The Revival of Prout’s Hypothesis

E. V. Shpolsky.

§ 1. In 1815, W. Prout proposed his attractive hypothesis that all elements are polymers of a single primary element—hydrogen. It is known that, under the pressure of very convincing facts, this hypothesis was soon abandoned. The classical works of J. B. Stas and Marignac showed that atomic weights, generally speaking, are not whole numbers, as follows from Prout’s hypothesis. Nevertheless, throughout the entire nineteenth century and the beginning of the twentieth, the researcher’s thought returned again and again to this fascinating hypothesis. Thus, Marignac already believed that Prout’s hypothesis is a kind of limiting law, like the Boyle–Mariotte and Gay-Lussac laws; he thought that perhaps there exists a principal cause by virtue of which simple relations should be observed among atomic weights, and secondary causes introducing small distortions into these simple relations. A number of other explanations were proposed by Lothar Meyer, Nägeli, Lundol and others.¹)

And indeed, if we consider the periodic system of the elements, it involuntarily strikes the eye that the deviations of atomic weights from whole numbers (especially at the beginning of the table) are very small. J. R. Rydberg²) and R. J. Strutt³) showed that, from the point of view of probability theory, there is very little chance that this fact is a matter of mere accident. In particular, Strutt calculated, for 9 elements (Br, C, Cl, H, N, O, K, Na, S), the probability that the small deviations of their atomic weights from whole numbers are a simple accident. It turned out that this probability is only \(1:1000\). Similar considerations prompted Rydberg to represent atomic weights in the form \(N + D\) (where \(N\) is a whole number, \(D\) a small fraction) and to seek regularities both in \(N\) and in \(D\).

The works of the very latest years have revived Prout’s idea with new force. In fact, we know well that radioactive transformations are associated with the emission of \(\alpha\)-particles, i.e. helium nuclei. Hence helium is a constituent part of the nucleus of radioactive elements. The works

¹) For the historical fortunes of Prout’s hypothesis, see C. Schmidt, Das periodische System der Chemischen Elemente. Leipzig, 1917, pp. 1–5; see also R. Swinne, Die Naturwissenschaften, 8, p. 727 (1920).

²) J. R. Rydberg, Bihang Sv. Vet.-Akad. Handlingar, Stockholm, 11, No. 13 (1886); cf. also R. Swinne, l. c.

³) See C. Schmidt, l. c., p. 3.

Rutherford1 and his pupils have shown, finally, that the same role must be played also by hydrogen, and moreover not only among radioactive elements but also among the light non-radioactive elements.

§ 2. Rydberg2 had already drawn attention to the fact that the integral part of the atomic weight can most often be represented by two formulas

$$ 4n \ \text{and}\ 4n+3 \quad (\text{or, what is the same, } 4n-1), $$

where \(n\) is an integer. In this case, as a rule, atomic weights of the first formula correspond to an even ordinal number, and atomic weights of the second formula to an odd one.

One may go still further and discern at the beginning of the periodic system something entirely analogous to the displacement rules established by Fajans and Soddy for radioactive elements3. Indeed, let us turn to Tables 1 and 2. On examining them, it is not difficult to find

Table 1.

Table 2.

that a change of the ordinal number by two units and the associated transition through one group of the periodic system leads to a change of the atomic weight by four units, i.e. here there occurs exactly the same thing as in radioactive \(\alpha\)-transformations;

when an $\alpha$-particle is ejected from the nucleus of a radioactive element, reducing the charge of the nucleus (= the ordinal number) by 2 units and the atomic weight by 4 units (the only exception is argon, marked with an asterisk). From this there naturally arises the hypothesis that helium is one of the principal components in the structure of the nuclei of elements in general1.

Thus a whole series of facts speaks in favor of returning to Prout’s hypothesis, which, from the modern point of view, should be formulated as follows: the atomic nuclei of all elements are built from nuclei of hydrogen, helium, and electrons.

The nucleus of helium must be regarded as a very important secondary unit in the structure of atoms; but it itself is built in a complex manner, and it is most natural to suppose that it consists of four hydrogen nuclei and two electrons2.

§ 3. What, however, are those “secondary causes” which determine the deviations of atomic weights from whole numbers?

One such cause has recently been pointed out very frequently by various investigators3. This is the relativistic energy of matter. It is known that every mass is equivalent to an enormous supply of “material” energy and, conversely, energy possesses an inertial mass. It may be considered, for example, that the decrease in mass due to the expenditure of energy liberated in radioactive decay, for one gram-atom of radium (225 gr.), amounts to $1.41 \cdot 10^{-2}$ gr. per hour, or $1.2 \cdot 10^{-3}$ gr. per year4. If we imagine that the formation of complex atoms, in the form of stable combinations of the primary structural units, was accompanied by a colossal “thermochemical” effect, then it should be expected a priori that the resulting atomic weight will not be exactly equal to the sum of the atomic weights of its components. Let us calculate, for example, what mass is equivalent to the kinetic energy of $\alpha$-particles $He^{++}$. The energy $E$ equivalent to the mass $m$ is expressed by $E = mc^2$, where $c$ is the velocity of light, and

\[ m = \frac{E}{c^2} \]

The kinetic energy of the $\alpha$-particle is

\[ E = \frac{1}{2} m_{He} v^2 = 2 m_H v^2 \]

The corresponding change in mass will be

\[ \Delta m=\frac{E}{c^{2}}=2m_H\left(\frac{v}{c}\right)^2 \]

or, putting \(m_H=1,\ v=2\cdot 10^9\), we obtain

\[ \Delta m=2\left(\frac{2}{30}\right)^2=0.01^{1}). \]

Thus it is clear that this cause can explain to us only small deviations of atomic weights from whole numbers. To explain such considerable deviations as in chlorine (35.45) or in magnesium (24.32), one must seek other causes.

1. Here an analogy with phenomena from the field of radioactivity gives us substantial help. The study of radioactivity has shown that the whole variety of elements is far from being exhausted by the 90–100 types that are listed in the usual tables of the periodic system. It turned out that there exists a very large number of elements which may differ in atomic weights by several units (up to 8), and which nevertheless are completely indistinguishable by the ordinary methods of chemical analysis. These are the elements isotopes. Without dwelling in detail on the phenomena of isotopy, we shall cite only a very curious table of Fajans’s2. A cursory glance at this table reveals, in separate places, whole clusters of elements. These are, in Fajans’s terminology, pleiads of isotopic elements. The chemical type of each pleiad is determined either by a nonradioactive element, or by the most stable radioactive element belonging to it.

The study of the final products of radioactive series has shown that the final products of the uranium-radium family (RaG) and of thorium (ThD) belong to the lead pleiad. The atomic weight of RaG \(=206\), the atomic weight of ThD \(=203\), and, finally, the atomic weight of ordinary lead \(=207.2\). All these three elements must be indistinguishable in chemical properties; all of them, in chemical analysis, we must take to be lead.

Thus one should expect that if we determine the atomic weights of lead obtained from pure uranium ores and from pure thorium ores, then numbers should result which differ from one another and from the atomic weight of ordinary lead, i.e. numbers close to 206 and 208. And indeed, it turned out that for the purest specimens of uranium lead the atomic weight is, in the best case, 206.05, in the worst—206.12; for thorium lead (from Norwegian thorite)—207.90. Meanwhile the atomic weight of lead isolated from Ceylon thorianite

Table 3.

Greek letters before the symbol of an element indicate the character of the transformation ($\alpha$- or $\beta$-transformation). In an $\alpha$-transformation the element is shifted by one group to the corresponding lower one; in a $\beta$-transformation, to the next higher one (Fajans’s and Soddy’s displacement rules). The symbol $\alpha\alpha$ before $U_{II}$ indicates the double character of the transformation of this element, which gives, besides $Io$ with a long lifetime, also the rapidly disintegrating $UY$ (both are placed in one row of group IV); $Pa$ is the symbol of the element protactinium, newly discovered by O. Hahn and L. Meitner, in all probability serving as the connecting link between the uranium and actinium families; $Z$ is a new element of the uranium family. The atomic weights of $UY$, $Pa$, and the members of the actinium series are hypothetical.

(68.9% thorium and 11.0% uranium), agrees exactly with the atomic weight of ordinary lead (207.2)¹). Hence there arises the entirely natural supposition that ordinary lead is, in essence, a mixture of uranium and thorium lead. But then one may take a further step and ask whether some of the elements of non-radioactive origin are not likewise mixtures of isotopes. Such a hypothesis would resolve the contradiction between Prout’s hypothesis and experiment. For, indeed, if an element which appears to us to be perfectly homogeneous is in reality a mixture of two or more isotopes, then the atomic weight determined by the usual chemical methods is a certain mean value. And if the atomic weights of these isotopes themselves are expressed exactly by whole numbers or are very close to them, then the mean atomic weight may differ from a whole number by any amount.

Aston’s work, to which the whole remaining part of our article is devoted, brilliantly confirmed this hypothesis and at the same time showed that isotopy is not a peculiarity belonging only to radioactive elements, but that in the periodic system it is a universal phenomenon.

§ 5. The first results in this direction were obtained by J. J. Thomson. Studying, by means of his method of electromagnetic analysis of canal rays, the gas obtained as a residue from the evaporation of liquid air, Thomson found on one of the photographs, besides parabolas corresponding to the known noble gases—helium, argon, and neon—also a parabola corresponding to a gas with atomic weight 22²). There is no element with such an atomic weight in the periodic system. Meanwhile the supposition that this parabola belongs to the compound NeH₂ is excluded, since it turned out that in the same mixture there occur particles with mass 22 and with two charges, which never happens with molecules³).

Since, in further experiments, this parabola appeared only when neon was taken and was not visible on hundreds of plates where neon was certainly absent, Thomson ascribed it to an isotope of neon, which he called metaneon.

Thomson’s pupil and collaborator F. W. Aston attempted to separate the new gas from neon (atomic weight 20.2). It turned out, however, that this was an extremely difficult task. Aston used chiefly two methods: fractionation over coconut charcoal cooled with liquid air, and repeated diffusion. In both cases,

¹) K. Fajans, l. c. pp. 50–58; there too (p. 106) and in K. Fajans’s review (Phys. ZS 16, p. 456, 1915) are further bibliographical references on this question.

²) J. J. Thomson. Rays of Positive Electricity and their application to chemical Analyses. London, 1913, p. 112 ff.

³) Thomson sets forth an empirical rule from which he did not once observe a departure. By virtue of this rule, only atoms, but by no means molecules, under the conditions of his experiments, can occur with two or several charges.

in view of the difference in the masses of the atoms, positive results were to be expected. Meanwhile it turned out that the first method in no way permits even a partial separation to be effected.¹) However, subsequently Lindemann²) showed that this failure was also theoretically inevitable.

Repeated diffusion through a Mundink clay tube gave, although only a weak one, nevertheless a positive result. Namely, after prolonged and difficult experiments it was possible to obtain two fractions with a difference in density of \(0.7\%\).³) However, Aston himself does not consider this result final and entirely convincing.

A preliminary theoretical investigation⁴) showed that the only method allowing the isotopes to be completely separated is the method of canal rays. This same method is the most convenient for detecting isotopes. And therefore Aston set himself the aim of so refining the electromagnetic analysis of canal rays as to bring it, in accuracy, close to optical spectrometry. Since the chief advantage of the latter is the possibility of focusing, Aston’s attention was directed precisely in this direction.

§ 6. Thomson’s method is based on the following simple considerations. A very narrow beam of canal rays is passed simultaneously through electric and magnetic fields arranged so that the deflections in the one and the other are mutually perpendicular. The deflection in the magnetic field will be

\[ y = A \frac{e}{mv}, \]

where the constant \(A\) does not depend on the quantities \(e\), \(m\), and \(v\); the deflection in the electrostatic field will be

\[ z = B \frac{e}{mv^{2}}, \]

where \(B\) likewise does not depend on \(e\), \(m\), and \(v\). From these two equations we have

\[ y^{2} = \frac{A^{2}}{B}\cdot \frac{e}{m}\, z. \]

Consequently, if a photographic plate is placed perpendicular to the initial direction of the beam, then all particles with the same \(\frac{e}{m}\) will leave on it a trace in the form of a parabola. Each parabola will be characteristic of the given kind of particle, and in this way one can carry out a chemical analysis of the gas contained in the discharge tube by a simple comparison of the parameters of these parabolas.⁵)

Aston’s arrangement differs somewhat from Thomson’s scheme.

¹) F. A. Lindemann and F. W. Aston, Phil. Mag., 37, p. 523 (1919).
²) F. A. Lindemann, Phil. Mag., 37 p. (1919).
³) F. A. Lindemann and Aston, l. c.
⁴) Lindemann and Aston, l. c.
⁵) For details of this method see Thomson’s cited book. See also the collection “New Ideas in Physics,” issue 7.

The general idea of this arrangement is shown in Fig. 11. \(S_1\) and \(S_2\) are two extremely narrow slits of special construction (for details see below).

Fig. 1.

The resulting thin bundle of canal rays is spread out into an electric spectrum while passing between the two plates of the condenser, \(P_1\) and \(P_2\), the dispersed bundle being, to a first approximation, regarded as issuing from the imaginary source \(Z\). Part of the rays of this dispersed bundle is again selected by the diaphragm \(D\) and is passed between the parallel poles of a large electromagnet. The poles, for simplicity, have a round shape; the field between them is uniform and has such a sign that the rays are deflected in it in the direction opposite to the electric deflection. In this lies the essential difference between Aston’s arrangement and Thomson’s.

Let \(\varphi\) and \(\theta\) be the algebraic values of the angles of deflection of the emitted bundle in the electric and magnetic fields; let \(ZO=b\). For simplicity of calculation, suppose that the magnetic field is concentrated at the point \(O\), and denote the length of the subsequent path of the bundle from this point by \(r\). Since, furthermore, the deflections in the electric and magnetic fields are opposite to one another, \(\theta\) is a certain negative angle; let \(\theta=-\theta'\). Taking into account that \(\varphi\) and \(\theta'\) are small angles (in the drawing they are greatly exaggerated), one can show2 that, under the condition

\[ r(\varphi-2\theta')=b\cdot 2\theta', \]

all particles having one and the same \(\frac{e}{m}\), but different velocities, will be collected at a certain focus \(F\). The equation just written can practically be satisfied by choosing the field in a suitable way, and thus we obtain the possibility of focusing canal rays.

Let us take the coordinate axes as shown in the drawing. The coordinates of \(F\) will be

\[ r \cos(\varphi - 2\theta') \quad \text{and} \quad r \sin(\varphi - 2\theta') \]

or, owing to the smallness of the angles,

\[ r,\quad r(\varphi - 2\theta') = b \cdot 2\theta'. \]

Thus, in the first approximation, for any field all foci must lie on the line \(ZF\), parallel to \(OX\), since the position of the diaphragm is unchanged. And if along this line one places a photographic plate (shown in the drawing by a heavy line), then on it there will be obtained a series of “spectral lines,” of which

each will correspond to a definite value of \(\dfrac{e}{m}\).

From the general idea of the method let us pass to the experimental details, which are so interesting that we consider it necessary to dwell on them. Fig. 2 gives the general scheme of the apparatus1. The X-ray tube \(B\) is an ordinary Röntgen tube, 20 cm in diameter. The aluminum anode \(A\) is surrounded by a polished aluminum cylinder serving as an anticathode. The cathode \(C\) (not shown in the drawing) is placed precisely at the beginning of the tube in order to fuse the opposite wall; directly opposite the cathode there is a quartz ball \(D\) (12 mm in diameter). Quartz is especially convenient as an anticathode because it emits the soft rays, desirable in this case.

Fig. 2.

The details of the apparatus are shown separately in Fig. 3. The flange is soldered with wax to the brass ring \(E\), by which the glass tube \(F\) ends; the evacuated extension-tube, carrying the cathode, branches off tangentially. The junction is cooled by a countercurrent of water circulating through the tube \(G\).

The gas under investigation flowed through a thin capillary via the opening \(O\); by means of the mercury pump of Gaede, a certain rarefaction was maintained continuously.

The cathode was drilled through at the center, the channel having a slightly conical form (diameter 3 mm). Into this channel was inserted—

the first main slit \(S_1\). The cathode was hermetically driven into a brass tube, in which, at a distance of 10 cm, there was a solid piece of brass \(H\), likewise drilled through in a slightly conical shape. This latter channel carried the second slit \(S_2\). The width of each slit was 0.05 mm, the length—2 mm; they had to be set strictly parallel, for which it was necessary to make use of diffraction phenomena. The space between the slits was evacuated as far as possible, with the aid of coconut charcoal and liquid air. This last circumstance is very important, for in this way losses due to scattering and neutralization of the rays as a result of collisions were reduced to a minimum.

Fig. 3.

On emerging from the slit \(S_2\), the rays entered an electrostatic field between two flat brass surfaces. The plate \(J_1\) could be charged to any potential by a battery of small accumulators; \(J_2\) was connected directly with the tube and together with it was led to earth. In order to make it possible to reduce the distance between the surfaces, they were placed somewhat at an angle to the initial direction of the beam.

Immediately after this the rays passed through two diaphragms \(K_1\) and \(K_2\). Of these, \(K_1\) is fixed and serves solely to prevent the rays from falling on the oily surface of the stopcock \(L\). The second diaphragm \(K_2\) is placed in the opening of the carefully earthed stopcock \(L\); it is movable, its width changing when the stopcock is turned.

Farther on the rays entered a magnetic field. The cylindrical pole pieces (diam.—8 cm) of a large Du Bois electromagnet were soldered into a brass tube \(O\), which forms part of the chamber \(N\); the distance between the poles is 3 mm.

Finally, the last stage of the path of the rays is the chamber \(N\). It is made of a strong brass tube 6.4 cm in diameter. For complete electrostatic shielding, the rays pass in a narrow space (3 mm) between two parallel brass plates \(ZZ\) (Fig. 4), closed from above by a third plate \(XX\). In this latter there is a slit (2 mm), behind which the photographic plate \(W\) is placed. The device \(V\), not shown in detail, makes it possible to move it parallel to itself and normal to the slit, so that on one

on the plate it was possible to obtain several photographs. \(Y\)—a small millimeter screen for observations, which could be made through the window \(P\), covered with red glass. Before the beginning and at the end of each photograph, the lamp \(T\) was lit for several seconds; the light from it, through two very fine openings in the tube \(R\), fell on the photographic plate and left there a small spot serving as the initial point in all measurements1.

Fig. 4.

In Fig. 5 several such photographs are shown. Aston calls them the mass spectra of elements (The Mass Spectra of Chemical Elements). As can be seen, the lines of these spectra are broad, but for some reasons of a geometrical character, their outer edge is always sharper and brighter; it is precisely along this edge that all the readings are made. Theoretically, it is sufficient to know the mass corresponding to one of the “spectral lines” in order to determine the masses corresponding to all the others. But Aston constructed an entire scale of known lines, and the mass for each new line is determined by comparison with two already known ones, located on either side of the new one. Under these conditions the accuracy of the determination of masses reaches 1 per mille.

As we have already seen, the position of the lines in the mass spectra depends on \(\dfrac{m}{e}\). If, in a beam of canal rays, a certain atom is encountered not only with one, but also with two or three charges, then in the spectrum there will be lines

\[ \frac{m}{e},\quad \frac{m}{2e},\quad \frac{m}{3e}. \]

Such lines, corresponding to multiple charges, are not difficult to recognize, for it is obvious that, in relation to the principal line, they will correspond to masses 2, 3, and so on times smaller,

\[ \left(\frac{m}{2},\quad \frac{m}{3}\right), \]

and so forth.

Aston calls these lines respectively lines of the 2nd, 3rd, and so on orders. In the examples of the analysis of spectrograms which we shall give below, this method of orientation will be clarified more fully. To distinguish atoms from complex molecules of the same mass, Aston used the rule, cited above, of Thomson, according to which molecules give lines only of the first order.

§ 7. Since all measurements in mass spectra are of a relative character, some element must be chosen as a basis, and the masses of all the remaining elements referred to it. For understandable reasons Aston settled on oxygen. Its molecule and atom with one and two charges give the principal lines 32, 16, and 8. Very exact integral ratios between the atomic weights of carbon and oxygen inspire confidence that both of them are “pure” elements (i.e. have no isotopes), and so far no fact has shaken this confidence. Direct comparison of the lines \(C\) (12) and \(CO\) (28) with the above-mentioned principal lines gave the expected integral ratios; moreover the additivity of masses \((CO = C + O)\) is also observed within the limits of observational error (1 per mille). Thanks to this we obtain several more “standard” lines: \(C^{++}\) (6), \(C\) (12), \(CO\) (28), and \(CO_2\) (44). Also very convenient as fundamental lines are the hydrocarbon radicals which in the free state exist in canal rays. These are the so-called groups \(C_1\) and \(C_2\): \(C_1\) (12), \(CH\) (13), \(CH_2\) (14), \(CH_3\) (15), \(CH_4\) (or \(O\)) (16), and \(C_2\) (24); \(C_2H\) (25), \(C_2H_2\) (26), \(C_2H_3\) (27), \(C_2H_4\) (or \(CO\)) (28), \(C_2H_5\) (29), \(C_2H_6\) (30)\(^1\). Thus an integral scale of masses is obtained, covering a fairly considerable interval. For some not entirely clear reasons, probably depending on the geometry of the apparatus\(^2\), a linear relation is fulfilled with sufficient rigor between the masses and the displacements of the corresponding lines. This circumstance greatly facilitates the work and increases the accuracy of the measurements.

§ 8. Let us turn to the analysis of several spectrograms (Fig. 5).

Neon (at. wt. 20.20).

In the mass spectrum of neon two lines, 20 and 22, are visible, which are also distinctly repeated in the second order (the spectrograms are not reproduced). In some photographs faint traces of line 21 are visible. Thus Thomson’s supposition of the existence of an isotope of neon is confirmed, with the only difference that both isotopes corresponding to the chemical type “neon” possess integral atomic weights.

Very interesting results have been obtained with chlorine (at. wt. 35.46) (photographs II, III, and IV). In studying this element phosgene \((COCl_2)\) was admitted into the apparatus. Considering spectrogram III, we see that in the region where the chlorine line ought to be there are 4 lines: 35, 36, 37, and 38. No traces of a line corresponding to the ordinary atomic weight

the structure of the alkali metals and beryllium, and also magnesium, was studied (Dempster). See F. W. Aston and G. P. Thomson, Nature 106, p. 642 (1920); F. W. Aston, Nature 107, p. 72 (1921); A. J. Dempster, Phys. Rev. 17, p. 427 (1921); F. W. Aston, Nature 107, pp. 520; G. P. Thomson, Nature 107, p. 395 (1921).

\(^1\) These lines appear almost always owing to the presence in the apparatus of liquid vapors.

\(^2\) Aston, Phil. Mag. 40, p. 628 (1920).

Fig. 5.

chlorine 35.46 is absent. In spectrogram II weak lines 17.5 and 18.5 are visible; they appear only when traces of chlorine are present in the apparatus and are undoubtedly second-order lines for 35 and 37. Lines 36 and 38, obviously, belong to \(HCl^{35}\) and \(HCl^{37}\). In spectrogram IV there are also lines 63 and 65; Aston ascribes them to \(COCl^{35}\) and \(COCl^{37}\).

From all this it follows that ordinary chlorine, with atomic weight 35.46, is a “mixed” element: it in fact consists of a mixture of two isotopes with atomic weights equal to 35 and 37. Consequently, the observed atomic weight is a statistical mean. But if this is so, then a priori one should expect that component 35 predominates in the mixture. And indeed, comparison of the intensities of the lines 35 and 37 fully confirms this, although it is still difficult to determine the mixing proportion.

Krypton (at. wt. 80.92) and xenon (at. wt. 130.2) proved to be likewise very complex elements (spectra VIII and IX). The first consists of at least six isotopes: in its mass spectrum there are five bright lines 80, 82, 83, 84, 86 and one weak line 78. All these lines are excellently repeated in the second and third orders, which makes it possible to determine the atomic weights of the isotopes with great accuracy. Xenon was available in a very small quantity (a few cubic millimeters), and therefore its investigation is of a preliminary character. However, the complex nature of this element is beyond doubt. As preliminary values for the atomic weights of its isotopes Aston gives the following figures: 128, 130, 131, 133 and 1351.

Mercury (at. wt. 200.6) also proved to be very complex. In it Aston counts up to six isotopes. In the spectrograms one sees, first, a blurred band 197—200 and, second, two lines 202 and 204. In the band 197—200 Aston finds it possible to count three or four isotopes. These results, of course, are still of a preliminary character.

We shall dwell only on helium and hydrogen, and shall give all the remaining results simply in the form of a table. The precise determination of the atomic weights of helium and hydrogen presents difficulties in that their lines are considerably removed from the standard ones. In view of this it was necessary to develop a special method of mass determination specifically for the present case. We shall not pause over this method, but shall give the results at once.

a) Helium.

\[ \begin{aligned} &\text{From comparison with } O^{++} = 8.00 \text{ at. wt.} = 3.994—3.996,\\ &\quad\quad\quad\quad\quad\quad\ \ C^{+++} = 6.00 \text{ at. wt.} = 4.005—4.010. \end{aligned} \]

Thus helium is an “even” element.

Table 4).

¹) The figures in parentheses are preliminary in character.
²) So far only one isotope has been discovered for $Cs$.

b) Hydrogen.

For the study of hydrogen, the molecules \(H_3\) (the Thomson molecule \(X_3\)) and \(H_2\) were considered. The results obtained were as follows:

\[ \begin{array}{rcll} H_3\ )\ \left\{ \begin{array}{l} \text{from } C^{++}=6{,}00\\ \text{ “ } He=4{,}00 \end{array} \right. & & \begin{array}{l} 3{,}025\text{—}3{,}027\\ 3{,}021\text{—}3{,}030 \end{array} \\ H_2 & \text{ “ } He=4{,}00 & 2{,}012\text{—}2{,}018 \end{array} \]

Thus, among all the elements investigated, hydrogen represents the sole exception. Being a “pure” element, it has an atomic weight (O = 16.00) differing from whole units, namely a half-integer weight, coinciding with the generally accepted value 1.008. We shall return somewhat below to the possible causes of this anomaly.

We shall now give a table of the final results (Table 4, p. 254).

§ 8. On the basis of this table one may make a generalization which Aston calls the Whole-number Rule: for the elements investigated, with the exception of hydrogen, all masses, whether atomic or molecular, are, within the limits of observational accuracy, whole numbers. The fairly considerable number and diversity of the elements already studied inspire confidence that this rule is valid in general.

The exceptional position of hydrogen, of course, requires explanation. Here it is necessary first of all to recall that not only hydrogen as such but, perhaps chiefly, also secondary units of the type of helium take part in the structure of the elements. However, if this is so, it still remains to be explained why in helium, whose nucleus itself is built of four hydrogen nuclei and two electrons, the atomic weight is exactly equal to four. We have already pointed out that, in order to explain small deviations from whole numbers, the relativistic inertia of energy is usually invoked. In particular, for the case of helium, Lenz2, precisely from this point of view, explains the unusual stability of the helium nucleus, which amazed Rutherford3. It is further necessary to point out that such small deviations

from the purely electromagnetic point of view is quite understandable. For the electromagnetic mass of a composite formation may be calculated additively so long as the components are sufficiently far removed from one another. If, for example, the molecule of hydrogen \(H_2\) is in question, then one may suppose that its mass is equal to twice the mass of the hydrogen atom. But when the components are situated extremely close together, as happens in the nucleus, then their fields are superposed upon one another, and à priori one must expect that the resulting mass will not be exactly equal to the sum of the masses of the original components (Harkins and Wilson wittily call this phenomenon the “Packeffekt”).

There is one more question on which it is necessary to dwell. For several years F. W. Richards, in the laboratory of Harvard University, has been carrying out remarkable determinations of atomic weights with the aim of establishing whether there is any difference in the atomic weights of elements taken from different places on the earth’s surface. The results so far have always been negative. Thus, in copper of German and American origin the atomic weights proved to be completely identical. The same was found for ordinary lead of the most diverse geographical and mineralogical origin, for chlorine, sodium, silver, etc. Still more curious is that the atomic weight of meteoric iron proved to coincide, within the limits of observational error, with the atomic weight of terrestrial iron. But if many elements in fact represent a mixture of isotopes, then such constancy of atomic weights testifies to the fact that these isotopes are everywhere mixed in the same ratio. The cause of this constancy is not yet entirely clear. It is possible that our elements were formed already at a time when the earth was still in a liquid or even gaseous state and could at that time mix uniformly1. However, as yet we have no experimental facts at all for resolving this question; here there is still an extensive field for various hypotheses2.

The works of Rutherford and Aston serve as a new powerful stimulus to the revival of Prout’s hypothesis. Hydrogen once again receives the role of the primary element, and Rutherford even proposed for it a new name, proton, corresponding to this role. But we have dwelt on Aston’s work in such detail also because, among the brilliant successes of physics in recent years, the discovery of isotopes in ordinary elements occupies one of the most notable places. And irrespective of whatever hypotheses there may be, the “whole-number rule” is a fact with which every investigator in this field will have to reckon.

1. See, for example, K. Fajans. Radioaktivität etc. ↩↩↩↩↩↩↩

2. We have only touched in passing (concerning methane) on other methods of isotope separation besides the canal-ray method. To this let us add that Harkins, Nature, 105, p. 230 (1920), succeeded in carrying out a partial separation of chlorine isotopes by repeated diffusion; Brönsted and Hevesy (Nature 106, p. 144, 1920) likewise obtained a partial separation of mercury isotopes by evaporating it under low pressure and condensing the evaporated mercury on a cooled surface; finally Hevesy (Nature 108, p. 000, 1921), by the same method, separated chlorine isotopes. F. W. Loomis (Phys. Rev. 17, 436, 1921) pointed out that the presence of isotopes must be reflected in the infrared absorption spectrum of a gas. Namely, individual lines of rotational absorption bands in the near infrared part of the spectrum should appear as doublets. And indeed, on the absorption curves of HCl given by Imes (Astrophys. Journal 50, p. 251, 1919), it is seen that each line in the band \(1.76\,\mu\) is accompanied, at a distance of \(14\,\text{Å}\) (toward longer wavelengths), by a weaker satellite; the distance calculated on the basis of the atomic weights of the isotopes is \(13.5\,\text{Å}\). These weak satellites are therefore attributed to \(Cl^{37}\). (See also the work of A. Kratzer, ZS. für Physik 3, p. 460, 1920.) ↩↩↩↩↩↩

3. Rutherford, in the conclusion of his historical paper (Collision of α-Particles with Light Atoms. IV. An anomalous effect in nitrogen, Phil. Mag. 37, p. 581, 1919), writes that he is not so much surprised that nitrogen is destroyed in the collision of \(\alpha\)-particles, as that the \(\alpha\)-particle itself withstands the enormous forces that are developed in the process. Using the formula given on p. 244, Lenz calculated that the “heat of formation” of the helium nucleus should amount, per gram-atom, to \(6.25\cdot 10^9\) large calories. For comparison it is worth recalling that the heats of formation in ordinary chemical processes are of the order of 100 Cal. Thus, from this point of view, the unusual stability of the helium nucleus becomes entirely comprehensible. ↩↩↩

4. M. v. Laue. Die Relativitätstheorie. B. I p. 209. 3 Aufl. Braunschweig, 1919. ↩↩