.

e

TABLE 127.-Mechanical efficiency based on coasting experiments of Benedict and Carpenter.

1 The friction value used by Benedict and Carpenter in these computations
(0.001547 per revolution) was erroneous.

One discrepancy between the earlier work and the more recent observations is in the computation of the effect on the efficiency of increasing the

a Benedict and Carpenter, U. S. Dept. Agr., Office Expt. Stas. Bull. 208, 1909.

Benedict and Cady, Carnegie Institution of Washington Publication No. 167, 1912, pp. 21 and 29.

c Benedict and Carpenter, loc cit., p. 39.

d See p. 110.

e Benedict and Carpenter, loc. cit., pp. 40 and 41.