TABLE 106.-Heat equivalent of muscular work and corrected amount of heat produced in experiments with A. L. L.,1 as reported by Benedict and Carpenter. (7 a.m. to 7 p. m.)

1 In deducting the heat production of resting metabolism from that in the work experiments, the averages of Nos. 65 and 66 were used. For the severe work experiment (No. 64), the heat production during the period from 7 a.m. to 4 a.m. of experiment No. 65 was used as the resting metabolism. This was found to be 2,205 calories. Deducting this from the total heat production of experiment No. 64 (6,843 calories) leaves 4,638 calories as the heat production necessary to produce mechanical work, the heat equivalent of which is 957 calories.

TABLE 107.-Heat produced in experiments with B. F. D. and E. F. S., as reported by Benedict and Carpenter.

1 No resting experiment with E. F. S. was made, as the subject left the city shortly after the conclusion of the work experiment. His body-weight was 80 kilos., and from a large amount of data obtained with other subjects, it is highly probable that his resting metabolism would have been not far from 1,400 calories for the period from 7 a.m. to 7 p.m. Accordingly, this resting metabolism has been assumed in the computations.

Finally, a series of experiments was made with a professional athlete, N. B., in which the metabolism was studied during short periods, usually 11⁄2 to 3 hours in length. The subject, who was 35 years old, weighed 66 kilograms, and was 172 centimeters in height, was one of the best-known professional bicycle riders in America. He was in excellent condition and an ideal subject for the experiment. The results, calculated on a one-hour basis, are abstracted in table 108. No data for oxygen consumption are given for the experiments made in October 1904, as the methods for the measurement of this factor had not then been perfected. Of special note is the net efficiency exhibited by this professional subject, the average being 21 per cent.

TABLE 108.-Results of experiments with N. B., as reported by Benedict and Carpenter.

A summary of the results obtained with all of the work experiments with these subjects is given in table 109, which shows the gross and net efficiency for each man.

TABLE 109.—Average mechanical efficiency of subjects in work experiments made by

Benedict and Carpenter.

[Amounts per hour.]

The authors also computed the mechanical efficiency based on the coasting or "no-load" values of these men; the results are abstracted in table 110. These values are wrong, owing to an erroneous assumption for the friction of the ergometer." Finally, the effect on the efficiency of increasing the ex

TABLE 110.-Mechanical efficiency based on coasting as reported by Benedict and Carpenter.

(See Benedict and

1 Later researches with the apparatus show that the values in this column are erroneous. Cady, Carnegie Institution of Washington Publication No. 167, 1912, p. 22.)

a For discussion of this point see p. 143 of this report.

ternal work or load was computed as shown in table 111. The authors point out that there was a disturbing factor in that the speed per minute was not uniform with all degrees of magnetization of the field, and state that the experiments must be looked upon as more or less tentative.

TABLE 111.-Effect on mechanical efficiency of increasing external work as reported by Benedict and Carpenter.

As an indication of the great difficulties that may be experienced in computing the heat efficiency of the bicycle rider from the energy intake and the mechanical measurements, we must cite the discussion of R. C. Carpenter," who computed the efficiency of two professional riders in a 6-day bicycle race, obtaining the apparent gross efficiencies of over 60 per cent in one case and nearly 45 per cent in the other. Computations of the effective muscular work in complicated muscular processes must always be of uncertain value.

One of the great difficulties incidental to computing the amount of external muscular work performed by going up and down stairs or walking along a horizontal or an inclined plane is strikingly indicated in certain experiments of Chauveau. This investigator computed that Tissot in his experiments on the respiratory exchange performed in 70 minutes 29,000 kilogrammeters of positive work and an equal amount of negative work. The total amount of work would thus be 58,000 kilogrammeters, or 136 calories, approximately 2 calories per minute. And yet Chauveau, in his computation of the respiratory quotients, maintains that the metabolism during work was but 4 times that of rest. In this laboratory in order to secure an effective output of 2 calories per minute on a bicycle ergometer, it was necessary for the subject to increase his metabolism over rest more than 10 times. It is thus obvious that either Chauveau's estimate of the amount of external muscular work performed must be erroneous or the analyses for the gaseous exchange are open to severe criticism. The technique of the ChauveauTissot apparatus has been carefully gone over in this laboratory by Mr. T. M. Carpenter, and when carried out according to the specific instructions of Chauveau and Tissot, the apparatus and method give admirable results. We are thus disinclined to consider the measurements of the gaseous exchange at fault, although the lengths of periods are short and the technique of sampling has not been adequately given. It is probable that the estimates of the work performed are erroneous.

Amar, using a bicycle ergometer in which the rear wheel was supplied with a steel ribbon as a brake, the amount of friction on the ribbon being

4 Atwater, Sherman, and Carpenter, U. S. Dept. Agr., Office Expt. Stas. Bul. No. 98, 1901, pp. 64 and 65. Chauveau, Comptes rendus, 1896, 122, p. 1163. Previously cited on p. 80 of this report.

Amar, Jules, Le rendement de la machine humaine. Recherches sur le travail, Paris, 1910.

continuously measured by a combination of weights and springs, determined the efficiency of a number of Arabs in Algeria. The net efficiency varied from 27 to 38 per cent, with an average of not far from 32.5 per cent, while the gross efficiency varied from 3.2 to 5.1 per cent, with an average of 4.5 per cent, these values being calculated from the ration eaten by the subjects. Amar also computed the net efficiency from the consumption of oxygen as measured by means of the Tissot apparatus, finding an average net efficiency of 27 per cent instead of the 32.5 per cent found when computed from the food intake. When the subject performed 13,748 kilogrammeters per hour for 4 consecutive hours, Amar computed the net efficiency from the oxygen consumption to be 29.33 per cent for the first hour, 31.23 per cent for the second, 33.81 for the third, and 35.03 for the fourth hour. Other experiments gave a similar increase in the efficiency as the work progressed. Of particular interest in connection with our research is his study of the effect upon the efficiency of the rate of speed. With 70 revolutions of the pedal he found with one subject 25.1 per cent, with 80 revolutions 26.7 per cent, with 90 revolutions 28.4 per cent, while with another subject with 90 revolutions he found 30.6 per cent, and with 100 revolutions 25.8 per cent, indicating approximately an optimum speed of about 90 revolutions of the pedal per minute. Considering the conditions under which Amar worked and the difficulties incidental to an inadequately equipped laboratory, these results are of special interest; yet, as pointed out by Lefèvre," the values must be taken with considerable reserve.

THE UNIT OF EFFICIENCY.

GROSS AND NET EFFICIENCY.

An examination of the earlier literature on the efficiency of the body shows that a large number of units of efficiency have been used by various writers. If the total energy output for the day is made the base-line, and the actual amount of energy transformed into external muscular work taken as the numerator, the percentage of efficiency can be obtained by the formula a x100 in which a represents the external work performed in calories and b b the total energy output in calories. This unit, which may be called the "gross efficiency," the "crude efficiency," or the "industrial efficiency," is naturally largely affected by the amount of work performed during the day and the number of hours in which work is done, since at least half of the day is usually spent in rest, during which time there is energy output but unaccompanied by effective external work. For computation of the energy output of a gang of laborers or artisans in a mill and for the provisioning of an army or navy under severe stress of muscular work, the gross efficiency is of particular value, but in physiological experiments per se it indicates but little of the potentialities of the human body for severe muscular work, and gives no conception of the possible efficiency of the human body as a machine.

To find this latter, it is obvious, to say the least, that the energy given off when the subject is at rest and not performing muscular work should be deducted from the total daily quota. Further than that, it can readily be assumed that a deduction should likewise be made of the energy required for

a Lefevre, Chaleur animale et bioenergétique, Paris, 1911, p. 212.

the maintenance of the body of a subject lying quietly during a period of time equal in length to the working period. A value, which may be termed the "net efficiency" or "pure efficiency," would thus be obtained by the formula ax 100

in which a is the external amount of muscular work performed, b b-c the total calorie output for the period during which work was performed, and c the resting requirement in calories during a similar period. Under these conditions, therefore, the value b-c represents the increment in oxygen or calories required to produce a calories of external muscular work.

METHODS OF COMPUTING THE NET EFFICIENCY.

This relationship has been used by many writers in their computations, but we find that there are many methods for computing this net efficiency. For instance, Durig " has emphasized the fact that when computing the net efficiency for a person walking along level ground, it is a question whether the resting lying metabolism should be deducted, or the metabolism while the person is standing. Similarly, for walking up an incline or climbing mountains it is difficult to select the exact base-line for comparison. In the work of mountain climbing, which has been studied so extensively by Zuntz, Durig, and their collaborators, it is legitimate to deduct not only the metabolism when the subject is lying quietly awake, but also logical to deduct the metabolism incidental to movement along a horizontal plane for a distance equivalent to that traveled on an ascent less the height; the actual amount of work involved in raising the body to a vertical height will then be shown by the increase in the oxygen consumption during the ascent over that required to move the body forward on the horizontal plane. This method of computation has been employed quite extensively. In the computations of the results of his mountain-climbing experiments, Durig has first deducted from the total katabolism the metabolism of the subject while lying quietly and then from the value remaining he has computed that for the "horizontal component;" deducting this, he obtains the value for the katabolism due to raising the body to a given height, i. e., the "vertical component." The difficulties incidental to this form of computation need not be pointed out.

Although somewhat extraneous to this discussion, it is not without interest to note that Durig states in his conclusions that experiments of this kind should be made in a respiration chamber since the Zuntz method does not take account of the cutaneous respiration and makes no provision for eliminating the influence of the resistance to the work of respiration. While the form of respiration apparatus used in the present series of experiments does not measure the cutaneous respiration, which is unquestionably considerable, yet, on the other hand, it does eliminate all resistance to the respiration since there are no valves to be actuated and no meter to be turned. A special calorimeter for severe muscular work is in process of construction in this laboatory which will give an opportunity for measuring the cutaneous respiration, but the results of this research may be taken as representing an intermediate step between results obtained by the Zuntz method and by the respiration chamber.

a Durig, Physiologische Ergebnisse Monte Rosa Expedition, Ueber den Gaswechsel beim Gehen, Denkschrift d. math.-natur. Klasse d. Kaiserl. Akad. d. Wiss., Wien. 1909, 86, p. 294. b Durig, loc. cit., p. 338.