UNSOLVED PROBLEMS OF SPACE PHYSICS1

W. F. G. Swann.

I have heard that when a student whose apparatus had not yielded the expected result came to Rowland for advice, Rowland replied: “Do something with it until you obtain something.” Every experimenter will recognize the wisdom of this advice; but, alas, a person studying space physics is unable to make use of it to any significant degree. He can do very little with many of the instruments with which he has to deal—with the Sun, the stars, and the planets. He can only look and wait for what will happen. How he would like to enclose our terrestrial sphere, together with all its atmosphere, in a lead box several meters thick and see what changes would then occur in the phenomena of atmospheric electricity; or to reverse the direction of the Earth’s rotation and study the changes in the Earth’s magnetic field over the course of several million years! However, he soon becomes convinced that it is very difficult to find someone who would wish to finance such projects, and therefore nothing remains for him but to wait, to observe, to reproduce the phenomena of nature, as far as he can, on a small scale in his laboratory, and, above all, to think persistently.

Fig. 1.

ATMOSPHERIC ELECTRICITY.

Fig. 1 shows a circle. The thickness of the line is small; nevertheless, in relation to the dimensions of the Earth represented by the circle, it is a layer whose thickness exceeds by 7 times that which is practically lim—

all our observations of atmospheric electricity begin. We know that within this region there exists an electric field, perpendicular to the surface of the earth and produced by a negative charge on the surface and a positive charge in the atmosphere. This field reaches approximately 150 volts per meter at the surface and undergoes extraordinarily regular variations over the course of the day and the year—variations amounting to 50 percent or more of its magnitude. It decreases with altitude and, at a height of about 10 km, reaches a value negligible in comparison with that which it has at the surface.

ELECTRICAL CONDUCTIVITY OF THE ATMOSPHERE.

The atmosphere is a conductor of electricity, although a very weak one, so that the positive charge in the atmosphere has a tendency to be neutralized by the negative charge of the earth’s surface. The electrical conductivity of the atmosphere is due to the presence in it of charged molecules of nitrogen and oxygen, called ions. The latter, by virtue of their charge, move in the electric field and give up their charges to surrounding bodies, which they thereby discharge. Under ordinary conditions, each cubic centimeter of air contains about 1000 ions of each sign—a figure extremely small in comparison with the 30 million million million molecules contained in this cubic centimeter of air. A positive ion is formed as a result of the removal from a neutral molecule of one of those electrons which modern physics teaches us to regard as one of the fundamental constituents of all matter. The negative electron sooner or later itself attaches to some neutral molecule and, charging it in this way, forms a negative ion. The ejection of an electron from an atom occurs under the influence of some external cause. There are three principal categories of such causes, corresponding to the radiations emitted by substances like radium, which is in a state of continuous spontaneous disintegration.

The first of these causes is the alpha particle—a positively charged helium atom moving at a speed of 20,000 kilometers per second. The second is beta rays, which are simply negative electrons moving with a speed close to that of light. Finally, the third is gamma rays, which are a certain kind of wave-like motion in the ether. When an alpha ray approaches an atom, it tends to tear an electron from its place, quite as a comet flying into our solar system might tend to tear the moon from its place. A beta ray tends to repel the electron by a force of repulsion, quite as a comet with a monstrous atmospheric whirlwind on its surface might tend to carry the moon along with the air current. Finally, gamma rays act by producing a certain kind of wav—

tion in the ether, by virtue of which the electron acquires a sufficiently great velocity to be able to leave the atom.

A considerable share of the ionization, and consequently also of the electrical conductivity of the atmosphere, is due to the presence in it of radium emanation. On average, there is only about one and a half molecules of emanation per cubic centimeter of atmosphere, whereas it contains about 30 million million million molecules of air; nevertheless, even such a quantity of emanation is sufficient to produce a very noticeable ionization effect. The alpha-, beta-, and gamma-rays emitted by radioactive emanations in the air, the gamma-rays emitted by the radium of the soil, and perhaps also penetrating radiation of cosmic origin, constitute the principal sources of ionization in the atmosphere. The circumstance that the ionization above the surface of the great oceans, where there are no radioactive substances, is of the same order as the ionization above the land surface suggests that cosmic radiation may play an important role, although recent experiments have given rise to some doubts as to the reality of this radiation, at least as regards its presence at low altitudes. Summing up what has been said, one may state that certain rays, namely $\alpha$-, $\beta$-, and $\gamma$-rays, and possibly also some cosmic radiation, are the cause of the emission of electrons by a small number of air molecules, thus bringing about the formation of positive and negative ions, which impart electrical conductivity to the atmosphere.

The conductivity of the atmosphere at the earth’s surface is utterly negligible in comparison with the conductivity of a substance such as copper. Thus, an air cylinder 1 inch long offers to an electric current the same resistance as would be offered by a copper cable of the same cross-section stretched 20 times from the earth to the star Arcturus and back. Nevertheless, even such electrical conductivity would be sufficient for 90% of the earth’s charge to disappear within 10 minutes, if these losses were not replenished. The explanation of the fact that the earth’s charge is maintained constitutes an important problem in the theory of atmospheric electricity. Quantitatively, this replenishment of charge requiring explanation is small. The current leaving the entire earth’s surface amounts to only about 1,000 amperes, i.e. the amount consumed by three thousand incandescent lamps; but our knowledge of the nature of electrical phenomena is so definite that we must impose substantial critical limitations on the possible processes by which such replenishment could be explained.

THE CONSERVATION OF THE EARTH’S CHARGE

It is evident that if negative electricity leaves the earth, or positive electricity enters it, owing to the potential gradient existing in the conducting atmosphere, then there must exist some...

which compensates the electric current arising as a result of processes acting in a direction opposite to the electric forces of the field. The proposed theories are, for the most part, divided into two classes: namely, those in which the principal acting agent forcing charges to move against the field is the force of gravity, and those in which the return of negative particles to the earth occurs, despite the opposing field, thanks to the very great velocity acquired by them in one way or another.

Theories based on gravitation. An example of a theory of the first kind is the theory of C. T. R. Wilson, which asserts that the replenishment occurs thanks to rain. Theoretical considerations show that raindrops should form on atmospheric ions—and, moreover, on negative ions in greater numbers than on positive ones—so that one may expect rain, in general, to have a negative charge. Charged drops, falling to the earth under the influence of gravity, will act against the electric field and will replenish the earth’s charge. This theory encounters two principal objections. First of all, rain is indeed charged, perhaps even to a sufficient degree to explain the necessary replenishment of charge; however, it has been established that 90% of the falling rain has a positive charge. Moreover, apparently, it is very difficult theoretically to admit the possibility of condensation of water on atmospheric ions in the form of drops of appreciable size, so that this theory has now been wholly abandoned.

Ebert’s theory comes close to solving the problem and, undoubtedly, partly explains the origin of the earth’s charge. This theory, which is a modification of the older theory of Elster and Geitel, proceeds from the fact that if ionized air passes through a thin tube, the negative ions diffuse to the walls of the tube more rapidly than the positive ones, so that the air issuing from the tube has a positive charge. Ebert applies this phenomenon to the explanation of the problem of atmospheric electricity, suggesting that air located in the pores of the soil and ionized by the action of radioactive substances in the soil emerges from these pores during periods of falling barometric pressure, leaving an excess negative charge on the walls of the pores. The positive charge emerging outward would have to remain in the immediate vicinity of the soil under the influence of the negative charge, but here Ebert invokes upward-directed air currents, which carry this charge, against the field, into higher regions of the atmosphere. This theory has been criticized on the grounds that the emission of ions by the soil is insufficient, and that upward-directed currents are too weak. I think—

I understand, however, that one of the most serious objections must be sought in the conclusion which follows comparatively simply from theoretical considerations; namely, from this kind of theory it would follow that before the ascending positive charge had risen to a height of approximately 1 km, it would have disappeared almost completely, being absorbed by the negative charge continuously supplied from below, from the earth, through the conducting atmosphere1. In such a case we would obtain a positive charge in the atmosphere, a negative charge on the earth’s surface, a conduction current and a potential gradient; but all these phenomena would be confined to an atmospheric layer approximately 1 km thick. The entire positive charge of the atmosphere would be contained in this layer and, being equal to the negative charge of the earth’s surface, as its former companion in the neutral substance, it would destroy the field at any more considerable height.

There are also other difficulties in Ebert’s theory and in the “ion-deposition” theory belonging to C. T. R. Wilson. Thus, according to both theories, the corresponding densities of positive and negative charge clearly ought to remain in the regions where they arise, as a consequence of which in other parts of the earth

there would be no electric field at all. It is useless to appeal to the wind for transporting the positive charge of the atmosphere into remote regions, for 90% of it would disappear within 10 minutes of travel owing to the electrical conductivity of the atmosphere. Every theory according to which the replenishment of the charge occurs by the separation of charges in isolated places, in such a way that positive and negative charges remain at a comparatively short distance from one another, encounters difficulties of the same kind. The difficulties become less serious if we adopt the plausible hypothesis that the lower layer of the atmosphere is surrounded by some conducting layer. The existence of such a layer appears necessary for explaining the fact of reflection of wireless-telegraph waves in the layers surrounding the earth; serious grounds for assuming the existence of such a layer are also provided by our information on the mechanism of the oscillations of terrestrial magnetism, which are considered below.

In the presence of such a layer, under the influence of a charged cloud, a difference of potentials must be established between the layer and the earth, transmitted around in all directions, since the difference of potentials between the earth and the layer must be everywhere the same. A detailed consideration of the action of such a layer shows that if a charged cloud \(C\) (Fig. 2) is at a height \(h\) above the surface of the earth, and if \(H\) is the height of the conducting layer and \(R\) the radius of the earth, then the hemisphere of the earth symmetrically remote from the charged cloud (the shaded semicircle in Fig. 2) would receive a number of lines of force \(\frac{R}{H}\) times greater than that which it would receive in the absence of the layer, or a fraction \(\frac{h}{H}\) of the number which it would receive if the charge of the earth and the charge of the cloud were distributed uniformly, the former over the earth and the latter in the atmosphere.

Fig. 2.

Thus, if rain fell from a cloud situated at a height of 5 km, and if the effective height of the conducting layer were 50 km, then the mean value of the potential gradient on the shaded hemisphere would be equal to 0.1 of the value which it would have if the charges were uniformly distributed over the earth and in the atmosphere, and would exceed by more than a factor of one hundred the value which it would have in the absence of a conducting layer. We see, therefore, that with the existence of a conducting layer any center of charge separation, such as, for example, a rain shower, can exert an influence—positive or negative—

…ultimate, depending on the circumstances—to the general gradient of potential in each part of the earth1.

However, although the difficulties connected with the assumption of a localization of the potential gradient are removed by the supposition of the existence of a conducting layer, there nevertheless remain other sufficiently serious difficulties, of which we have spoken, and which make it improbable that Ebert’s theory takes account of the principal cause of the earth’s charge.

Corpuscular theories. We turn now to theories in which the replenishment of the charge is ascribed to the action of electrified particles (“corpuscles”) of high velocity falling upon the earth. The first of such theories was proposed by G. C. Simpson. This theory assumes that the sun emits negative and positive particles with great penetrating power. It is assumed that the former (negative ones) pass straight through our atmosphere and charge the earth, while the latter possess a smaller penetrating power and are stopped in the atmosphere. In this way the earth will continuously receive a negative charge, and the atmosphere—a positive charge. At the same time the usual process of atmospheric electrical conductivity will create a constant current of electricity between the atmosphere and the earth, so that a stationary state will be attained in the case when the neutralization of the charge under the influence of this latter process is, quantitatively, exactly balanced by the charging action of the influx of particles. This theory requires the existence of particles with so considerable a range that they can pass through the entire thickness of the earth’s atmosphere, which in absorbing power is equivalent to a column of mercury approximately 76 cm high. The greatest range observed in air for the β-rays of radium is approximately 7 or 8 meters. Electrons having a velocity of 99% of the velocity of light can pass only through a layer of aluminum 1.3 cm thick, which in absorbing power is equivalent to approximately 10 meters of air at atmospheric pressure.

Although, according to electromagnetic theory, the velocity of light represents the maximum velocity that a particle can attain, nevertheless it would be rash to suppose, on the basis of the fact that particles with a velocity equal to 99% of the velocity of light have a range in air of only 10 meters, that no particles can have a greater range. In fact, electromagnetic theory shows that particles with a velocity even of 99% of the velocity of light are, in their properties, still very far from particles which approach this limit to a much greater degree. As is known, the mass of a particle increases together with

velocity of the latter, so that the particle must possess infinitely large energy in order to attain the velocity of light. The theory of the absorption of electrons in matter for large velocities was developed by N. Bohr, and Table I gives, for various velocities approaching the velocity of light, the ranges computed on the basis of Bohr’s formula, in connection with the experimental values obtained by R. W. Varder (R. Varder) for lower velocities reaching up to 0.99 of the velocity of light. According to Bohr’s theory, at a velocity equal to the velocity of light, the range theoretically attains an infinite value.

TABLE I.

CHANGE OF THE MEAN RANGE AS A FUNCTION OF VELOCITY.

Usually, for velocities still closer to the velocity of light than those given in Table I, additional considerations are taken into account; the nature of these considerations is such that they yield still greater ranges than those following from Bohr’s formula.

Simpson’s theory, and others like it, lead to interesting conclusions concerning the change in the density of the atmospheric current as a function of altitude. The ideas that follow from this can be studied most simply if one considers the case in which the entire corpuscular flux through the troposphere consists of negative particles, since the carriers of positive electricity become trapped in the upper layers of the atmosphere.

It is self-evident that, in the stationary state, the density of the corpuscular current directed downward must be equal throughout

at every point in the atmosphere to the density of the conduction current directed upward. But if the particles are completely absorbed during their descent, then the density of the descending corpuscular current will decrease as it approaches the earth’s surface, so that the density of the ascending conduction current will increase with height. If, for example, the density of the corpuscular current during descent from a height of 10 km to 5 km were reduced by half in comparison with its initial value, then the density of the conduction current would increase by 100% during its ascent from a height of 5 km to 10 km. The data we have concerning the change in the density of the vertical conduction current as a function of height are not very abundant. Nevertheless, insofar as they exist, they do not reveal large changes as a function of height. We see, therefore, that the range required by the theory of Simpson and similar theories exceeds the value of this range that is necessary for a simple explanation of the fact that particles reach the earth. It is also necessary to explain this fact under the condition of absence of absorption, as follows from the constancy of the density of the conduction current at different heights1.

We would feel more satisfied if we could devise a theory that would not require so high a limit of penetration as Simpson’s theory. There are one or two ways by which we can achieve this. Let us imagine that, owing to radioactivity or to some other cause, a certain number of air molecules will be destroyed every second with the emission of a negative particle of high velocity.

In such a case, although these particles may in general be emitted in all directions, some particles will enter the earth from the atmosphere, and the latter will thus acquire a charge, until the conduction current directed back into the atmosphere balances the corpuscular current. Practically all the particles entering the earth will flow in from a distance comparable with the mean range of the particle. However short this range may be, we can provide the necessary replenishment of the earth’s charge if we assume a sufficiently abundant emission of these particles by every cubic centimeter. However, unless we assume a very large value of the range, we shall encounter difficulties connected with the change of the conduction current as a function of height. Suppose, for example, that the mean range is 10 meters, so that practically all particles,

entering the earth come from a layer whose thickness is comparable with the indicated figure. At a height of the order of 10 meters, the resulting corpuscular current will be zero, since just as many particles will be emitted upward by the lower layer of air as will be emitted downward by the upper layer. In fact, the corpuscular current will vary in strength, beginning with a maximum at the surface of the earth down to zero at the named height, and so likewise both the conduction current and the potential gradient will vary.

We thus see that if one assumes an equal emission of particles by every cubic centimeter of the atmosphere and a uniform decrease in the magnitude of the range with each centimeter of path, then in practice it will be necessary to assume that the mean total range is equal to that height up to which we wish to explain the potential gradient. The result will be the same if we assume a definite emission of particles by every gram of the atmosphere, for although in this case the pressure and density will decrease with height, the magnitude of the range will nevertheless increase in the same measure. We can avoid this undesirable conclusion by assuming an increase of the emission per gram together with height; we would have a similar case if we imagined that the emission is caused by some kind of external radiation, gradually absorbed as it descends. In order actually to obtain a constant density of the conduction current, it would be necessary to assume an increase of the emission as a function of height comparable with twice the magnitude of the required corpuscular current, for a mass of air corresponding to the mean range of the particles.

It is not without interest to consider the order of magnitude required by a theory of this kind. It turns out that if the range is assumed equal to 5 km, it is necessary only to suppose that every 200 cubic cm emit approximately one particle per second. But we know that about 6 ions are formed in each cubic cm per second; thus it is necessary only to assume that only one out of 1200 such ions is formed with the emission of a particle of large range.

We can avoid the hypothesis of spontaneous emission and obtain certain other advantages by adopting a hypothesis to some extent similar to the preceding one. It has become a common assumption that strongly penetrating radiation passes through our atmosphere, originating either from the outer regions of the atmosphere or from some cosmic source, for example, from the sun. This supposition has been advanced in order to explain the formation of ions which occurs, as is known, in a closed vessel freed, as far as possible, from radioactive air—an occurrence which cannot otherwise be explained, even if one takes into account the $\gamma$ rays emanating from the soil, which can penetrate through the walls of the vessel. In view of the funda-

...in the details of which I have no need to enter here, it was proposed that this radiation is a certain kind of γ-rays, but of a more penetrating type than the usually observed radiation of radium. But γ-rays possess the ability to produce ionization, i.e. to compel the gas through which they pass to emit electrons, and the nature of their action is such that the direction of motion of the emitted electron almost entirely coincides with the direction of the γ-rays.

We may, therefore, expect that radiation of this kind, arriving from above, will cause electrons to be emitted by the air, and that the latter will be directed downward and will travel some distance before coming to rest. Electrons emitted within the corresponding distance from the earth will reach it and charge it. Their places will be taken by other electrons arising in the upper layers, which will be absorbed before they have time to reach the earth. One of the advantages of this type of corpuscular theory is that, in order to explain the formation of particles, it appeals to a factor whose existence has already been recognized on other grounds; its other advantage consists in the fact that it does not require an artificial adaptation of the theory in order to explain the conduction current, practically independent of height. As the height increases, the emission of particles per cubic centimeter will decrease, but the distances traversed by the particles will correspondingly increase, so that if the intensity of the penetrating radiation is in itself independent of height, then the corpuscular current will also remain independent of height.

Further, by subjecting the theory to mathematical treatment, we arrive at quantities which are by no means inconceivable. Thus, if we assume that in each cubic centimeter only 3 particles with a high velocity are emitted per second—a quantity comparable with that which is assumed to be emitted under the influence of penetrating radiation—then it is only necessary to assume that these particles have a range of 9 meters in air, and we obtain an explanation of the replenishment of the earth’s charge1. We shall see presently that, in order to explain ionization, it is desirable to ascribe to the particles a greater range than 9 meters; but, in order to explain merely the replenishment of the earth’s charge, a range of 9 meters is sufficient.

Objections to corpuscular theories.—I now turn to the two chief objections which may be advanced against corpuscular theories of every kind. The first of them arises from the failure of attempts to discover any effect in

in the sense of the acquisition of charge by an isolated body subjected to the action of particles. If the particles flow onto the earth from above, then an isolated mass of metal should gradually acquire a charge from the particles falling into it, unless, however, these particles possess such great penetrating power that they pass straight through the mass. In order that the corresponding experiment should be valuable, it is necessary to take a very thick piece of metal, since particles that have passed through the earth’s atmosphere, equivalent to 76 cm of mercury, do not show much absorption in passing through an additional few centimeters of metal. I performed an experiment of this kind in 1915, but was unable to detect any electrification of the desired type. More recently the same effect was sought by Schweidler, but without success. However, even then I felt that my own experiments, which were carried out with a copper bar about 25 cm long and 5 cm in diameter, placed vertically, ought to be repeated with a larger mass of metal, whereas Schweidler’s experiments were made with an even smaller mass. In any case, if we find that a metal sphere, say one meter in diameter, experiences no electrification, then theories that ascribe the replenishment of charge to an influx of particles would encounter a serious difficulty. This difficulty, however, is not insurmountable if we adopt the last of the views set forth by me, namely that according to which the ejection of particles by molecules of air is produced under the influence of extraordinarily hard $\gamma$-rays falling from above. In fact, if, according to this view, the $\gamma$-rays are sufficiently penetrating to pass straight through the metal, then on the one hand they will knock particles out of the lower part of the mass, and on the other hand knock them into its upper part. A simple calculation shows that, assuming the intensity of the $\gamma$-rays not to change in passing through the metal, one easily arrives at the conclusion that just as many electrons will be knocked out of the lower part of the mass as will be knocked into the upper part; for this it is only necessary to assume that the ratio of the number of particles ejected per cubic centimeter of air and of metal is equal to the ratio of the densities of these substances, and that the mean free path of a particle in air and in metal is inversely proportional to the densities. Both these assumptions are in full agreement with what is known to us about the laws relating to the action of $\gamma$-rays and to the passage of particles through matter.

The second major and, perhaps at first glance, most serious objection to any corpuscular theory consists in the fact that, when particles pass at high speed on their way to the earth through the atmosphere, one might expect a stronger ionization than that actually observed. The situation is as follows: the corpuscular current necessary for balancing the atmospheric elec-

of the electric current, is equal to an influx of 1500 particles per square centimeter per second. But we know that an electron with a speed approaching the speed of light produces, per centimeter of its path, about 40 ions; therefore we may expect that in each cubic cm approximately 60,000 ions per second will arise, whereas experiment shows that they are formed only in an amount equal to one ten-thousandth of the number just given. In order to understand how we can avoid this difficulty, it is of interest to consider somewhat more closely the mechanism of ionization.

Fig. 3.

Fig. 4.

The absence of an ionizing action in corpuscles whose velocity approaches the velocity of light.—Let us suppose that in Fig. 3 \(E\) is an electron in an atom and that another electron—\(e\), which for distinction I shall call a particle, approaches the atom. As the particle approaches the electron, it will begin to repel it and will continue to exert the same action as it recedes; as a result, the electron will receive energy, and the momentum acquired by it will be in a more or less perpendicular direction to the line of flight of the particle. The greater the velocity of the particle, the shorter is the interval of time during which the electron has an opportunity to receive an impulse from it. Thus the effective force of the particle, in the sense of its ability to push the electron out of the atom, decreases as its velocity increases and would reduce, one might say, to zero if the particle could attain infinite velocity. But the particle cannot attain a velocity greater

than the speed of light, and, since the matter concerns the effect described above, no very considerable weakening of the ionizing power is observed as the velocity increases, beginning, say, with \(95\%\) of the speed of light, at which the ionization was measured, and up to the speed of light itself.

However, as the speed of light is approached, a new phenomenon is found. The field of the particle does not remain uniformly distributed. According to the well-known laws of electromagnetism, its lines of force will shift more and more into the equatorial plane, as indicated by the dashed lines in Fig. 4. In view of this, the time during which the particle exerts an action on the electron is diminished to a still greater degree; however, the intensity of the action during this time increases; as a result, as Bohr showed, if we do not take other considerations into account, the energy imparted to the electron by the passage of the particle will undergo no change whatever as a consequence of the indicated concentration of the lines of force.

Yet we must take into account one more very important consideration.

If an electron acquires even a small velocity during a very short interval of time, then, as is known, it will radiate a large amount of energy. Its sudden motion will give a strong impulse to the ether. The corresponding mathematical calculation shows that even if we wished to impart to the electron only a small amount of energy, but during an infinitely small interval of time, we would have to pay a kind of tax in the form of an infinitely large amount of energy in the form of radiation. But the closer the speed of the particle comes to the speed of light, the more rapidly it imparts energy to the electron. Without going into excessive detail, we may represent the situation in the following way. If a particle moves with a speed approaching the speed of light (for example, reaching \(95\%\) of the speed of light), but not so close to it as that at which the considerations just set forth regarding radiation come into force, then, as it turns out, the particle must approach the electron of an oxygen atom to a distance not exceeding \(0.7 \times 10^{-10}\) cm in order to be able to expel this electron from the atom. But it is possible to ascribe to the particle a speed so close to the speed of light that, if it were to approach the electron to a distance of \(0.7 \times 10^{-10}\) cm, then the “tax” alone, in the form of the radiation accompanying the expulsion of the electron, would exceed the amount of energy that the particle can impart to it, and the conditions are such that the situation is still more unfavorable for expelling the electron if the particle approaches it closer than \(0.7 \times 10^{-10}\) cm. There is no doubt that, in the absence of radiation, the electron will receive the more energy, the closer to it the particle approaches.

particle; but if radiation is taken into account, then the electron, to which the particle with sufficiently great velocity would come within a distance not exceeding \(0.7\times 10^{-10}\) cm, is in the position of a man whose earnings are so high that, if he receives them, the appropriate tax falling upon him will exceed all his earnings, owing to the very heavy taxation of high incomes, so that he will gain more by having a smaller income. The electromagnetic equations, however, are merciful to the electron and allow it, under such conditions, to renounce its earnings. The direct result of all this is that, if the velocity of the particle is sufficiently high, it will be unable to expel the electron if it passes from it at a distance of \(0.7\times 10^{-10}\) cm. It will also be unable to expel it if it approaches it at a smaller distance, owing to the reaction of the radiation. But it would be unable to expel it, in passing also at a greater distance than the one indicated, if the considerations relating to radiation were absent. As a result, it proves in all cases to be generally incapable of expelling the electron. Carrying out the corresponding mathematical calculation, we shall find that a particle with a velocity 200 meters per second less than the velocity of light will certainly be unable to expel an electron from an atom of nitrogen or oxygen1.

It is interesting to note the following remark: if we make the supposition that the particles are brought to the earth from space outside the atmosphere, then,

completely independently of any absorption in the atmosphere, it is necessary to assume some minimum velocity in order to explain their reaching the earth, at least in the neighborhood of the equator. Indeed, the path of a moving particle is bent under the influence of the magnetic field, and this bend may turn out to be so strong as to turn the particle back in space. The closer the velocity of the particle approaches the velocity of light, the less its path is bent. The decrease in curvature is not so much a direct result of the increase in velocity as of the increase in mass brought about by the increased velocity. As it turns out, in order that a particle which has entered our atmosphere in the neighborhood of the equator should be able to reach the surface of the earth without being turned back by the action of the earth’s magnetic field, it must have a velocity too great for it to be able to ionize the air through which it passes.

Birkeland tried to explain the chief properties of the aurora by supposing that it is produced by the intrusion into our atmosphere of particles of high velocity emitted by the sun. In order to explain the facts connected with the curvature undergone by the paths of the particles in the earth’s magnetic field, he was compelled to assume that the velocities vary within limits from 400 to 4 meters per second less than the velocity of light. Thus the velocity at which ionization must cease fits well within the limits indicated by Birkeland. As follows from the theory now accepted, Birkeland’s particles will have no ionizing action at all, so that they cannot give a satisfactory explanation of the aurora; but at the present time it is generally accepted that the aurora is not the result of ionization produced by negative electrons, and I recall these calculations of Birkeland only in order to show that, in resorting to velocities only 200 meters per second less than the velocity of light, we are by no means resorting to means still more “powerfully acting” than those which have already been used in other fields of our science.

Let us note, moreover, that if we extrapolate Bohr’s theory of absorption to velocities comparable with the value 200 meters per second less than the velocity of light, we find that particles possessing such a velocity can traverse distances in the atmosphere comparable with one kilometer. If we remember that the transfer of energy to the electrons in atoms is the process by which particles, according to Bohr’s theory, lose energy, then we shall see that a decrease in such transfer, expressed in the absence of ionization, will result in a still greater increase in the magnitude of the possible range. Thus the nature of all the considerations that bear on this matter is such that they all converge in the following view: if a...

particles must enter our atmosphere with velocities sufficiently close to the velocity of light in order to be able to reach the earth’s surface in the vicinity of the equator, without undergoing a deflection in the reverse direction under the influence of the earth’s magnetism; then, in doing so, they must pass straight through the atmosphere with limited absorption and will not ionize the air through which they pass.

Thus the difficulties consisting in the fact that any corpuscular theory of the earth’s charge, as might seem at first sight, must lead to ionization of the air, are not insurmountable. But we encounter new difficulties: it is true that, in explaining merely the fact of the replenishment of the earth’s charge, we can avoid the hypothesis of large paths, which is necessary for the theory according to which the air emits particles under the influence of penetrating radiation; however, on the other hand, we must assume velocities for the particles very close to the velocity of light in order to explain the absence of ionization, and this by itself already leads, as a consequence, to large paths.

Attempts have been made to overcome the presumed difficulties to which the absence of an electrifying effect in the case of an insulated body should lead, by making the assumption that the influx of particles occurs in the zone of the aurora borealis. It may be useful to point out that, even if we make such an assumption, we shall not avoid the difficulties to which the fact of the ionizing action of such particles leads, unless we adopt some theory like the one I have outlined; indeed, if we adopt the usual ionization per centimeter of path, it will be necessary to admit recombination of ions in order to reduce the density of ions, and moreover to such a degree that we would have to assume an area of incidence of the particles amounting to less than one-thousandth of the earth’s area; on the other hand, the electrical conductivity thereby imparted to the air will be so great that, with a potential gradient of 150 volts per meter, the entire current of conductivity for this region alone will have, as the calculation shows, a value greater than the corpuscular current.

THE ORIGIN OF TERRESTRIAL MAGNETISM.

The fact that the earth possesses the capacity to determine the direction of a magnetic needle was known even to the ancients. Indeed, the earth behaves approximately as if it were a gigantic magnet with two poles, one of which lies not far from the northern geographic pole, and the other not far from the southern. The problem of explaining this fact was one of the most fascinating fields in cosmic physics.

Of course, we may say that the interior of the earth contains a large quantity of substance possessing magnetic properties, such as iron, which acquired magnetism in one way or another and at one time or another. However, we cannot so easily rid ourselves of responsibility for this explanation; in fact, we know that if a steel magnet is heated to a temperature of 785 degrees Celsius, it loses its magnetism, and we have grounds to think that within the earth the temperature is far higher than the one indicated. We can escape this conclusion if we suppose that the great pressures prevailing inside the earth raise the temperature at which magnetism is lost. But until further and real data have been obtained concerning the influence of pressure in this direction, we may try to seek a more fundamental cause for explaining the magnetic state of the earth.

It is difficult to resist the temptation (to which many have yielded) to suppose that terrestrial magnetism is connected in one way or another with the rotation of the earth. There is no doubt that the simplest theories based on this view lead to a state of magnetization symmetrical with respect to the geographical axis, and, moreover, the remarkable feature of terrestrial magnetism, expressed in its secular variations, does not follow from them of itself. Nevertheless, we could feel great satisfaction with our successes if we were able to indicate some way by which such a body as the earth could acquire a magnetization comparable in magnitude with the terrestrial magnetism actually observed.

Theories resorting to the rotation of electrostatically charged systems.—We know that an electric current flowing through a circular conductor creates a magnetic field, and if we were to wind the surface of a sphere with one layer of rings and then pass a current through the rings, we would obtain a magnetic field approximately analogous to the field of the earth. But since the earth is electrically charged, the first thought that may occur to us is whether the current formed by the rotation of this charge together with the earth will not give an appreciable field. The charge density is known, and the speed of the earth’s rotation is also known, so that it is comparatively easy to compute the result. Neglecting the action of the positive charge of the atmosphere, we find that the magnetic field produced in this way reaches a magnitude of only one hundred-millionth part of the terrestrial field. Since the charge of the earth creates a very considerable electric field on its surface, we see that the charge density required to form a magnetic field comparable with the terrestrial field would have to create an electric field of enormous magnitude. Moreover, it is well known that, owing to the motion of the observer together with the earth’s surface, the field will appear to him different from that which is observed

...gave a stationary observer, and the character of this effect is such that the vertical component of the field receives the wrong sign, if we choose the sign of the charge so as to obtain the correct sign for the horizontal component.

If we take into account the motion of the atmospheric charge, we obtain an even more curious result. For a stationary observer the vertical component will now everywhere be equal to zero1, whereas for an observer participating in the motion of the earth, both the vertical and the horizontal components will be zero.

There is, however, another way by which we can obtain a magnetic field by the rotation of charges, without making use of an external electric field. If we imagine a sphere of positive electricity and set it into rotation, it will produce a magnetic field; but for a given total charge the strength of the equivalent magnet will be the greater, the larger the diameter of the sphere. Thus, if we superpose two spheres of somewhat different volumes, of which one consists of positive and the other of negative electricity, but the magnitude of the charge in both is the same, then they will act as oppositely directed magnets of different strength, and a residual magnetic effect will result. As regards the electric field, however, there will be no residual effect outside the sphere. But modern physics comes to the view that matter consists exclusively of positive and negative electricity and, apparently, at a time when a cubic centimeter, say, of iron is on the whole neutral, the quantities of positive and negative electricity contained in it are nevertheless so great that, if we could separate them and concentrate them at two points one centimeter apart, they would attract one another with a force equivalent to \(10^{20}\) tons. In view of the presence of so large a quantity of electricity of each sign, we can, as it turns out, explain a magnetic field comparable with the field of the earth, if we agree—

that positive electricity in the earth is distributed over a sphere whose radius is smaller than the radius of the sphere of negative electricity by only \(2 \times 10^{-8}\) cm; in other words, we need only assume that the diameters of the two spheres differ from one another by an amount equal to the diameter of a single molecule.

However, despite the very strong temptation to adopt this view, which was first advanced by Sutherland, we encounter a very serious difficulty when we begin to seek an explanation of why the positive and negative electricities remain separated even by so insignificant an amount; in fact, calculation shows that at the surface of transition there would be an electric field of a thousand million volts per centimeter, resisting such a separation of charges.

There are not a few reasons which might act to some extent in the direction of producing such a separation of charges, which as a result of the earth’s rotation would create a magnetic field. Thus, it is usually assumed that in a solid body a considerable fraction of the electrons is not bound to atoms, but can wander freely in the spaces between molecules, resembling the motion of air molecules among the leaves of a tree. Owing to the centrifugal force of the earth’s rotation these electrons will tend toward the surface of the earth. This tendency will encounter resistance in the form of attraction by the positive electricity which they will leave behind. Nevertheless, some tendency in this direction will exist, and as a result of the rotation of such a system, in which the charges have been displaced, we shall obtain a magnetic field. However, mathematical calculation shows that the field obtained in this way reaches a magnitude of only \(10^{-23}\) of the earth’s magnetic field and, moreover, is of a type quite different from it.

On the other hand, by virtue of the earth’s gravity the electrons will tend to move in the direction toward the center. If we leave aside the sign, this leads to the type of displacement assumed in Sutherland’s theory; but upon analyzing the magnetic field we find that in magnitude it reaches only \(10^{-21}\) of the earth’s field and, moreover, has the wrong direction.¹

¹ P. N. Lebedev, who in the last years of his life was interested in the problem of the origin of terrestrial magnetism, attempted to subject Sutherland’s theory to experimental verification on models. The calculation showed that, using masses and velocities with which it is still convenient to operate in the laboratory, one should expect the appearance of magnetic forces readily accessible to measurement if the substances under investigation, when rotated, excite magnetic forces to approximately the same degree as the substance of the earth. The experiments, however, gave negative results, which led P. N. Lebedev to the conviction that Sutherland’s hypothesis was untenable. Ed.

I shall point out still another possibility. We know that within the earth there prevails a higher temperature than at the surface. With a temperature gradient in a gas, the latter becomes, where the temperature is high, less dense than where it is low, so that the density of electrons will tend to become smaller in regions with a higher temperature than in those with a lower one; this tendency is opposed by the electrostatic attraction that appears as a result of the separation of charges. In working out this case we shall find that the magnetic field produced as a result reaches only \(10^{-17}\) of the earth’s field, although it happens to have the correct direction.

Fig. 5.

There are many other possibilities, to some extent analogous to those indicated; but, as calculations show, they all give fields of an order of magnitude infinitely small in comparison with the earth’s field. I think we may infer, as a general rule, that it is practically hopeless to seek an explanation of terrestrial magnetism on the basis of the rotation of charges separated against electrostatic attraction, since the mechanical forces necessary to produce the required separation must in all cases be immeasurably great.

Theories based on the properties of the gyroscope. Allow me now to turn to another possibility. We know that iron molecules behave like small magnets, and the magnetization of a steel bar consists in the phenomenon of the partial orientation of these small magnets, arranged in more or less the same direction. A circular conducting ring carrying a current acts like a magnet with an axis perpendicular to the plane of the ring; in this case it is generally assumed that the atom acquires magnetic properties as a result of the circulation within it of electrons. This circulation of electrons makes the atom behave like a gyroscope. But it is well known that if a gyroscope is set into rotation about its axis \(AB\) (see Fig. 5), for example in the direction indicated by the arrow \(C\), and if this axis is set into rotation about another axis \(GH\) in the direction indicated by the arrow \(D\), then the gyroscope will tend to turn so as to become parallel to \(GH\). Therefore, if the earth consists to a considerable extent of iron, then its molecular magnets will have a tendency to turn their axes parallel to the axis of rotation. That a piece of iron can be magnetized by rotation was experimentally shown by S. J. Barnett; but if we apply these conclusions to the earth, we shall find that in this way

in this way it is impossible to explain a magnetic field exceeding, in its magnitude, the earth’s field by \(2 \times 10^{-10}\).

It is known that various substances may be magnetized to different degrees by the action of one and the same magnetizing force. Of readily magnetizable substances it is said that they possess great permeability. The supposition has been put forward that, owing to high pressure or to some other cause, the interior of the earth may possess an unusually high permeability and that, consequently, a very weak magnetizing force, for example that produced by the gyroscopic effect, may suffice to impart to it a perceptible magnetization. Such a view, however, meets with a very serious objection, which I can illustrate by calling your attention to a well-known experiment. If a horseshoe electromagnet is excited by the action of an electric current and is made to support, say, a hundred-pound weight tied to its armature, it turns out that the weight continues to hang after the current has been switched off, provided only that the surfaces of the poles and of the armature are regular planes.

Fig. 6.

A closed iron ring, made up of the horseshoe and the armature, once magnetized, remains so even after the current has been stopped. If the armature is now forcibly torn away from the horseshoe, magnetic poles appear at the points of separation, as shown in Fig. 6. The action of these magnetic poles is such that it destroys the magnetization in the horseshoe and in the armature, and as a result it turns out that the horseshoe can no longer support not only the armature with the 100-pound weight, but even the armature alone (“self-demagnetizing force”). A short piece of iron is much more difficult to magnetize than a long one, because of the closeness of the poles to the main mass of the iron in the former case. Indeed, these poles create inside the iron a magnetic field of such a direction as tends to demagnetize it. In the case of a magnetized sphere, the action of the poles consists in the fact that, inside the iron mass, a demagnetizing field is formed equal to the field which the sphere itself produces at external points of its equator. Therefore a certain primary magnetizing force, which ultimately brings about the formation of the earth’s field by means of the orientation of molecular magnets, must have so high an intensi-

need to act on molecular magnets with a force at least equal to that with which a magnetic field, equal in intensity to the earth’s magnetic field at the equator, acts upon them.

Theories based on the action of terrestrial currents.—The earth’s field can be explained if we prove the existence of a corresponding circulation of currents within the earth. However, such an attempt at explanation immediately entails the necessity of explaining the electromotive forces that maintain the currents. In this connection it is not without interest to recall a calculation made many years ago by G. Lamb (H. Lamb), the significance of which I shall try to explain.

If we excite a current in a wire and then leave it to itself, it will fall to zero almost at once, owing to the resistance offered by the wire. The situation is analogous to this: suppose we took a hollow ring-shaped armature, filled it with water, and suddenly imparted to it a rotational motion. If there were no friction, the water would enter into a vortical circular motion forever; but owing to friction it will soon stop. If the water were less dense and therefore possessed less inertia, it would stop sooner. The analogy between the motion of water and the motion of electricity is not very close, but an electric current possesses the property of inertia, and, as it turns out, the inertia of the current is greater in a large ring than in a small one. When, however, we are dealing with a body of the volume of the earth, this inertia acquires such great importance that, as Lamb showed, if a system of currents were excited in a body of the volume of the earth, with its electrical conductivity equal to that of copper, and if the electromotive forces that caused this excitation ceased to act, about ten million years would be required for the current strength to fall to one third of its initial value. Attempts to explain the earth’s field in this way have met with criticism, since in that case one would have to admit the existence of gigantic currents which could be traced by extrapolation into past times as far as epochs no more remote than the epoch of the solidification of the earth’s crust; so that, unless we find some basis for supposing that the conductivity of the earth at present or in the past is greater than the conductivity of copper, we shall be faced with the necessity of accounting for the enormous stores of energy originally required to create the magnetic field.

The actual current density within the earth required to explain the earth’s field is very small, being, for example, only one hundred-millionth of an ampere per square centimeter of surface at the equator, if the current density is proportional to the distance from the axis of rotation. I have already reported on the enormous quantity of stores of positive and negative electricity in one cubic

centimeter of earth. If we imagine an iron sphere of the volume of the earth and assume that it contains \(10^{23}\) free electrons per cubic centimeter—a figure not devoid of foundation—then it is only necessary to suppose that the electrons on the earth’s surface differ in velocity from the matter in which they are situated by \(\frac{1}{7\times 10^{16}}\) of the velocity of the matter, in order to account for a current of one millionth of an ampere. It may be that the hope is not too greatly exaggerated that a fuller acquaintance with the mechanism of the conduction of electricity in solid bodies may lead to an explanation of this small difference as a direct result of the rotation of the earth. In that case the problem would not consist in explaining the electromotive force by means of which the electrical resistance of the substance of the earth could be overcome; rather, we should have to show that the continuously occurring motion of electrons in a rotating body, which must exist in order to avoid a further degradation of energy into heat, is such that there must be a definite relative velocity between the free electrons and the substance of the rotating body.

The small relative velocity between the free electrons and the substance of the earth can be explained rather simply if we suppose that the velocity of the earth is diminished as a result of the action of tides and ebbs. If the retarding forces exerted an influence on the earth and not on the free electrons, then the latter would tend to preserve their angular velocity undiminished. Of course, they would in fact lag behind the matter that had left them by such a distance that the force which would begin to act on them as a result of this lag, and which can be calculated on the basis of the specific electrical resistance, would be just sufficient to compel them to follow the earth in its retarded motion. However, if the corresponding calculations are carried out, it turns out that, in order to cause in this way the formation of a current of sufficient strength to explain the terrestrial field, the retardation in the motion of the earth would have to occur to such a degree that it would lose all its velocity in less than a day.

We can explain the small magnetic field if we assume that the negative electrons, while taking part in the displacement of the substance in which they are contained, do not rotate with respect to axes fixed in space. In this case we shall in fact obtain, as a result, a magnetic field entirely equivalent to the field that we would have if the whole system were at rest, with the exception of the electrons, which would all rotate about their own axes in a direction opposite to the rotation of the earth, making one revolution per day. The magnetic field formed in this case is equal to only

\(1.6 \times 10^{-25}\) of the terrestrial field and, moreover, has the opposite direction. Curious, however, is the following remark, which is of purely mathematical interest and does not claim to explain terrestrial magnetism: if we were to divide all the positive electricity contained in the earth into groups with an average radius of approximately \(1\ \mathrm{cm}\), and then in some way make these small groups move together with the earth without participating in its rotation, while all the negative electricity participated both in the rotation and in the translational motion of the earth, then we would obtain the possibility of explaining a magnetic field of the order of magnitude of the earth’s field.

Possibilities connected with a slight alteration of the fundamental laws of electrodynamics.—There is always the possibility that the origin of the terrestrial field lies in some fundamental, though small, departure from the usual laws of electrodynamics. In this connection I shall remind you of a somewhat analogous modification proposed by H. A. Lorentz to explain gravitation. As Lorentz showed, if we imagine that the attraction between a positive and a negative electron exceeds the repulsion between two positive or two negative electrons only by the fraction

\[ \frac{1}{3 \times 10^{33}}, \]

then the excess attraction will be sufficient to explain gravitation. Noting the extreme caution required in this connection in defining the concept of a neutral body, we point out that Lorentz’s theory leads to the following conclusion: for the equilibrium of the electrons in a body, the latter must possess a charge density not entirely determined by the weight of the electrons. Schuster analyzed this question; apparently, however, even under the most favorable assumptions this additional density is insufficient for a magnetic field comparable with the earth’s field to arise during rotation.

Greater success has been achieved by means of an assumption, to some degree analogous, concerning the magnetic field produced by a moving charge. I shall remind you that when a charge moves in a magnetic field, a force acts on it in a direction perpendicular to the plane containing the direction of its velocity and the direction of the magnetic field. This is precisely the force that sets an electric motor in action. Even when we measure a magnetic field by its action on a magnet, the same force underlies its action, since the magnet obtains its properties from the electrons rotating inside it. By analogy with what is observed in electrostatics, where we have the action of a positive charge on a positive one, of a negative on a negative one, and of a positive on a negative one, we also observe, with respect to moving electrons, the additional force of the action of the motion of a positive electron on a moving positive one

electron, of the motion of a negative electron upon a moving negative electron, of the motion of a negative electron upon a moving positive electron, and of the motion of a positive electron upon a moving negative electron1.

If, for similar motions, all these four forces are equal, then the rotation of the earth as a whole will exert no influence whatever on a moving electron or magnet. But if the forces arising between unlike moving charges differ sufficiently from the same forces between like charges in the same states of motion, then it follows directly from this that the electrically neutral earth will, by its rotation, act upon magnets and moving electrons with forces such as we ascribe to magnets in their usual definition. If we assume that the forces between electrons of like signs are equal for both signs, but that the force with which the motion of a negative electron acts upon a moving positive electron is greater, and the force of the action of the motion of a positive electron upon a moving negative electron is less, than the forces between like electrons by approximately the amount \(2.10^{-16}\), then in this way we can explain a field equivalent to the magnetic field of the earth2. If these changes are combined with the corresponding changes in electrostatic forces, then we can also include gravitation in the complete scheme.

The significance of secular oscillations.—There is some evidence in favor of the view that the earth’s magnetic axis rotates about the geographical axis, making one revolution in approximately 500 years. But we know that if, in some way, the number of lines of magnetic induction passing through a certain area of a conductor is changed, induction currents arise in the conductor. This is merely the result of the inertia, inherent in electromagnetic phenomena, of which I have already spoken. Therefore the displacement of the earth’s magnetic axis within the earth itself will excite induction currents, and the magnetic field observed by us will be, on the one hand, created by these induction currents (the secondary field), and, on the other hand, by the primary causes (the primary field). If, for illustration, we take an iron sphere of the volume of the earth, it turns out that the flux of the magnetic lines of induction of the secondary field through the sphere reaches such a magnitude that it almost completely reduces to zero the component of the primary flux perpendicular to the axis of rotation. As a result there remains only a small excess not

axial component. Thus, in order for the resultant current to have a noticeable inclination to the geographic axis, it is necessary that the primary axis lie very close to the plane of the equator, and that at the same time the primary current be so large that its axial component, small in comparison with it, would constitute the axial component observed by us. This practical coincidence of the primary magnetization axis with the equatorial plane would, of course, be very remarkable if it actually existed. The considerations by which it has been derived are based on the assumption of an electrical conductivity comparable with that of iron; and although we do not assert that the principal mass of the earth possesses an electrical conductivity of this order of magnitude, it is nevertheless interesting to draw attention to the curious results which would follow from secular variations if this electrical conductivity were such.

Diurnal variations.—The magnitudes of the earth’s magnetic elements undergo extremely regular variations over the course of the day and the year; and we are in a far better position in explaining these variations than in explaining the terrestrial field as a whole.

When a conductor moves across the lines of force of a magnetic field, induced currents are excited in it; as is known, this phenomenon underlies the operation of a dynamo machine. But the air is in constant motion under the influence of the tides and ebbs, just like the sea, and in its motion it crosses the magnetic lines of force of the earth. In consequence of this, electromotive forces are formed in the atmosphere; these latter cause the formation of currents in amounts determined by the conductivity of the atmosphere. The currents create magnetic fields, and these magnetic fields, being thus connected with the atmospheric tides and ebbs, will, as may be expected, undergo diurnal and seasonal variations. Such is the supposition originally put forward by Balfour Stewart, and subsequently worked out in detail by Schuster.

Let us note that the magnitude of the expected effects depends on the conductivity which we ascribe to the atmosphere. The lower layer of the atmosphere is so poor a conductor that its participation in the phenomenon indicated is negligibly small. However, there are grounds for supposing that the conductivity of the upper layer of the atmosphere is considerably greater; and on certain grounds, into which I need not enter, Schuster has suggested that appreciable conductivity may be regarded as characteristic of a layer of the atmosphere 300 km thick, situated at such a height that the mean pressure is equal to one millionth of an atmosphere. However, the conductivity whose existence he considers necessary for explaining the phenomena is 300,000 million times greater than the conductivity of the atmosphere at the earth’s surface.

To form an idea of what this means, one may point out that, with such conductivity, a column of air extending around the whole earth in the upper layer of the atmosphere must have no greater resistance than a column of the same cross-section, but only \(1/30\) cm long, at the earth’s surface. In other words, such an assumption essentially means that the earth may be regarded as surrounded by a conducting shell. However unexpected such an assumption may be, it agrees well with what is required for the explanation of other phenomena. Thus, in discussing the origin of the earth’s charge, we had occasion to consider the possibility of the existence of such a layer. On the other hand, the question was long a matter of dispute why the waves of wireless telegraphy travel such great distances above the earth’s surface. On the basis of elementary considerations we should have had to suppose that their energy would be scattered in space and that only a very small portion of it would succeed in passing a great distance around the earth. On the other hand, a conducting shell gives us the possibility of removing this difficulty. In fact, such a shell will reflect waves, analogously to what happens with sound waves transmitted through a tube or by means of a horn. The same considerations, of course, could have been applied to show that wireless waves arriving from outside could not enter into the conducting layer, since they would be reflected from its surface. We must not, however, attach too general a significance to this argument, since light also is in reality an electromagnetic disturbance with a very short wavelength—a kind of very short wireless wave—and it would be unfortunate for the theory if it proved that light cannot pass through the layer described.

It seems probable that ultra-violet light does not play an important role, because with its aid one can explain only a conductivity amounting to not even one millionth part of the required value. Other factors, often invoked in explaining electrical conductivity, are the corpuscular radiations of the sun. Some radiation of this kind appears necessary for the explanation of the aurora.

Aurora.—The aurora assumes various forms and has different colors and shades, but the phenomenon is confined chiefly to high latitudes. A characteristic feature of the aurora is the sharp boundary of its lower edge. The height of this boundary has been measured by various observers and, it seems, fluctuates between 70 and 300 km, with a maximum approximately at 115 km. The activity of auroras in most cases is confined to two zones of the atmosphere, situated at an angle of approximately \(20^\circ\) to the earth’s axis. One of the best-known theories of auroras explains them by light produced as a result—

the ionization of our atmosphere by negative electrons emitted by the Sun. As laboratory experiments show, beams of rapidly moving charged particles are deflected by a magnetic field; Birkeland—in the field of experiment—and Störmer—in the field of mathematical analysis—devoted much effort to determining to what extent the characteristic features of the aurora can be explained from the point of view that its cause is a stream of negatively charged particles issuing from the Sun and rushing into our atmosphere, while being subjected to the deflecting action of the Earth’s magnetic field. The two zones of active deposition of electrons are thereby satisfactorily explained, if one does not take into account the fact that they turn out to lie at higher latitudes than observation indicates. The cause of the difficulty is the small mass of the electron, which leads to an excessively large deflection of its path under the action of the Earth’s magnetic field. But, as I noted above in this article, the mass of a particle increases with its velocity and becomes theoretically infinite when the particle reaches the velocity of light. In order to bring the theory into agreement with the facts, Birkeland had to assume that the particles which cause the formation of auroras have velocities less than the velocity of light by only an amount from 400 to 4 meters per second.

To overcome the difficulty arising from the small mass of the electron, Vegard and others proposed that the particles which cause the formation of auroras are not electrons, but alpha particles emitted by the Sun. Alpha particles possess the proper velocity and mass to give the required deflection. Moreover, characteristic features of alpha particles are the rectilinearity of their paths and the very sharp boundary of the extent of their action. Both of these features are clearly expressed in the phenomenon of auroras: the rectilinearity of the path—in the rectilinearity of the auroral rays, and the sharp boundary of the range—in the sharpness of the lower boundary of the aurora. The circumstance that $\alpha$-particles travel only a distance of a few meters in air at atmospheric pressure presents no difficulty, because the pressure in the regions of auroras is very small. The range of an alpha particle is quite sufficient to explain the depth of penetration; and since there is in general some difficulty on this point, it arises from the fact that, judging by the trustworthy conceptions of the composition of the upper layers of the atmosphere, the range of ordinary alpha particles is rather too great to explain the facts.

The alpha particles emitted by the Sun have been invoked to explain not only auroras, but also those sudden disturbances in the Earth’s magnetic field which are known as magnetic storms. These disturbances are most frequent in periods of maximum sunspots, so that it is natural to attribute them to some substance emitted by sunspots.

To illustrate the difficulties encountered by any explanation of these storms by means of alpha particles, I shall cite some of the objections raised by Lindemann. To explain the facts it is necessary to assume that the particles are emitted in the form of some kind of cone. But Lindemann points out that, first of all, the dimensions of the phenomenon are such that they make necessary an incredibly large store of radioactive material in the sun; further, owing to mutual repulsion, alpha particles cannot remain together in the form of a beam during their journey from the sun to the earth. A beam of the required intensity would have to exhibit lateral scattering corresponding to an acceleration of the order of \(10^{13}\ \text{cm}/\text{sec}^{2}\) at its edges. Finally, even if alpha particles could reach the terrestrial atmosphere in the form of a beam, they would charge it to such a degree that, after the lapse of a few seconds, not a single one could any longer enter the atmosphere because of repulsion by those particles which had arrived there earlier.

Lindemann himself advances the view that the particles arriving in the atmosphere from the sun and causing magnetic storms, as well as the aurora borealis, are in fact gaseous ions ejected by solar prominences. These prominences, as we shall recall, consist of incandescent masses of gas, and some of them reach the incredible height of 300,000 miles; their forms change with such rapidity that the gases composing them must move with gigantic velocities. Velocities of the order of 80 million cm per second are not uncommon.

We know that if light falls upon a particle, its surface experiences pressure; moreover, the smaller the particle, the more strongly light acts upon it in the sense of increasing its velocity. Let us recall the usual opinion that the cause of the observed direction of comet tails, which are more often bent away from the sun and not toward it, as might have been expected by virtue of gravitation, is the pressure of light; owing to the small size of the particles, this pressure repels them from the sun with a force greater than that with which they are attracted to it by gravity. On this basis Lindemann proposed that the enormous velocities attained by gases in solar prominences are acquired owing to the pressure of light; he further showed that, as a result of this, some of the particles constituting these gases, as might be expected, will be thrown out into space with such velocities that the properties of the corresponding atoms will prove similar to the properties of alpha particles. He assumes that the gas is almost completely ionized owing to the high temperature in the prominences, so that particles of both signs are ejected in the direction of the earth—an circumstance which ensures the absence of scattering due to mutual repulsion.

I have no need to go into the details of the theory of these phenomena proposed by Lindemann. I shall note, however, that from different points of view we arrive at the conclusion that particles of one kind or another are ejected into our atmosphere by the sun at enormous velocity and are probably the principal causes of magnetic storms, of the high conductivity of the upper layers of the atmosphere, and of the phenomena of the aurora borealis; unfortunately, our knowledge of the upper layers of the atmosphere is practically based entirely on inferences, and we have no direct experimental data concerning the electrical conditions at the heights in question. If we could investigate them with the aid of some kind of apparatus, we should have better luck.

GRAVITATION.

It is impossible to consider fully the great problem of gravitation within the limits of a short article. Therefore I must confine myself to only a few remarks on this question. In searching for an explanation of such a phenomenon as gravitation, it might be appropriate to ask to what extent we are entitled to expect from nature an indication of the cause of this phenomenon. We say, or some of us say, that Newton discovered the force of gravitation, and since then we have been trying all the time to discover the cause of gravitation. Yet what sort of explanation could satisfy us? The picture of the earth revolving around the sun and not flying away from it very closely recalls to our imagination the picture of a stone whirling at the end of an elastic cord, and therefore we have tried to imagine some sort of elastic tension emanating from the sun. But suppose that someone has succeeded in explaining gravitation by the elastic properties of an intervening medium. How much would that reassure us? Shall we say that now everything is clear: that in fact the sun is surrounded not by a great “nothing,” but by a medium with elastic properties, and that this medium produces the tension. If we do this, then some future philosopher may ask: but why does an elastic medium produce tension? To this we shall reply that tension is the result of cohesion. An elastic medium consists of a multitude of small molecules, and when they separate from one another, they strive to return back. But why—says the philosopher—do they behave in this way? We shall reply that, although the molecules appear to be separated from one another, in reality between them there is a medium endowed with elastic properties and producing tension. But why—says the philosopher—does the elastic medium produce tension? And such reasoning may continue to infinity. In reality, we cannot arrive at the ultimate explanation of the question. The best we can do is to conclude that the phenomenon of gravitation, which we are unable to explain,

in many respects behaves analogously to another phenomenon, connected with elasticity, which we are likewise unable to explain.

But in presenting Newton’s law of gravitation there is in fact no basis at all for speaking of force. Newton’s whole discovery consists in this: if, for example, a particle is moving far from other bodies, then it moves in a straight line with constant velocity; but if two particles approach one another, they move with an acceleration inversely proportional to the square of the distance between them. In general, he found that the motion of a particle \(A\) can be described in the following way: connect the particle with some other particle \(B\) in the universe. Represent for particle \(A\) an acceleration in the form of a line joining it with particle \(B\), inversely proportional to the square of the distance between them and directly proportional to the masses of both particles. Then draw a line to another particle \(C\), and represent the second acceleration in the form of a line joining \(A\) and \(C\) and proportional to the inverse square of the distance and to the masses possessed by \(A\) and \(C\). Do this for all particles in the universe. Add the accelerations by the usual method of adding vectors, and the result will represent the acceleration of particle \(A\). In such a presentation of the law as a simple empirical fact, we have no need at all to use the word “force.” The law is, even without it, fully sufficient to give us the possibility of calculating all the motions of the planets. However, the circumstance that the resultant acceleration is composed of a certain number of noninterfering parts, each of which depends on another particle and on the line joining \(A\) with that particle, suggests to our mind the idea of an elastic tension. The mind prefers to think of elasticity or of something similar; in fact, it is in general exceedingly difficult for the human mind to think if it has no definite object for reflection. If Newton had found, for example, that the acceleration produced by particle \(B\) is not expressed by the line joining it with \(A\), if the acceleration made an angle of \(45^\circ\) with this line, then it would still have been possible to speak of a force produced by \(B\) and \(A\); but our mind would to a considerable degree have been freed from the obsessive representation evoked by reflection on elasticity. A slight further complication of the situation would have led to the analogy with elasticity being of even less use to us. We

of the correctness of such an explanation and ask me whether I am certain that there really is a fire hose in this house. Of course, if you are very persistent, it will be difficult for me to prove that I am right. However, if you annoy me greatly, I shall become angry with you and call you an impractical philosopher; but, feeling the need to say something in order to convince you, I may in the end make the following speech: “I am not interested in whether there is a fire hose in the house or not. But since, having made the assumption of its existence and representing the motion of the traveler in accordance with its action, I can predict results which turn out to be correct, I stand on perfectly firm ground. And I bear no responsibility to anyone for the devices of my thinking so long as my conclusions are correct.” Having said this, I shall feel that I have justified my position and brought you into final confusion. I myself shall feel like a little philosopher, but quietly I shall continue to amuse myself with the picture of the hose and the various details of its action. I shall think all sorts of things about it, but I shall never dare communicate them to you, since otherwise you will ridicule me. I shall ponder what the density of the liquid discharged by the hose is, what its boiling point may be, and so on. Suppose now that, while I am giving myself up to such reflections, you report to me certain observations showing that the traveler’s motion does not correspond quite exactly to the conception of it which we had formed. The difference may be very slight, but it may be of such a character as completely to overthrow the simplicity of the action which I had regarded as being due to the hose. Naturally, I first of all again turn to my hose, but I shall have to modify it somewhat. I shall say: “Of course, this is a hose—not of the ordinary type. It is possible that it gives an impulse not quite in the direction in which the liquid is moving.” But I shall have to face the fact that, although the deviations may be small quantitatively, they may at the same time be so essential in principle and lead to such radical changes in my conceptions of the mechanism of the process that the hose which I shall have to assume will prove to be entirely different from any hose I have ever seen. I shall have to follow this path, modifying and adapting the hose, making it more and more difficult to understand; and, forgetting that the original justification for its existence was its supposed ability to explain the observed phenomenon by means of something that I consider perfectly familiar to me, I shall soon be forced to spend 99% of my ingenuity on attempts to understand the hose, leaving only 1% of it for the law of the traveler’s motion.

Suppose now that, while I am occupied with this matter and feel rather embarrassed by my success, you come to

to me and say: “I have made a discovery. I do not know why a man moves exactly as he does, and I think that you do not know this either, but I have established precisely how he moves. He moves from \(A\) to \(E\) by a path which is the shortest distance between these two points, but not like the flight of a bird; rather, through a crater, the form of which I can describe to you.” Let us suppose that you say this and then add: “I intend to take such a formulation of the law as my starting point. If in this phenomenon there should prove to be some remarkable gut, then it is the gut that must be explained in accordance with this fundamental law, and not the fundamental law in accordance with the gut.” I think I should have to admit that your position is at least reasonable.

But this position is to some extent analogous to that embodied in Einstein’s formulation of the law of gravitation. It is true that this formulation does not remain wholly within the bounds of experience. Its construction is furnished with many embellishments of which I have no need to speak. But as regards the law itself, the language of its formulation is not very different from that which we gave for the law of motion of our traveler. It asserts that a planet, passing from one point to another, moves along a path which is the longest distance between these points; but, unfortunately for the convenience of the non-mathematical mind, this path does not lie in the world of three dimensions, but is a path in a certain non-Euclidean four-dimensional space, of such a type that the fourth dimension is time, and whose properties are expressed in such a way that they are in accord with certain philosophical requirements of the theory of relativity.

Philosophers of past centuries said that the planets move in circles because the circle is perfect symmetry, and we are inclined to laugh at their opinion; but we see that the Einsteinian formulation of the law of gravitation, avoiding mention of forces and formulating the law exclusively in accordance with the properties of the path described by the planets, contains an element of the same position. In reality the law of the ancient philosophers would not have been so bad if it had defined the magnitude of the circles somewhat more precisely, and if they had altogether abandoned the word “because.”

Translated by S. A. Alekseev.

1. The first two actions may serve to determine the magnetic fields formed, respectively, by the motions of positive and negative electricity, since in this case each of them must be determined independently. ↩↩↩↩↩↩↩↩

2. I note in passing that it is possible to give a statement of this law in a form consistent with the special theory of relativity. ↩