Section 82).

The ions which are produced in gases at ordinary pressure have an apparent size, as determined from their rates of diffusion, large compared with the molecule of the gas in which they are produced. The negative ion consists of an electron with a cluster of molecules attached to and moving with it; the positive ion consists of a molecule from which an electron has been expelled, with a cluster of molecules attached. At low pressures under the action of an electric field the electron does not form a cluster. The positive ion is always atomic in size, even at low pressures of the gas. Each of the ions carries a charge of value 3·4 × 10⁻¹⁰ electrostatic units.

=41. Ions produced by collision.= The greater part of the radiation from the radio-active bodies consists of a stream of charged particles travelling with great velocity. In this radiation, the α particles, which cause most of the ionization observed in the gas, consist of positively charged bodies projected with a velocity about one-tenth the velocity of light. The β rays consist of negatively charged particles, which are identical with the cathode rays generated in a vacuum tube, and travel with a speed about one-half the velocity of light (chapter IV.). Each of these projected particles, in virtue of its great kinetic energy, sets free a large number of ions by collision with the gas molecules in its path. No definite experimental evidence has yet been obtained of the number of ions produced by a single particle, or of the way in which the ionization varies with the speed, but there is no doubt that each projected body gives rise to many thousand ions in its path before its energy of motion is destroyed.

It has already been mentioned (section 29) that at low pressures ions moving under the action of an electric field are able to produce fresh ions by collision with the molecules of the gas. At low pressures the negative ion is identical with the electron set free in a vacuum tube, or emitted by a radio-active substance.

The mean free path of the ion is inversely proportional to the pressure of the gas. Consequently, if an ion moves in an electric field, the velocity acquired between collisions increases with diminution of the pressure. Townsend has shown that fresh ions are occasionally produced by collision when the negative ion moves freely between two points differing in potential by 10 volts. If the difference be about V = 20 volts, fresh ions arise at each collision.

Now the energy W, acquired by an ion of charge e moving freely between two points at a difference of potential V, is given by

W = Ve.

Taking V = 20 volts = ²⁰⁄₃₀₀ E. S. units, and e = 3·4 × 10⁻¹⁰, the energy W required in the case of a negative ion to produce an ion by collision is given by

W = 2·3 × 10⁻¹¹ ergs.

The velocity u acquired by the ion of mass m just before a collision is given by

1 --- mu² = Ve, 2

and

$$ u = \sqrt{\frac{2Ve}{m}} $$

Now e/m = 1·86 × 10⁷ electromagnetic units for the electron at slow speeds (section 82).

Taking V = 20 volts, we find that

u = 2·7 × 10⁸ cms. per sec.

This velocity is very great compared with the velocity of agitation of the molecules of the gas.

In a weak electric field, the negative ions only produce ions by collision. The positive ion, whose mass is at least 1000 times greater than the electron, does not acquire a sufficient velocity to generate ions by collision until an electric field is applied nearly sufficient to cause a spark through the gas.

An estimate of the energy required for the production of an ion by X rays has been made by Rutherford and McClung. The energy of the rays was measured by their heating effect, and the total number of ions produced determined. On the assumption that all the energy of the rays is used up in producing ions, it was found that V = 175 volts—a value considerably greater than that observed by Townsend from data of ionization by collision. The ionization in the two cases, however, is produced under very different conditions, and it is impossible to estimate how much of the energy of the rays is dissipated in the form of heat.

=42.= Variations are found in the saturation current through gases, exposed to the radiations from active bodies, when the pressure and nature of the gas and the distance between the electrodes are varied. Some cases which are of special importance in measurements will now be considered. With unscreened active material the ionization of the gas is, to a large extent, due to the α rays, which are absorbed in their passage through a few centimetres of air. In consequence of this rapid absorption, the ionization decreases rapidly from the surface of the active body, and this gives rise to conductivity phenomena different in character from those observed with Röntgen rays, where the ionization is in most cases uniform.

=43. Variation of the current with distance between the plates.= It has been found experimentally that the intensity of the ionization, due to a large plane surface of active matter, falls off approximately in an exponential law with the distance from the plate. On the assumption that the rate of production of ions at any point is a measure of the intensity I of the radiation, the value of I at that point is given by

$$ \frac {i}{i₀} = 1 − e^{–λ x} $$

where λ is a constant, x the distance from the plate, and I₀ the intensity of the radiation at the surface of the plate.

While the exponential law, in some cases, approximately represents the variation of the ionization with distance, in others the divergence from it is wide. The ionization, due to a plane surface of polonium, for example, falls off more rapidly than the exponential law indicates. The α rays from an active substance like radium are highly complex; the law of variation of the ionization due to them is by no means simple and depends upon a variety of conditions. The distribution of ionization is quite different according as a thick layer or a very thick film of radio-active matter is employed. The question is fully considered at the end of chapter IV., but for simplicity, the exponential law is assumed in the following calculations.

Consider two parallel plates placed as in Fig. 1, one of which is covered with a uniform layer of radio-active matter. If the distance d between the plates is small compared with the dimensions of the plates, the ionization near the centre of the plates will be sensibly uniform over any plane parallel to the plates and lying between them. If q be the rate of production of ions at any distance x and q₀ that at the surface, then q = q₀e^{–λx}. The saturation current i per unit area is given by

$$ i = \int₀^d qe' dx $$, where e´ is the charge on an ion,

$$ = q₀e' \int₀^d e^{–λ x} dx = \frac{q₀e'}{λ} (1 - e^{–λ d}) $$

hence, when λd is small, i.e. when the ionization between the plates is nearly constant,

i = q₀e´d.

The current is thus proportional to the distance between the plates. When λd is large, the saturation current i₀ is equal to q₀e´/λ, and is independent of further increase in the value of d. In such a case the radiation is completely absorbed in producing ions between the plates, and

$$ \frac {i}{i₀} = 1 − e^{–λ d} $$

For example, in the case of a thin layer of uranium oxide spread over a large plate, the ionization is mostly produced by rays the intensity of which is reduced to half value in passing through 4·3 mms. of air, i.e. the value of λ is 1·6. The following table is an example of the variation of i with the distance between the plates.

Distance Saturation Current

2·5 mms. 32 5 „ 55 7·5 „ 72 10 „ 85 12·5 „ 96 15 „ 100

Thus the increase of current for equal increments of distance between the plates decreases rapidly with the distance traversed by the radiation.

The distance of 15 mms. was not sufficient to completely absorb all the radiation, so that the current had not reached its limiting value.

When more than one type of radiation is present, the saturation current between parallel plates is given by

$$ i = A (1 − e^{λ d}) + A1 (1 − e^{–λ1 d}) $$ &c.

where A, A₁ are constants, and λ, λ₁ the absorption constants of the radiations in the gas.

Since the radiations are unequally absorbed in different gases, the variation of current with distance depends on the nature of the gas between the plates.

=44. Variation of the current with pressure.= The rate of production of ions by the radiations from active substances is directly proportional to the pressure of the gas. The absorption of the radiation in the gas also varies directly as the pressure. The latter result necessarily follows if the energy required to produce an ion is independent of the pressure.

In cases where the ionization is uniform between two parallel plates, the current will vary directly as the pressure; when however the ionization is not uniform, on account of the absorption of the radiation in the gas, the current does not decrease directly as the pressure until the pressure is reduced so far that the ionization is sensibly uniform. Consider the variation with pressure of the saturation current i between two large parallel plates, one of which is covered with a uniform layer of active matter.

Let λ₁ = absorption constant of the radiation in the gas for unit pressure.

For a pressure p, the intensity I at any point x is given by

$$ \frac {I} {I₀} = e^{- p λ_1 x} $$

The saturation current i is thus proportional to

$$ \int₀^d pI dx = \int₀^d pI₀e^{-pλ1 x} dx = \frac{I₀}{λ1} (I − e^{pA_1d}) $$

If r be the ratio of the saturation currents for the pressures p₁ and p₂,

$$ r = \frac {1 − e^{-p1λ1 d}} {1 − e^{-p2λ1 d}} $$

The ratio is thus dependent on the distance d between the plates and the absorption of the radiation by the gas.

The difference in the shape of the pressure-current curves is well illustrated in Fig. 8, where curves are given for hydrogen, air, and carbonic acid for plates 3·5 cms. apart.

For the purpose of comparison, the current at atmospheric pressure and temperature in each case is taken as unity. The actual value of the current was greatest in carbonic acid and least in hydrogen. In hydrogen, where the absorption is small, the current over the whole range is nearly proportional to the pressure. In carbonic acid, where the absorption is large, the current diminishes at first slowly with the pressure, but is nearly proportional to it below the pressure of 235 mms. of mercury. The curve for air occupies an intermediate position.

In cases where the distance between the plates is large, the saturation current will remain constant with diminution of pressure until the absorption is so reduced that the radiation reaches the other plate.

An interesting result follows from the rapid absorption of radiation by the gas. If the current is observed between two fixed parallel plates, distant d₁ and d₂ respectively from a large plane surface of active matter, the current at first increases with diminution of pressure, passes through a maximum value, and then diminishes. In such an experimental case the lower plate through which the radiations pass is made either of open gauze or of thin metal foil to allow the radiation to pass through readily.

The saturation current i is obviously proportional to

$$ \int{d1}^{d2} pI₀e^{-pλ1 d} $$,

i.e. to

$$ \frac{I₀}{λ1} (e^{-pλ1 d1} − e^{-pλ1 d_2}) $$

This is a function of the pressure, and is a maximum when

$$ \loge \frac{d1}{d2} = − pλ1 (d2 − d1) $$

For example, if the active matter is uranium, pλ₁ = 1·6 for the α rays at atmospheric pressure. If d₂ = 3, and d₁ = 1, the saturation current reaches a maximum when the pressure is reduced to about ⅓ of an atmosphere. This result has been verified experimentally.

=45. Conductivity of different gases when acted on by the rays.= For a given intensity of radiation, the rate of production of ions in a gas varies for different gases and increases with the density of the gas. Strutt has made a very complete examination of the relative conductivity of gases exposed to the different types of rays emitted by active substances. To avoid correction for any difference of absorption of the radiation in the various gases, the pressure of the gas was always reduced until the ionization was directly proportional to the pressure, when, as we have seen above, the ionization must everywhere be uniform throughout the gas. For each type of rays, the ionization of air is taken as unity. The currents through the gases were determined at different pressures, and were reduced to a common pressure by assuming that the ionization was proportional to the pressure.

With unscreened active material, the ionization is almost entirely due to α rays. When the active substance is covered with a layer of aluminium ·01 cm. in thickness, the ionization is mainly due to the β or cathodic rays, and when covered with 1 cm. of lead, the ionization is solely due to the γ or very penetrating rays. Experiments on the γ rays of radium were made by observing the rate of discharge of a special gold-leaf electroscope filled with the gas under examination and exposed to the action of the rays. The following table gives the relative conductivities of gases exposed to various kinds of ionizing radiations.

Gas Relative α β γ Röntgen Density rays rays rays rays

Hydrogen 0·0693 0·226 0·157 0·169 0·114

Air 1·00 1·00 1·00 1·00 1·00

Oxygen 1·11 1·16 1·21 1·17 1·39

Carbon dioxide 1·53 1·54 1·57 1·53 1·60

Cyanogen 1·86 1·94 1·86 1·71 1·05

Sulphur dioxide 2·19 2·04 2·31 2·13 7·97

Chloroform 4·32 4·44 4·89 4·88 31·9

Methyl iodide 5·05 3·51 5·18 4·80 72·0

Carbon 5·31 5·34 5·83 5·67 45·3 tetrachloride

With the exception of hydrogen, it will be seen that the ionization of gases is approximately proportional to their density for the α, β, γ rays of radium. The results obtained by Strutt for Röntgen rays are quite different; for example, the relative conductivity produced by them in methyl iodide was more than 14 times as great as that due to the rays of radium. The relative conductivities of gases exposed to X rays has been recently re-examined by McClung and Eve, who have found that the conductivity depends upon the penetrating power of the X rays employed. The results obtained by them will be discussed later (section 107).

This difference of conductivity in gases is due to unequal absorptions of the radiations. The writer has shown that the total number of ions produced by the α rays for uranium, when completely absorbed by different gases, is not very different. The following results were obtained:

Gas Total Ionization

Air 100

Hydrogen 95

Oxygen 106

Carbonic acid 96

Hydrochloric acid gas 102

Ammonia 101

The numbers, though only approximate in character, seem to show that the energy required to produce an ion is probably not very different for the various gases. Assuming that the energy required to produce an ion in different gases is about the same, it follows that the relative conductivities are proportional to the relative absorption of the radiations.

A similar result has been found by McLennan for cathode rays. He proved that the ionization was directly proportional to the absorption of the rays in the gas, thus showing that the same energy is required to produce an ion in all the gases examined.

=46. Potential Gradient.= The normal potential gradient between two charged electrodes is always disturbed when the gas is ionized in the space between them. If the gas is uniformly ionized between two parallel plates, Child and Zeleny have shown that there is a sudden drop of potential near the surface of both plates, and that the electric field is sensibly uniform for the intermediate space between them. The disturbance of the potential gradient depends upon the difference of potential applied, and is different at the surface of the two plates.

In most measurements of radio-activity the material is spread over one plate only. In such a case the ionization is to a large extent confined to the volume of the air close to the active plate. The potential gradient in such a case is shown in Fig. 9. The dotted line shows the variation of potential at any point between the plates when no ionization is produced between the plates; curve A for weak ionization, such as is produced by uranium, curve B for the intense ionization produced by a very active substance. In both cases the potential gradient is least near the active plate, and greatest near the opposite plate. For very intense ionization it is very small near the active surface. The potential gradient varies slightly according as the active plate is charged positively or negatively.

=47. Variation of current with voltage for surface ionization.=

Some very interesting results, giving the variation of the current with voltage, are observed when the ionization is intense, and confined to the space near the surface of one of two parallel plates between which the current is measured.

The theory of this subject has been worked out independently by Child and Rutherford. Let V be the potential difference between two parallel plates at a distance d apart. Suppose that the ionization is confined to a thin layer near the surface of the plate A (see Fig. 1) which is charged positively. When the electric field is acting, there is a distribution of positive ions between the plates A and B.

Let n₁ = number of positive ions per unit volume at a distance x from the plate A,

K₁ = mobility of the positive ions,

e = charge on an ion.

The current i₁ per square centimetre through the gas is constant for all values of x, and is given by

$$ i1 = K1n_1e \frac{dV}{dx} $$

By Poisson’s equation

$$ \frac {d^2 V} {da^2} = 4\pi n_1 e $$

Then

$$ i1 = \frac {K1} {4\pi} \frac {dV} {dx} \frac {d^2 V} {dx^2} $$

Integrating

$$ (\frac {dV} {dx})^2 = \frac {8\pi i1x} {K1} + A $$

where A is a constant. Now A is equal to the value of

dV ---- dx

when x = 0. By making the ionization very intense, the value of

dV ---- dx

can be made extremely small.

Putting A = 0, we see that

$$ \frac {dV} {dx} = \pm \sqrt {\frac {8\pi i1 x} {K1}} $$

This gives the potential gradient between the plates for different values of x.

Integrating between the limits 0 and d,

$$ V = \pm \frac{2}{3} \sqrt {\frac {8\pi i1} {K1} d^{ rac{3}{2}}} $$

$$ i1 = \frac {9V^2} {32\pi d^3} K1 $$

If i₂ is the value of the current when the electric field is reversed, and K₂ the velocity of the negative ion,

$$ i2 = \frac {9V^2} {32 \pi d^3} K2 $$

and

i₁ K₁ ---- = ---- . i₂ K₂

The current in the two directions is thus directly proportional to the velocities of the positive and negative ions. The current should vary directly as the square of the potential difference applied, and inversely as the cube of the distance between the plates.

The theoretical condition of surface ionization cannot be fulfilled by the ionization due to active substances, as the ionization extends some centimetres from the active plate. If, however, the distance between the plates is large compared with the distance over which the ionization extends, the results will be in rough agreement with the theory. Using an active preparation of radium, the writer has made some experiments on the variation of current with voltage between parallel plates distant about 10 cms. from each other.

The results showed

(1) That the current through the gas for small voltages increased more rapidly than the potential difference applied, but not as rapidly as the square of that potential difference.

(2) The current through the gas depended on the direction of the electric field; the current was always smaller when the active plate was charged positively on account of the smaller mobility of the positive ion. The difference between i₁ and i₂ was greatest when the gas was dry, which is the condition for the greatest difference between the velocities of the ions.

An interesting result follows from the above theory. For given values of V and d, the current cannot exceed a certain definite value, however much the ionization may be increased. In a similar way, when an active preparation of radium is used as a source of surface ionization, it is found that, for a given voltage and distance between the plates, the current does not increase beyond a certain value however much the activity of the material is increased.

=48. Magnetic field produced by an ion in motion.= It will be shown later that the two most important kinds of rays emitted by radio-active substances consist of electrified particles, spontaneously projected with great velocity. The easily absorbed rays, known as α rays, are positively electrified atoms of matter; the penetrating rays, known as β rays, carry a negative charge, and have been found to be identical with the cathode rays produced by the electric discharge in a vacuum tube.

The methods adopted to determine the character of these rays are very similar to those first used by J. J. Thomson to show that the cathode rays consisted of a stream of negatively electrified particles projected with great velocity.

The proof that the cathode rays were corpuscular in character, and consisted of charged particles whose mass was very small compared with that of the hydrogen atom, marked an important epoch in physical science: for it not only opened up new and fertile fields of research, but also profoundly modified our previous conceptions of the constitution of matter.

A brief account will accordingly be given of the effects produced by a moving charged body, and also of some of the experimental methods which have been used to determine the mass and velocity of the particles of the cathode stream.

Consider an ion of radius a, carrying a charge of electricity e, and moving with a velocity u, small compared with the velocity of light. In consequence of the motion, a magnetic field is set up around the charged ion, which is carried with it. The charged ion in motion constitutes a current element of magnitude eu, and the magnetic field H at any point distant r from the sphere is given by

eu sin θ H = --------- r²

where θ is the angle the radius vector makes with the direction of motion. The lines of magnetic force are circles around the axis of motion. When the ion is moving with a velocity small compared with the velocity of light, the lines of electric force are nearly radial, but as the speed of light is approached, they tend to leave the axis of motion and to bend towards the equator. When the speed of the body is very close to that of light, the magnetic and electric field is concentrated to a large extent in the equatorial plane.

The presence of a magnetic field around the moving body implies that magnetic energy is stored up in the medium surrounding it. The amount of this energy can be calculated very simply for slow speeds.

In a magnetic field of strength H, the magnetic energy stored up in unit volume of the medium of unit permeability is given by

H² ---- 8π

Integrating the value of this expression over the region exterior to a sphere of radius a, the total magnetic energy due to the motion of the charged body is given by

$$ \inta^{\infty} \frac{H^2}{8\pi} d(vol) = \frac{e^2 u^2}{8\pi} \int₀^{2\pi} \int₀^{\pi} \inta^{\infty} \frac{\sin^2 \theta}{r^4} r \sin \theta d\phi rd\theta dr $$ $$ = \frac{e^2 u^2}{4} \int₀^{\pi} \inta^{\infty} \frac{(1−\cos^2 \theta)}{r^2} \sin \theta d\theta . dr $$ $$ = \frac{e^2 u^2}{3} \inta^{\infty} \frac{dr}{r^2} = \frac{e^2 u^2}{3a} $$

The magnetic energy, due to the motion, is analogous to kinetic energy, for it depends upon the square of the velocity of the body. In consequence of the charge carried by the ion, additional kinetic energy is associated with it. If the velocity of the ion is changed, electric and magnetic forces are set up tending to stop the change of motion, and more work is done during the change than if the ion were uncharged. The ordinary kinetic energy of the body is

1 --- mu² 2

In consequence of its charge, the kinetic energy associated with it is increased by

e²u² ------ 3a

It thus behaves as if it possessed a mass m + m₁ where m₁ is the electrical mass, with the value

2e² ---- 3a

We have so far only considered the electrical mass of a charged ion moving with a velocity small compared with that of light. As the speed of light is approached, the magnetic energy can no longer be expressed by the equation already given. The general values of the electrical mass of a charged body for speed were first worked out by J. J. Thomson in 1887. A more complete examination was made in 1889 by Heaviside, while Searle worked out the case for a charged ellipsoid. Recently, the question was again attacked by Abraham. Slightly different expressions for the variation of electrical mass with speed have been obtained, depending upon the conditions assumed for the distribution of the electricity on the sphere. The expression found by Abraham, which has been utilized by Kaufmann to show that the mass of the electron is electromagnetic in origin, is given later in section 82.

All the calculations agree in showing that the electrical mass is practically constant for slow speeds, but increases as the speed of light is approached, and is theoretically infinite when the speed of light is reached. The nearer the velocity of light is approached, the greater is the resisting force to a change of motion. An infinite force would be required to make an electron actually attain the velocity of light, so that, according to the present theory, it would be impossible for an electron to move faster than light, i.e. faster than an electromagnetic disturbance travels in the ether.

The importance of these deductions lies in the fact that an electric charge in motion, quite independently of any material nucleus, possesses an apparent mass in virtue of its motion, and that this mass is a function of the speed. Indeed, we shall see later (see section 82) that the apparent mass of the particles constituting the cathode stream can be explained in virtue of their charge, without the necessity of assuming a material body in which the charge is distributed. This has led to the suggestion that all mass may be electrical in origin, and due purely to electricity in motion.

=49. Action of a magnetic field on a moving ion.= Let us consider the case of an ion of mass m carrying a charge e and moving freely with a velocity u. If u is small compared with the velocity of light, the ion in motion corresponds to a current element of magnitude eu. If the ion moves in an external magnetic field of strength H, it is acted on by a force at right angles both to the direction of motion, and to that of the magnetic force and equal in magnitude to Heu sin θ, where θ is the angle between the direction of the magnetic force and the direction of motion. Since the force due to the magnetic field is always perpendicular to the direction of motion, it has no effect upon the velocity of the particle, but can only alter the direction of its path.

If ρ is the radius of curvature of the path of the ion, the force along the normal is equal to

mu² -----, ρ

and this is balanced by the force Heu sin θ.

π θ = ---, 2

i.e. if the ion is moving at right angles to the direction of the magnetic field

mu² Heu = ----- ρ

m Hρ = ---- u e

Since u is constant, ρ is also constant, i.e. the particle describes a circular orbit of radius ρ. The radius of the circular orbit is thus directly proportional to u, and inversely proportional to H.

If the ion is moving at an angle θ with the direction of the magnetic field, it describes a curve which is compounded of a motion of a particle of velocity u sin θ perpendicular to the field and u cos θ in the direction of the field. The former describes a circular orbit of radius ρ, given by

m Hρ = --- u sin θ; e

the latter is unaffected by the magnetic field and moves uniformly in the direction of the magnetic field with a velocity u cos θ. The motion of the particle is in consequence a helix, traced on a cylinder of radius

mu sin θ ρ = ----------, eH

whose axis is in the direction of the magnetic field. Thus an ion projected obliquely to the direction of a uniform magnetic field always moves in a helix whose axis is parallel to the lines of magnetic force.

=50. Determination of e/m for the cathode stream.= The cathode rays, first observed by Varley, were investigated in detail by Crookes. These rays are projected from the cathode in a vacuum tube at low pressure. They travel in straight lines, and are readily deflected by a magnet, and produce strong luminosity in a variety of substances placed in their path. The rays are deflected by a magnetic field in the same direction as would be expected for a negatively charged particle projected from the cathode. In order to explain the peculiar properties of these rays Crookes supposed that they consisted of negatively electrified particles, moving with great velocity and constituting, as he appropriately termed it, “a new or fourth state of matter.” The nature of these rays was for twenty years a subject of much controversy, for while some upheld their material character, others considered that they were a special form of wave motion in the ether.

Perrin and J. J. Thomson showed that the rays always carried with them a negative charge, while Lenard made the important discovery that the rays passed through thin metal foil and other substances opaque to ordinary light. Using this property, he sent the rays through a thin window and examined the properties of the rays outside the vacuum tube in which they were produced.

The absorption of the rays by matter was shown to be nearly proportional to the density over a very wide range, and to be independent of its chemical constitution.

The nature of these rays was successfully demonstrated by J. J. Thomson in 1897. If the rays consisted of negatively electrified particles, they should be deflected in their passage through an electric as well as through a magnetic field. Such an experiment had been tried by Hertz, but with negative results. J. J. Thomson, however, found that the rays were deflected by an electric field in the direction to be expected for a negatively charged particle, and showed that the failure of Hertz to detect the same was due to the masking of the electric field by the strong ionization produced in the gas by the cathode stream. This effect was got rid of by reducing the pressure of the gas in the tube.

The experimental arrangement used for the electric deflection of the rays is shown in Fig. 10.

The cathode rays are generated at the cathode C, and a narrow pencil of rays is obtained by passing the rays through a perforated disc AB. The rays then passed midway between two parallel insulated plates D and E, d centimetres apart, and maintained at a constant difference of potential V. The point of incidence of the pencil of rays was marked by a luminous patch produced on a phosphorescent screen placed at PP´.

The particle carrying a negative charge e in passing between the charged plates, is acted on by a force Xe directed towards the positive plate, where X, the strength of the electric field, is given by

V ---- . d

The application of the electric field thus causes the luminous patch to move in the direction of the positive plate. If now a uniform magnetic field is applied at the plates D and E, perpendicular to the pencil of rays, and parallel to the plane of the plates, and in such a direction that the electric and magnetic forces are opposed to one another, the patch of light can be brought back to its undisturbed position by adjusting the strength of the magnetic field. If H is the strength of the magnetic field, the force on the particle due to the magnetic field is Heu, and when a balance is obtained

Heu = Xe,

or X u = --- (1). H

Now if the magnetic field H is acting alone, the curvature ρ of the path of the rays between the plates can be deduced from the deflection of the luminous patch. But we have seen that

mu H = ----- (2). e

From equations (1) and (2), the value of u and e/m for the particle can be determined.

The velocity u is not constant, but depends upon the potential difference between the electrodes, and this in turn depends upon the pressure and nature of the residual gas in the tube.

By altering these factors, the cathode particles may be made to acquire velocities varying between about 10⁹ and 10¹⁰ cms. per second. This velocity is enormous compared with that which can be impressed ordinarily upon matter by mechanical means. On the other hand, the value of e/m for the particles is sensibly constant for different velocities.

As a result of a series of experiments the mean value e/m = 7·7 × 10⁶ was obtained. The value of e/m is independent of the nature or pressure of the gas in the vacuum tube and independent of the metal used as cathode. A similar value of e/m was obtained by Lenard and others.

Kaufmann and Simon used a different method to determine the value of e/m. The potential difference V between the terminals of the tube was measured. The work done on the charged particle in moving from one end of the tube to the other is Ve, and this must be equal to the kinetic energy

1 -- mu² 2

acquired by the moving particle. Thus

e u² --- = ---- (3). m 2V

By combination of this equation with (2) obtained by measurement of the magnetic deflexion, both u and e/m can be determined.

Simon found by this method that

e --- = 1·865 × 10⁷. m

It will be seen later (section 82) that a similar value was deduced by Kaufmann for the electrons projected from radium.

These results, which have been based on the effect of a magnetic and electric field on a moving ion, were confirmed by Weichert, who determined by a direct method the time required for the particle to traverse a known distance.

The particles which make up the cathode stream were termed “corpuscles” by J. J. Thomson. The name “electron,” first employed by Johnstone Stoney, has also been applied to them and has come into general use.

The methods above described do not give the mass of the electron, but only the ratio of the charge to the mass. A direct comparison can, however, be made between the ratio e/m for the electron and the corresponding value for the hydrogen atoms set free in the electrolysis of water. Each of the hydrogen atoms is supposed to carry a charge e, and it is known that 96,000 coulombs of electricity, or, in round numbers, 10⁴ electromagnetic units of quantity are required to liberate one gram of hydrogen. If N is the number of atoms in one gram of hydrogen, then Ne = 10⁴. But if m is the mass of a hydrogen atom, then Nm = 1. Dividing one by the other e/m = 10⁴. We have seen already that a gaseous ion carries the same charge as a hydrogen atom, while indirect evidence shows that the electron carries the same charge as an ion, and consequently the same charge as the atom of hydrogen. Hence we may conclude that the apparent mass of the electron is only about ¹⁄₁₀₀₀ of the mass of the hydrogen atom. The electron thus behaves as the smallest body known to science.

In later experiments J. J. Thomson showed that the negative ions set free at low pressures by an incandescent carbon filament, and also the negative ions liberated from a zinc plate exposed to the action of ultra-violet light, had the same value for e/m as the electrons produced in a vacuum tube. It thus seemed probable that the electron was a constituent of all matter. This view received strong support from measurements of quite a different character. Zeeman in 1897 found that the lines of the spectrum from a source of light exposed in a strong magnetic field were displaced and doubled. Later work has shown that the lines in some cases are trebled, in others sextupled, while, in a few cases, the multiplication is still greater. These results received a general explanation on the radiation theories previously advanced by Lorenz and Larmor. The radiation, emitted from any source, was supposed to result from the orbital or oscillatory motion of the charged parts constituting the atom. Since a moving ion is acted on by an external magnetic field, the motion of the charged ions is disturbed when the source of light is exposed between the poles of a strong magnet. There results a small change in the period of the emitted light, and a bright line in the spectrum is, in consequence, displaced by the action of the magnetic field. According to theory, the small change in the wave-length of the emitted light depends upon the strength of the magnetic field and on the ratio e/m of the charge carried by the ion to its mass. By comparison of the theory with the experimental results, it was deduced that the moving ion carried a negative charge, and that the value of e/m was about 10⁷. The charged ion, responsible for the radiation from a luminous body, is thus identical with the electron set free in a vacuum tube.

It thus seems reasonable to suppose that the atoms of all bodies are complex and are built up, in part at least, of electrons, whose apparent mass is very small compared with that of the hydrogen atom. The properties of such disembodied charges has been examined mathematically among others by Larmor, who sees in this conception the ultimate basis of a theory of matter. J. J. Thomson and Lord Kelvin have investigated mathematically certain arrangements of a number of electrons which are stable for small disturbances. This question will be discussed more in detail in section 270.

=51. Canal rays.= If a discharge is passed through a vacuum tube provided with a perforated cathode, within certain limits of pressure, luminous streams are observed to pass through the holes and to emerge on the side of the cathode remote from the anode. These rays were first observed by Goldstein and were called by him the “Canal-strahlen.” These rays travel in straight lines and produce phosphorescence in various substances.

Wien showed that the canal rays were deflected by strong magnetic and electric fields, but the amount of deflection was very small compared with that of the cathode rays under similar conditions. The deflection was found to be opposite in direction to the cathode rays, and this indicates that the canal rays consist of positive ions. Wien determined their velocity and the ratio e/m, by measuring the amount of their magnetic and electric deflection. The value of e/m was found to be variable, depending upon the gas in the tube, but the maximum value observed was 10⁴. This shows that the positive ion, in no case, has a mass less than that of the hydrogen atom. It seems probable that the canal rays consist of positive ions, derived either from the gas or the electrodes, which travel towards the cathode, and have sufficient velocity to pass through the holes of the cathode and to appear in the gas beyond.

It is remarkable that, so far, no case has been observed where the carrier of a positive charge has an apparent mass less than that of the hydrogen atom. Positive electricity always appears to be associated with bodies atomic in size. We have seen that the process of ionization in gases is supposed to consist of the expulsion of an electron from the atom. The corresponding positive charge remains behind on the atom and travels with it. This difference between positive and negative electricity appears to be fundamental, and no explanation of it has, as yet, been forthcoming.

=52. Radiation of energy.= If an electron moves uniformly in a straight line with constant velocity, the magnetic field, which travels with it, remains constant, and there is no loss of energy from it by radiation. If, however, its motion is hastened or retarded, the magnetic field is altered, and there results a loss of energy from the electron in the form of electromagnetic radiation. The rate of loss of energy from an accelerated electron was first calculated by Larmor and shown to be

2e² ---- × (acceleration)², 3V

where e is the charge on the electron in electromagnetic units, and V the velocity of light.

Any alteration in the velocity of a moving charge is thus always accompanied by a radiation of energy from it. Since the electron, set free in a vacuum tube, increases in velocity in passing through the electric field, energy must be radiated from it during its passage from cathode to anode. It can, however, readily be calculated that, in ordinary cases, this loss of energy is small compared with the kinetic energy acquired by the electron in passing through the electric field.

An electron moving in a circular orbit is a powerful radiator of energy, since it is constantly accelerated towards the centre. An electron moving in an orbit of radius equal to the radius of an atom (about 10⁻⁸ cms.) would lose most of its kinetic energy of motion in a small fraction of a second, even though its velocity was originally nearly equal to the velocity of light. If, however, a number of electrons are arranged at equal angular intervals on the circumference of a circle and move with constant velocity round the ring, the radiation of energy is much less than for a single electron, and rapidly diminishes with an increase in the number of electrons round the ring. This result, obtained by J. J. Thomson, will be discussed in more detail later when the stability of systems composed of rotating electrons is under consideration.

Since the radiation of energy is proportional to the square of the acceleration, the proportion of the total energy radiated depends upon the suddenness with which an electron is started or stopped. Now some of the cathode ray particles are stopped abruptly when they impinge on the metal cathode, and, in consequence, give up a fraction of their kinetic energy in the form of electromagnetic radiation. Stokes and Weichert suggested that this radiation constituted the X rays, which are known to have their origin at the surface on which the cathode rays impinge. The mathematical theory has been worked out by J. J. Thomson. If the motion of an electron is suddenly arrested, a thin spherical pulse in which the magnetic and electric forces are very intense travels out from the point of impact with the velocity of light. The more suddenly the electron is stopped, the thinner and more intense is the pulse. On this view the X rays are not corpuscular like the cathode rays, which produce them, but consist of transverse disturbances in the ether, akin in some respects to light waves of short wave-length. The rays are thus made up of a number of pulses, which are non-periodic in character, and which follow one another at irregular intervals.

On this theory of the nature of the X rays, the absence of direct deflection, refraction, or polarization is to be expected, if the thickness of the pulse is small compared with the diameter of an atom. It also explains the non-deflection of the path of the rays by a magnetic or electric field. The intensity of the electric and magnetic force in the pulse is so great that it is able to cause a removal of an electron from some of the atoms of the gas, over which the pulse passes, and thus causes the ionization observed.

The cathode rays produce X rays, and these in turn give rise to a secondary radiation whenever they impinge on a solid body. This secondary radiation is emitted equally in all directions, and consists partly of a radiation of the X ray type and also of electrons projected with considerable velocity. This secondary radiation gives rise to a tertiary radiation and so on.

Barkla has shown that the secondary radiation emitted from a gas through which the rays pass consists in part of scattered X rays of about the same penetrating power as the primary rays as well as some easily absorbed rays.

Part of the cathode rays is diffusely reflected on striking the cathode. These scattered rays consist in part of electrons of the same speed as in the primary beam, but also include some others of much less velocity. The amount of diffuse reflection depends upon the nature of the cathode and the angle of incidence of the rays.

We shall see later (chapter IV.) that similar effects are produced when the rays from radio-active substances impinge upon solid bodies.

* * * * *

In this chapter an account of the ionization theory of gases has been given to the extent that is necessary for the interpretation of the measurements of radio-activity by the electric method. It would be out of place here to discuss the development of that theory in detail, to explain the passage of electricity through flames and vapours, the discharge of electricity from hot bodies, and the very complicated phenomena observed in the passage of electricity through a vacuum tube.

For further information on this important subject, the reader is referred to J. J. Thomson’s Conduction of Electricity through Gases, in which the whole subject is treated in a full and complete manner. A simple account of the effect of moving charges and the electronic theory of matter was given by the same author in the Silliman Lectures of Yale University and published under the title Electricity and Matter (Scribner, New York, 1904).

Footnote 44:

J. J. Thomson and Rutherford, Phil. Mag. Nov. 1896.

Footnote 45:

The word ion has now been generally adopted in the literature of the subject. In using this word, it is not assumed that the ions in gases are the same as the corresponding ions in the electrolysis of solutions.

Footnote 46:

A minute current is observed between the plates even if no radio-active matter be present. This has been found to be due mainly to a slight natural radio-activity of the matter composing them. (See