On Two Modifications of Hydrogen

Yu. Khariton, Leningrad

Introduction

The separation of the two modifications of hydrogen was accomplished, practically simultaneously, by Bonhoeffer and Harteck in Berlin and by Eucken in Breslau. Preliminary communications by both groups of authors were printed side by side in the March issue of the German journal Naturwissenschaften for 1929.

The question of the existence of two modifications of hydrogen, however, had been posed somewhat earlier.

The distribution of intensities in the spectrum of molecular hydrogen¹ and of some other diatomic gases, on the one hand, and the behavior of the heat capacity of hydrogen at low temperatures,² on the other, could not be calculated from the standpoint of the usual quantum-mechanical conceptions. The explanation of these “anomalies” is one of the triumphs of wave mechanics.

The first attempts to explain these anomalies were made by Heisenberg³ and Hund⁴ and were then refined by Dennison. Considering the hydrogen molecule from the point of view of wave mechanics, Heisenberg comes to the conclusion that there must exist two states of hydrogen molecules. For molecules of one type, rotational

¹ R. Mecke. Phys. ZS. 25, 597, 1924.
² A. Eucken. Sitzber. Preuss. Akad. Wiss. S. 141, 1912.
³ W. Heisenberg. Z. Physik. 41, 239, 1927.
⁴ F. Hund. Z. Physik. 42, 93, 1927.

states only with odd quantum numbers, and for molecules of the other type—with even ones. We shall call the former molecules orthohydrogen, and the latter parahydrogen.

Hund tries to obtain the ratio between the numbers of molecules of the two kinds from experimental data on the dependence of the rotational heat capacity of hydrogen on temperature. For the two configurations the heat-capacity curves are different, and both differ from the experimental curve as well as from the curve corresponding to the classical rotator. Hund found that a curve close to the experimental one can be obtained if the statistical weight of parahydrogen molecules is taken to be half the statistical weight of orthohydrogen molecules. Dennison,^1 using in his calculations the more recent data of Hori^2 on the moment of inertia of the hydrogen molecule, found that the experimental data are best satisfied when the concentrations of para- and orthohydrogen are in the ratio \(1:3\).

Fig. 1

Without going into the history of the question, let us consider its present state.

The hydrogen molecule consists of two protons and two electrons. At very low temperatures most of the molecules will possess only kinetic energy, and the rotational heat capacity (the part of the heat capacity due to rotational motion) will be equal to zero. As the temperature is raised, part of the internal energy will go into rotational motion. If hydrogen molecules behaved according to classical quantum theory, then at first chiefly the first rotational level would begin to be populated, then

^1 Dennison. Proc. Roy. Soc. 115, 483, 1927.
^2 Hori. Z. Physik. 44, 834, 1927.

ON TWO MODIFICATIONS OF HYDROGEN

second, etc. The heat capacity of hydrogen as a function of temperature would in that case be expressed (i.e., on the assumption that each molecule can occupy any rotational level) by curve I in Fig. 1. Experiment, however, gives something quite different, namely curve II in the same figure.

Wave mechanics indicates to us that each molecule cannot occupy just any rotational state. Some molecules can have only even rotational quantum numbers, others only odd ones.

The characteristic function of the molecule, in the first approximation, can be expressed as the product of the characteristic functions for the nuclei and the electrons,

\[ \psi=\psi_{\mathrm{nuc}}\cdot\psi_{\mathrm{el}}, \]

where both \(\psi\) of the nuclei and \(\psi\) of the electrons must be antisymmetric. With respect to \(\psi\) of the nuclei one may write:

\[ \psi_{\mathrm{nuc}}=\psi_{\mathrm{rot}}\cdot\psi_m, \]

where \(\psi_{\mathrm{rot}}\) depends only on the rotation of the nuclei, and \(\psi_m\) on the arrangement of the nuclear moments (if such exist). The solution of Schrödinger’s equation for the case of rotation shows that \(\psi_{\mathrm{rot}}=\theta_n\), where \(\theta_n\) is the \(n\)-th spherical function corresponding to the \(n\)-th rotational quantum number. Consequently \(\psi_{\mathrm{rot}}\) is a symmetric function for even \(n\) and an antisymmetric one for odd \(n\). Accordingly \(\psi_m\) must be antisymmetric or symmetric, i.e.

\[ \psi_{\mathrm{nuc}}^{-}=\psi_{\mathrm{rot}}^{+}\cdot\psi_m^{-} \]

or

\[ \psi_{\mathrm{nuc}}^{-}=\psi_{\mathrm{rot}}^{-}\cdot\psi_m^{+} \]

Upon permutation of the moments the following arrangements relative to some axis may occur

\[ \uparrow\uparrow \qquad \downarrow\downarrow \qquad \uparrow\downarrow \qquad \downarrow\uparrow \]

One of the last two cases must be rejected, since we cannot distinguish the individuality of each of the two nuclei; thus in fact we have the following combinations

\[ \uparrow\uparrow \qquad \downarrow\downarrow \qquad \uparrow\downarrow \]

Obviously, the first two combinations can give only symmetric \(\psi_m\), while the last can give both \(\psi_m\) and \(\psi_m^{-}\). In other words, we can realize \(\psi_m^{+}\) in three ways and \(\psi_m^{-}\) in only one way. Therefore \(\psi_{rot}^{-}\), which can combine with the three \(\psi_m^{+}\), will have a statistical weight three times greater than \(\psi_{rot}^{+}\). Since the displacement of energy levels caused by different configurations of the moments is quite negligible, as a result we obtain only a tripled intensity of the lines corresponding to transitions between odd \(n\), as compared with the lines obtained from transitions between even \(n\). Such a distribution of intensities in the hydrogen spectrum was noted by Mecke1 in 1925.

In the case where the nuclei of identical atoms making up the molecule have no magnetic moment, we shall have an even more characteristic phenomenon. Since here it is already impossible to obtain an antisymmetric \(\psi_m\), the molecules will exist only in states with antisymmetric \(\psi_{rot}\). Therefore, for example, in the spectrum of \(\mathrm{He}_2\) all lines corresponding to transitions between even \(n\) are simply absent.

If, however, the nuclei have a large magnetic moment, then the ratio of statistical weights

\[ \frac{g(\psi_{rot}^{-})}{g(\psi_{rot}^{+})} \]

will no longer be \(3:1\), but another. For \(\mathrm{N}_2\), apparently, \(2:1\). For \(\mathrm{I}_2\) and \(\mathrm{Na}_2\)—\(1:1\).

Molecules for which \(n\) is even and \(\psi_{rot}\) is symmetric are called parahydrogen molecules; those for which \(n\) is odd are called orthohydrogen molecules. Under ordinary conditions both configurations are stable with respect to one another (like parhelium and orthohelium), and hydrogen thus represents a mixture of para- and orthohydrogen in the proportion \(1:3\).

The probability of a spontaneous transition from one state to another was approximately calculated by Wigner2 (his calculations are given in the paper by Bonhoeffer and Harteck).

On Two Modifications of Hydrogen

Its calculation gives, for the transition probability, \(10^{-10}\ \mathrm{sec}^{-1}\), which corresponds to a half-life of about 300 years.

Let us now return to the question of the heat capacity of hydrogen.

Because para- and orthohydrogen have different \(n\), their rotational heat capacities differ from one another. Curve III (Fig. 1) represents the calculated temperature course of the heat capacity of parahydrogen; curve IV, likewise, that for orthohydrogen. If we now construct the heat-capacity curve of hydrogen according to the formula

\[ C_{\mathrm{H}_2}=\frac{1}{4}C_{para}+\frac{3}{4}C_{orto}, \]

i.e., assuming that the ratio \(1:3\) is preserved at all temperatures,^1 then the resulting curve will pass exactly through the points obtained from the measurements of Eucken et al., i.e., along curve II.

The ratio \(1:3\) for the amounts of parahydrogen and orthohydrogen, however, will be an equilibrium one only for relatively high temperatures, when the heat capacities of the two modifications differ little from one another. For low temperatures, where the heat capacities and entropies are very different, the equilibrium will shift toward parahydrogen. Eucken gives the following (calculated) table of equilibrium concentrations:

It may therefore be expected that at low temperatures hydrogen will, with time, become enriched in parahydrogen.

^1 K. F. Bonhoeffer und P. Hartek. Z. Phys. Chem. Abt. B 4, S. 126, 1929.

Preparation and Detection of Parahydrogen

The works of Bonhoeffer and Harteck¹ and the work of Eucken² were undertaken with the aim of detecting such a change in the composition of hydrogen. In both works, the change with time of the heat capacity of hydrogen kept at low temperature was measured. Eucken measured the heat capacity of hydrogen directly. Bonhoeffer and Harteck measured the thermal conductivity of hydrogen, which is proportional to the heat capacity.

The measurement of thermal conductivity was carried out as follows. In a narrow glass tube a Wollaston wire of thickness \(0.01\) mm was stretched. The ends of the wire were soldered to copper leads of thickness \(0.3\) mm. For the measurement the vessel was immersed in a bath of liquid hydrogen. It should be noted that, in this case, all difficulties that might be caused by contaminants and admixtures in the hydrogen fall away, since everything except hydrogen simply freezes out. The measuring Wollaston wire, connected in a Wheatstone bridge, is heated by a 12-volt battery, whose voltage is controlled by a standard cell. In the tube a pressure of about \(40\) mm Hg is maintained, at which convection no longer has any effect. Depending on the thermal conductivity of the gas filling the tube, the Wollaston wire has one temperature or another and consequently also a resistance, which is measured by means of the Wheatstone bridge. At the temperature of liquid hydrogen the resistance of the wire was \(32.21\,\Omega\). When voltage was applied to the bridge, the resistance (in an atmosphere of ordinary hydrogen) rose to \(111.85\,\Omega\), which corresponds to \(203.9^\circ\) abs.

In the first experiments of Bonhoeffer and Harteck, the measuring vessel filled with hydrogen was immersed in liquid air, in which it was kept for several weeks. After four weeks’ stay at the temperature of liquid air, the thermal conductivity of the hydrogen remained—in the pre-

¹ Bonhoeffer und Harteck, l. c. 113.
² A. Eucken und K. Klusius. Ztschr. Phys. Chem. (B) 4, 142, 1929.

within the limits of experimental error—constant. That is, there was no shift in the concentrations of para- and orthohydrogen toward equilibrium.

If, however, the hydrogen is under high pressure, the situation is different. In a brass cylinder filled at room temperature to a pressure of 350 atm and cooled with liquid air, a noticeable change in concentration is already observed within twenty-four hours. In the course of two days the concentration of parahydrogen rises from 25 to 35%. In these experiments one might have suspected a catalytic action of the metal walls and therefore considered the results not entirely reliable. But experiments with liquid hydrogen in glass vessels gave approximately the same rate of conversion. Since experiments at low pressure showed that glass walls do not catalyze the conversion, it may be concluded that brass walls also do not appreciably affect the reaction rate.

Rapid attainment of equilibrium is effected by means of catalysts. For example, practically pure (99.7%) parahydrogen is obtained in the following way. A quartz vessel of about 50 cm³ volume is filled with coconut charcoal and heated in vacuum to red heat for a quarter of an hour (until gas evolution ceases). After cooling, the charcoal is saturated with hydrogen at a pressure of one atmosphere, first at room temperature, then at the temperature of liquid air, and finally at the temperature of liquid hydrogen. As a result, about 9 l of hydrogen is absorbed. If the gas absorbed in the charcoal is then pumped off at the temperature of liquid hydrogen, practically pure parahydrogen is evolved.

Owing to the better thermal conductivity of parahydrogen in comparison with orthohydrogen, the temperature of the filament in the measuring instrument, when it is filled with parahydrogen, must be lower, and accordingly its resistance is less than in the case of normal hydrogen. The table below shows the resistance of the filament in a vessel filled with gas pumped out of charcoal after various intervals of time following adsorption.

The course of the change in resistance with time shows that the conversion of orthohydrogen into parahydrogen on the catalyst does not occur instantaneously, but is completed in approximately 20 minutes.

A completely analogous result was obtained by Eucken by another method. Eucken and Hiller, and also Clusius, directly measured the heat capacity of hydrogen. In one series of experiments, hydrogen under a pressure of about 100 atm. was kept for several days in a vacuum calorimeter. The calorimeter consisted of a solid-drawn steel cylinder \(A\) (see Fig. 2) with welded-on spherical caps, placed in a vessel \(O\), which could be filled with helium for heat exchange with the surrounding cooling bath, or else evacuated. The calorimeter was filled with hydrogen by means of a neusilber capillary. A substantial improvement over Eucken’s old calorimeter was the introduction of a cylindrical brass jacket \(B\), the upper part of which, in order to increase the heat capacity, was filled with lead \(C\). By means of electrical heating the jacket was maintained at the same temperature as cylinder \(A\). The absence of a temperature difference between \(A\) and \(B\) was monitored by a copper-constantan thermocouple. The equality of the temperatures of \(A\) and \(B\) excluded the possibility of exchange of radiant energy between \(A\) and the surrounding space. To heat the calorimeter itself, i.e. \(A\), a constantan winding with a resistance of \(580\ \Omega\) was placed on it. By passing a certain

Fig. 2.

of the current for a definite interval of time the calorimeter is supplied with an amount of energy that can easily be calculated. The heating current was in all cases 40.73 milliamperes.

The rise in temperature was measured from the resistance of a platinum wire 0.05 mm in diameter wound on the same cylinder; its resistance at \(0^\circ\mathrm{C}\) was about \(110\,\Omega\). Both windings were wound on thin tissue paper and fastened with turpentine varnish.

Under the experimental conditions, the total heat capacity of the hydrogen injected into the cylinder amounted to about 25% of the heat capacity of the cylinder; the rotational heat capacity \(C_{rot}\) was consequently an even smaller part. Accordingly, the measurement of the heat capacity had to be made with very great accuracy. In fact, the deviations from the mean value in measuring the heat capacity of the empty cylinder did not exceed 0.2%.

The duration of the passage of the current was measured by means of a stopwatch with a reading accuracy of up to \(1/50\) sec. Usually the heating lasted about a minute.

The heat capacity of the hydrogen filling the calorimeter under a pressure of 100–200 atm. was measured immediately after filling, and then after several days. The table given provides an idea of the changes taking place. (See Table III, p. 104.)

As has already been indicated, the conversion of orthohydrogen into parahydrogen at the temperature of liquid hydrogen proceeds very rapidly upon adsorption on charcoal. Bonhoeffer and Harteck also investigated the action of other catalysts. The investigation was carried out as follows. A U-shaped tube was filled with the catalyst and maintained at a definite temperature. Hydrogen was passed through it at a rate of \(200\ \mathrm{cm^3/min}\), and the shift of the concentrations toward equilibrium was studied.

At the temperature of liquid hydrogen, ordinary hydrogen (25% parahydrogen) was passed through the tube. It turned out that filling the U-shaped tube with palladium or platinum black produced no shift of the concentrations at all.

When the tube was filled with charcoal, the para-hydrogen content at the outlet from the tube increased to 27.5%.

TABLE III

Placed in the calorimeter: 0.24118 mole of H₂

At room temperature hydrogen with 50% para-hydrogen was introduced into the tube (in this case the equilibrium state corresponds to 25% para-hydrogen). The following table gives the para-hydrogen content after passage through a tube filled with various catalysts.

At room temperature the action of platinum and palladium black already significantly exceeds the action of charcoal. Probably the mechanism of their effect on hydrogen is of some kind

of a different character than in the case of charcoal, which is active at low temperatures.

At room temperature the character of the surface, as is evident from Table IV, does not play a particularly large role. The role of the surface becomes significant at higher temperatures. Thus, for example, the conversion of parahydrogen into orthohydrogen requires a time on the order of seconds if the hydrogen flows through a quartz or glazed porcelain tube at \(800—900^\circ\) C. In an unglazed porcelain tube the conversion proceeds at the same rate at a temperature of \(300—400^\circ\) C. As yet no definite assumptions can be made about the mechanism of the conversion on the surface.

Heat Capacity of Liquid and Solid Parahydrogen, Its Vapor Elasticity, and the Heats of Fusion and Evaporation

The heat capacity of liquid and solid parahydrogen was measured by K. Clusius and K. Hiller.\(^1\) Pure parahydrogen was condensed into a small (\(10\ \mathrm{cm}^3\)) steel bulb placed in an atmosphere of helium cooled to \(10^\circ\) abs. by means of hydrogen evaporating at low pressure. After condensation was complete the helium was removed and the bulb served as a vacuum calorimeter,\(^2\) for which purpose it was provided with a heating and measuring winding.

The results of measuring the heat capacity of solid and liquid parahydrogen coincided, within the accuracy of the measurements, with the corresponding data for ordinary hydrogen.\(^3\) The same applies to the heat of fusion (which, of course, can be measured on the same apparatus). For it Clusius and Hiller obtained (for parahydrogen) \(28.03\ \mathrm{cal}/\mathrm{mol}\). Simon and Lange, working with ordinary hydrogen, obtained \(28.0 \pm 0.12\ \mathrm{cal}/\mathrm{mol}\).

\(^1\) K. Klusius und K. Hiller. Ztschr. Phys. Chem. 4, 158, 1929. 41, 1929.

\(^2\) For a description of an analogous apparatus see Ztschr. Phys. Chem. 3.

\(^3\) A. Fucken. Verhandlg. Deutsch Phys. Ges. 18, 4, 1916. F. Simon und F. Lange. Z. Physik 15, 312, 1923.

The melting temperature of parahydrogen was measured with the aid of the same apparatus and proved to be equal to 13.88° abs. (for ordinary hydrogen, 13.95° abs. Bonhoeffer and Harteck,¹ determining this value by an indirect method, obtained 13.83° abs.).

Bonhoeffer and Harteck also traced the course of the pressure saturating the vapor space of parahydrogen. The apparatus they used made it possible to measure simultaneously both the difference between the vapor pressures of para- and ordinary hydrogen and the absolute value for one of the substances. The apparatus consisted (see Fig. 3) of vessels \(A\) and \(A'\), which were cooled to the temperature of liquid air and were filled respectively with parahydrogen and ordinary hydrogen. The vessels were connected by tubes with a copper block \(B\), immersed in vessel \(G\) with liquid hydrogen. Then the liquid air was removed from \(A\) and \(A'\); the excess hydrogen and parahydrogen then condensed on the copper block, and in the vessels there was established the pressure corresponding to the temperature of the hydrogen in Dewar \(G\). Vessels \(A\) and \(A'\) then communicated with the differential manometer \(C\) and the absolute manometer \(D\).

Fig. 3.

When the hydrogen in \(G\) boiled under normal pressure (\(T = 20.39^\circ\) abs.), the difference of levels in the differential manometer was 25 mm. Final processing of the observational results gave the following values of the vapor pressure

¹ A. Euken, l. c., p. 135.

saturating the vapor space at \(20.39^\circ\) abs.: \(787 \pm 1\) mm for parahydrogen and \(751 \pm 1\) for orthohydrogen.

At the triple points, the pressures of ordinary hydrogen and parahydrogen were respectively: \(53.9 \pm 0.1\) mm and \(53.1 \pm 0.1\) mm. The measurement was carried out by means of the very simple apparatus shown in Fig. 4. The whole apparatus is immersed in liquid hydrogen, and tube \(D\) communicates with a reservoir containing ordinary hydrogen or parahydrogen. When the pressure is raised above atmospheric, the parahydrogen in bulb \(C\) is compressed and flows into bulb \(B\), surrounded by the evacuated space \(A\). Then the hydrogen was pumped out of \(B\) for a short time, as a result of which it froze there and, finally, the tube was connected to a manometer. The solid hydrogen in \(B\) gradually began to warm, and the pressure rose correspondingly. This continued until the triple point was reached, where the pressure remained constant during the time of melting of the hydrogen—approximately \(1/4\) hour—and could be carefully measured. The lower pressure of parahydrogen at the triple point indicates that its temperature is lower than that for ordinary hydrogen, since at equal temperatures parahydrogen has a greater vapor elasticity, near the melting temperature greater by \(2.9\) mm. From this Bonhoeffer and Harteck obtained \(13.83^\circ\) abs. for the melting temperature of parahydrogen.

Fig. 4.

For orthohydrogen, assuming a linear dependence of melting on the concentrations of the components, one obtains:

\[ P_{13.95\text{ abs.}} = 52.9\ \text{mm} \qquad P_{13.99\text{ abs.}} = 54.2\ \text{mm}\quad(\text{triple point}). \]

The calculation shows that, if the difference between the vapor pressures of para- and orthohydrogen is due to different heats of evaporation, then the heat of evaporation of parahydrogen must be approximately \(0.65\%\) less than that of orthohydrogen.

In general, all the results reduce to the conclusion that the heats of evaporation and melting of para- and orthohydrogen differ by no more than \(1\%\). And if this is so, then one may say that in the solid state the molecules of para- and orthohydrogen differ—

are energetically the same as in the gaseous state. At temperatures below \(20^\circ\) abs., all orthohydrogen molecules may already be regarded as possessing the minimum possible amount of rotational energy for them—one quantum. The parahydrogen molecules, for which the first rotational level is 2 (after 0), are in general already practically devoid of rotational energy. (At \(20^\circ\) abs., \(T = 380\) cal/mol, just of the same order as the energy of the first rotational level—336 cal/mol.) Thus also in solid hydrogen the orthohydrogen molecules are richer in energy by one quantum than the parahydrogen molecules, i.e. they rotate both in the liquid and while situated in the crystal lattice.

In solid and liquid parahydrogen, consisting of non-rotating molecules, the van der Waals forces ought, as it were, to manifest themselves more strongly than in orthohydrogen. Correspondingly, the mutual energy, and hence also the heat of vaporization of parahydrogen, should exceed the same quantities for orthohydrogen. From experiment, however, one must draw the opposite conclusions, since the greater elasticity of vapor over parahydrogen indicates a smaller heat of vaporization. This contradiction remains unexplained for the present.

It is interesting to note that the energy of the first rotational state in which parahydrogen molecules are found at low temperatures, namely 336 cal/mol, is approximately one and a half times greater than the heat of vaporization of hydrogen. Therefore ordinary liquid hydrogen, in which orthohydrogen gradually transforms into parahydrogen, will always evaporate somewhat faster than liquid orthohydrogen.

CHEMICAL AND SPECTRAL PROPERTIES OF PARA- AND ORTHOHYDROGEN

The chemical activities of both modifications of hydrogen, within the limits of error of the experiments so far carried out, have proved to be identical, although the experimental data here are very scanty. Goldmann1 determined the limiting (na-

...the smallest and the largest) concentration of hydrogen in air at which propagation of the explosion still occurs after the mixture is ignited by a spark. No difference between parahydrogen and ordinary hydrogen was observed.

During the experiments Goldman discovered the following fact. In cases where the concentrations of the components of the mixture were such that the combustion of hydrogen did not proceed to completion, the hydrogen remaining after the passage of the flame was always ordinary hydrogen, even if the mixture had been composed of pure parahydrogen and air.

The temperature of the flame under the experimental conditions was of the order of \(900^\circ\text{C}\). The passage of the flame through each point of space lasted approximately \(10^{-4}\) sec, and this time proved sufficient for the complete attainment of the ordinary ratio \(1:3\). In the experiments of Bonhoeffer and Harteck, at \(900^\circ\text{C}\), about one second was required for this purpose. Apparently, the presence of energy-rich molecules in the flame considerably facilitates the process of the transition of parahydrogen into orthohydrogen.

Bonhoeffer and Harteck1 obtained the spectrum of parahydrogen when exciting it in a discharge tube. Since the discharge rapidly converts parahydrogen into normal hydrogen, the discharge tube had to be supplied with flowing parahydrogen. Under these conditions it was possible to obtain a spectrum in which precisely those lines were strongly expressed which, in the ordinary spectrum of hydrogen, have an intensity three times smaller than the others. All the bright lines of the spectrum of ordinary hydrogen were greatly weakened, and in the case of a weak current in the discharge tube they disappeared altogether.

In conclusion, let us touch on analogous phenomena in other substances. According to the theoretical considerations set forth at the beginning of the article, different modifications of one and the same molecule will exist in those cases where both nuclei are identical, for example, in the molecules \(C_2\), \(Na_2\), \(F_2\), \(Cl_2\), \(Br_2\). However, for heavier molecules the separation of modifications will be considerably more difficult. Owing to the greater—

of the moment of inertia the energy ladder of the rotational levels will have smaller steps, and the curves of the rotational heat capacity of the two modifications will differ appreciably only at very low temperatures. Therefore the equilibrium will likewise shift appreciably only at very low temperatures (of the order of 3° absolute). These are temperatures attainable only with the aid of liquid helium. Therefore one should rather hope for separation of the modifications by fractional distillation.

Although up to now the existence of two modifications has been observed experimentally only for hydrogen, the fundamental significance of the experiments of Bonhoeffer and Harteck, as well as of Eucken and his collaborators, is exceptionally great. First, the hypothesis of the existence of a magnetic moment of the proton is seriously confirmed; second, all the facts described once again confirm the correctness and power of the methods of wave mechanics.

1. L. c. S. 138. ↩↩↩

2. Dennison, l. c. ↩