maximum temperature to be expected, on certain assumptions, for layers of different thicknesses. The following factors, which affect the temperature gradient near the surface, are considered :

(1) Variation of thermal conductivity with temperature.

(2) Effect of underground water. Some results of experiments on convection in vertical water-columns show that we might expect large effects with water in fissures of moderate size, but only very slight effects with pores. (3) Secular variation of climate.

(4) Heat evolved during volcanic eruptions.

As it is shown that all these effects conspire to reduce the temperature gradient, it is contended that the smallness of the latter is no evidence against the uniform distribution of radioactivity throughout the continental layer.

It is suggested that owing to tidal stresses and consequent crustal motions the continents towards the end of revolutionary periods become "stranded" on solidified magma, and that during inter-revolutionary periods the heat evolved in their lower layers is largely used in re-melting this magma.

Royal Dublin Society

June 8, 1923.

XLII. Grouping of the Lines of the Secondary Spectrum of Hydrogen. By K. BASU *.

TH

HE problem of the secondary spectrum of hydrogen continues to be as interesting as ever, as can be easily seen from the large number of experimental and theoretical papers appearing on the subject. It seems now to be fairly well established that the secondary spectrum is due to the molecule of hydrogen. But we are still in the dark about the mechanism underlying the combination of two Bohrhydrogen atoms to form the molecule and the genesis of radiation in the process. In considering the process of combination of two atoms which, according to Langmuir, is attended with the evolution of 82,000 calories of heat per gm.-molecule, it is often assumed that a molecular spectrum is emitted, the limiting frequency of which is given by the Bohr relation

hy W (heat evolved).

* Communicated by Prof. Megh Nad Saha. Phil. Mag. S. 6. Vol. 46. No. 273. Sept. 1923.

2 E

The assumption is based upon the analogy of the origin of the atomic spectrum. We know that when one electron combines with an ionized atom, the atomic spectrum is produced. If W is the heat of ionization, the limiting frequency of the atomic spectrum is given by the relation

hy W (heat of ionization).

But a little consideration will show that this law cannot hold in the case of molecular dissociation. For then the limiting frequency of the molecular spectrum of hydrogen would lie at x=3600 A.U. But the fact that ordinary H-gas is quite transparent to radiation of this wave-length shows that Bohr's rule cannot be applied to any case of molecular dissociation. The secondary spectrum extends to about λ=3300, which is also against Bohr's rule, provided this spectrum is regarded as the molecular spectrum.

It is also evident that in view of the enormous number of lines in this spectrum, any attempt at grouping will meet with a certain amount of success, which, after all, may turn out to be quite fortuitous.

The laws are expected to be more complicated than in the case of line spectra, since the distance between the nuclei must, as a matter of course, occur in the formula. An attempt was made to see if any of the lines may be regarded as due to H, i. e. two hydrogen nuclei at a definite distance I em. from each other with an electron revolving about them. The case has been already treated by F. Tank (Ann. d. Phys. Bd. lix.) and L. Silberstein, because the dynamics can be handled by the Hamilton-Jacobian method, but it has not been applied to the case of the secondary spectrum. Using Bohr's rule, the frequency comes out in the form

v = 4N

[

_ (n + ng + Any])? — (nj' + ng' + Ang')2.

where NRydberg number, n, n' are azimuthal quantum numbers, ng, ng' are radial quantum numbers, and

Ang = 16mm2e+ / h*ng3.

Thus Ang involves the distance between the nuclei. The value of I can only be guessed. Let us assume l=1 x 10-8 cm., which is slightly less than 2a, a radius of the Bohr H-atom.

Let us classify the lines under the following heads :

where A1 =21191 16, obtained by putting n1 = 0 in the second term of the right-hand member of (i.); in the same way (A2, As, A4, Box)=(22254-17, 25720-5, 26680.6, 21191-91), when we put respectively n=2, 1, 0, 0 in the corresponding second terms of the right-hand members of (ii.), (iii.), (iv.) and (v.).

But the above coincidences, though interesting, can hardly be claimed to have solved the problem of the molecular spectrum, because the distance between the nuclei has been taken

arbitrarily. If some other value were assumed, we should probably get some other coincidences.

In view of the fact that we are yet far removed from the satisfactory solution of the coupling of two Bohr H-atoms to form an H-molecule, which is by far the simplest problem of this class we can think of, is it not a bit too premature to attempt the general solution of the problems of chemical combination of more complicated atoms like Na and Cl, as has been done in the theories of Lewis and Langmuir? To the same category must belong the large number of radiation theories of monomolecular reaction, which are all based upon the Bohr rule hy-heat of dissociation.

University College of Science and Technology,
Calcutta, India.

XLIII. The Absorption of Light by Sodium Vapour. By F. H. NEWMAN, D.Sc., A.R.C.S., Professor of Physics, University College, Exeter *.

THE

[Plate VIII.]

1. INTRODUCTION.

HE normal operation of an arc below ionization results in the excitation of the first line of the principal series, providing that the energy of the electrons is equal to, or greater than, the resonance potential. As the accelerating potential in the arc is increased, the intensity of this line increases, approximately proportional to the total number of electrons, until the ionization potential is reached. At this point there should be, according to the Bohr theory of the atom, a pronounced decrease in the intensity of the line, and this decrease takes place at the voltage at which the complete line spectrum is produced. The line 15 S-2p is the result of inelastic collision with electrons having energy equal to the resonance potential, but as this voltage is exceeded, electrons which at a slightly lower value would give rise to this line, now produce the complete spectrum. Any line of the series 15 S-mp, where m is greater than 2, is necessarily excited at the sacrifice of the line 1.5 S-2p. After a certain voltage has been reached, however, the intensity of any line per unit number of electrons present per c.c. attains a saturation value, in agreement with the quantum theory, for the number of quanta radiated is proportional to the number of

• Communicated by the Author.

collisions, and hence, approximately, to the number of electrons present.

In a previous communication by the author it has been shown that under certain physical conditions in the sodium vapour arc, the D lines of sodium are relatively much brighter than the lines of the subordinate series, although of course these latter lines are always much fainter than the D lines. In this work the applied potential difference was so large that the saturation value of the intensity of any line must have been attained, and the effect was explained by the self-reversal of the subordinate series lines. The atoms of sodium vapour in this case must be in an abnormal state, by which is meant that the valency electron, instead of being in the 1.5 S stable orbit, must be displaced to the first p ring. This condition can be brought about by an electrical stimulus, the density of the electrons being very great. Then the energy necessary for the displacement of the electron to the first p ring may be obtained either by direct impact with electrons possessing the requisite resonance potential, or it may be absorbed as radiation emitted by neighbouring atoms in which the electron is temporarily in the first p ring. At high vapour-pressure and considerable current density, it is probable that most of the energy in the abnormal atom is derived from the second of these sources. Under ordinary conditions nearly all the atoms of a vapour exist in the normal state, and the value of the energy is a minimum. Light corresponding to a given line in the spectrum will be absorbed when the atoms pass from this state to a state in which the electron revolves in one of the p rings. Unexcited sodium vapour shows, therefore, absorption corresponding to the principal series lines only. If, however, the atoms can be brought to the condition that a considerable proportion have the electron in the 2p ring, then the radiation absorbed when white light is passed through the vapour will be the lines which in the emission spectrum arise when the electron is displaced from the 2p ring to outer stationary orbits, i. e. the subordinate series lines.

It appears probable that this abnormal state of the vapour can be produced not only by electrical stimulation, but also by high temperature, for King † observed absorption in the subordinate series lines of the alkalies with his electric furnace. Using a special plug at the centre of the tube, by which temperatures above 3200° C. could be obtained, and excluding oxygen, these absorption lines in the subordinate * Phil. Mag. vol. xlvi. (1923). † Phys. Rev. vol. xviii. (1921).