The Zeeman Effect of the Hyper-Fine Structure Components of 2537 of Mercury

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familiar one of the rotating nuclei with a force between them drawing them to a definite distance apart, the force being different for each electronic quantum number. It is easy to see, since the potential V in (2) includes repulsive terms between the nuclei, that Ec(x2) must become positively infinite as any two nuclei approach each other. Thus in problem (3) the nuclei will have .apparent repulsive forces if they are brought too close together. On the other hand, as the nuclei draw far apart, in many cases the function e, also increases, giving a position of equilibrium between and possible vibrational stationary states. In other cases there would be no such increase of e, for increasing r, no finite stationary states are possible, no molecule can form and our problem becomes one of the collision of two atoms. The qualitative side of the application of our method to band spectra has been noticed by Hund ;8 our perturbation method as applied to molecules may be regarded as a mathematical formulation of his ideas on the subject of intermolecular forces. 1 Heisenberg, W., Zeitschr. Physik, 39, 499 (1926); Wailer, J., Ibid., 38, 635 (1926); UnsOld, A., Ann. Physik, 82, 355 (1927). 2 Wentzel, Zeitschr. Physik, 38, 518 (1926); Kramers, H. A., Ibid., 39, 828 (1926). 8 SchrOdinger, E., Ann. Physik, 80, 437 (1926).4 Heisenberg, W., Zeitschr. Physik, 38, 411 (1926). 5Fues, E., Zeitschr. Physik, 11, 364; 12, 1; etc.; Hartree, D. R., Proc. Camb. Phil. Soc., 21, 625 (1923), etc. 6 Burrau, O., Kgl. Danske Vid. Selskab, Mat.-fys. Med., 7, 14 (1927). 7 Kramers, H. A., Oc. cit. 8 Hund, F., Zeitschr. Physik, 40, 742 (1927).

THE ZEEMAN EFFECT OF THE HYPER-FINE STRUCTURE COMPONENTS OF X 2537 OF MERCUR Y* By WALTER A. MAcNAIR1 BUREAU OFP STANDARDS, WASHINGTON, D. C.

Communicated May 14, 1927

The hyper-fine structure of X 2537 of mercury has been shown by Professor R. W. Wood2 to consist of five lines of very nearly equal intensity. Choosing the central component as the reference line, the separations he reports may be interpreted into relative positions and expressed in milliangstroms as follows: -24, -10, 0, +11, +22. The optical analysis in the present work was carried out with a Hilger Lummer-Gehrcke plate of crystalline quartz, 4.24 mm. thick, in a manner similar to that employed earlier.3 The present observations on the Zeeman effect were made with four different sources of 2537A radiation, all of which gave mutually consistent

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results. The data obtained from over twenty exposures chosen from more than two hundred fifty show that each of the five hyper-fine structure lines has a triplet Zeeman pattern. The results of the work deal with the position and separation of each triplet and the relative intensity of the fine triplets. In zero magnetic field the positions of the lines, expressed in milliangstroms, are (taking the central one as the reference), -25.6, -10.3, 00.0, +11.6, +22.1. In a magnetic field the latter four become triplets with 3/2 the normal separation. There is no Paschen-Back effect evident up to 5800 gausses, the highest field employed, though if there is such an effect it should set in at about 1100 gausses. The parallel components of these four triplets maintain the same relative positions whatever the magnetic field strength. Several special observations were made from which it was established that these components also show no wave-length shift as a group. The behavior of the hyper-fine structure line at -25.6 is not so simple. The perpendicular components behave as the perpendicular components of a 3/2 normal triplet which starts at -25.6. The parallel component, however, increases in wave-length with increasing field strength. The following equation represents its position in various field strengths: AX= -25.6 + 0.089 V/H where A X is the position of this component measured from the parallel component of the central reference line, and H is the field strength in gausses. The estimated relative intensities of the five lines in zero field are, in order of increasing wave-length, 13, 8, 10, 10 and 9. A remarkable change takes place as the field strength is increased. In a field of 5000 gausses it is estimated that the relative intensities of the parallel components (the same holds for the perpendicular components) are 3, 6, 18, 19 and 4. The change in intensity of each component appears to be uniform with the magnetic field strength. It is very probable that the anomalous behavior of the -25.6 line will, in some way, account for the fact that the polarization of resonance radiation of mercury in zero magnetic field is only 80 per cent instead of 100 per cent as predicted by theory which assumes that the Zeeman pattern of X 2537 is a 3/2 normal triplet. This belief is supported by recent work of v. Keussler4 who obtains 100 per cent polarization when the resonance bulb is placed in a magnetic field of 7900 gausses, the lines of force being parallel to the electric vector of the polarized exciting light. The present work shows that in this field the absorption lines of the resonance bulb are at -17.7, -10.3, 00.0, +11.6, +22.1, while the emission lines of the source are at -25.6 (approximately), -10.3, 00.0, +11.6, +22.1. Con-

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sequently, all the light absorbed in the bulb is contained in the parallel components of the four longer wave-length lines, which are the ones that have 3/2 normal triplet Zeeman patterns. This condition satisfies the requirements of the theory and the results of v. Keussler are in agreement with the prediction. No doubt in the above case the fact that the intensity of the anomalous line is practically zero plays some part, but if a source giving narrower lines were used, for example, a resonance bulb instead of a water-cooled arc, 100 per cent polarization should be obtained in field strengths as low as 2000 gausses, at which field the intensity of the anomalous line is of considerable magnitude. * Published with the approval of the Director of the Bureau of Standards of the U. S. Department of Commerce. 1 NATIONAL RS3sARCH FaLLoW. 2 Wood, R. W., Phil. Mag., 50, pp. 761-774 (1925).

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MacNair, W. A., Phil. Mag., 2, pp. 613-621 (1926). v. Keussler, V., Ann. d. Physik, 82, Nr. 6, pp. 820-825 (1927).

THE DIELECTRIC CONSTANT OF ATOMIC HYDROGEN IN UNDULATORY MECHANICS By PAUL S. EPSTmIN CALIFORNIA INsTIrUTe

or

TiCmNoLoGY

Communicated April 20, 1927

1. In a recent paper J. H. Van Vleck1 used the expressions for the energy of a hydrogen atom in an electric field, derived by I. Waller2 and the writer,3 for computing the dielectric constant. The interesting method he applies is analogous to that used by J. H. Jones4 for the same purpose in Bohr's quantum theory, and is outlined in section 1 of the following paper by Evelyn F. Aylesworth.5 It appears from this last paper that, in Bohr's theory, the atomic energy has a different expression for weak and for strong fields. If the strength of field is above a certain critical value, the atoms acquire an orientation with respect to it, if it is below this value, their orientation is arbitrary and not affected by the field. The critical value is particularly high for the normal state of the atom, so that here we have the largest deviation from the behavior of the gas in strong fields. On the Qther hand, Van Vleck shows by a very convincing argument that, from the point of view of undulatory mechanics, an atom in the normal state must change its energy in weak and in strong fields according to the same law. It seemed, therefore, desirable to treat the problem of the energy change