and has the roots a(1

(6)

i) and 1/A in addition to -a(1 — i); two of the roots therefore give increasing motions. The root 1/4 is the large extraneous root that comes in when the force (1) is used;2 the root a(1) gives a non-radiating orbit. Any orbit of the whole set

is also non-radiating.

z = C1 e ̄a(1−i)1 + C2 ea(1−i)¿

(7)

The orbits (4) have been described as non-radiating because the force (1), being normal to the path, does no work. It is only in this sense that they are free from radiation: the equation of energy holds, the sum of the kinetic and potential energies is constant. (As the motions are supposed to be small, quasi-stationary, relativity effects have been ignored.) From the point of view of electro-magnetic theory the rate of radiation varies as the square of the acceleration and can never vanish in accelerated motion; and there is a coördinate radiation of momentum. The relation between the two rates of radiation is shown by the equation

The total radiation is the same according to both points of view whenever estimated between two instants for which v.dv/dt has the same values; but the instantaneous rates cannot be indentically equal except for orbits in which v.dv/dt is always the same constant independent of the time. I have discussed elsewhere the effect of replacing the law (1) by its alternative in the case of the rectilinear oscillation,3—which then ceases to be an oscillation.

From the point of view of relativity the rate of radiation of energy (and momentum) has been treated by several authors and has been shown to vary with the square of the generalized curvature of the path when regarded as a space-time locus in four dimensions. For any real motion, where the velocity is less than that of light, the radiation must be positive and radiationless orbits, other than straight lines uniformly described, are impossible. If, however, velocities greater than light were possible and if the formula for the rate of radiation still held, the orbits would be those for which the curvature vector was a minimum line. Although this state of affairs may have no present

physical interest, it does have a purely mathematical interest, and I shall therefore determine also these orbits.

The expression which must be integrated is '

dv dv - (vxdv). (vxdr),

dt dt

dt

(8)

The

provided the units are so chosen that the velocity of light is 1. Let R be the radius of curvature of the orbit (in ordinary space). tangential and normal resolution of acceleration throws (8) into

If then any space curve be given intrinsically by the equation R = f(s), equation (9) determines the velocity at which the curve must be traced if there is to be no radiation as estimated by the usual electro-magnetic formula.

1 See H. A. Lorentz, Theory of Electrons, Art. 37, B. G. Teubner, Leipzig, 1916.

2 See M. Planck, Theorie der Wärmestrahlung, p. 110, J. A. Barth, Leipzig, 1906.

3 * Wilson, E. B., Boston, Proc. Amer. Acad. Arts Sci., 50, 1914, (105–128).

♦ See Wilson and Lewis, Ibid., 48, 1912, (387-507), especially p. 481.

THE EFFECT UPON THE ATOM OF THE PASSAGE OF AN
ALPHA RAY THROUGH IT1

BY R. A. MILLIKAN, V. H. GOTTSCHALK AND M. J. KELLY
RYERSON PHYSICAL LABORATORY, UNIVERSITY OF CHICAGO

Read before the Academy, November 11, 1919

In 1910, by catching at the instant of ionization the positive residues of atoms ionized by X-rays, and by beta and gamma rays of radium, it was conclusively shown that the act of ionization by these agencies uniformly consists in the detachment of a single negative electron from a neutral atom.

The method consisted in balancing the force of gravity acting upon a minute oil-drop by a strong vertical electrical field, holding the oil-drop under observation in a telescope with the aid of a powerful beam of light,

passing a sharply limited beam of X-rays, beta rays or y rays immediately underneath the drop, catching upon the drop the positive ion, formed by the ionization of a neutral molecule by the rays under investigation, and finally measuring the charge communicated to the drop by the advent of the ion upon it through observing the speed imparted to the drop by its new increment in charge.

Just before the war, Millikan attacked the more difficult and the more interesting problem of catching by the same general method, the ions formed by the passage of an alpha particle through an atom, expecting in this case to find that this relatively huge and powerful ionizing agent would often detach more than one negative electron from a single atom. When he was called to other duties by the war, the experimental work already begun was continued and completed by Gottschalk and Kelly. The results are as follows:

1. Alpha rays have been shot through atoms of the most diverse sorts (H, C, O, N, Cl, I, Hg) and of atomic weights from 1 to 200, without bringing to light in any case evidence of the formation of multiply-valent ions.

2. Twenty-nine hundred ions formed by the passage of a rays through neutral molecules have been caught on oil drops at the instant of ionization and the charges carried by each of these ions individually measured. Of these 2900 captures, 5 might possibly have corresponded to double charges, though even these were in all probability due to the nearly simultaneous advent upon the drop of two singly charged ions.

3. In no single case has an a particle been observed to form an ion carrying three or more charges, even though mercury, from which octivalent ions had been expected, was one of the substances tested.

4. Alpha ray ionization consists, then at least 99 times out of a 100, in the case of all the gases and vapors studied, in the detachment of a single negative electron from a neutral molecule.

1 A detailed report of these experiments will shortly be published in the Physical Review. 2 * Millikan, R. A., and Fletcher, H., London Phil. Mag., (Ser. 6) 21, 1911, (753).

ON THE EMBRYOLOGICAL BASIS OF HUMAN MORTALITY1

BY RAYMOND PEARL

DEPARTMENT OF BIOMETRY AND VITAL STATISTICS, JOHNS HOPKINS UNIVERSITY

Read before the Academy, November 11, 1919

1. In order to get a clearer idea of the underlying biological factors in human mortality I have rearranged the 'causes of death' listed in the International Classification of the Causes of Death, which is the code used generally by vital statisticians, into a new classification on a biological basis. It is not possible with our present statistical material to make a completely and precisely logical classification, but I have endeavored to come as close to it as is possible. The underlying idea of this new classification is, as the first operation, to group all causes of death under the heads of the several organ systems of the body, the functional breakdown of which is the immediate or predominant cause of the cessation of life. All except a few of the statistically recognized causes of death in the International Classification can be assigned places in such a biologically grouped list. It has a sound logical foundation in the fact that, biologically considered, death results because some organ system, or group of organ systems, fails to continue its functions. Practically, the plan involves the reassignment of all of the several causes of death now grouped by vital statisticians under heading 'I. General diseases.' It also involves the re-distributing of causes of death now listed under the puerperal state, malformations, early infancy, and certain of those under external causes.

The headings finally decided upon for the new classification are as follows:

I. Circulatory system, blood, and blood-forming organs

II. Respiratory system

III. Primary and secondary sex organs

IV. Kidneys and related excretory organs

V. Skeletal and muscular systems

VI. Alimentary tract and associated organs concerned in metabolism VII. Nervous system and sense organs

VIII. Skin

IX. Endocrinal system

X. All other causes of death

It should be emphasized that the underlying idea of this rearrangement of the causes of death is to put all those lethal entities together which bring about death because of the functional organic breakdown of the same general organ system. The cause of this functional breakdown may be anything whatever in the range of pathology. It may be due to bacterial infection; it may be due to trophic disturbances; it may be due to mechanical disturbances which prevent the continuation of normal function; or to any other cause whatsoever. In other words, the basis of the present classification is not that of pathological causation, but it is rather that of organological breakdown. We are now looking at the

TABLE 1

SHOWING THE RELATIVE IMPORTANCE OF DIFFERENT ORGAN SYSTEMS IN HUMAN

question of death from the standpoint of the pure biologist, who concerns himself not with what causes a cessation of function, but rather with what part of the organism ceases of function, and therefore causes death.

2. In table 1 the death rates per 100,000 are arranged in descending order of importance (for the United States Registration Area 1906-10) by organ systems. Four sets of data are used: (a) the United States Registration Area for the five years, 1906-10 inclusive; (b) the same, 1901-05; (c) England and Wales, 1914; and (d) Sao Paulo, Brazil, 1917. 3. The data show that in the United States, during the decade covered, more deaths resulted from the breakdown of the respiratory system than from the failure of any other organ system of the body. The same thing