where W is the velocity of thermal agitation of the electron, K' is the mobility of the electron, L is its mean free path, V is the voltage, d is the distance between the plates, and n is the chance of ion formation per impact.

Let us assume that when the voltage V is equal to V. all the Q. carriers starting from P at atmospheric pressures can reach E. This simplifying assumption is contrary to fact for at V. the carriers actually only begin to reach E. We may with this assumption impose the conditions implied in equation (1) on the equation (2). This will lead to the conclusion that out of a maximum possible current Io, the real current I which reaches E as a function of the frequency N = 1/T, the pressure p, the plate distance d, and the voltage V, is given by the equation

I = I。e ̄μK'L(d2(p/760)2,

W

K(p/760)

(3)

where p is in mm. of mercury, and K is the mobility of the normal ion. Now it is possible to evaluate W from the mean kinetic energy of the molecules, for it is assumed in the theory that the electrons move in the electric field with a velocity small compared to W. Let us further assume K' to be constant and equal to 200 cm./sec., 73 while we take L as 4√2 times the mean free path of the molecules, and K as about 2.5. We thus have the equation

This equation is open to experimental verification for it contains but one unknown quantity n, as I/I。 can be determined experimentally under known conditions of N, p, V and d.

I have recently made a series of determinations of the mobilities of the carriers produced in air at different pressures under essentially the simple conditions in the foregoing discussion. These determinations yielded mobility curves of which the set of curves shown in figure II are typical. As is seen at once the form of the curves resembles the curves to be expected from the qualitative discussion above. The values of I/I。 may be determined in such curves from the ratio of the current to E caused by a given alternating potential between P and E and that caused by an equal fixed negative potential on P. By substituting this value of I/I。 in the equation with the corresponding values of N, P, V and d one may solve for n. As the result of a large number of determinations the value of n obtained under conditions best conforming to the theoretical assumptions was 250,000. With n determined the theory may be further tested by computing the curves for I/I。 as a function of V for different values of d, N and p. A large number of curves were thus computed. A typical comparison of the theoretical curves so obtained and the curves actually observed under the same conditions may be seen in figures III, IV and V.

The dotted curves are the observed and the full curves are the computed ones. The experimental data are given in the legend. The shapes of the curves at atmospheric pressures or at low values of N, where the carriers are all ions, should not agree. For in deducing the theory we assumed that at V. all carriers succeeded in reaching E, which is not the case in fact. Also at the lower pressures close agreement is not to be expected, for the velocity acquired in the field becomes commensurable with the velocity of agitation W. Barring these points the general shapes of the theoretical and observed curves, and the changes in shape of these curves with p and N, are quite similar. It is also evident that the points of in

flection, or the asymptotic feet, of the corresponding observed and computed curves fall on values of V which lie close together. This means that the values of the hybrid, or abnormal, mobilities estimated from the two sets of curves are nearly the same. There is, therefore, sufficient similarity in the two sets of curves to permit one to assert that the curves are represented by the same type of equation. We may then conclude that the Thomson theory is in good qualitative agreement with the results observed.

With the evidence before us I believe we are justified in concluding that the mechanism of negative ion formation in air consists in the electron attaching itself to a molecule to form a negative ion on the average in one out of 250,000** molecular impacts. Now it has been shown that in pure nitrogen34 the electron does not attach to form an ion to any appreciable extent. We must, therefore, assume that the electron attaches to the oxygen molecule in air. Measurements made in pure oxygen give n as about 50,000. As there are four molecules of nitrogen in air to one of oxygen this agrees quite well with our conclusion. What the significance of n is, whether it depends on the electronic ring in the molecule struck, whether it depends on some particular state of the molecule struck, or whether it depends on the energy conditions of the impact remains for the future to say.

In conclusion I desire to express my thanks to Professor R. A. Millikan for his kind advice and criticism.

* A more detailed description of these experiments will later appear in the Physical Review.

† NATIONAL Research FELLOW of the NATIONAL RESEARCH COUNCIL.

Such mobilities have been obtained below 100 mm pressures in air by all the experimenters in this field up to the time of Wellisch. Until Thomson proposed his theory they had never been adequately explained.

** This value depends on the correctness of the assumptions as to the numerical values of K' and L for the electron.

1 Thomson, J. J., London Phil. Mag., Sept., 1915.

2 Kovarik, A. F., Physic. Rev., Ithaca, 30, 1910 (415).

3 Franck, J., Verh. deuts. physik. Ges., 12, 1910 (613).

4 Loeb, L. B., These PROCEEDINGS, June, 1920.

5 Loeb, L. B., Physic. Rev., 8, 1916 (6).

6 Yen, K. L., Ibid., 9, 1918 (5).

7 Wellisch, E. M., Amer. J. Sci.; New Haven, (Ser. 4) 44, 1917 (1); Phil. Mag., 34, July, 1917.

THE BASAL METABOLISM OF GIRLS 12 TO 17 YEARS OF AGE BY FRANCIS G. BENEDICT, MARY F. HENDRY AND MARION L. BAKER NUTRITION LABORATORY, CARNEGIE INSTITUTION OF WASHINGTON, BOSTON

Read before the Academy, November 17, 1920

The Nutrition Laboratory's task of charting the field of basal metabolism of humans from birth to old age has resulted in a reasonable completion of the study of boys and girls from birth to puberty, of both sexes, from the college age to 35 years, and of women about 50 years of age. The metabolism during the important age-range from 12 to 17 years, representing as it does a period of rapid growth as well as the period of the establishment of puberty, has recently been studied, so far as girls are concerned, in a large respiration chamber permitting the simultaneous measurement of the carbon-dioxide production of a dozen or more subjects. Groups of twelve Girl Scouts each volunteered as subjects, and a typical experiment involved their entering the respiration chamber after a light standard supper and sleeping quietly throughout the night. The entire carbon-dioxide production during the period of "bed rest," as well as the "minimum" carbon-dioxide production found throughout the night, are the bases for the computations of the energy needs for "bed rest" and for the basal metabolism. The quiet, resting morning pulse rate was obtained with all groups and the insensible perspiration was also measured with most of the groups.

Special interest centres around the gaseous metabolism or, more particularly, the energy computations therefrom. It was found that 55.0 calories represented the average hourly heat production per- individual, with very little difference due to either average age or average weight.

For groups of girls, therefore, from 12 to 17 years of age the energy requirement for 10 hours of "bed rest" may be taken as 550 calories. The basal 24-hour heat production with all these groups of girls closely approximated 1250 calories per individual, irrespective of age or weight.

The computation of the heat per kilogram of body weight per 24 hours, the classic method of equalizing, in so far as possible, differences in the weights of the groups, showed that in general the younger the average age, the higher the heat production. Similarly, computations of the heat production per square meter of body surface (obtained from the Du Bois height-weight chart) indicated a distinct tendency for the higher values to be found with the younger girls. These data for the basal metabolism measurements are given in table 1 herewith.

TABLE 1

BASAL HEAT PRODUCTION OF GIRLS 12 TO 17 YEARS OF AGE

1 Eleven girls were studied on Jan. 16-17 and April 9-10; 12 girls on all other dates. All girls in the 15, 16 and 17 year old groups had reached puberty; none of the girls studied on April 9-10 and March 12-13 had reached puberty; 5 girls on Jan. 23-24, 2 on March 19-20, 4 on Feb. 13-14, and 11 on March 5-6 had not reached puberty. 2 Using a respiratory quotient of 0.79 and 3.086 calories as the calorific equivalent of a gram of carbon dioxide.

The striking influence of age is shown by the values for the heat production per kilogram of body weight, which indicate a specific high metabolism with the younger ages. These values for the heat per kilogram have been plotted, referred to age, in figure 1, and a line representing the general trend of the metabolism has been laid on the chart. From this chart we have derived the predicted values for the heat per kilogram of body weight of girls, depending upon age, and these values we present in table 2 as representing the best available standard for predicting the heat production of young girls of this age-range.

TABLE 2

BASAL HEAT PRODUCTION PER KILOGRAM PER 24 HOURS PREDIcted from Age, for GIRLS FROM 12 TO 17 YEARS OF AGE

Other general conclusions derived from the study are the following: The average, minimum, resting pulse rate per minute of girls from 12 to 17 years of age, just before rising in the morning, was found to be 81 at 12 years, 77 at 13 years, 77 at 14 years, 83 at 15 years, 71 at 16 years, and 74 CALORIES PER KILO. REFERRED TO AGE. (GIRLS)

Cals. 32

Basal heat production of girls per kilogram per 24 hours referred to age

17

The first of the two figures accompanying each point on this chart represents the number of girls in the group who had not as yet menstruated; the second figure indicates the number who had.