METHODS AND RESULTS OF ISOTOPE RESEARCH*

I. Mattauch

Contents

I. Introduction.
II. Methods of investigating canal rays. 1. Parabola method. a) General remarks and survey of older works. b) New works. 2. Aston’s velocity focusing. a) General remarks. b) Aston’s first instrument. α) Measurement of mass numbers. β) Resolving power. γ) Aston’s work with the first instrument. c) Aston’s second instrument: α) Measurement of relative mass defects. β) Measurement of relative abundances. γ) Work done by Aston with the second instrument. d) Works of other authors. 3. Focusing of directions. a) Dempster’s works and general remarks. b) New works. c) Modifications of the method. 4. Velocity filters. a) Wien filter. b) Smythe filter. 5. Multiple acceleration. 6. Focusing of velocities and directions. a) Simultaneous electric and magnetic deflection. b) Separate deflection.
III. Spectroscopic methods. 1. Shifts in band spectra caused by isotopy. a) General remarks (diatomic molecules). α) Isotopy effect in electronic terms. β) Isotopy effect in vibrational terms. γ) Isotopy effect in rotational terms. b) Measurements of isotopy by means of band spectra. α) General remarks. β) Discovery of new isotopes. γ) Measurements with unknown isotopes. c) Shift caused by isotopy in the spectra of triatomic and polyatomic molecules. 2. Shifts caused by isotopy in line spectra. a) Systems with one electron. b) Systems with many electrons. c) Investigation of hyperfine structure. α) General considerations. β) New discoveries. γ) Investigation of known isotopes.
IV. Results. 1. Survey of methods. a) Investigation of canal rays. b) Spectroscopy. c) Other methods. 2. Table of isotopes. a) Isotopes and methods of their detection. b) Nonexistent and doubtful isotopes. c) Relative abundances. d) Weights of isotopes and relative mass defects. 3. Attempts to create a systematics of isotopes.

I. Introduction

The fruitless attempts of Boltwood¹,** Kettmann², Auer von Welsbach³, Markwald⁴, Soddy⁵ and others to separate from one another the elements ionium from thorium and mesothorium from radium—elements differing in their radioactive properties—led Soddy⁶ in 1910 to consider the possibility of the existence of a mixture of atoms of various kinds also among nonradioactive elements. After Russell and Rossi⁷ established the identity of the spectra of thorium and ionium

* I. Mattauch, Phys. Zeitschr., 35, 567, 1934, translated by P. A. Lambina.
** See the literature at the end of the article.

in the visible region, and after Fajans ^8 and others had formulated the displacement law for radioactive elements, Soddy defined the concept of isotope in the following way: “Elements with the same algebraic sum of negative and positive charges in the nucleus but with a different arithmetical sum constitute what I call ‘isotopes’ or ‘isotopic elements,’ since in the periodic system they occupy one and the same place. Chemically they are identical; physically they are also identical, if one disregards those few physical properties which depend directly on the atomic mass.” Soon after this, Rutherford and Andrade ^9 demonstrated the spectroscopic identity of radium D and lead also in the X-ray region.

Even earlier, J. J. Thomson ^10, in studying positive rays, had detected near the strong neon line a weak satellite, to which he assigned mass 22 and which he regarded as an isotope of neon. Irrefutable proof of the existence of this isotope was given only by Aston ^23, after in his mass spectrograph he succeeded, in an ingenious way, in increasing the precision of the study of positive rays, thereby providing an excellent method for studying isotopes. Subsequently Aston discovered a large number of isotopes of nonradioactive elements. The discoveries followed one another with extraordinary rapidity. Almost simultaneously, Dempster ^46, using another method of investigating positive rays, succeeded in finding the isotopes of magnesium.

Very soon a subtle difference in the spectra of isotopes was established by the optical method. For the line \(\lambda = 4058\ \text{Å}\) in the spectrum of lead, Aronberg ^208 found a small shift for radiogenic lead and ordinary lead. The direction of the shift corresponded to Bohr’s predicted theory; however, it was approximately one hundred times larger. The experiment was checked by Merton ^209. For the first time Ames ^125, in band spectra in the study of HCl, observed a splitting of the maxima into doublets of about \(1.75\ \mu\), which Loomis ^93 and Kratzer ^94 explained as an isotopic shift caused by Cl isotopes. However, several more years passed before optical methods could be used for the study of isotopes, namely for the discovery of new isotopes, the measurement of mass ratios, and the relative abundances of isotopes. Until that time, the study of isotopes remained connected with the investigation of positive rays, and in this field there reigned almost without rival one single investigator—F. W. Aston.

II. METHODS OF INVESTIGATING POSITIVE RAYS

As is well known, measurement of \(\frac{e}{m}\) for positive rays, in contrast to cathode rays, always gives a series of different values characteristic of the ions in the discharge tube. To determine \(\frac{e}{m}\) it is always ne-

the action on the ions of at least two fields is necessary (for example, with static fields, one electric and one magnetic, or one static electric field and one alternating electric field). At the same time, together with \(\frac{e}{m}\) there always appears a second unknown—the velocity \(v\), which must either be measured or eliminated. For an electric field it is characteristic (used are: homogeneous electrostatic fields—the direction of the velocity perpendicular or parallel to them, a static radial field, and an alternating field) that the combination

\[ \frac{e}{mv^2}, \]

appears invariably, while for a magnetic field (always only static, homogeneous and sometimes with an associated stray field) the combination

\[ \frac{e}{mv} \]

appears.

In contrast to the determination of \(\frac{e}{m}\) for electrons, in the study of isotopes one can speak only of the relative determination of mass with respect to some arbitrarily chosen standard \(({}^{16}\mathrm{O}=16)\).* Nevertheless, almost all methods of measuring \(\frac{e}{m}\) for ions have found a more or less exact analogue in the methods of determining \(\frac{e}{m}\) for electrons. The only exception is Aston’s method, precisely because it is best adapted to the special features of isotope study.

Fig. 1.

1. The Parabola Method

a) General remarks and review of earlier work

This method was first applied by J. J. Thomson\(^{18}\). Its arrangement is shown schematically in Fig. 1. Canal rays, which are produced and accelerated in a discharge tube, pass through a channel whose length is \(2\ \mathrm{cm}\) and whose internal diameter is \(0.1\ \mathrm{mm}\), and emerge from it as a slightly divergent beam. The beam contains particles with all possible energies, up to the maximum determined by the voltage on the tube. After this they pass through two parallel or antiparallel fields \(E\) and \(H\) (not necessarily of the same length). Thus the directions of def—

\[ \text{* According to an old proposal by C. Meyer, mass indices will here be written at the upper left.} \]

deflections \(y\) and \(z\), caused by the two fields, are perpendicular to one another and both are perpendicular to the direction \((x)\) of the incident beam. As is easy to show, the deflected rays then appear to originate from the midpoint of the two fields, independently of what their \(v\) and \(\frac{e}{m}\) are. For small deflections on a plane located at an arbitrary distance \(l\) from the beginning of the fields, the following equalities hold:

\[ y=\frac{e}{mv^{2}}\,A \quad \text{and} \quad z=\frac{e}{mv}\,B, \tag{1} \]

where \(A\) and \(B\), for constant fields, are constants, which are obtained from

\[ \int_{0}^{l}(l-x)F(x)\,dx, \]

where \(F\) in one case must be replaced by the electric-field strength \(E(x)\), and in the other by the magnetic-field strength \(H(x)\). Eliminating \(\frac{e}{m}\) and \(v\) from equalities (1) gives:

\[ z=\frac{A}{B}\,vy \quad \text{and} \quad y=\frac{A}{B^{2}}\,\frac{e}{m}\,z^{2}. \tag{2} \]

This means that particles with equal velocities meet a plane perpendicular to the \(x\)-axis on straight lines passing through the origin, while particles with the same mass and charge are arranged on parabolas whose common vertex lies at the origin of coordinates. Since the charge can be only an integral multiple of the charge of the electron, at a constant value of the abscissa \(y\), the masses of the ions are inversely proportional to \(z^{2}\)—the squares of the ordinates. Of course, as in any other method for investigating canal rays, ions with double charge and with half the mass cannot be distinguished from one another. However, it is precisely the parabola method, as we shall see, that provides the greatest amount of information on this question. This occurs because only in this method is resolution along two coordinates carried out. It therefore gives the broadest possibilities for judging the processes taking place in the discharge tube and on the path to the deflecting fields. Since the electric field gives, according to equation (1), an energy spectrum, and the maximum energy is the same for all ions, all parabolas must begin from some abscissa \(y_{0}\), provided only that these ions have not undergone recharging.

Near this value the parabolas exhibit a maximum of intensity owing to the fact that the majority of ions, being formed in the region of positive glow, traverse a large part of the voltage applied to the tube. If, on the path between the tube and the deflecting fields, an ion undergoes a change of charge (loses half of its initial charge or doubles it), then the parabolas

respectively begin at \(\frac{1}{2}y_0\) or \(2y_0\) and have a second maximum near these values. These relations are well illustrated by Fig. 2 (photograph by R. Conrad \(^{16}\)). The second maximum of the H parabola cannot, of course, be due to atoms with half charge. It is explained, as Aston \(^{11}\) showed, by the dissociation of \(\mathrm{H}_2\) molecules. In dissociation, one atom retains the charge, while the other (neutral) falls at the origin.* According to the first equality (2), the corresponding points of the first maximum of the \(\mathrm{H}_2\) parabola and the second maximum of the H parabola must lie on a straight line passing through the origin, exactly as do the corresponding points of the parabolas C and \(\mathrm{C}^{++}\) or the parabolas O and \(\mathrm{O}^{++}\), since they are due to particles having identical velocities.

As already mentioned, J. Thomson initiated the study of the isotopy of nonradioactive elements by the discovery of the \({}^{22}\mathrm{Ne}\) parabola. Aston \(^{12}\) tried to carry out a macroscopic separation of the Ne isotopes from one another by fractional distillation and fractional diffusion. Density measurements showed that the separation had in fact succeeded, though only to an insignificant degree. However, photographs taken by the parabola method did not make it possible to detect any change in relative intensity. Further, J. Thomson established, as a rule, the circumstance that atoms often acquire a double charge and in some cases even a multiple charge, whereas molecules can occur only in the form of singly charged ions. J. P. Thomson \(^{13}\) investigated the isotopy of Li and Be.

Fig. 2.

b) New work

Several years ago R. Conrad \(^{14}\) considerably improved the technique, chiefly by, following Aston’s example, replacing the canal by two narrow (0.1 mm) diaphragms placed at a large distance (20 cm) from one another. He evacuated the space between the slits with the aid of a separate pump (Fig. 3).

* If dissociation in Aston’s mass spectrograph occurs between the electric and magnetic fields, this is recorded by the appearance of particles with mass 0.5 (see F. W. Aston, Mass-Spectra and Isotopes, p. 60, London 1933).

Together with O. Eisenhut,^15 Konrad carried out interesting experiments on the regular construction and decomposition of hydrocarbons. Later Konrad^16 succeeded in detecting in canal rays, in the form of a neutral molecule, the molecule \(\mathrm{H}_3\), already known to J. Thomson in ionic form, and in indicating the lower limit of its lifetime, namely \(3 \cdot 10^{-8}\) sec. Of special importance for the mass-spectrographic discovery of rare isotopes is Konrad’s work,^14 in which he established the existence of a double positive charge in a large number of molecules (Fig. 4). Thus Thomson’s rule, already shaken by the discovery by Aston of \((\mathrm{BF}_3)^{+++}\)^25 and \((\mathrm{Hg}_3)^{++++}\),^31 lost its force. Thanks to this, the explanation of the parabolas with masses 9, 6.5, and 7.5, found by E. Rückhardt,^17 as being due to the existence of \({}^{18}\mathrm{O}^{++}\), \({}^{13}\mathrm{C}^{++}\), and \({}^{15}\mathrm{Ne}^{++}\), becomes doubtful. Konrad^14 also succeeded in obtaining at least fivefold charged positive ions of \(\mathrm{Cl}\) (Fig. 5). When filling the discharge tube with helium with an admixture of \(\mathrm{Cl}\), he observed the appearance of \(\mathrm{He}^{++}\) (Fig. 6). He was therefore able to obtain artificial \(\alpha\)-particles.

Fig. 3.

Recently G. Hertz^18 succeeded in actually carrying out a considerable macroscopic separation of isotopes, which he could demonstrate also by the parabola method. In the development of this work, Harmsen^19 succeeded in obtaining 99% \({}^{20}\mathrm{Ne}\) and \({}^{22}\mathrm{Ne}\) and in enriching the rare isotope \({}^{21}\mathrm{Ne}\) (Figs. 7, 8, and 9). The photographs were made with the aid of apparatus by means of which two of Hertz’s pupils, G. Lukanow and W. Schütze,^20 enormously increased the resolving power of the parabola method. They achieved a resolving power of \(1:600\), as is shown by the separation of \({}^{1}\mathrm{H}_2^{+}\) and \(\mathrm{He}^{++}\) (Fig. 10).

Fig. 4.

This was achieved, on the one hand, thanks to an increase in the in—

Fig. 5.

Fig. 6.

Fig. 7. Neon 20, 22, and 21.

Fig. 8. Neon 22.

intensity as a result, on the one hand, of using a metal discharge tube with an appendage, whose channel is extended to the place where the beam of canal rays has the greatest intensity and density, and, on the other hand, of using extremely narrow slits. The first of these was made in the form of a channel 1 to 2 cm long, so that it played the role of a large aerodynamic resistance in comparison with the resistance of the discharge tube, since it was desirable to make do with an insignificant amount of gas and low-power pumps. The diameter of the channel was from 0.02 to 0.008 cm. The diameter of the second slit was from 0.005 to 0.001 cm.

Fig. 9. Neon 20.

Fig. 10. Helium—hydrogen (magnified 20 times).

Precise measurements of masses (measurements of binding energy) had not yet been made. For these measurements, the nonlinearity of the mass scale in the parabola method was an obstacle. Lukanov and Schütze showed in an elegant way the enrichment in the new heavy isotope \({}^{2}\mathrm{H}\) by Hertz’s method with the aid of negative ions (Figs. 11 and 12, Table 7).

Zeemann and de Gier\(^{21}\), with the aid of the parabola method, detected ions of all triatomic hydrogen molecules \(({}^{1}\mathrm{H}_{2}{}^{2}\mathrm{H})^{+}\), \(({}^{1}\mathrm{H}{}^{2}\mathrm{H}_{2})^{+}\), and \(({}^{2}\mathrm{H}_{3})^{+}\), as well as all OH combinations up to \((\mathrm{O}^{1}\mathrm{H}^{2}\mathrm{H}_{2})^{+}=21\). They were further able to resolve the doublets: \(\mathrm{He}—({}^{1}\mathrm{H}_{2}{}^{2}\mathrm{H})\), \(\mathrm{He}^{1}\mathrm{H}—{}^{1}\mathrm{H}^{2}\mathrm{H}\), and \(\mathrm{He}^{2}\mathrm{H}—{}^{2}\mathrm{H}_{3}\), and to compute with great accuracy the corresponding mass differences, using only Thomson’s interpolation formula (without a calibration curve). The results, with an accuracy of from 1 to 1.5%, agree with Bainbridge’s data\(^{21,26}\). Thanks to the appearance in enriched hydrogen of mass 42 \((\mathrm{A}^{2}\mathrm{H})\) alongside 41 \((\mathrm{A}^{1}\mathrm{H})\), these authors were able convincingly to prove the possibility of hydride formation even among noble gases and to show that 41 is not an isotope of A. Recently Zeemann and de Gier\(^{21a}\) succeeded in discovering a new isotope of argon—\({}^{38}\mathrm{A}\).

For measurements of \(e/m\) of electrons by the parabola method, J. J. Thomson himself made use of it.

2. Aston’s Focusing of Velocities

a) General Remarks

Historically, the increase in resolving power did not proceed by way of improving the parabola method. With the aid of his apparatus, Aston succeeded in carrying out a method which, precisely because of its adaptation to the requirements and experimental features of isotope research by the method of canal-ray analysis, found no analogue among the methods for determining \(e/m\) for cathode rays.

Fig. 11. Ordinary hydrogen (natural size).

Fig. 12. Hydrogen enriched by diffusion (natural size).

Aston, by compressing (velocity focusing) Thomson parabolas, or parts of them, achieved a strong increase in intensity, which could be increased still further here by the possible use of rectangular diaphragms instead of round ones.

For comparing the intensities of different lines, it is essential that corresponding pieces be cut out from all the parabolas, i.e., pieces bounded by the same abscissas, for example the vertices of the parabolas. Since for isotopes of one

element, a velocity distribution (expressed in volts) is one and the same thing as the distribution of intensity along the parabola, Aston could make quite reliable measurements of intensity. He could also make accurate measurements of masses, owing to the fact that, as it unexpectedly turns out, the mass scale in the region where the measurements are made shows only slight deviations from linearity.

Aston’s apparatus, rightly called by him a mass spectrograph, and the measurements made by Aston, recently described with exhaustive completeness,* are so well known that, for lack of space at the author’s disposal, we omit their detailed discussion. The path of the rays is shown schematically in Fig. 13

Fig. 13.

approximately as it occurs in Aston’s second (precision) apparatus.^33 A ray selected by two collimating slits \(S_1\) and \(S_2\), \(0.02\) mm wide and separated from one another by a distance of \(20\) mm, is deflected by the radial electric field \(J_1\) and \(J_2\) (radius of curvature \(30\) cm, arc length \(5\) cm) through an angle \(\theta\). The slits \(S_1\) and \(S_2\) are made so as to act as an aerodynamic resistance. The diaphragm \(K\) passes only those rays for which \(\theta_0 < \theta < \theta_0 + d\theta\), where \(\theta_0\) is constant, and \(d\theta\) is a small angle, also constant for a fixed position of the diaphragm. At a distance \(l\) from the midpoint of the electric field lies the midpoint \(O\) of the magnetic field \(M\). The magnetic field is directed so that it causes the ray to be deflected through an angle \(\varphi\) in the direction opposite to that in which the ray is deflected in the electric field. The angle \(\varphi\) depends on the mass of the ions. The pole pieces on the exit side are made so that the path lengths \(L\) for rays with different \(\varphi\) are identical. The pencil of rays selected by the diaphragm \(K\), having approximately the same energy, is separated in the magnetic field according to masses and, for different masses, is focused at points \(F \ldots F\) at different distances \(\rho\) from the midpoint of the magnetic field. The question is: what is the geometrical locus of these focal points?

Aston’s focusing condition requires that the width of the pencil at the point \(F\) vanish; this means that:

\[ (l+\rho)\,d\theta-\rho\,d\varphi=0. \tag{3} \]

* F. S. W. Aston, Mass-Spectra and Isotops, London 1933.

For small values of \(\theta_0\), with constant \(E\), from equations (1) one readily obtains

\[ d\theta=-2\theta_0\frac{dv}{v}. \tag{4} \]

As long as \(dv\) is small, for any values of \(\theta_0\) in a radial field the following expression is valid, as is seen after a simple calculation from equation (24) of the work of P. Herzog and Mattauch \(^{83}\):

\[ d\theta=-\sqrt{2}\sin(\sqrt{2}\theta_0)\frac{dv}{v}. \tag{4a} \]

For small \(\theta_0\) this expression becomes equality (4). The curvature of a circular path in a magnetic field is determined by the familiar relation: \(\frac{\varphi}{L}=\frac{e}{mv}H\), from which, for constant \(L\) and \(H\), one obtains:

\[ d\varphi=-\varphi\frac{dv}{v}. \tag{5} \]

Substitution of equations (4) and (5) into the focusing condition (3) gives:

\[ \frac{dv}{v}\,[\rho(\varphi-2\theta_0)-2l\theta_0]=0. \]

Since \(dv\) is different from zero, this condition can be fulfilled only when the expression in brackets is equal to zero. If the angle of deflection in the magnetic field is measured from the axis drawn in Fig. 13 with a dotted line, i.e., if we put \((\varphi-2\theta_0)=\psi\), then in polar coordinates we obtain the equation of the geometrical locus of focal points:

\[ \rho\psi=2l\theta_0=\text{const} \tag{6} \]

or, according to equations (4a) and (5), putting:

\[ \psi=\varphi-\sqrt{2}\sin(\sqrt{2}\theta_0), \]

we have

\[ \rho\psi=\sqrt{2}\cdot l\sin(\sqrt{2}\theta_0)=\text{const} \tag{6a} \]

for any values of \(\theta_0\).

This is the equation of a hyperbolic spiral, which is shown in Fig. 13 (from \(\psi=0\) to \(\psi=2\pi\)). At \(\psi=0\) it comes from infinity and makes an infinite number of revolutions around the origin without falling into it. For \(\psi=0\) it has an asymptote parallel to the polar axis and separated from it by \(2l\theta_0\) [for sufficiently small angles \(\sqrt{2}\,l\sin(\sqrt{2}\theta_0)\)], since for the perpendicular \(d\), dropped from any point of the spiral to the polar axis, the relations hold:

\[ d=\rho\sin\psi=2l\theta_0\frac{\sin\psi}{\psi} \quad\text{and}\quad d_{\psi=0}=2l\theta_0\lim_{\psi=0}\frac{\sin\psi}{\psi}=2l\theta_0. \]

In the plane containing this asymptote (shown in Fig. 13 by a dashed line), Aston places a photographic plate. As is evident from the figure, the contact with the spiral is excellent, and, with the aid of three screws fixing the position of the plate, its most advantageous position can be found experimentally.

b) Aston’s first apparatus

With the aid of the first apparatus, which differed from that described above by a smaller distance between the slits (10 cm), a larger aperture of the slits (approximately 0.05 mm), and a smaller angle of deflection (\(1/12\) radian), Aston \(^{23-31}\) determined the mass ratio \(M\) of isotopes by two different methods, by directly measuring the distance \(D\) of a line from some selected and fixed point on the plate. Owing to the asymmetric shape of the lines, caused by the shape of the slits and diaphragms, and also by the peculiar polarization effect due in its origin to the incidence of channel rays on the plates of the condenser, the measurements are made along the most deflected edges of the lines, since the position of these edges depends least of all on changes in intensity.

a) Measurement of mass numbers. The first method is based on the fact that \(D=f\left(\dfrac{M}{M_0}\right)\), where \(f\) is a function in which all the quantities entering into it are determined by the geometrical dimensions of the apparatus, while the field strengths \(E\) and \(H\) change only the value of the mass \(M_0\). Hence it follows at once that, on each photograph, the mass ratio for two specified values \(D_1\) and \(D_2\) is one and the same, provided only that the field strengths were changed, but not the constants of the apparatus. Using masses whose ratios are known, such as, for example, the masses of the molecule and the atom \((\mathrm{O}_2:\mathrm{O})\), or with the aid of singly and doubly charged ions of the same atom \((\mathrm{O}^{+}:\mathrm{O}^{++},\ \text{etc.})\), one can construct a calibration curve, the gaps in which can be filled by photographing the same points at other values of the magnetic-field strength \(H\). In this way the curve can be constructed with any desired accuracy. For this purpose the groups \(\mathrm{C}_1\) and \(\mathrm{C}_2\), with mass numbers 12 and 24, prove very valuable (see, for example, Figs. 3 and 4).

The calibration curve obtained in this way has only slight deviations from linearity, which considerably facilitates the attainment of high accuracy. Aston and Fowler \(^{22}\) theoretically found the form of the function \(f\). The results of their calculations are presented in Fig. 14 (solid line). The points of Aston’s calibration curve plotted on the same graph show a brilliant agreement of theory with experiment. Since the equality

\[ \frac{d}{dM}\left(\frac{f\left(\dfrac{M}{M_0}\right)}{\dfrac{M}{M_0}}\right)=0 \]

is valid for angles of deflection \(\varphi = 40\), and since under the conditions of the experiment the angles of deflection lie near this region, the almost linear course of the curve also finds a theoretical explanation.

In the second method (the coincidence method) Aston does not at all make use of the dependence between \(D\) and \(M\). The method is based on the relation:

\[ \frac{M}{M'}=\frac{E}{E'}\left(\frac{H'}{H}\right)^2, \]

obtained, for example, from equality (1). This relation is valid if the masses \(M\) and \(M'\) fall on one and the same place of the photographic plate. Since exact coincidence cannot be detected, the coincidence method is replaced by the “inclusion” method. For this method it is necessary, at unchanged magnetic-field strength, to use two values of the voltage \(V\) and \(V'\); \(V'\) must differ from \(V\) by an amount \(\pm h\) (small in comparison with \(V\) and \(V'\)), which can be precomputed from the expected mass ratio. Thus, for example, the coincidence of the value of the mass ratio \(\mathrm{H}:\mathrm{H}_2\) with \(1:2\) was proved, and the deviation from this value of the ratio \(\mathrm{H}_2:\mathrm{He}\) was detected and measured.

Fig. 14.

\(\beta)\) Resolving power. The resolving power of the apparatus is limited by the width of the lines, which, with the assumed ideal focusing of velocities, is determined by the divergence caused by the finite dimensions of the slits and the distance between them. The line width calculated by Aston and Fowler\(^{22}\) on the basis of these assumptions agrees very well with that observed. This indicates that the inaccuracy of the velocity focusing hardly affects the broadening of the lines. The calculated resolving power proved to be \(1:100\). This means that masses differing from one another by \(1\%\) can still give separate lines. In fact, the resolving power is still somewhat higher, because it is precisely the narrowest parts of the slit that give the image. Further, Aston and Fowler showed that, by narrowing the slits and increasing the distance between them, the resolving power can be increased only with a simultaneous increase of \(\varphi\) and \(\theta\). Further, they investigated the question of whether, by choosing a suitable path length \(L\) in the magnetic field at different angles \(\varphi\), one can improve the position of the photographic plate (incidence closer to normal) or

improve the focusing of velocities (second-order focusing). The first is hardly practically feasible owing to the excessively great curvature of the line bounding the magnetic field. The second appears possible by imparting to the pole pieces bounding the magnetic field on the side of entry of the rays a curvature that is practically realizable.

γ) Aston’s work with the first apparatus. With the aid of his first mass spectrograph Aston carried out a series of studies in which he investigated the constellations of isotopes of a large number of elements. The results of these works led him to establish the well-known whole-number rule. It turned out that, within the limits of attainable accuracy (1:1000), the weights \(M\) of isotopes are expressed, relative to \({}^{16}\mathrm{O} = 16\), by integers \(m\), the so-called mass numbers. Only hydrogen gave a distinctly measurable deviation. The weight of this isotope measured by Aston, \(M = 1.008\), was in good agreement with the chemical atomic weight. In some other elements as well there appeared deviations from integrality lying at the limit of measurability. The following elements were investigated, listed here in the order of publication: \(\mathrm{Ne}^{23}\); H, He, C, N, O, Ne, Cl, A, Kr, X and \(\mathrm{Hg}^{24}\); B, F, Si, P, S, As and \(\mathrm{Br}^{25}\); Se, Te, J, Sb and Sn, of which only for J was a final value obtained \({}^{26}\); Li, Na, K, Rb and \(\mathrm{Cs}^{27}\); He from Canadian gas sources; Al, Fe, Ni, Se, Sn, Sb and X; then, however without result, Pb, Zn, Cd, Tl, Te and \(\mathrm{Be}^{28}\); Li and Be, for which a small deviation from integrality was measured; Mg and Ca, in which, at any rate, not all the isotopes found by Dempster \({}^{46,47}\) were discovered; further, Sc, Ti, V, Cr, Mn, Co, Cu, Ga, Ge, Sr, Y and Ag, and also, however without result, Zr and \(\mathrm{Hf}^{29}\); In, Sr, Ba, La, Pr, Nd, Ce, Zr, Cd, Te, Bi, Si, Fe and \(\mathrm{Pb}^{30}\); and finally, persistent but unsuccessful searches for atmospheric-air components heavier than X, which led to the discovery of two new isotopes of X \({}^{31}\).

c) Aston’s second apparatus

Of outstanding interest are the deviations of isotope weights from the mass numbers \(m\). Under the assumption made concerning the composition of the nucleus, these deviations, on the basis of the equivalence of mass and energy, give the binding energy of the constituent parts of the nucleus. In order to be able to measure these deviations, Aston \({}^{33}\) constructed the already described precision apparatus, in which he succeeded in considerably increasing the resolving power and the accuracy of the measurements. This was achieved, as indicated above, by reducing the diaphragms and increasing the distance between them, and also by increasing \(\theta_0\) to \(1/6\) radian while simultaneously increasing \(\varphi\) in such a way that on average \(\varphi\) remained equal to \(4\theta\). Next, an attempt was made to realize second-order focusing by imparting to the entrance side of the magnetic field the necessary curvature (Fig. 13).

Several mass spectra obtained with this instrument are presented in Fig. 15 (Table 8). The length of the spectra, almost 16 cm, comprises somewhat more than one octave. As can be seen, for example, from spectra I or VI, the distribution of lines along the entire length

Fig. 15.

of the spectrum is strikingly close to linear. For a one-percent change in mass, the dispersion changes from 1.5 mm at the left end of the plate, corresponding to the greatest deflection, to somewhat more than 3 mm at the other end of the plate. In Fig. 15, with the aid of the natural doublet (O and CH₄), this change can easily be traced (on the left and in the middle of spectrum IV, in the first half of spectrum I, and at the right end of spectrum III). The resolving power is suffi-

accurate for the separation of masses differing from one another by \(1/600\), and, according to the prediction of the theory, is not very different at the two ends. Owing to the fact that the curvature of the lines is not uniform and their shape changes along the spectrum, direct measurement of the mass ratio by measuring the distance \(D\) from some point on the plate, as was done formerly (the first method), becomes impossible. Since the accuracy must be very high \((1:10\,000)\), it can be attained only by measuring the distance between lines of approximately equal intensity and, consequently, of identical shape (if they are located very close to one another). The measurement of small distances between lines is carried out with the aid of a special comparator. However, when such high accuracy is required, the second method (the coincidence or “switching-on” method) also becomes unusable in its former form, since, owing to the polarization effect mentioned above, on the plates of the deflecting condenser the field strength can no longer be determined sufficiently accurately by measuring the applied voltage. The “switching-on” method gave, for the deviation of the mass ratio \(\mathrm{H}:\mathrm{H}_2\) from the value \(1:2\), a value equal to almost one-hundredth. This value could be reduced to \(5\cdot10^{-4}\) by using clean gold-plated plates (of the condenser), but still proved to be too high. In those cases where the effect was still greater, measurements showed that it remains very constant as long as the discharge conditions are not changed.

Therefore, in the method described below, Aston used the beams themselves to measure the ratio of the fields.

a) Measurements of relative mass defects. Proceeding from the whole-number rule, the weight of isotopes may be represented in the following form:

\[ M=m(1+\pi), \tag{7} \]

where \(\pi\) is the relative mass defect, a small quantity whose second order may be neglected (Aston expresses this quantity in \(10^{-4}\) fractions of a unit of atomic weight). It should be noted here that the masses measured with the mass spectrograph are the masses of ions, which—where this is necessary in order to obtain the masses of neutral atoms—must be further corrected by the value of the electron mass

\[ M_e=5.4\cdot10^{-4}. \]

The relative mass defect of the ion is \(\pi'=\pi-\dfrac{M_e}{m}\), where for doubly charged ions \(m\) must be replaced by one half of the mass number. The accuracy with which the distances of lines to some point can be measured is sufficient for determining both the mass numbers and the values of the dispersion constant at different points. These values, in the region where the measurements are usually made, lie on a straight line, so that interpolation can easily be performed. However, an exact comparison of the lines, as has already been said,

can be carried out only on doublets of identical intensity. Therefore, to compare the masses of the lines \(x\) and \(a\), they are photographed twice, so that, at fields \(E\) and \(E'\), the ratio of which is taken to be approximately equal to the ratio of the mass numbers, and with an unchanged magnetic field, the lines on one and the same plate would be arranged in the form of a conveniently measurable doublet. In order not to be dependent on small fluctuations of the magnetic-field voltage, the voltages \(V\) and \(V'\), which determine the strength of the electric field, are applied alternately, by means of a special interrupter, changing rapidly throughout the entire exposure time; moreover, the relative duration can be regulated so that the lines receive approximately the same intensity.

With ideal coincidence—which, however, could not be established on the photographic plate—there should be:

\[ M_x \cdot E' = M_a E. \]

By measuring the length of the interval between \(x\) and \(a\) with a comparator and multiplying the value obtained by the dispersion constant, taken for the midpoint of the interval, Aston obtained the corresponding percentage increase in mass \(\left(\frac{\Delta M}{M}\right)\), expressed in units of mass. This means that, using the coincidence relation, \(M'\) must be replaced in it by \(M\left(1 + \frac{\Delta M}{M}\right)\). But the coincidence relation also contains the fields \(E\) and \(E'\), which are not measured sufficiently accurately by the voltages \(V\) and \(V'\) (owing to the presence of a polarization effect). In order to eliminate them, photographs of two other lines \(b\) and \(c\), for which the mass ratio is well known, are taken at the same field voltages on another plate. To avoid the influence of an error in the dispersion constant, it is desirable to make the photograph so that the lines \(b\) and \(c\) lie, as far as possible, in the same region of the plate as the lines \(x\) and \(a\). This can be achieved by selecting another constant value of the magnetic-field voltage. In order for these two lines to form a narrow doublet, they must be chosen so that their mass numbers are in the same, or, if this cannot be accomplished, approximately the same, ratio as the mass numbers corresponding to the lines \(x\) and \(a\), i.e. the following relation must hold:

\[ m_x \cdot m_c = m_a \cdot m_b (1 + \varepsilon), \tag{8} \]

where \(\varepsilon\) is a small quantity. Since, besides the constancy of \(V\) and \(V'\), the constancy of the discharge conditions is also maintained, \(E\) and \(E'\) are one and the same for both photographs, and:

\[ \begin{aligned} M_x E' &= M_a \left[1 + \left(\frac{\Delta M}{M}\right)_1\right] E \\ M_b E' &= M_c \left[1 + \left(\frac{\Delta M}{M}\right)_2\right] E \end{aligned} \tag{9} \]

When equations (9) are divided by one another, the unknowns \(E\) and \(E'\) are eliminated. Substitution in place of \(M\) of expression (7), after calcu-

tion according to the rules of operations with small quantities gives the following relation between the relative mass defects of the ions:

\[ (\pi'_x-\pi'_a)-(\pi'_b-\pi'_c)=\Delta-\varepsilon . \tag{10} \]

Here \(\Delta\) represents the difference or the sum of the two measured mass intervals \(\frac{\Delta M}{M}\), depending on whether the lines \(b\) and \(c\) follow in the same order as the lines \(x\) and \(a\), or in the reverse order. To obtain the relative mass defects of neutral atoms, in some cases the electronic correction must be added to the right-hand side of equation (10):

\[ M_e\left[\left(\frac{1}{m_x}-\frac{1}{m_a}\right)-\left(\frac{1}{m_b}-\frac{1}{m_c}\right)\right] = M_e\,\frac{(m_x-m_a)-(m_b-m_c)}{m_a m_b}. \tag{11} \]

The right-hand side of equation (11) is exact only for the case \(\varepsilon=0\).

For the first relative mass defects measured by this method, certain assumptions naturally had to be made concerning the lines \(a\), \(b\), \(c\). Aston used the circumstance that the masses of molecules are formed by additive summation of the masses of the atoms entering into them, since the magnitude of the binding energy for molecules is many orders of magnitude below the order of magnitude of the accuracy of measurement; the mass defect of a molecule is

\[ \pi_{\mathrm{mol}}=\frac{\Sigma m_i\pi_i}{\Sigma m_i}, \tag{12} \]

where \(m_i\) and \(\pi_i\) denote the mass number and mass defect of the \(i\)-th component. Further, the mass defects of singly and doubly charged ions are identical. Therefore, as the lines \(b\) and \(c\) serving for comparison, one may choose an atom and a molecule of an element (\(\mathrm{H}\) and \(\mathrm{H}_2\), or \(\mathrm{C}\) and \(\mathrm{C}_2\), etc.) or singly and doubly charged ions of an atom (\(\mathrm{O}^{+}\) and \(\mathrm{O}^{++}\), or \(\mathrm{C}^{+}\) and \(\mathrm{C}^{++}\), etc.); for such pairs \(\pi_b-\pi_c=0\).

The mass defect of \({}^{16}\mathrm{O}\), by definition, is taken to be zero. The choice of this isotope as the standard has great advantages. O lies most precisely in the middle of the scale, since \({}^{1}\mathrm{H}:{}^{16}\mathrm{O}={}^{16}\mathrm{O}:{}^{238}\mathrm{U}\), and this greatly facilitates the achievement of high accuracy in mass comparison. With this choice of standard the mass defects obtained are the smallest and have positive and negative signs with almost equal frequency, whereas if, for example, hydrogen or the proton were chosen as the standard, all relative mass defects would be of the same sign and of considerably greater magnitude, so that treating them as small quantities would be permissible with much lower accuracy. In addition, the practical identity with the scale of atomic weights speaks in favor of this choice of standard.

Since for the first measured line \(x\), the lines serving for comparison must be chosen so that \(\pi_b-\pi_c=0\), then for

the value of the ratio of its mass number to the mass number \(a\) can in practice be chosen only between \(1:2\) and the reciprocal value. Since, moreover, \(\pi_a\) must be equal to zero, i.e. for \(a\) one of the simultaneously appearing oxygen lines must be chosen: 8, 16, or 32 (\(\mathrm{O}^{++}\), \(\mathrm{O}^{+}\), or \(\mathrm{O}_2^{+}\)), and the line \(x\) must be well distinguishable from them, only the mass numbers 4 or 64 can be adopted. For this reason Aston\({}^{33}\), as the first element to be measured, chooses He, and as comparison lines he takes \(\mathrm{O}^{++}\) for \(a\), \(\mathrm{C}^{++}\) for \(b\), and \(\mathrm{C}^{+}\) for \(c\). Owing to this, \(\varepsilon\) vanishes, which considerably increases the accuracy of the measurement. The mean of four measurements gives, for the difference \(\Delta\) of the two intervals, the value 5.2; to this is added the electron correction according to equation (11), \(\frac{1}{24}M_e = 0.2\). Thus \(\pi_{\mathrm{He}} = 5.4\), and hence, according to equation (7), the weight of the isotope \(M_{\mathrm{He}} = 4.00216\).

Now, for the second isotope to be measured, He can be chosen as \(a\), and owing to the fact that \(\pi_e - \pi_c\) must still be equal to zero, this isotope must stand to \({}^{4}\mathrm{He}\) in the ratio \(1:2\). Therefore, \({}^{1}\mathrm{H}_2\) is taken as the second isotope, and as comparison lines: \({}^{1}\mathrm{H}\) as \(b\) and \({}^{1}\mathrm{H}_2\) as \(c\). Since again \(\varepsilon = 0\), \(\Delta\), which by equation (10) was obtained as the mean of three measurements to be 73.73, is equal to the difference of the relative mass defects of \({}^{1}\mathrm{H}^{+}\) and \({}^{4}\mathrm{He}^{+}\). Here \(\Delta\) is the sum of the two mass intervals \(\frac{\Delta M}{M}\), since, in order to increase the accuracy, the voltages were chosen so that the \({}^{1}\mathrm{H}_2\) line in both doublets lay on one and the same side. The electron correction (11) gives \(-\frac{1}{4}M_e = -1.35\); therefore \(\pi_{\mathrm{H}} - \pi_{\mathrm{He}} = 72.4\), and with the preceding value of \(\pi_{\mathrm{He}}\) one obtains \(\pi_{\mathrm{H}} = 77.8\), whence by equation (7) \(M_{\mathrm{H}} = 1.00778\).*

For the following isotopes the ratio \(1:2\) between the lines serving for comparison is no longer prescribed. \({}^{12}\mathrm{C}\) can be measured with the aid of the lines \(\mathrm{O}^{++}\) as \(a\), \(\mathrm{OH}_2^{+}\) as \(b\), while for \(c\) \({}^{12}\mathrm{C}^{+}\) itself is again chosen. \(\varepsilon\) is again equal to zero. The mean of four measurements gives, for the difference \(\Delta\), the value \(-2.7\). According to equation (10), \(2\pi_{\mathrm{C}} - \pi_{\mathrm{H_2O}} = -2.7\), since in this case the electron correction (11) may be neglected. Relative—

* With so large a relative mass defect in \({}^{1}\mathrm{H}\), one should, strictly speaking, take into account in equation (10) terms of the second order and therefore add one more term \(\Delta^2(1-x)\), where \(x = \frac{\Delta M}{M}\Delta\). Since \(0 < x < 1\), \(\pi_{\mathrm{H}}\) lies between 77.8 and 78.3 in accordance with the value \(\left(\frac{\Delta M}{M}\right)_1\). In Aston’s work this value is not given. However, this correction lies within the limits of the experimental error.

the mass defect of the hydrogen molecule according to equation (12) is 8.7; therefore \(\pi_C = 3.0\), whence, by equation (7), \(M_C = 12.0036\).

In general, the lines used for comparison cannot always be chosen so that \(\varepsilon = 0\), and this greatly lowers the accuracy of the measurements. Thus, for example, for the lighter isotope B the exact relation can still be used

\[ {}^{10}\mathrm{B}\cdot{}^{12}\mathrm{C} = {}^{16}\mathrm{O}^{++}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H}_3, \]

whereas for the heavier one the inexact relation \({}^{11}\mathrm{B}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H} = {}^{12}\mathrm{C}\cdot{}^{12}\mathrm{C}\) must already be used. The results were checked by means of the relation \({}^{11}\mathrm{B}\cdot{}^{11}\mathrm{B} = {}^{12}\mathrm{C}\cdot{}^{10}\mathrm{B}\) and were found to agree. Other examples of this (Fig. 15, Table 8):

\[ {}^{19}\mathrm{F}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H}_3 = {}^{12}\mathrm{C}_2\cdot{}^{12}\mathrm{C} \quad \text{for F (spectra III and IV);} \]

\[ {}^{31}\mathrm{P}\cdot{}^{31}\mathrm{P} = {}^{12}\mathrm{C}^{16}\mathrm{O}\cdot{}^{31}\mathrm{P}^{1}\mathrm{H}_3 \quad \text{for P (spectrum VI).} \]

A very exact relation

\[ {}^{81}\mathrm{Br}^{++}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H} = {}^{12}\mathrm{C}^{16}\mathrm{O}_2\cdot{}^{12}\mathrm{C} \]

for the heavier isotope Br (spectrum VI):

\[ {}^{86}\mathrm{Kr}^{++}\cdot{}^{81}\mathrm{Br} = {}^{12}\mathrm{C}^{16}\mathrm{O}_2\cdot{}^{79}\mathrm{Br} \quad \text{(spectrum XI, \(a\) and \(f\))} \]

and

\[ {}^{86}\mathrm{Kr}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H}_3 = {}^{198}\mathrm{Hg}^{++}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H} \quad \text{(spectrum VIII)} \]

for the heavier isotope Kr.

This method, the method of double spectra, called by Aston method III, has the widest application, and it was precisely for it that the instrument was constructed. Method I, according to which the measurement is carried out on natural doublets, is a special case of method III under the condition \(E = E'\). In this case only the first equation (9) is used, the need for auxiliary lines \(b\) and \(c\) disappears, and since the electronic correction is equal to zero, the difference of the relative mass defects is simply equal to the measured interval \(\frac{\Delta M}{M}\). An example of this may be the doublet \({}^{16}\mathrm{O} — {}^{12}\mathrm{C}^{1}\mathrm{H}_4\) at mass number 16 (see, for example, spectrum I), by means of which Aston checked the relative mass defect of \({}^{12}\mathrm{C}\).

In those cases where the masses being compared form an arithmetic series with a not too large difference, Aston could use yet another method (II—“series shift”). An example of its application is the measurement of the lighter isotope Br by means of the series \({}^{79}\mathrm{Br}\), \({}^{79}\mathrm{Br}^{1}\mathrm{H}\), \({}^{81}\mathrm{Br}\), \({}^{81}\mathrm{Br}^{1}\mathrm{H}\) (spectrum II, \(a\) and \(b\)), or the measurement of the deviations from whole-number values of Kr isotopes by means of a series of even isotopes.

Two voltages, differing little from one another, corresponding to small differences of the chosen series, cause the formation of a double spectrum. The double spectrum is photographed as many times with different relative durations of the voltages as is necessary to form a doublet of equal intensity for each pair of lines. The advantage of this method is that there is no need for an exact determination of the dispersion constant. If all the lines formed an exact arithmetic series, the doublet distance 80, 81 would be equal to the average

from the doublet distances 79, 80 and 81, 82, since the dispersion constant changes linearly. When, however, as in the present case, this does not occur, the deviation from the mean measured in this way immediately gives the sought ratio between \(^{79}\mathrm{Br}\) and \(^{81}\mathrm{Br}\). Direct measurements show that the five even isotopes of Kr form an arithmetical series with an accuracy even greater than \(1:10^4\). It is easy to convince oneself that in this case what is measured are the deviations from integrality, i.e. the products \(m\pi\). To determine mass defects or isotope weights in this case, the corresponding data for one of the isotopes must, of course, first be measured—by the method described above.

Aston’s method of measuring mass defects is set forth here in such detail because the opinion is sometimes expressed in the literature that Aston made direct measurements of the relative weights of isotopes and computed from them relative mass defects characterizing the binding energy in nuclei, whereas in fact precisely the opposite was the case. The relative mass defects \(\pi\) have, as compared with deviations from integrality \((m\pi)\), the advantage that the error with which they are measured is the same over the whole scale of elements, whereas the error in determining \(m\pi\), for example for Hg, is 200 times greater than for \({}^{1}\mathrm{H}\). We shall denote by \(E\pi_x\) the relative mass defect of the atom \(x\), calculated on the assumption that the mass of the element \(E\), taken as the standard, is expressed by an integer and that its mass defect is therefore taken equal to zero. \(E\pi_x\), after multiplication by \(c^2\), represents the relative gain or loss of energy in the case in which the energy of intranuclear binding of the element \(E\) is recalculated to the element \(x\). For converting relative mass defects from one standard \(E\) (for example oxygen) to another \(E'\) (for example helium or hydrogen), the following exact expression exists:

\[ E'\pi_x\left(1+E\pi_{E'}\right)=E\pi_x-E\pi_{E'}, \tag{13} \]

or approximately:

\[ E'\pi_x=E\pi_x-E\pi_{E'}-E\pi_{E'}\cdot E\pi_x+E\pi_{E'}^{\,2}=E\pi_x-E\pi_{E'}. \tag{13a} \]

Here attention should be paid to the fact that, in the case of choosing the neutron as the standard, owing to its abnormally high mass defect and in view of the great accuracy of the measurements achieved by Aston, terms of the second order must also be taken into account.

For nuclear reactions, or for questions connected with the structure of nuclei, mass defects are of great importance; they can be calculated from relative mass defects. The mass defect of a nucleus, for its given (hypothetical) composition, is defined* as

* See, for example, B. F. G. Houtermans, Erg. d. exakt. Naturw. 9, 189, 1930.

the difference between the total weight of the particles entering into its composition and the true weight of the given nucleus. It is measured in grams and, when multiplied by \(c^2\), gives the binding energy of the particles in the nucleus under study.

Since the binding energies of the electron shells may be neglected, the mass defect is obtained most simply by replacing, in the total weight, the masses of the particles forming the nucleus (\(\alpha\)-particles, protons, etc.) by the corresponding isotopic weights (\(\mathrm{He}\), \({}^{1}\mathrm{H}\), etc.), and the weight of the nucleus under study by its isotopic weight. If the isotopic weight, the mass number, and the relative mass defect of the \(i\)-th particle entering into the composition of the nucleus are supplied with the index \(i = 1, 2, 3 \ldots s\), then

\[ \sum_{1}^{s} n_i m_i = m_x, \]

where the integer \(n\) shows how many \(i\)-th particles are contained in the nucleus. Then the mass defect \(\Delta M\), for the given composition of the nucleus, will be

\[ \Delta M = \frac{E}{m_E} \left[ \sum_{1}^{s} n_i E M_i - E M_x \right] = \frac{E}{m_E} \sum_{1}^{s} n_i m_i \left( E_{\pi_i} - E_{\pi_x} \right), \tag{14} \]

where \(E\) denotes the weight, expressed in grams, of the standard element, and \(m_E\) its mass number.

b) Measurement of relative abundances. In addition to measuring relative mass defects, Aston, on his second instrument, also carried out for various elements a series of very accurate measurements of the relative abundance of the isotopes of a given element and, on the basis of these measurements, calculated the physical atomic weights. It would seem that the most reliable method for investigations of this kind is the method of measuring the ion current due to the ions of individual isotopes. However, technical difficulties compelled Aston\({}^{34}\) to stop at the photometric method. In choosing the method, the consideration also played a role that, in the event of a transition to an electrical method, the instrument would have proved unsuitable for normal photographic measurements. The photographic method is based on the assumption that isotope \(A\) produces the same photographic action as isotope \(B\). This is true only approximately, but since the masses of isotopes, especially of heavy elements, differ from one another by only a few percent, and since, moreover, in Aston’s method the ions possess the same energy, the above assumption can hardly be the cause of serious errors. Further, the question arises of the validity of the law of reciprocity, which, as is known, is not entirely valid for light quanta. For electrons and canal rays, however, it is valid with a sufficient degree of accuracy. In other words: if, with the source of rays constant, isotope \(B\), during an exposure \(R\) times longer, gives the same photographic action as isotope \(A\), then the relative abundance of isotope \(A\) is \(R\) times greater than that of isotope \(B\). For photographs

at first\(^{32, 34, 35}\) flat-parallel “Paget-Half-Tone” plates were used, and later\(^{36}\) the so-called Ilford company \(Q\)-plates, which have 5–7 times greater sensitivity to canal rays. Schumann plates, which are about 20 times more sensitive than \(Q\)-plates, proved unsuitable for photometric measurements; however, they are used for detecting weak isotopes. In photometry, for each line the maximum blackening is determined, not the integral intensity. When comparing the intensities of two lines far removed from one another, a correction must be introduced that depends on the position of the line on the photographic plate, since the width of the lines, even with ideal focusing of the velocities, changes along the plate as a result of divergence.

In order to obtain the gradation curve of plates for canal rays, an exposure is made of a certain definite line (for example, \({}^{1}\mathrm{H}_{2}\), \({}^{84}\mathrm{Kr}\), \({}^{132}\mathrm{X}\), or \({}^{200}\mathrm{Hg}\)); moreover, two voltages \(V\) and \(V'\), differing from each other by \(1/2\%\), are alternately applied to the condenser plates. With good resolving power of the mass spectrograph, a clearly separated doublet is obtained, the components of which, however, are so close together that they permit accurate comparison. The ratio of the total exposure time at one and at the other voltage, the alternating switching-on of which is carried out in order to equalize the effect of the nonconstancy of the source of rays, can be accurately regulated by means of a rotating switch. The error arising because, in these measurements, different segments of the Thomson parabolas are taken for comparison is not cause for concern. First, the spherical discharge tube used by Aston gives a very uniform distribution of intensity over the electric spectrum; and secondly, even this minimal difference is eliminated by the fact that the mean is always taken from two measurements at voltages \(V\) and \(V'\). Thus, the dependence between the photometer readings and the logarithm of the product of intensity by exposure time is established experimentally. This dependence, for the above-mentioned ions, proves to be linear over sections of various length.

To determine the relative abundance (r. a.) of two isotopes by the method of alternating exposures, two lines of comparable intensity are photographed. The lines of both isotopes must lie in the linear region of the logarithmic curve for the corresponding element. The difference of the photometric readings, usually representing the average of the result of photometry of 6–7 separate photographs, gives, with the aid of the logarithmic curve, after introducing the above-mentioned correction connected with the position of the line on the plate, the relative abundance of both isotopes. For weak isotopes, owing to the formation of a halo from neighboring intense lines of abundant isotopes, a further correction must be introduced.

The smaller the relative abundance of a given isotope, the greater the error in its measurement. In determining the atomic weight from isotope weights and their relative abundances, the larger errors in determining the relative abundances of rare isotopes are automatically compensated precisely by their rarity. Furthermore, the influence of systematic errors for each symmetrical group of isotopes disappears, and the more isotopes there are on both sides of the mean, the more likely one may expect random errors to cancel. For heavy elements, the first of the two conditions indicated for measurements of relative abundances is fulfilled better. Therefore, for them all three sources of error in the measurement of the physical atomic weight—the relative mass defect, the transition from the scale \(^{16}\mathrm{O}=16\) to the scale \(\mathrm{O}=16\), and relative abundances—give one and the same error, namely: \(1:10^4\).

γ) Work done by Aston with the aid of the second instrument. With the aid of the second (precision) mass spectrograph Aston carried out a series of measurements of relative mass defects and abundances of isotopes, and also discovered new isotopes. The dependence of the relative mass defects on the mass numbers is represented by a smooth curve (Fig. 30), from which, by interpolation, the relative mass defects may be found for those elements for which measurements could not yet be made. For light elements the curve forms a second branch, on which lie the isotopes \(^{4}\mathrm{He}\), \(^{12}\mathrm{C}\), and \(^{16}\mathrm{O}\), which must be attributed to the greater stability of the bonds of the structural elements of these nuclei. Measurements of relative abundances revealed no regularity of a general character. They did, however, provide a physical method for determining atomic weights which in its accuracy is comparable with the best chemical methods. In some cases disagreement between the results of these two methods led to a revision of the international values. The advantage over the chemical method consists in the fact that, in general, the purity of the substance under investigation plays no role, and the amount required for measurement is usually a fraction of a milligram. The works published at various times contain the following: the discovery of new isotopes of S, Sn, X, and Hg; measurement of the relative mass defects and calculation of the weights of the isotopes \(^{1}\mathrm{H}\), \(^{4}\mathrm{He}\), \(^{10}\mathrm{B}\), \(^{11}\mathrm{B}\), \(^{12}\mathrm{C}\), \(^{14}\mathrm{N}\), \(^{16}\mathrm{O}\), \(^{19}\mathrm{F}\), \(^{20}\mathrm{Ne}\), \(^{22}\mathrm{Ne}\), \(^{31}\mathrm{P}\), \(^{35}\mathrm{Cl}\), \(^{37}\mathrm{Cl}\), \(^{36}\mathrm{A}\), \(^{40}\mathrm{A}\), \(^{75}\mathrm{As}\), \(^{79}\mathrm{Br}\), \(^{81}\mathrm{Br}\), \(^{78}\mathrm{Kr}\), \(^{80}\mathrm{Kr}\), \(^{82}\mathrm{Kr}\), \(^{83}\mathrm{Kr}\), \(^{84}\mathrm{Kr}\), \(^{86}\mathrm{Kr}\), \(^{120}\mathrm{Sn}\), \(^{127}\mathrm{J}\), \(^{134}\mathrm{X}\), and \(^{200}\mathrm{Hg}\) \(^{34}\); determination of the relative abundances of the isotopes of Kr, X, and Hg and calculation from them of the atomic weights of these elements \(^{34}\); a report on the discovery of new isotopes of Cr and Mo and confirmation of the existence of the Zn isotope discovered by Dempster \(^{47}\), and also a report on the discovery of two new isotopes of Zn which, however, as Bainbridge recently showed \(^{68}\), are hydrides; further, determination of the relative abundances of the isotopes of Zn, Sn, Cr, and Mo, calculation from them of the atomic weights of these elements, and a report on unsuccessful experiments with Cd and Ge \(^{35}\); discovery of new isotopes of Ru, Te, W, Re, Os, Ge (three of them...

which Bainbridge^75 had identified as hydrides); the determination of the relative mass defects of ^78Se, ^80Se, ^28Si, ^184W, ^190Os, ^192Os, ^126Te, ^128Te, ^187Re, the relative abundances of the isotopes of Se, Br, B, W, Sb, Os, Ru, Te, Ge, Re, and Cl, and the calculation of the atomic weights of these elements^36; the report of the discovery of new isotopes of Sr, Ba, Tl, and U (protactinium); the measurement of the relative mass defects for ^133Cs, ^138Ba, ^203Tl, and ^205Tl, the relative abundances of the isotopes of Cs (protactinium), Sr, Li, Rb, Ba, Se (protactinium), and Tl, and the derivation by calculation of the atomic weights of these elements^37; the study of the isotopic composition and atomic weights of Pb taken from different sources^38; the determination of the relative abundances of the isotopes of O^39, the relative mass defects of ^93Nb and ^181Ta^40; and, finally, the report of the discovery of new isotopes of the rare earths Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tu, Yb, and Cp^41, as well as Hf, Ti, Ca, Zr, Rh, Th, and Sm^41a.

d) Work of Other Authors

The Aston method for the study of isotopes, apart from Aston himself, was used only by Da Costa^42, who, even before the construction of Aston’s second mass spectrograph, built his own instrument. With this instrument he measured the weights of the isotopes (chiefly relative to the standard He = 4) of several light elements with an accuracy of 1 : 3,000. The results of his measurements of the isotopes of Li, recalculated by Aston to ^16O = 16, remained until very recently the only measurements made for this element. K. P. Yakovlev^43, using Aston apparatus, carried out a macroscopic separation of the isotopes 20 and 22 of neon, using separate receivers. Unfortunately, the dispersion of the optical spectrograph he employed proved insufficient for detecting differences in the spectra. In the Norman Bridge Laboratory an Aston mass spectrograph was also constructed for measurements analogous to those of Eizengut and Konrad^15; however, the reviewer is not aware of any published work from this laboratory. For determining \(\frac{e}{m}\) of the products of nuclear decay and of natural H-rays, G. Stetter^44 used an Aston mass spectrograph, which he redesigned in accordance with the special features of these experiments.

3. Focusing of Directions

a) Dempster’s Work and General Remarks

Almost simultaneously with Aston, A. J. Dempster developed another method for investigating canal rays. He made use of the focusing of a weakly divergent beam of rays when it is turned through 180° in a magnetic field. J. Classen used such focusing in determining \(\frac{e}{m}\) for electrons. Fig. 16 shows the superposition, on the circular path of the mean ray, of circular paths turned about the point \(S_1\) through the angle \(\pm \alpha\). From this figure it is clear wherein

consists in the focusing of the directions. The ions of the metal under investigation, obtained by slow evaporation of this metal or of its salts, while being simultaneously bombarded by electrons, all pass through one and the same potential difference \(V\), applied between \(A\) and \(S_1\) (Fig. 17). In this case the electric spectrum in Parabola’s method would consist of only one point. For further analysis, therefore, only one magnetic field is sufficient. Applying the known equations:

Fig. 16.

we have:

\[ \left. \begin{aligned} \frac{mv_0^2}{2} &= eV;\quad \frac{1}{r}=\frac{eH_0}{mv_0},\\ \frac{m}{e} &= \frac{H_0^2 r^2}{2V} \end{aligned} \right\} \tag{15} \]

Since the intensity \(H_0\) of the homogeneous magnetic field is kept constant, the masses are inversely proportional to the voltage \(V\), and comparison of the weights of isotopes can in principle be made with the same accuracy with which this voltage can be measured.

The paths from the anode \(A\) to the entrance into the homogeneous magnetic field pass through the stray field of a rather strong electromagnet. Therefore, near the point \(B\), they will be turned through a small angle and will be displaced somewhat. This is sufficient to destroy the focusing. Moreover, it creates an inaccuracy in the value of \(r\) in equation (15). Dempster overcame this difficulty by means of a simple device. He placed the entrance slit \(s_1\) at a distance \(b\) from the entrance into the homogeneous field. On the basis of the considerations illustrated by Fig. 16, Dempster asserts that the focusing condition consists in the points \(S_1\), \(O\), \(S_2\) lying on one straight line. Although the paths now have, over a certain stretch, a non-circular form, the focusing condition remains valid as long as the influence of the stray field is small. Dempster calculates the magnitude \(b\) as follows: on the one hand, \(\operatorname{tg}\gamma\) is equal to \(\frac{b}{2r}\); on the other hand, it

Fig. 17.

is equal to the angular coefficient of the tangent to the trajectories at the point \(B\). The angle of inclination of the tangent is composed of the angle of deflection in the segment between \(K\) and \(S_1\) and the angle of deflection in the segment between \(S_1\) and \(B\). Between \(K\) and \(S_1\) an electric field acts. The first integral of the equations of motion:

\[ m\frac{d^2x}{dt^2}=\frac{eV}{AS_1},\ \text{and}\ m\frac{d^2z}{dt^2}=eH\frac{dx}{dt} \]

with the aid of equation (15) gives, for the first segment, the expression:

\[ \left(\frac{dz}{dx}\right)_{S_1}=\frac{1}{rH_0}\int_K^{S_1} H(x)\,dx . \tag{16} \]

Exactly the same expression is also valid for the second segment, i.e. for particles moving only in the magnetic field:

\[ b=\frac{2}{H_0}\int_K^B H(x)\,dx . \]

Measurement of the stray field, carried out by compensating it at the point \(K\) with another magnet, gave for the magnitude \(b\) the value \(0.93\ \mathrm{cm}\). Accordingly, \(S_1\) was advanced by this distance from the homogeneous magnetic field. The second integral (cf. equation 1a) gives the magnitude of the displacement of \(S_1\) relative to \(B\) in the direction \(z\). This quantity proved to be \(0.25\ \mathrm{mm}\). Half of this quantity represents a correction (which may be neglected) to the value of the radius \(r\) \((=5\ \mathrm{cm})\).* If one assumes that the directional focusing is ideal, then, for equal width \(S\) of both slits, the maxima for the individual masses, as is easy to see, must have the form of isosceles triangles. The width of these triangles at half height is equal to \(S\), if distances are laid off along the axis of abscissas. The resolving power is determined from the last equation (15).

\[ \frac{\Delta m}{m}=\frac{2\Delta r}{r}=\frac{2\Delta d}{d}=\frac{2S}{d}. \]

Dempster \(^{45-47}\), in his experiments, finds that this relation is justified quantitatively and qualitatively, at any rate for the light elements. The slight broadening of the maxima observed experimentally is explained by Dempster \(^{47}\) by the small but finite width of the electric spectrum (3 V at 900 V accelerating-field voltage). Dempster even then proposed using, in addition to the analyzing magnetic field, also a radial electric field, which would give, simultaneously with focusing in direction, focusing of velocities.

* For a more detailed calculation of the influence of the stray field, see R. Herzog \(^{90}\).

Detection of ions at slit \(S_1\) is carried out electrometrically, by the null method. The charging of the receiver by positive ions is balanced by means of a negative ion current produced in an ionization chamber by the \(\beta\)-particles of a radioactive preparation, the flux of which is regulated by a slit with a micrometer screw. Readings on the scale of the micrometer screw are calibrated according to the negative ion current and provide an easily reproducible and accurate method for measuring the positive ion current.

Dempster’s method makes possible the direct measurement of the relative intensities of isotopes, since here too segments (or points) of Thomson parabolas corresponding to the same (electric) abscissae are used. However, for some elements (above all for Li) Dempster\(^{46}\) finds a very variable and nonreproducible intensity ratio, which he explains by surface conditions and by different rates of evaporation of the isotopes at different temperatures.

Dempster found the isotopes of Li (simultaneously with Aston\(^{27}\) and J. J. Thomson\(^{13}\)) and Mg\(^{46}\); subsequently he found the isotopes of Ca and Zn\(^{47}\) and confirmed the existence of the isotopes of K. The atomic weights calculated from the relative abundances and mass numbers agree so well with the chemical ones that Dempster proposes carrying out the calculation of relative mass defects.

b) New works

Dempster’s method has been applied many times, especially by Smyth, Hogness and Lunn, Kallmann and others, for investigating the emission of positive ions and for identifying ions in experiments with electron impacts. Here we shall confine ourselves to works devoted to isotopes. M. Moran\(^{48}\), in one of his experiments using Dempster’s apparatus, obtained a macroscopic separation of the isotopes of Li and found constancy of the intensity ratio by simultaneously measuring the ion currents for both isotopes. J. L. Hendley\(^{49}\), as well as earlier J. J. Thomson\(^{13}\) and Dempster\(^{46}\), found a strongly varying intensity ratio for the isotopes of Li. The intensity ratio, apart from its dependence on the isotope source, appeared to depend strongly on temperature. Later Bainbridge\(^{53}\) explained these contradictions. T. R. Hogness and H. M. Kvalnes\(^{5}\) succeeded in establishing the authenticity of the existence of \({}^{21}\mathrm{Ne}\) as a genuine isotope. The nature of this particle, discovered earlier by Aston\(^{24}\), had remained in question even for him.

Using Dempster’s method, K. T. Bainbridge\(^{51-54}\) carried out important investigations. The first paper\(^{51}\) was devoted—though unsuccessfully—to searches for an ion of mass 223 or 224 (eka-cesium) in vapors of cesium salts taken from minerals in which eka-cesium was presumed to be present. In these experiments the radius \((r = 3.2\ \mathrm{cm})\) and resolving power \(\left(\dfrac{\Delta m}{m} = \dfrac{1}{42}\right)\) were still small. Both these quantities

...were enormously increased through the use of the large magnet of the Franklin Institute \(\left(r = 9.2\ \text{cm},\ \frac{\Delta m}{m}=\frac{1}{279}\right.\) in the assumption of ideal focusing and for a beam limited by an angle of \(\pm 4^\circ\), allowing for actually attainable focusing \(\left.\frac{\Delta m}{m}=\frac{1}{208}\right)\). On this apparatus Bainbridge showed with complete clarity the homogeneity of Cs. The chemical atomic weight of Cs is 132.81; for the relative mass defect of \(^{133}\mathrm{Cs}\), Bainbridge gives the value \(-14.3\), quite outside Aston’s curve (Fig. 30). The atomic weight should be \(0.077\%\) higher. Bainbridge succeeded in establishing that mass numbers 132, 131, 130, or 129 do not appear even with \(1/10\) of the intensity that would have been sufficient to explain this discrepancy.

A direct measurement of the relative mass defect for Cs, carried out by Aston \(^{37}\), gives the value \(-5.0 \pm 2\), which lies on the curve. The corresponding physical atomic weight is \(132.917 \pm 0.02\). In good agreement with this is the new chemical atomic weight measured by J. P. Baxter and J. S. Thomas (223a). Further, Bainbridge precisely measured the ratio for the isotopes of Li and undertook searches for unknown isotopes of Na and K, for which he succeeded in establishing upper limits of relative abundance.

The nonconstancy of the isotope ratio of Li, discovered by Dempster, Bainbridge attributes to the circumstance that, before entering the homogeneous magnetic field, the two isotopes describe different paths in the accelerating field, since the voltage \(V\) is applied in two parts, the first usually being kept constant and only the second part varied in accordance with the masses of the isotopes. Thus, even before \(S_1\) a weak separation of the isotopes occurs, which, naturally, is much more pronounced for light elements, for which the differences of the masses in percentage terms are greatest. For heavy elements Dempster in most cases obtained constant ratios. The dependence of the intensity ratio on temperature, found by Hande \(^{49}\), Bainbridge explains by the fact that in Hande’s apparatus the ion current was limited by space charges, owing to which the effective dimensions of the ion source become correspondingly greater than the physical dimensions of the filament emitting the ions. This circumstance, together with that indicated above, also leads to separation of the isotopes already before \(S_1\). As the probable value for the relative abundance Bainbridge gives \(^{7}\mathrm{Li}:{}^{6}\mathrm{Li}=11.28 \pm 0.07\). If the isotopic effect in free evaporation is taken into account, one obtains* 12.18. J. P. Garnwell and W. Bleakney \(^{55}\) recently found for this ratio—despite the fulfillment of Bainbridge’s condition—an average value equal to 8.4, which is in agreement with measurements made by means of band spectra. Further, with the alkali metals Bainbridge \(^{55}\) carried out photo-

* F. W. Aston, Mass-Spectra and Isotops, p. 110, London 1933.

graphical measurements, linking them with electrometric ones, and investigated the absorption coefficient, especially for copper (up to \(4602\ \mathrm{eV}\)) rays.

Kalman and Lazarev \(^{56}\) reported on their investigations of the isotopes of O, N, and Cl. They used Dempster’s method with the sole difference that instead of \(V\), \(H\) was varied. For the abundance ratio of \({}^{18}\mathrm{O}:{}^{16}\mathrm{O}\), by comparing the maxima of the pairs \({}^{12}\mathrm{C}{}^{16}\mathrm{O}\) and \({}^{12}\mathrm{C}{}^{18}\mathrm{O}\), \({}^{1}\mathrm{H}_{2}{}^{18}\mathrm{O}\) and \({}^{1}\mathrm{H}_{2}{}^{16}\mathrm{O}\), and also \({}^{16}\mathrm{O}_{2}\) and \({}^{16}\mathrm{O}{}^{18}\mathrm{O}\), they found the mean value \(1:630 \pm 8\%\), which practically coincides with the result of Mecke and Childs \(^{113}\). Further, they asserted that they had discovered an isotope of Ne with mass 23, whose abundance relative to \({}^{20}\mathrm{Ne}\) is \(1:2000\). This assertion was disputed by Bleakney \(^{57}\), and also by Bainbridge. Both authors were able to give \(1:10^{4}\) as the upper limit, so that, apparently, Kalman and Lazarev were dealing with the hydride \({}^{22}\mathrm{NeH}\). Their repeated reports on the discovery of \({}^{39}\mathrm{Cl}\) (abundance ratio \({}^{39}\mathrm{Cl}:{}^{35}\mathrm{Cl}=1:6000\)) should not be trusted especially. Le Roy, L. Barnes, and R. K. Gibbs \(^{52}\) also work by Dempster’s method; in a sample of alkaline sulfates they discovered an ion with mass 220 and attributed it to eka-cesium. One should also mention the work of H. Muravkin, which is devoted to the development of the method and to the question of the emission of ions by glasses. Among other things, it contains completely implausible values for the ratio \({}^{16}\mathrm{O}:{}^{18}\mathrm{O}\).

J. T. Tate, P. T. Smith, and A. L. Vaughan \(^{59a}\), in experiments with electron impacts in acetylene \((\mathrm{C}_{2}\mathrm{H}_{2})\), found mass 27, which they represented as \({}^{12}\mathrm{C}{}^{13}\mathrm{C}{}^{1}\mathrm{H}_{2}\); for the abundance ratio \({}^{12}\mathrm{C}:{}^{13}\mathrm{C}\) one obtains \(100:1\), which is in good agreement with spectroscopic measurements. When filling the tube with Co, N, and A, A. L. Vaughan, J. G. Williams, and J. T. Tate \(^{59b}\), comparing the relative heights of maxima on numerous curves, find the following values for the abundance ratios:
\({}^{12}\mathrm{C}:{}^{13}\mathrm{C}=91.6 \pm 2.2,\quad {}^{14}\mathrm{N}:{}^{15}\mathrm{N}=265 \pm 8,\quad {}^{40}\mathrm{A}:{}^{36}\mathrm{A}=304 \pm 12,\quad {}^{20}\mathrm{Ne}:{}^{21}\mathrm{Ne}=337 \pm 20\) and \({}^{20}\mathrm{Ne}:{}^{22}\mathrm{Ne}=9.25 \pm 0.08\).

c) Modifications of the method

W. Bleakney modified Dempster’s method in an original way, using a current-carrying coil to obtain the magnetic field. The coil serves two purposes. First, thanks to the magnetic field, the expansion of the electron beam traveling along its axis is impeded. The electrons serve to form ions in a gaseous atmosphere at a pressure from \(10^{-4}\) to \(10^{-7}\ \mathrm{mm}\ \mathrm{Hg}\). Owing to the application of the magnetic field, the ions are formed in a definite part of the volume and can therefore be accelerated by a definite voltage \(V\). The voltage is applied in two stages. The first (smaller) serves to extract the ions from the electron beam; the second (larger) is what actually brings about the acceleration. The ions then pass through two long narrow coaxial slits. Secondly, the magnetic field, as in Dempster’s apparatus, serves for the analysis of the ions and for focusing on a third slit, located where the beam

rotated by \(180^\circ\), and behind which there is a receiver connected to an electrometer. A second receiver, arranged in a special way, makes it possible, for a given deflection of the beam, to measure the total current of ions passing through the first two slits. Soon after the discovery of the hydrogen isotope with mass 2, Bleakney \(^{61}\) undertook to measure its abundance in natural and enriched H. The resolving power (the magnitude of the radius \(r\) is not given), calculated from Bleakney’s maxima for \({}^{1}\mathrm{H}\) and \({}^{1}\mathrm{H}_2\), is approximately \(1/60\). It is, of course, not high enough to separate, at mass 2, the maxima from \({}^{1}\mathrm{H}\) and \({}^{1}\mathrm{H}_2\), or, at mass 3, the maxima from \({}^{1}\mathrm{H}{}^{2}\mathrm{H}\) and \({}^{1}\mathrm{H}_3\). Bleakney’s method is, strictly speaking, not mass-spectrographic, since what is measured is the dependence of the total intensity of the maximum at mass 3 on the pressure \(p\). The number of diatomic molecules \({}^{1}\mathrm{H}{}^{2}\mathrm{H}\), representing a primary combination, must be proportional to \(p\), whereas the number of triatomic molecules \({}^{1}\mathrm{H}_3\), formed as a result of secondary processes, must be proportional to \(p^2\). The total intensity at mass 3 will therefore be \(I = ap + bp^2\), or \(\dfrac{I}{p} = a + bp\), where \(b\) is a constant which must have one and the same value for both curves (for natural and for enriched hydrogen). The pressure \(p\), whose measure is the intensity of the maximum at mass 2, caused chiefly by \({}^{1}\mathrm{H}_2\) ions, is also checked by the fact that the tube itself is used as an ionization manometer (measurement of the total ionic current at constant electron current). Thus the measurement of the abundance of \({}^{2}\mathrm{H}\) is reduced to the measurement of the constant \(a\). The result of measuring the relative abundance for \({}^{2}\mathrm{H}:{}^{1}\mathrm{H}\) is as follows: \(1:3\cdot10^4 \pm 20\%\). This result was also confirmed from another side \(^{64,130,175,176}\), and therefore for some time was regarded as reliable, despite the fact that it was in contradiction with the data obtained by R. T. Birge and D. H. Menzel \(^{22}\) by calculation from the atomic weight of H and from the weight of the isotope \({}^{1}\mathrm{H}\). Recently, Bleakney and A. J. Gould \(^{62}\) have resolved this contradiction, finding in hydrogen obtained by the decomposition of rain water with iron at a temperature of \(510^\circ\), for \({}^{2}\mathrm{H}:{}^{1}\mathrm{H}\), the value \(1:5000 \pm 10\%\). Evidence of the accuracy of the method is provided by the fact that for commercial electrolytic hydrogen, which Bleakney \(^{61}\) had also used previously, they found the ratio \(1:25000\). In this hydrogen, \({}^{2}\mathrm{H}\) was probably depleted owing to the process that was later discovered by Washburn and Urey \(^{225}\), and also by Lewis and Macdonald \(^{226}\). Bleakney and Gould were able, using \({}^{2}\mathrm{H}_3\), to verify experimentally their assumption that the number of triatomic molecules formed is proportional to the square of the pressure.

Furthermore, Bleakney succeeded in showing that in He there are no isotopes with masses 3 or 5 whose abundance would exceed \(1:5\cdot10^4\). The ion \(({}^{1}\mathrm{H}_2\,{}^{2}\mathrm{H}_1)^+\), which H. Kalman and V. Lazarev \(^{63}\) had unsuccessfully sought by Dempster’s method, was soon detected by Bleakney’s method, at any rate in enriched ...

in the sample, the presence of \({}^{2}\mathrm{H}\). They also found \({}^{5}\mathrm{He}:{}^{4}\mathrm{He}<1:4\cdot10^{4}\); the same was found by J. P. Tait and P. T. Smith \(^{64}\) for He from Precambrian beryl, using Bleakney’s method. For \({}^{3}\mathrm{He}\) in He under discharge, A. J. Dempster, J. H. Williams, and J. T. Tait \(^{59b}\) give the ratio \({}^{3}\mathrm{He}:{}^{4}\mathrm{He}<1:3.5\cdot10^{4}\).

P. T. Smith, W. W. Locher, and W. Bleakney refined and automated Bleakney’s apparatus. The accuracy was increased to such an extent that, with the aid of the new apparatus, much smaller relative abundances can be measured. Bleakney and Gould \(^{62}\), in concentrated \({}^{2}\mathrm{H}\), searched for the isotope \({}^{3}\mathrm{H}\) and found \({}^{3}\mathrm{H}:{}^{2}\mathrm{H}<1:10^{5}\). This ratio for natural hydrogen gives \({}^{3}\mathrm{H}:{}^{1}\mathrm{H}<1:5\cdot10^{8}\). On the new apparatus W. W. Locher, P. T. Smith, and W. Bleakney succeeded mass-spectrographically in detecting \({}^{3}\mathrm{H}\), whose existence, among other things, had been assumed by M. L. Oliphant, P. Harteck, Lord Rutherford \(^{221a}\), and others on the basis of experiments on the disintegration of atomic nuclei. In concentrated \({}^{2}\mathrm{H}\) they found \({}^{3}\mathrm{H}:{}^{2}\mathrm{H}=5\cdot10^{6}\), whence it follows that for natural hydrogen \({}^{3}\mathrm{H}:{}^{1}\mathrm{H}=1:10^{9}\) and even less. J. P. Harnwell, H. D. Smyth, C. N. Van Voorhis, and J. B. H. Kuper \(^{65b}\) subjected \({}^{2}\mathrm{H}\), under high pressure, to bombardment by very fast \({}^{2}\mathrm{H}\)-channel rays. In agreement with the above-mentioned authors, an enrichment in the isotope \({}^{3}\mathrm{H}\) was found, for which \({}^{3}\mathrm{H}:{}^{2}\mathrm{H}=1:5\cdot10^{3}\) was measured. This enrichment occurs by the reaction proposed by Oliphant, Harteck, and Rutherford \(^{221a}\):

\[ {}^{2}\mathrm{H}+{}^{2}\mathrm{H}\longrightarrow{}^{3}\mathrm{H}+{}^{1}\mathrm{H}. \]

Thanks to a modification of another kind, consisting in the “correction” of the magnetic lens, carried out by giving a suitable shape to the entrance side of the magnetic field while at the same time considerably increasing the primary intensity of the ions, W. R. Smythe and his collaborators L. H. Rumbaugh and S. S. West \(^{66}\) succeeded in constructing a mass spectrograph of especially high intensity, in which, for example, a current of \({}^{39}\mathrm{K}\) ions of 0.1 mA could be maintained for 20 hours. Therefore macroscopic separation of Li isotopes in amounts of several micrograms proved feasible on this instrument. In this instrument (in contrast to how it is done by Dempster) a very large entrance slit, admitting emission from \(30\ \mathrm{cm}^{2}\), is located perpendicular to the lines of force of the magnetic field. The magnetic field is bounded by two circles, so that the rays passing through the entrance slit along its entire length are focused into one point.

4. Velocity filters

As early as 1926 W. R. Smythe \(^{79}\) proposed a velocity filter for electrons and ions, based on the use of rapidly alternating fields (we shall return to this question in point b). Regarding the application of his method he reports successful experiments on

for the identification of positive ions, produced by Dr. Klein. After passing through a constant voltage \(V\), the positive ions were passed through a velocity filter. Measurement of the frequency applied to the filter and of the voltage \(V\) immediately gives both \(v\) and \(\dfrac{mv^{2}}{e}\), and consequently \(\dfrac{e}{m}\). He then describes (constructed jointly with Referent) a mass spectrometer, consisting of a velocity filter, to which, for mass analysis, either a magnetic field or a radial electric field can be applied at will. Among the advantages of this method one must note the strict linearity of the mass scale, as well as the possibility of direct comparison with a standard element.

Related to this method is the method used by Kirchner, and also by Perry and Chaffee, for precise measurements of \(\dfrac{e}{m}\) of cathode rays. At the basis of the Vin method of “compensated scales” there likewise lies a velocity filter. The latter method was used by Bestelmeyer, Bucherer, and others to determine \(\dfrac{e}{m}\) of cathode and \(\beta\)-rays. Only rays with velocity

\[ v_{0}=\frac{E}{H} \tag{17} \]

can pass through two crossed fields \(E\) and \(H\) of equal length without undergoing deflection. This condition is easily obtained by subtracting equations (1), or simply from the condition of equilibrium of the forces \(eE=ev_{0}H\).

a) Vin Filters

Even before the use of his apparatus described in the preceding section, W. Bleakney proposed an analogous arrangement and used it for measuring ionization potentials. He increased the concentration of the electron beam producing the ions by using the magnetic field of a coil. The ions are accelerated by a constant voltage \(V\) and therefore have the same value of \(\dfrac{mv^{2}}{e}\).

The analysis of the ions, however, is carried out not as before—not only by the magnetic field of the coil. The ions pass simultaneously through a magnetic field and an electric field perpendicular to it, which is possible only for ions having a velocity determined by equation (17). Therefore

\[ \frac{e}{m}=\frac{E^{2}}{2VH^{2}}; \]

the measurement of masses is carried out at constant \(v\) and \(H\) by varying \(E\), similarly to the way this is done in Klein’s apparatus described by Smythe[^79]. For isotope research this method has not yet been applied.

K. T. Bainbridge[^68,^70,^72,^78] described an instrument operating analogously to that described by Smythe[^79], with the sole difference that in it Smythe’s filter is replaced by a Vin filter. Fig. 18

schematically depicts this apparatus. By means of the collimating slits \(S_1\) and \(S_2\), a narrow beam of canal rays is selected, which may contain ions of all possible velocities. Bainbridge extended the field of his magnet upward and to the right and, by placing a capacitor \(P_1, P_2\) between the slits \(S_1\) and \(S_2\), realized Wien’s velocity filter. Thus ions with different masses, but with the very narrowly limited velocity \(v_0\), the same for all ions, can pass through the slit \(S_3\). Therefore, according to the second equation (15), the radius \(r\) in the analyzing magnetic field is strictly proportional to the mass. The distances of the lines from some line arbitrarily chosen for comparison are likewise, consequently, strictly proportional to the masses. Further, Bainbridge asserts that the path of the rays corresponds to that shown in Fig. 18. There is no focusing of directions (Fig. 16) in this case; the rays emerging from the slit \(S_3\) as a parallel beam intersect when turned through \(90^\circ\), and when turned through \(180^\circ\) they meet the plate at a right angle, the rays again becoming parallel. This leads to the lines on the plate having a symmetrical form, whereby comparison of lines is made possible, even of lines that differ greatly from one another in intensity.

Fig. 18.

This circumstance, together with the linearity of the mass scale, gives a great advantage in comparison with Aston’s apparatus. It should be noted here that the effect of the finite width of the slit, as well as the effect of those rays passed by the slit for which the velocity differs somewhat from \(v_0\), may be neglected.* In fact, photometric measurement gives a very symmetrical form of the lines, so that the accuracy indicated by Bainbridge (in favorable cases the error does not exceed \(1:100\,000\)) appears justified.

The calibration of the first eight centimeters of the plate, made with the aid of the \(C_1\) group and the lines O, OH\(_1\), OH\(_2\), OH\(_3\), shows that the linearity prescribed by the theory is fulfilled with an accuracy of up to \(1:10\,000^{71}\) (cf. Fig. 20, Table 9, spectrum \(e\)). Toward the end of the plate the deviations increase to approximately \(10:10\,000^{74}\). For a change in mass of 1% the dispersion is \(1.6\) mm at one end of the plate and changes along the plate so that at its other end it is \(3.8\) mm

* For discussion of this question, see R. Herzog\(^{30}\).

(cf., for example, the doublet \(^{4}\mathrm{He}^{++}—{}^{1}\mathrm{H}_{2}\), Fig. 20, spectrum c). In comparison with the data of Aston’s second mass spectrograph (from \(1.5\ \mathrm{mm}\) to somewhat more than \(3\ \mathrm{mm}\)), these figures, if one takes into account the sharpness of the lines obtained by Bainbridge, testify to the success achieved in increasing the resolving power. In any case, for measuring the relative abundances the Aston apparatus retains its superiority. Since, as in any method in which a velocity filter is used before mass separation, the lines are points of Thomson parabolas lying on straight lines passing through the origin (according to the first equation \(^{2}\)), comparison of the intensities of the lines of different isotopes, without information on the distribution of intensity along the parabolas, does not give a measure of the relative abundances of the isotopes. For isotopes of heavier elements, whose masses differ little from one another, the intensity along the investigated portion of the parabola may be considered constant, and the ratio of the intensities of the lines may be taken as the ratio of the intensities of the isotopes themselves.

Fig. 19.

In Fig. 19 Bainbridge’s apparatus is shown in detail. A voltage from 5,000 to 20,000 V, obtained from two 25,000 V transformers, is applied to the discharge tube \(A\), which is filled through \(P\) with the gas under investigation. Rectification of both half-waves is carried out, with no additional smoothing of the voltage being used. \(K\) is water cooling of the cathode. The end of the dark space is, as a rule, at a distance of \(2—5\ \mathrm{cm}\) above the cathode. On the cathode there is a slit (\(0.0025\) to \(0.007\ \mathrm{cm}\)) which can be adjusted; the ions pass through it. \(C\) and the other shaded parts constitute the magnetic shielding of the discharge tube and of the path of the rays up to their entrance into the filter \(D\). In front of the filter there is a slit of \(0.005\ \mathrm{cm}\). The condenser plates, separated from one another by \(3\ \mathrm{mm}\), are carefully set parallel to one another and to slit \(B\). The voltage on the plates is supplied by radio batteries. To prevent the influence of induced alternating voltages, the plates are connected to ground through condensers. The chamber is bounded by pole pieces \(N\), spaced \(1.6\ \mathrm{cm}\) apart; a thin copper shell \(J\) makes it possible to create a vacuum in the chamber. Three volumes, separated by slits, are evacuated through branches \(Q\), \(R\), and \(O\). \(L\) is a liquid-air trap, which for condensable vapors plays the role of a powerful pump. The photographic plate \(F\) (\(25.4 \times 2.54\ \mathrm{cm}\)) is located

in holder E and can be shifted sideways for successive exposures. With the aid of lens I, target H is photographed on plate F; its image serves as the line with respect to which the measurements are made. After the plate is inserted, the camera cover, centered by pins G, is put on and then sealed with glyptal lacquer.

With this apparatus Bainbridge undertook a series of very precise measurements of relative mass defects and isotopic weights, using chiefly Aston’s methods I and III. Owing to the accurate linearity of the mass scale, direct measurement of M also becomes possible. Since \(kM = D + E\), where \(D\) is the distance of the given line from the line with respect to which the measurements are made, and \(E\) is the distance of the latter from the source \((S_3)\), two known masses are sufficient to determine the constants \(k\) and \(E\). To obtain metal ions, Bainbridge made use of cathode sputtering in a discharge in Ne or A. He deposited the metal under investigation on the cathode, or else deposited it on the walls of the discharge tube by evaporation. This method is especially suitable for studying elements that form hydrides, since the strong affinity of ionized Ne and A for hydrogen ensures purification of the gas in the discharge tube from accidental hydrogen impurity. Bainbridge \(^{68}\) showed that the Zn isotopes discovered by Aston \((^{65}\mathrm{Zn}\) and \(^{69}\mathrm{Zn})\) are hydrides. He succeeded in explaining the disagreement between the physical and chemical atomic weights of Te by the discovery of three (four) new, lighter isotopes in addition to those discovered by Aston (Fig. 20, spectrum a). He then measured the isotopic weights of \(^{2}\mathrm{H}\) \(^{71,76}\) (Fig. 20, Table 9, spectrum b and spectrum f) by means of natural doublets with masses 4, 5, and 6: \(^{4}\mathrm{He}^{+}—(^{1}\mathrm{H}_{2}\,^{2}\mathrm{H})^{+}\), \((^{4}\mathrm{He}\,^{1}\mathrm{H})^{+}—(^{2}\mathrm{H}_{2}\,^{1}\mathrm{H})^{+}\) and \((^{4}\mathrm{He}\,^{2}\mathrm{H})^{+}—^{2}\mathrm{H}_{3}^{+}\); \(^{1}\mathrm{H}^{72}\) (Fig. 20, Table 9, spectrum d) by means of a doublet with mass number 2; \(^{4}\mathrm{He}^{++}—^{1}\mathrm{H}_{2}^{+}\); \(^{9}\mathrm{Be}^{73}\) (Fig. 20, spectrum d) by means of the ratios: \(^{9}\mathrm{Be}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H}_{4}=^{12}\mathrm{C}\cdot{}^{12}\mathrm{C}\) and \(^{9}\mathrm{Be}\cdot{}^{12}\mathrm{C}^{1}\mathrm{H}=^{20}\mathrm{Ne}^{++}\,^{12}\mathrm{C}\); the isotopes \(^{35}\mathrm{Cl}\) and \(^{37}\mathrm{Cl}^{75}\); the isotopes \(^{20}\mathrm{Ne}\), \(^{11}\mathrm{B}\), and \(^{22}\mathrm{Ne}\) \(^{74}\) (Fig. 20, spectrum e) by direct measurement; \(^{6}\mathrm{Li}\) and \(^{7}\mathrm{Li}^{76}\) (Fig. 20, spectrum g) by means of a doublet of mass 6: \(^{6}\mathrm{Li}—^{2}\mathrm{H}_{3}\) and by direct measurement.

Measurement of the masses of Li makes it possible to verify experimentally the expression for the equivalence of mass and energy \(\Delta E = c^{2}\Delta m\) \(^{77}\) with the aid of data on energy obtained from experiments on the artificial disintegration of nuclei. For the reaction \(^{7}\mathrm{Li}+\mathrm{p}\rightarrow 2\alpha\), investigated by Cockcroft and Walton et al., excellent agreement is obtained, whereas for the reaction \(^{6}\mathrm{Li}+{}^{2}\mathrm{H}\rightarrow 2\alpha\), proposed by Lewis, Livingston, and Lawrence, agreement is not obtained. Next, a study \(^{75}\) was made of the isotopes of Kr, Hg, Cd, and Ge, and the existence of the isotopes discovered by Aston was confirmed, with the exception of \(^{71}\mathrm{Ge}\), \(^{75}\mathrm{Ge}\), \(^{77}\mathrm{Ge}\) (Fig. 20, spectrum h). These latter

To the article by I. Mattauch

[Figure: a multi-panel diagram with photographic mass-spectrographic lines. The panels are labeled а, б, в, г, д, е, ж, з. Repeated labels in the figure include “stable lines” and “radioactive lines”; many isotope and ion designations are printed next to the dark line groups, but most are too faint to read with certainty in the page image. Legible or partly legible inscriptions include: “stable lines,” “radioactive lines,” \( \mathrm{He}^{++} \), \( \mathrm{H}_2^+ \), \( \mathrm{Li}^+ \), \( \mathrm{Be}^+ \), \( \mathrm{C}^+ \), \( \mathrm{CH}^+ \), \( \mathrm{CH}_2^+ \), \( \mathrm{CH}_3^+ \), \( \mathrm{OH}^+ \), and several additional isotope/ion labels [[unclear: faint formulas and mass numbers throughout the figure]].]

Fig. 20.

almost all, if not all, are in all probability hybrids. Owing to the excessively short exposure time on the plate, the rare isotopes \({}^{196}\mathrm{Hg}\), \({}^{197}\mathrm{Hg}\), and also the isotopes \({}^{118}\mathrm{Cd}\) and \({}^{108}\mathrm{Cd}\), recently discovered by Swensson \({}^{124}\), were not detected.

b) Smythe’s Filter

W. R. Smythe and I. Mattauch \({}^{80}\) described a mass spectrograph differing from all the others in that the use of a magnetic field is completely excluded in it, while measuring and limiting, as well as maintaining the constancy, of such a field is experimentally much more difficult than in the case of an electric field. Fig. 21 shows the scheme of such an instrument. \(S_1\) and \(S_2\) are narrow collimating

Fig. 21.

slits, which select a thin beam of canal rays. It passes through Smythe’s velocity filter. A charged particle, as Smythe \({}^{79}\) showed, will move parallel to the \(x\)-axis only if the rapidly alternating electric field, whose lines of force are perpendicular to the \(x\)-axis, first, satisfies the relation \(E(x)=E(x-a)\), i.e. when the field is identically repeated with period \(a\), and second, if the velocity of the particle is

\[ v_0=\frac{2a\nu}{n}, \tag{18} \]

where \(\nu\) is the frequency of the field, and \(n\) is an odd number.

After passing through the first (double) condenser, the transverse section of the beam of rays having velocity \(v_0\) will undergo oscillations whose amplitude is proportional to the high-frequency voltage. These oscillations are compensated by a second exactly similar (double) condenser in the case when, during the passage of the ray, the voltage on it is in the opposite phase, i.e. in the case when it is at a distance \(D=\dfrac{sa}{n}\) from the first, where \(s\) is an integral odd number. Therefore, if this condition is fulfilled, only rays with velocity \(v_0\) can pass through the filter along the \(x\)-axis undeflected and undisplaced. If in choosing \(s\) and \(n\) incommensurable numbers are chosen, then the next velocity transmitted at the same distance \(D\) is \(\dfrac{1}{3}v_0\).

Mass separation can be carried out, as is known, by means of a magnetic field or by means of a radial electric field. Up to now, in experiments only the first method has been used. A particle passes through a radial electric field along a circle of radius \(r\) only when the equation of equilibrium of forces is satisfied:

\[ \frac{mv_0^2}{r}=\frac{eX}{\ln \frac{r_1}{r_2}}, \]

where \(X\) is the voltage between the cylindrical surfaces, which bound the field, of radii \(r_1\) and \(r_2\).

For an arc of circular path I. Mattauch\({}^{81}\) chooses the value \(\varphi=\frac{\pi}{2}\sqrt{2}=127^\circ\). By this, as A. Yuz and F. Rozhanskii\({}^{82}\) showed, a complete analogy is achieved with the focusing of directions in a magnetic field upon rotation through \(180^\circ\). In this case the rays entering as a divergent beam from the slit \(S_3\) are focused at \(S_4\), while the rays entering in parallel intersect at the middle of the arc and near \(S_4\) will again be parallel. In this arrangement the latter is justified to an even greater degree than in Bainbridge’s, first, because of the greater distance between the collimating slits and, second, because even rays with velocities lying near \(v_0\) emerge as a parallel beam. For the angle \(\varphi\) any value may be chosen lying within the limits from \(\frac{\pi}{4}\sqrt{2}\) to \(\frac{\pi}{2}\sqrt{2}\), provided only that \(S_3\) and \(S_4\) are arranged so that the first is advanced by a segment \(x=\frac{r}{\sqrt{2}}\operatorname{tg}\left(\sqrt{2}\varphi\right)\) before the beginning of the field, and the second is moved back beyond the end of the field by the same segment (see the work of R. Herzog and I. Mattauch\({}^{83}\)). Mass separation is greatest at \(\varphi=\frac{\pi}{4}\sqrt{2}\), but in this case \(x\) becomes equal to infinity. For the magnetic field, as P. Herzog\({}^{90}\) showed,* the same generalization can be made.

Since the slit cannot be made infinitely narrow, particles with velocities differing somewhat from \(v_0\) will pass through it. Smaiz\({}^{79}\) also calculated the form of the expected maxima for the slit \(S_3\) and for parallelism of the beam entering it. He notes, moreover, that the resolving power can be increased with a relatively small loss of intensity by cutting off the marginal rays with special diaphragms \(B\). This would lead to trimming the edges of the lines (maxima) and, what is especially important, would make possible the detection of weak lines near very intense ones. The width of the lines is obtained—

* Independently of him, E. Stephens\({}^{90a}\) made this generalization, but only for the magnetic field, and carried out an experimental test using electron rays.

is inversely proportional to \(n\), so that especially heavy elements with large values of \(n\) must be profiled out. Herzog and Mattauch\(^{83}\) extended this calculation to the beam of rays actually selected by the collimator slits, and took into account the influence of the radial field on the shape of the maxima. If \(S_1 — S_2 — S_3\) do not lie on one straight line, then, besides a change in intensity, there is also a change in the shape of the lines, which may ultimately lead to line splitting. Asymmetric grounding of the high-frequency voltage also leads to broadening and may cause splitting of the line. An error in setting \(D\) causes a displacement of the lines, which, in the first approximation, is proportional to it. The loss of intensity for an incorrect \(D\) increases with increasing \(n\). A displacement of the lines depending on \(n\) is also caused by an error in Smythe’s condition: \(E(x)=E(x-a)\). Therefore only those maxima that have been recorded with identical \(D\) and \(n\) can be subjected to exact comparison. This was confirmed experimentally by J. Mattauch\(^{81}\). Since Smythe’s assumption that the lines of force are everywhere perpendicular to the \(x\)-axis is not strictly fulfilled at the edges of the high-frequency fields, acceleration or deceleration of the marginal rays consequently takes place; as a result, complete compensation in the second (double) condenser becomes impossible. Moreover, after passing through the condenser, rays with velocities \(v_0\) will, for the same reason, execute minimal residual oscillations. This hinders the attainment of the great resolving power that could be achieved by increasing the high-frequency voltage.

A great advantage of this mass spectrograph is its theoretically strictly linear mass scale. Since overtones of a quartz-controlled generator are used for the voltage frequency \(\nu\), \(\nu=f\nu_0\), where \(f\) is an integer and the constancy of \(\nu_0\) can be maintained only with an accuracy of \(1:10^6\). Therefore, according to equations (18) and (19),

\[ M=\operatorname{const} X \frac{n^2}{f^2}, \tag{20} \]

where all constants of the instrument enter into \(\operatorname{const}\). Measurement of one single mass thus gives the mass scale. By switching the generator from one overtone to another, a direct comparison of such masses can be made, whose ratio is equal to the ratio of the squares of integers, as, for example, \({}^{1}\mathrm{H}:{}^{4}\mathrm{He}\), \({}^{4}\mathrm{He}:{}^{16}\mathrm{O}\), or \({}^{1}\mathrm{H}:{}^{16}\mathrm{O}\), etc.

This comparison of masses can be carried out with great accuracy, similarly to the way it is done by Aston’s first doublet method. Another advantage is the possibility, by changing the high-frequency voltage within wide limits, of varying the magnitude of the resolving power. Small voltages cause the formation of broad intense lines, which very much facil-

prevents their detection. For precise measurements the lines, by increasing the voltage, can be made as narrow as desired. Despite the focusing of velocities, in special cases measurements of intensities can also be made, namely when the distribution of intensity along all the parabolas may be considered identical (a discharge in a homogeneous gas mixture). With the filter capacitors grounded, the measurement directly gives the electrical spectrum (the sum of the intensities of all the parabolas). Smythe and Mattauch \(^{80}\), with the aid of this instrument, gave the first unobjectionable quantitative mass-spectrographic proof of the existence of the new rare isotope \(^{18}\mathrm{O}\), discovered in the study of band spectra (previously oxygen was considered a simple gas—only \(^{16}\mathrm{O}\)). A comparison was made of the intensities for both molecules \(\mathrm{O}_2 : {}^{16}\mathrm{O}_2\) and \(^{16}\mathrm{O}—{}^{18}\mathrm{O}\). Since for the latter an increase of the maximum was observed, due to the equivalent molecule \(^{204}\mathrm{Hg}_6^{+}\), which could not be excluded because of the use of mercury pumps, the magnitude of the ratio \(^{16}\mathrm{O} : {}^{18}\mathrm{O}\) was found to be equal to 600 or more, which is in good agreement with the international value. Recently W. R. Smythe \(^{83a}\) repeated the experiments with oxygen, using oil diffusion pumps; the oxygen was obtained from \(\mathrm{PbO}_2\), heated in a special branch of a calcium discharge tube. He found the highest of the values hitherto known for \(^{18}\mathrm{O}\), namely
\(^{16}\mathrm{O} : {}^{18}\mathrm{O} = 503 \pm 10\). For the best separation of the masses the angle of rotation \(\varphi\) in the radial field was taken equal to \(70^\circ\); accordingly, the receiving slit was at a distance \(x = 25\ \mathrm{cm}\) beyond the end of the radial field \((r = 5\ \mathrm{cm})\).

5. Multiple Acceleration

The apparatus of E. O. Lawrence, D. H. Sloan, and M. S. Livingston \(^{84,85}\) for obtaining ions of high energy is at the same time a mass spectrometer with very great resolving power. A characteristic feature here is that the high-frequency field employed serves not to deflect the rays, as in Smythe’s apparatus, but to accelerate the particles. Between the round pole pieces of a large electromagnet are two flat semicircular metal boxes, made like the sectors of a quadrant electrometer. Between them is applied a high-frequency field, serving for the successive acceleration of ions formed at the center of the field. The ions describe spiral paths, made up of semicircles of ever-increasing radius. At a precisely determined moment, namely when the acceleration reaches its greatest value, the ions must pass through the slit between the two semicircular boxes, between which an alternating high-frequency voltage is imposed. For this, first, the time of passage along each semicircle must be constant and, second, this time must be

is equal to a half-period of the high-frequency oscillation. The first condition is satisfied according to the second equation (15), since

\[ t=\frac{r\pi}{v}=\frac{\pi m}{eH} \]

does not depend on the radius or the velocity. To satisfy the second condition it is necessary that \(t=\dfrac{\lambda}{2c}\). Therefore

\[ \frac{m}{e}=\frac{\lambda}{2\pi c}\,H . \tag{21} \]

At the boundary of the magnetic field, ions are extracted by means of an auxiliary electric field, and their number is then measured electrometrically. The mass scale in this case is also linear. With an unchanged voltage frequency, the mass is measured from the magnetic-field strength. It could, however, also be measured from the wavelength \(\lambda\), while keeping the magnetic-field strength constant.

In this case as well, obtaining a high intensity is due to the focusing action both of the alternating field acting between the halves of the apparatus and of the curvature of the magnetic lines of force at the edge of the magnetic field. Both of these factors keep the beam in the median plane. For details one should consult the original papers.

Fig. 22.

Up to now this method has not been used for isotope research. By essentially the same method, F. J. Dunnington\(^{86}\) undertook a precision measurement of \(\dfrac{e}{m}\) for cathode rays.

6. Focusing of velocities and directions

a) Simultaneous electric and magnetic deflection

W. Bleakney and A. J. Dempster\(^{87}\) proposed an arrangement in which, owing to simultaneous deflection by an electric and a magnetic field, the broadening of the maxima found by Dempster in his own method and ascribed by him to the nonuniformity of the rays in energy is eliminated. H. Bondy and K. Popper\(^{88}\), by measuring the maxima for \(^{23}\mathrm{Na}\) and \(^{39}\mathrm{K}\), showed the applicability of this method. Ions in the space between the anode \(A\) (Fig. 22) and the slit \(S_1\) are accelerated by the voltage \(V\); by a magnetic field (perpendicular to the plane of the drawing) the ions are turned along a circular path toward \(S_2\), passing thereby through the field of the cylindrical capacitor \(K\), whose electric field, with strength \(X\), tends to deflect them outward. Rays that have passed through \(S_1\) with somewhat differ-

...from one another by angles and with not quite identical velocities, after traversing an arc \(\frac{\pi}{2}\sqrt{2}\) will be focused at \(S_2\) in the case that:

\[ \frac{X}{\ln \frac{r_1}{r_2}}=\frac{1}{4}\frac{e}{m}r^2H^2 \quad \text{and} \quad V=\frac{1}{8}\frac{e}{m}r^2H^2, \tag{22} \]

i.e., if the magnetic force acting inward is twice as great as the electric force acting outward.

With constant \(H\), measurement of masses can be carried out only with simultaneous variation of \(X\) and \(V\). Since, according to equation (22), \(X=2V\ln\frac{r_1}{r_2}\) does not depend on \(\frac{e}{m}\), Bondy and Popper used a magnetic field for their measurements. On the former Dempster instrument, measurement of \(r\) and of the mass when the velocity was varied by \(15\%\) could be carried out only with an accuracy up to \(15\%\), even with ideal focusing of directions, whereas by the Bartky and Dempster method, owing to the additional focusing of velocities, it could be carried out with an accuracy up to \(1\%\). W. Henneberg^89 considered the Bartky–Dempster method as a special case of a combination of fields that contains focusing both in a magnetic field (Dempster^45) and in a radial electric field (Juz and Rozhanskii^82), and that also includes Wien’s velocity filter. Further, Henneberg finds the conditions for focusing of directions of the second order, without, however, taking velocity focusing into account. Almost simultaneously and independently of him, R. Herzog^90 made an even more general consideration of this combination of fields, in addition to the generalization made by R. Herzog and I. Mattauch^83 concerning focusing in a radial field.

A. E. Shaw^91 used the Bartky–Dempster apparatus for determining \(\frac{e}{m}\) in the case of electrons. He points to the great sharpness of the maxima in comparison with their sharpness obtained with Dempster focusing. He also made interesting measurements of the polarization effect that occurs on the plates of a cylindrical condenser. In the reviewer’s opinion, this effect is identical with the disturbing effect already observed by Aston.

b) Separate Deflection

While compiling this review, it became clear to the reviewer that in Aston’s apparatus there is, in addition, focusing of directions. Since the necessity of restricting oneself to small angles \(\theta\) and \(\varphi\) has now disappeared, it is clear that, with a corresponding choice of \(\theta\) and \(\varphi\), it is possible, at least for one mass, to obtain both focusing of directions and of velocities. After R. Herzog^90 developed the optics of the radial and magnetic field and

their combinations, we (I. Mattauch and R. Herzog^92) succeeded in showing that this is possible for all masses. Aston and Fowler^22 showed that the width of Aston’s lines is determined by divergence. In accordance with this, Aston expressed the opinion that if it were possible to increase the sharpness of the lines, the accuracy of the measurements could be significantly improved. We think that simultaneous focusing of directions would be essential. Here we briefly report on a special case that promises success.

A narrow beam of rays separated by the slit \(S\) (Fig. 23) first passes through a radial electric field, the wide slit \(B\), serving to limit the region of velocity focusing, and then

Fig. 23.

enters a magnetic field, in which the rays undergo deflection in the opposite direction by \(\varphi = 90^\circ\). As the calculation shows, in order for velocity focusing to take place, i.e., so that rays (the upper and lower beam, Fig. 23) whose energy differs somewhat from the mean, meet again on the plate with the mean ray, the angle of the radial field \(\Phi_e\) must be equal to \(\frac{\pi}{8}\sqrt{2} = 31^\circ 50'\). In order that, in addition, focusing of directions should take place, the radius of the middle path in the radial field \(a_e\) must be equal to \(\sqrt{2}\,l_e\), where \(l_e\) denotes the distance from \(S\) to the beginning of the field. Rays of a certain velocity, diverging from \(S\) at a small angle, after leaving the radial field proceed as a parallel beam. By the laws of geometrical optics, a correct image of the slit is obtained on the plate. For greater clarity, Fig. 23 schematically shows two beams of rays of different velocities. A great convenience in experimentation consists in the fact that the images for different masses lie on one straight line, thanks to which a photographic plate can be used. The plate makes an angle of \(45^\circ\) with the direction of the rays. The distance \(\rho\) of the lines from the point where the rays enter the magnetic field is proportional to the square root of the mass.

(To be continued)