LXIX. Remarks regarding the Series Spectrum of Hydrogen and the Constitution of the Atom. By L. Vegard, Dr.Phil., Lecturer of Physics at the University of Christiania [Communicated by the Author.]. IN the number of the Phil. Mag. for Jan. 1915, Dr. H. Stanley Allen has published two interesting papers, where he considers the case in which the circulating electrons of the atom, in addition to the electrical forces, are acted on by a magnetic field equivalent to that of an elementary magnet placed at the centre and with its axis perpendicular to the plane of the orbit. Generally, he finds that the magnetic effects u are not in themselves sufficient to account for more than a small fraction of the effect that would be necessary to give the observed distribution of lines in spectral series. " In the case of hydrogen, however, he finds that the deviation from the Balmer formula as found by Curtis would be explained, when in certain states of motion the electron was acted on by the field of an elementary magnet with a moment of 5 or 6 magnetons and placed at the centre, and he states that ' ; in support of the view that the core contains 5 magnetons we have the fact first pointed out by Chalmers that the magnetic moment produced by an electron moving in a circular orbit with angular momentum of [formula redacted] is exactly 5 magnetons." Regarding this last point I should like to make a few remarks. The 5 or 6 magnetons which are necessary to explain the deviations from the Balmer formula in the way proposed by Dr. Stanley Allen must be due to a magnetic system near the centre, and are of course not to be identified with the 5 magnetons produced by the light-emitting electron in the normal state of the atom; and if the explanation of Dr. Stanley Allen is correct, it would have important consequences with regard to our conception of the inner nucleus. The inner magnetic system might either be produced by circulating electrons or by the rotation of the positive nucleus. The angular momentum [mu] of a sphere is [formula redacted], where M is the mass, a the radius, and co the angular velocity. The 652 [header] magnetic moment [formula redacted] the kinetic energy [formula redacted] [It is supposed that the inner nucleus can be treated as a charged solid body]. If the mass of the nucleus is of purely electromagnetic origin, its radius is equal to [formula redacted] when the charge is supposed to be on the surface o£ the nucleus. For a volume distribution we can assume the formula to give a radius of the right order, or about 10 _16 cm. for the hydrogen nucleus. In order to get a magnetic moment o£ 5 magnetons we should have to assume an angular momentum of 1800 [formula redacted] and the number of rotations (v) in unit time would be [formula redacted], and the kinetic energy [formula redacted], or about 10 19 times the energy of the outer electron in the normal state of the atom. As long as we know so little about the interior of the atom we are perhaps not allowed to say that the existence of such rotations and the enormous store of energy are impossible, although there seems no special reason for the assumption unless we would suppose that the internal energy of the atom which is brought to light through the atomic disintegration is to be of a rotational nature, and that the rotations are preserved also for the lighter elements like hydrogen. Let us next consider the case in which the inner magnetic system is composed of (N — 1) electrons circulating round the nucleus with a positive charge [formula redacted]. If the angular momentum of all inner electrons [formula redacted]. is equal to [formula redacted] they would produce a magnetic moment of 5 magnetons. Let all electrons form one ring, then [formula redacted] and [formula redacted] Ai and Wt are radius and energy of inner ring, a and W the corresponding quantities for the light-emitting electron in the normal state. In order that the inner system shall act electrically on the outer electron as a single charge [formula redacted] must be a small quantity. In fact, [formula redacted] diminishes rapidly with increase of N. Thus with an inner ring of 1 electrons [formula redacted]. and [formula redacted], [header] 653 and we see that toe energy of the magnetic system also in this case would be very great compared with that of the light- emitting electron in the normal state. Even if we take it for granted, however, that the assumption of an inner magnetic system is a legitimate one, we should still meet with the difficulty that, according to Dr. Stanley Allen, the magnetic moment must vary considerably with the state of motion of the light-emitting electron. In fact, it is assumed that for the state of motion corresponding to an angular momentum of [formula redacted] the magnetic moment of the inner system is equal to zero, while for the stationary circles of greater momentum the magnetic moment is 5 magnetons. Dr. Allen gives no indication as to how the passage of the electron from one stationary circle to the next can increase the magnetic moment from to 5 magnetons. With certain modifications of Dr. Allen's assumptions we might, however, in quite a formal way explain the formula of Curtis through the effect of an internal magnetic field. We suppose the inner magnetic system to be produced by circulating electrons, and that the inner magnetic system and the outer electron maintain a constant difference of momentum equal to [formula redacted] [formula redacted] putting [formula redacted] and the magnetic moment of the inner system would be [formula redacted] magnetons, where c is the velocity of light [Mg and c are give in electrostatic units.]. Now Dr. Allen has deduced the following general formula for the magnetic influence on the spectrum: [formula redacted] where [formula redacted] 654 [header] Putting [formula redacted] [formula redacted] and [formula redacted], we get [formula redacted] and [formula redacted] This formula is somewhat different from that found by Dr. Stanley Allen, but it will equally well represent the observed facts. For the six lines considered in Dr. Allen's paper we get: [table redacted] It happens that for these lines [formula redacted] comes out practically constant equal to 1/9, and we get the formula [formula redacted] which has exactly the same form as the empirical formula found by Curtis. Using the values [formula redacted] and [formula redacted], we find [formula redacted], while the corresponding constant in Curtis' formula is equal to [formula redacted] . Thus the deviation from the Balmer formula would be satisfactorily explained through the magnetic influence of the inner core, when a constant difference of momentum of [formula redacted] is supposed to be maintained between the outer and inner system. It may be granted that in dealing with atomic structure we have a fairly great freedom for making assumptions, but still I think we ought to hesitate in assuming any connexion between the outer and inner system which would change the magnetic moment of the latter from zero to 5 magnetons when the outer electron passes from the circle corresponding to t = 2 to that for which t = 3. We have previously seen that the magnetic core of 5 magnetons, whether it consists of a rotating nucleus or a system of electrons, would store an energy which is enormously [header] 655 greater than the kinetic energy of the outer electron ; and it seems hardly possible to suppose a system with so much energy to be essentially affected by the passage of the outer electron from one stationary circle to the next ; for it must be kept in mind that in the passage of the electron from t = 2 to t = 3 the inner system should take up the whole energy involved in the production of the magnetic field of 5 magnetons. As, however, the assumption of a mutual connexion between the inner core and the outer electron seems essential for the explanation of the correction term of the Balmer formula through magnetic influences as proposed by Dr. Stanley Allen, it seems that we shall have to seek another explanation for these deviations. Christiania, Feb. 8, 1915.