THE ORIGIN AND MAINTENANCE OF THE EARTH'S CHARGE It is obvious that, if negative electricity is leaving our earth and positive electricity entering it in virtue of the potential gra dient operating in a conducting atmosphere, any compensating stream must take place in opposition to the forces of the electric field. The theories which have been proposed divide themselves mainly into two classes, those in which gravity is the primary agent instrumental in moving the charges against the field, and those in which the flux of negative corpuscles towards the earth is brought about in opposition to the field through the agency of a very high velocity produced in them by some means or other.
Theories Invoking Gravitation. As an example of the former class we have the theory of C. T. R. Wilson (1897-190o) to the effect that the replenishment takes place through the agency of rain. Theoretical considerations have been thought to suggest that the raindrops should form on the atmospheric ions, and more copiously on the negative than on the positive ions, so that rain might be expected to be, on the whole, negatively charged. The charged drops, falling to earth under gravity, would do so in opposition to the electric field, and would constitute the replenish ment. This theory is open to two primary objections. In the first place, while rain is charged, and to a degree probably sufficient to account for the necessary replenishment, it is found that 90% of the rain which falls is positively charged. Again, it appears that there are grave theoretical difficulties concerned with the possi bility of condensation of water upon atmospheric ions, in the form of drops of appreciable size, so that this theory is now generally regarded as inadequate to account for the facts.
A theory which came near to being successful, and which un doubtedly plays a part in the origin of the earth's charge, is one due to H. Ebert 0904). Ebert's theory, which constitutes a modification of an earlier theory due to Elster and Geitel, invokes the fact that if ionized air be passed through a fine tube the nega tive ions diffuse to the walls of the tube more rapidly than do the positive ions, so that the air which emerges from the tube is positively charged. Ebert applies this to the atmospheric electric problem, by supposing that the air which is to be found in the interstices of the soil, and which is ionized by the radioactive material therein, is drawn out during the periods of falling barometric pressure, leaving an excess of negative charge on the walls of the interstices. The positive charge which emerges would be held in the immediate vicinity of the ground by the negative charge, but here Ebert invokes the aid of upward air currents which carry it, against the field, into the higher regions of the atmosphere. The theory has been criticized on the basis that the emission of ions from the ground would be insufficient, and the upward currents too feeble. One of the most serious objections is to be found in a conclusion, which, however, follows comparatively simply from theoretical considerations, to the effect that, on such a theory, it would result that, before the ascending positive charge had risen to an altitude of a kilometre or so, it would have dis appeared almost completely, devoured, as it were, by the negative charge continually fed into it from the earth below, through the medium of the conducting atmosphere. We should obtain a posi tive charge in the atmosphere, a negative charge on the earth's surface, a conduction current and a potential gradient ; but all of these phenomena would be confined to a layer of the atmosphere about a kilometre or so in thickness. The whole of the positive charge in the atmosphere would be found in this layer, and, being equal to the negative charge on the earth's surface, since that was formerly its partner in neutrality, it would annul the field at all greater altitudes.
Both C. T. R. Wilson's theory and also that of Ebert's suffers from the fact that the positive charge in the atmosphere, which is the counterpart of the negative left on the earth, holds that nega tive to the spot immediately beneath it, and so fails to provide for the existence of a potential gradient where the primary phe nomenon, falling barometric pressure or precipitation, is not going on. Difficulties of these kinds become greatly minimized by the assumption, justified by considerations from other sources, as to the existence of a region of very high conductivity, a conducting layer in the upper atmosphere. For, under such conditions the combined actions of even an isolated positive charge in the atmosphere and its counterpart of negative on the earth would be to set up between the earth and the conducting layer a potential difference which would be handed around more or less uniformly all over the earth.
Corpuscular Theories.—Turning now to theories in which the replenishment of the charge comes about by the agency of high-speed electrified corpuscles shot into the earth, the first of these was proposed by G. C. Simpson (1904). In this theory it was supposed that the sun emitted negative and positive cor puscles of high penetrating power. The former were supposed to pass right through our atmosphere and charge the earth, while the latter were of less penetrating power and were caught in the atmosphere. In this way the earth would continually receive negative, and the atmosphere positive, charge. The ordinary processes of atmospheric conduction would, moreover, cause a con tinual conduction of electricity between atmosphere and earth, so that a steady state would be reached when the amount of neutralization of charge by this latter process just balanced the charging effect due to the influx of the corpuscles. This theory requires that we suppose the existence of corpuscles of pene trating power so great that they could pass through the whole of the earth's atmosphere, which is comparable in absorbing power with a column of mercury about 76cm. high. The greatest range which has been observed in air, for the (3-rays of radium, is about 7 or 8 metres. Electrons having a velocity 99% of that of light can travel through only 1.3cm. of aluminium, which is equivalent in absorbing power to about loin. of air at atmospheric pressure.
Although, according to electromagnetic theory, the velocity of light represents the maximum velocity which a corpuscle can attain, one must guard against the supposition that, because corpuscles with velocity 99% of that of light have ranges of only in air, no corpuscles can have ranges much greater than this. For electromagnetic theory shows that corpuscles with velocity even 99% of that of light are very far removed in their properties from those which approach that limit much more closely. As a matter of fact, the mass of a corpuscle increases with its velocity in such a way that the corpuscle must have infinite energy in order to attain the velocity of light.
We may, however, avoid the assumption of exceptionally long ranges by a device in which the penetrating radiation becomes invoked as the primary cause responsible for the earth's charge (W. F. G. Swann, 1917; E. v. Schweidler, 1918). The penetrating radiation is probably of the nature of a gamma-ray radiation. Now gamma-rays possess the power of ionizing, i.e., of ejecting elec trons from a gas through which they pass, and the nature of their action is such that the ejected electron is sent out almost entirely in the direction of the gamma-ray. (See COMPTON EFFECT.) We may thus expect that such a radiation coming from above will eject electrons from the air, and these will travel certain distances in a downward direction before coming to rest. Those electrons which are shot out within striking distance of the earth will reach it and charge it. Their places will be taken by other electrons, which have been shot out from layers above and have become absorbed before reaching the earth. One advantage possessed by this type of corpuscular theory is that it invokes, for the production of the corpuscles, an agency which is already recognized for other reasons, and another advantage lies in the fact that no artificial adjustments of the theory are necessary in order to provide for a conduction current which is practically independent of altitude.
Further, on submitting the theory to calculation, we arrive at magnitudes for the quantities involved which are by no means unreasonable. Thus, if we assume that only three high-speed cor puscles are emitted per cu.cm. per second, a number comparable with that which the penetrating radiation is supposed to eject, it is only necessary to assume that these corpuscles have a range of 9m. in air in order to account for the replenishment of the earth's charge. We shall presently see that, for reasons concerned with the ionization which would be produced by the corpuscles, it is desirable to endow them with a range greater than 9m.; but for the mere requirements of the replenishment of the earth's charge an average range of 9m. is sufficient.
Objections to Corpuscular Theories.—Two main objections may be raised against all forms of corpuscular theories. The first of these comes from failure to detect any charging effect on an insulated body exposed to the corpuscles (E. v. Schweidler, 1918; W. F. G. Swann, 1917) . If corpuscles are being shot into the earth from above, an insulated mass of metal should gradually acquire a charge from the corpuscles which enter it, unless, indeed, the corpuscles are so penetrating as to pass right through it. Experi ments of this kind have failed to reveal any corpuscular current of amount sufficient to correspond to the requirements. The diffi culty it not insurmountable, however, if one adopts the last of the views referred to above, i.e., that the ejection of the corpuscles from the molecules of air is brought about by exceptionally hard gamma-rays from above. For, on this view, if the gamma-rays are sufficiently penetrating to pass right through the metal, they will eject corpuscles from the bottom of the mass as well as inject them at the top. A simple calculation shows that, provided the intensity of the gamma radiation does not alter in passing through the metal, all that is necessary in order to conclude that as many electrons would be shot out of the bottom of the mass as were shot in at the top is the assumption that the ratio of the numbers of corpuscles shot out per cu.cm. of air and metal is equal to the inverse of the ratio of the average ranges of a corpuscle in air and in the metal. This assumption is entirely consistent with our knowledge of the laws pertaining to the action of gamma-rays and the passage of corpuscles through matter.
The second great objection, and perhaps the most serious ob jection, at first sight, to any corpuscular theory is the fact that we might expect the passage of high-speed corpuscles through the atmosphere, on their way to the earth, to be accompanied by a much greater ionization than is observed. The situation is this : The corpuscular current necessary to balance the atmospheric electric current amounts to an influx of 1,5oo corpuscles per sq.cm. per second. We know that an electron approximating in velocity to that of light produces about 4o ions per cm. of its path, so that in each cu.cm. we might expect ions to be produced to the extent of about 6o,000 per cu.cm. per second, whereas experiment shows that they are only produced to the extent of one ten-thousandth of this amount. In order to see how we may escape this difficulty it may be of interest to probe a little more closely the mechanism of the ionization.
Absence of Ionization by Corpuscles with Velocities Approximating That of Light.—Consider an electron in an atom, and suppose that another electron which we shall distin guish by calling it a corpuscle, approaches the atom. The corpuscle will start to repel the electron as it approaches, and will continue to do so as it recedes, with the result that the electron receives energy, the momentum which it acquires being more or less in a direction perpendicular to the line of flight of the corpuscle. The greater the velocity of the corpuscle the shorter the time during which the electron has opportunity to receive momentum from it. The effi ciency of the corpuscle as regards its power to hurl the electron out of the atom thus diminishes with increase of its velocity, and would, as a matter of fact, become zero if the corpuscle could attain an infinite velocity. The velocity of the corpuscle cannot attain a value greater than that of light, however, and, as regards the above effect, there is not very much reduction in ionizing effi ciency for an increase of velocity from, say, 95% of that of light, where the ionization has been measured, to the velocity of light itself. As the velocity of light is approached, however, another phe nomenon comes in. The field of the corpuscle does not remain uni formly distributed. According to known electromagnetic laws, its lines of force close up more and more into its equatorial plane. The time which the corpuscle has for acting effectively on the electron is therefore reduced still further on this account; but the intensity of the action during that time is increased; and, it turns out that, if we take nothing else into consideration, the energy communicated to the electron by the passage of the corpuscle will be unaffected by this concentration of the lines of force. There is one other very important consideration which we must take into account, however. If an electron receives even a small velocity in a very short time, it is known that it will radiate a large amount of energy. Its sudden start results in a violent jerk in the aether. On submitting this matter to calculation it turns out that, even if we should wish to give to an electron but a small amount of energy, in an infinitesimal time, it would be necessary to pay a sort of tax, of an infinite amount of energy, in the shape of radiation. Now the more nearly the corpuscle approaches the velocity of light the more suddenly does it com municate to the electron such energy as it imparts. Without entering too greatly into details, we may describe the situation as follows : In the case of a corpuscle moving with a velocity approx imating that of light (say 95% of the velocity of light) it turns out that the corpuscle must approach an electron of an oxygen atom within o• 7x 1 o–i ocm. in order that it shall be able to eject that electron from the atom. If the minimum distance of approach is less than this amount the energy imparted to the electron will be greater, if it is more the energy imparted will be less. It is, however, possible to assign to the corpuscle a velocity so high that, irrespective of the distance of approach, if we should sup pose it to transmit to the electron an amount of energy corre sponding to the ionization potential of oxygen (15.5 volts), we should lead ourselves to the impossible conclusion that the elec tron's acceleration would be so large that the energy radiated by it in acquiring its velocity would be greater than the work done on it by the corpuscle. Thus corpuscles having the velocity in question, or any higher velocity, would be unable to eject an electron from an atom of oxygen, the more easily ionizable of the two main constituents of the atmosphere. When we work out this velocity, we find that it comes out as only 45 metres per sec. less than the velocity of light. In spite of the very close approxima tion of the velocity to the velocity of light, the value found hap pens to be exactly the velocity which Birkeland has found it necessary to assign to solar corpuscles if the bending which these corpuscles suffer in the earth's magnetic field is to be consistent with their accounting for the aurora. Corpuscles of lower speeds would suffer too large deviations in the field to permit of their accounting for the facts. The diminution of bending, resulting from approximation of the velocity to that of light, results not so much from the direct influence of high speed as from the increase in the mass of the corpuscle which approximation to the velocity of light implies. It is, of course, a fact that, if the present theory were true, it would lead to difficulty as regards Birkeland's corpuscles being responsible for the aurora, since they could not ionize. This difficulty may be of a secondary nature, however. It may perhaps be worth while pointing out that closeness of approx imation to the conditions pertaining to the velocity of light is not well symbolized by closeness of approximation of v to c; for, as regards the energy of a corpuscle, for example, there is an infinite range from that corresponding to v less than c by 45 metres per second and v = c.
As a special aspect of the above comparison with Birkeland's data, it is of interest that, if an electron were shot from infinity into our atmosphere—in the equatorial plane, for example—it would not reach the earth, but would be turned back into space by the earth's magnetic field, unless it had a velocity nearer to that of light than the velocity which we have calculated as suffi ciently great to ensure absence of ionization. Indeed, with this velocity (45m. per second below the velocity of light) the cor puscle would not succeed in approaching nearer the earth than about eight times the earth's radius before being turned back by the earth's magnetic field.
The Possibility of Spontaneous Generation of Charge.— The possibility of a spontaneous generation of charge within the earth was first tentatively suggested by G. C. Simpson (1916). This possibility has been elaborated by W. F. G. Swann (19 2 7 ) into a theory in which a modification of the ordinary laws of electromagnetism is made in a form consistent with the theory of relativity and of such a type as to secure a slow death of positive charge as a result of the earth's rotation. The surplus negative electricity accumulates until it has built up a potential gradient adequate to drive negative electricity away from the earth at a rate sufficient to balance the rate of death of positive electricity. The necessary rate of death of positive electricity is very small. It amounts to only one proton per cu.cm. per day, or, in other words, it corresponds to a diminution of only o. 5 % of the earth's mass in years. The modification in the electro dynamic scheme is also made to provide for the origin of the earth's magnetism and gravitation.