Chapter XIII: Radio-Active Processes (3)

The sudden rise of temperature observed in the mineral fergusonite, at the time the helium is released, has been found to have nothing to do with the presence of helium, for it also takes place in minerals not containing helium. The old view that helium was in a state of chemical combination with the mineral must be abandoned in the light of these more recent experiments.

Since the helium is only released from some minerals by the action of high temperatures and solution, it appears probable that a large proportion of the helium found in the minerals is unable to escape under normal conditions. Thus if the rate of production of helium by the radio-active substance were definitely known, it should be possible to calculate the age of the mineral by observing the volume of helium liberated from it by solution.

In the absence of such definite information, an approximate calculation will be made to indicate the order of magnitude of the time that has elapsed since the mineral was formed or was at a temperature low enough to prevent the escape of the helium.

Let us take, for example, the mineral fergusonite, which was found by Ramsay and Travers[373] to evolve 1·81 c.c. of helium. The fergusonite contained about 7 per cent. of uranium. Now uranium in old minerals probably contains about 8 × 10⁻⁷ of its weight of radium (see section 262). One gram of the mineral thus contained about 5·6 × 10⁻⁸ grams of radium. Now if the α particle is helium, it has been shown that 1 gram of radium produces 0·24 c.c. of helium per year. The volume of helium produced per year in 1 gram of fergusonite is thus 1·3 × 10⁻⁸ c.c. Assuming that the rate of production of helium has been uniform, the time required to produce 1·81 c.c. per gram is about 140 million years. If the calculated rate of production of helium by radium is an over-estimate, the time is correspondingly lengthened.

I think that, when the constants required for these calculations are more definitely fixed, this method will probably give fairly trustworthy information as to the probable age of some of the radio-active minerals of the earth’s crust, and indirectly as to the age of the strata in which they are found.

In this connection it is of interest to note that Ramsay[374] found that a Ceylon mineral, thorianite, contained as much as 9·5 c.c. of helium per gram. According to the analysis by Dunstan, this mineral contains about 76 per cent. of thorium and 12 per cent. of uranium. The unusually large amount of helium evolved from this mineral would indicate that it was formed at an earlier date than the fergusonite previously considered.

=270. Possible causes of disintegration.= In order to explain the phenomena of radio-activity, it has been supposed that a certain small fraction of the radio-atoms undergoes disintegration per second, but no assumptions have been made as to the cause which produces the instability and consequent disintegration. The instability of the atoms may be supposed to be brought about either by the action of external forces or by that of forces inherent in the atoms themselves. It is conceivable, for example, that the application of some slight external force might cause instability and consequent disintegration, accompanied by the liberation of a large amount of energy, on the same principle that a detonator is necessary to start some explosives. It has been shown that the number of atoms of any radio-active product which break up per second is always proportional to the number present. This law of change does not throw any light on the question, for it would be expected equally on either hypothesis. It has not been found possible to alter the rate of change of any product by the application of any known physical or chemical forces, unless possibly it is assumed that the force of gravitation which is not under our control may influence in some way the stability of the radio-atoms.

It seems likely therefore that the cause of the disruption of the atoms of the radio-elements and their products resides in the atoms themselves. According to the modern views of the constitution of the atom, it is not so much a matter of surprise that some atoms disintegrate as that the atoms of the elements are so permanent as they appear to be. In accordance with the hypothesis of J. J. Thomson, it may be supposed that the atoms consist of a number of small positively and negatively charged particles in rapid internal movement, and held in equilibrium by their mutual forces. In a complex atom, where the possible variations in the relative motion of the parts are very great, the atom may arrive at such a phase that one part acquires sufficient kinetic energy to escape from the system, or that the constraining forces are momentarily neutralised, so that the part escapes from the system with the velocity possessed by it at the instant of its release.

Sir Oliver Lodge[375] has advanced the view that the instability of the atom may be a result of radiation of energy by the atom. Larmor has shown that an electron, subject to acceleration, radiates energy at a rate proportional to the square of its acceleration. An electron moving uniformly in a straight line does not radiate energy, but an electron, constrained to move in a circular orbit with constant velocity, is a powerful radiator, for in such a case the electron is continuously accelerated towards the centre. Lodge considered the simple case of a negatively charged electron revolving round an atom of mass relatively large but having an equal positive charge and held in equilibrium by electrical forces. This system will radiate energy, and, since the radiation of energy is equivalent to motion in a resisting medium, the particle tends to move towards the centre, and its speed consequently increases. The rate of radiation of energy will increase rapidly with the speed of the electron. When the speed of the electron becomes very nearly equal to the velocity of light, according to Lodge, another effect supervenes. It has been shown (section 82) that the apparent mass of an electron increases very rapidly as the speed of light is approached, and is theoretically infinite at the speed of light. There will be at this stage a sudden increase of the mass of the revolving atom, and, on the supposition that this stage can be reached, a consequent disturbance of the balance of forces holding the system together. Lodge considers it probable that, under these conditions, the parts of the system will break asunder and escape from the sphere of one another’s influence.

It seems probable that the primary cause of the disintegration of the atom must be looked for in the loss of energy of the atomic system due to electromagnetic radiation (section 52). Larmor[376] has shown that the condition to be fulfilled in order that a system of rapidly moving electrons may persist without loss of energy is that the vector sum of the accelerations towards the centre should be permanently zero. While a single electron moving in a circular orbit is a powerful radiator of energy, it is remarkable how rapidly the radiation of energy diminishes if several electrons are revolving in a ring. This has recently been shown by J. J. Thomson[377], who examined mathematically the case of a system of negatively electrified corpuscles, situated at equal intervals round the circumference of a circle, and rotating in one plane with uniform velocity round its centre. For example, he found that the radiation from a group of six particles moving with a velocity of ⅒ of the velocity of light is less than one-millionth part of the radiation from a single particle describing the same orbit with the same velocity. When the velocity is ¹⁄₁₀₀ of that of light the amount of radiation is only 10⁻¹⁶ that of a single particle moving with the same velocity in the same orbit.

Results of this kind indicate that an atom consisting of a large number of revolving electrons may radiate energy extremely slowly, and yet, finally, this minute but continuous drain of energy from the atom must result either in a rearrangement of its component parts into a new system, or of an expulsion of electrons or groups of electrons from the atom.

Simple models of atoms to imitate the behaviour of polonium in shooting out α particles, and of radium in shooting out β particles have been discussed by Lord Kelvin[378]. It is possible to devise certain stable arrangements of the positively and negatively electrified particles, supposed to constitute an atom, which, on the application of some disturbing force, break up with the expulsion of a part of the system with great velocity.

J. J. Thomson[379] has mathematically investigated the possible stable arrangements of a number of electrons moving about in a sphere of uniform positive electrification. The properties of such a model atom are very striking, and indirectly suggest a possible explanation of the periodic law in chemistry. He has shown that the electrons, if in one plane, arrange themselves in a number of concentric rings; and generally, if they are not constrained to move in one plane, in a number of concentric shells like the coats of an onion.

The mathematical problem is much simplified if the electrons are supposed to rotate in rings in one plane, the electrons in each ring being arranged at equal angular intervals. The ways in which the number of electrons group themselves, for numbers ranging from 60 to 5 at intervals of 5, are shown in the following table:—

Number 60 55 50 45 40 35
of
electrons

Number in 20 19 18 17 16 16
successive
rings

16 16 15 14 13 12

13 12 11 10 8 6

8 7 5 4 3 1

3 1 1

Number 30 25 20 15 10 5
of
electrons

Number in 15 13 12 10 8 5
successive
rings

10 9 7 5 2

5 3 1

In the next table is given the possible series of arrangements of electrons which can have an outer ring of 20:—

Number 59 60 61 62 63 64 65 66 67
of
electrons

Number in 20 20 20 20 20 20 20 20 20
successive
rings

16 16 16 17 17 17 17 17 17

13 13 13 13 13 13 14 14 15

8 8 9 9 10 10 10 10 10

2 3 3 3 3 4 4 5 5

The smallest number of electrons which can have an outer ring of 20 is 59, while 67 is the greatest.

The various arrangements of electrons can be classified into families, in which the groupings of the electrons have certain features in common. Thus the group of 60 electrons consists of the same arrangement of electrons as the group of 40 with the addition of an outer ring of 20 electrons; the group of 40 is the same as the group of 24 with an additional ring outside; and the group of 24 in turn is the same as the group of 11 with an extra ring. A series of model atoms may be formed in this way, in which each atom is derived from the preceding member by an additional ring of electrons. Such atoms would be expected to possess many properties in common, and would correspond to the elements in the same vertical column of the periodic table of Mendeléef.

Different arrangements of electrons vary widely in stability. Some may acquire an extra electron or two and yet remain stable, others readily lose an electron without disturbing their stability. The former would correspond to an electro-negative atom, the latter to an electro-positive.

Certain arrangements of electrons are stable if the electrons move with an angular velocity greater than a certain value, but become unstable when the velocity falls below this value. Four electrons in motion, for example, are stable in one plane, but when the velocity falls below a certain critical value, the system is unstable, and the electrons tend to arrange themselves at the corners of a regular tetrahedron. J. J. Thomson (_loc. cit._) applies this property to explain why an atom of radio-active matter breaks up, as follows:—

“Consider now the properties of an atom containing a system of corpuscles (electrons) of this kind. Suppose the corpuscles were originally moving with velocities far exceeding the critical velocity; in consequence of the radiation from the moving corpuscles, their velocity will slowly—very slowly—diminish; when, after a long interval, the velocity reaches the critical velocity, there will be what is equivalent to an explosion of the corpuscles, the corpuscles will move far away from their original position, their potential energy will decrease, while their kinetic energy will increase. The kinetic energy gained in this way might be sufficient to carry the system out of the atom, and we should have, as in the case of radium, a part of the atom shot off. In consequence of the very slow dissipation of energy by radiation the life of the atom would be very long. We have taken the case of the four corpuscles as the type of a system which, like a top, requires for its stability a certain amount of rotation. Any system possessing this property would, in consequence of the gradual dissipation of energy by radiation, give to the atom containing it radio-active properties similar to those conferred by the four corpuscles.”

=271. Heat of the sun and earth.= It was pointed out by Rutherford and Soddy[380] that the maintenance of the sun’s heat for long intervals of time did not present any fundamental difficulty if a process of disintegration, such as occurs in the radio-elements, were supposed to be taking place in the sun. In a letter to _Nature_ (July 9, 1903) W. E. Wilson showed that the presence of 3·6 grams of radium in each cubic metre of the sun’s mass was sufficient to account for the present rate of emission of energy by the sun. This calculation was based on the estimate of Curie and Laborde that 1 gram of radium emits 100 gram-calories per hour, and on the observation of Langley that each square centimetre of the sun’s surface emits 8·28 × 10⁶ gram-calories per hour. Since the average density of the sun is 1·44, the presence of radium in the sun, to the extent of 2·5 parts by weight in a million, would account for its present rate of emission of energy.

An examination of the spectrum of the sun has not so far revealed any of the radium lines. It is known, however, from spectroscopic evidence that helium is present, and this indirectly suggests the existence of radio-active matter also. It can readily be shown[381] that the absence of penetrating rays from the sun at the surface of the earth does not imply that the radio-elements are not present in the sun. Even if the sun were composed of pure radium, it would hardly be expected that the γ rays emitted would be appreciable at the surface of the earth, since the rays would be almost completely absorbed in passing through the atmosphere, which corresponds to a thickness of 76 centimetres of mercury.

In the Appendix E of Thomson and Tait’s _Natural Philosophy_, Lord Kelvin has calculated the energy lost in the concentration of the sun from a condition of infinite dispersion, and concludes that it seems “on the whole probable that the sun has not illuminated the earth for 100,000,000 years and almost certain that he has not done so for 500,000,000 years. As for the future we may say, with equal certainty, that inhabitants of the earth cannot continue to enjoy the light and heat essential to their life for many million years longer, unless sources now unknown to us are prepared in the great storehouses of creation.”

The discovery that a small mass of a substance like radium can emit spontaneously an enormous quantity of heat renders it possible that this estimate of the age of the sun’s heat may be much increased. In a letter to _Nature_ (Sept. 24, 1903) G. H. Darwin drew attention to this probability, and at the same time pointed out that, on Kelvin’s hypotheses, his estimate of the duration of the sun’s heat was probably much too high, and stated that, “The lost energy of the sun, supposed to be a homogeneous sphere of mass _M_ and radius _a_, is (⅗)μ_M²_/_a_ where μ is the constant of gravitation. On introducing numerical values for the symbols in this formula, I find the lost energy to be 2·7 × 10⁷ _M_ calories where _M_ is expressed in grams. If we adopt Langley’s value of the solar constant, this heat suffices to give a supply for 12 million years. Lord Kelvin used Pouillet’s value for that constant, but if he had been able to use Langley’s, his 100 million would have been reduced to 60 million. The discrepancy between my results of 12 million and his of 60 million is explained by a conjectural augmentation of the lost energy to allow for the concentration of the solar mass towards its central parts.” Now it has been shown (section 266) that one gram of radium emits during its life an amount of heat corresponding to 1·6 × 10⁹ gram-calories. It has also been pointed out that there is every reason to suppose that a similar amount of energy is resident in the chemical atoms of the inactive elements. It is not improbable that, at the enormous temperature of the sun, the breaking up of the elements into simpler forms may be taking place at a more rapid rate than on the earth. If the energy resident in the atoms of the elements is thus available, the time during which the sun may continue to emit heat at the present rate may be at least 50 times longer than the value computed from dynamical data.

Similar considerations apply to the question of the age of the earth. A full discussion of the probable age of the earth, computed from its secular cooling from a molten mass, is given by Lord Kelvin in Appendix D of Thomson and Tait’s _Natural Philosophy_. He has there shown that about 100 million years after the earth was a molten mass, the gradual cooling due to radiation from its surface would account for the average temperature gradient of ¹⁄₅₀° F. per foot, observed to-day near the earth’s surface.

Some considerations will now be discussed which point to the probability that the present temperature gradient observed in the earth cannot be used as a guide to estimate the length of time that has elapsed since the earth has been at a temperature capable of supporting animal and vegetable life; for it will be shown that probably there is sufficient radio-active matter on the earth to supply as much heat to the earth as is lost by radiation from its surface. Taking the average conductivity _K_ of the materials of the earth as ·004 (C.G.S. units) and the temperature gradient _T_ near the surface as ·00037° C. per cm., the heat _Q_ in gram-calories conducted to the surface of the earth per second is given by

_Q_ = 4π_R²KT_,

where _R_ is the radius of the earth.

Let _X_ be the average amount of heat liberated per second per cubic centimetre of the earth’s volume owing to the presence of radio-active matter. If the heat _Q_ radiated from the earth is equal to the heat supplied by the radio-active matter in the earth,

_X_ . (⁴⁄₃)π_R³_ = 4π_R²KT_,

or
3_KT_
_X_ = ------ .
_R_

Substituting the values of these constants,

_X_ = 7 × 10⁻¹⁵ gram-calories per second
= 2·2 × 10⁻⁷ gram-calories per year.

Since 1 gram of radium emits 876,000 gram-calories per year, the presence of 2·6 × 10⁻¹³ grams of radium per unit volume, or 4·6 × 10⁻¹⁴ grams per unit mass, would compensate for the heat lost from the earth by conduction.

Now it will be shown in the following chapter that radio-active matter seems to be distributed fairly uniformly through the earth and atmosphere. In addition, it has been found that all substances are radio-active to a feeble degree, although it is not yet settled whether this radio-activity may not be due mainly to the presence of a radio-element as an impurity. For example, Strutt[382] observed that a platinum plate was about ¹⁄₃₀₀₀ as active as a crystal of uranium nitrate, or about 2 × 10⁻¹⁰ as active as radium. This corresponds to a far greater activity than is necessary to compensate for the loss of heat of the earth. A more accurate deduction, however, can be made from data of the radio-activity exhibited by matter dug out of the earth. Elster and Geitel[383] filled a dish of volume 3·3 × 10³ c.c. with clay dug up from the garden, and placed it in a vessel of 30 litres capacity in which was placed an electroscope to determine the conductivity of the enclosed gas. After standing for several days, they found that the conductivity of the air reached a constant maximum value, corresponding to three times the normal. It will be shown later (section 284) that the normal conductivity observed in sealed vessels corresponds to the production of about 30 ions per c.c. per second. The number of ions produced per second in the vessel by the radio-active earth was thus about 2 × 10⁶. This would give a saturation current through the gas of 2·2 × 10⁻¹⁴ electromagnetic units. Now the emanation from 1 gram of radium stored in a metal cylinder gives a saturation current of about 3·2 × 10⁻⁵ electromagnetic units. Elster and Geitel considered that most of the conductivity observed in the gas was due to a radio-active emanation, which gradually diffused from the clay into the air in the vessel. The increased conductivity in the gas observed by Elster and Geitel would thus be produced by the emanation from 7 × 10⁻¹⁰ gram of radium. Taking the density of clay as 2, this corresponds to about 10⁻¹³ gram of radium per gram of clay. But it has been shown that if 4·6 × 10⁻¹⁴ gram of radium were present in each gram of earth, the heat emitted would compensate for the loss of heat of the earth by conduction and radiation. The amount of activity observed in the earth is thus about the right order of magnitude to account for the heat emission required. In the above estimate, the presence of uranium and thorium minerals in the earth has not been considered. Moreover, it is probable that the total amount of radio-activity in the clay was considerably greater than that calculated, for it is likely that other radio-active matter was present which did not give off an emanation.

If the earth is supposed to be in a state of thermal equilibrium in which the heat lost by radiation is supplied from radio-active matter, there must be an amount of radio-active matter in the earth corresponding to about 270 million tons of radium. If there were more radium than this in the earth, the temperature gradient would be greater than that observed to-day. This may appear to be a very large quantity of radium, but recent determinations (section 281) of the amount of radium emanation in the atmosphere strongly support the view that a large quantity of radium must exist in the surface soil of the earth. Eve found, on a minimum estimate, that the amount of emanation always present in the atmosphere is equivalent to the equilibrium amount derived from 100 tons of radium. There is every reason to believe that the emanation found in the atmosphere is supplied both by the diffusion of the emanation from the soil and by the action of springs. Since the emanation loses half its activity in four days, it cannot diffuse from any great depth. Assuming that the radium is uniformly distributed throughout the earth, the quantity of the radium emanation produced in a thin shell of earth about thirteen metres in depth, is sufficient to account for the amount ordinarily observed in the atmosphere.

I think we may conclude that the present rate of loss of heat of the earth might have continued unchanged for long periods of time in consequence of the supply of heat from radio-active matter in the earth. It thus seems probable that the earth may have remained for very long intervals of time at a temperature not very different from that observed to-day, and that, in consequence, the time during which the earth has been at a temperature capable of supporting the presence of animal and vegetable life may be very much longer than the estimate made by Lord Kelvin from other data.

=272. Evolution of matter.= Although the hypothesis that all matter is composed of some elementary unit of matter or protyle has been advanced as a speculation at various times by many prominent physicists and chemists, the first definite experimental evidence showing that the chemical atom was not the smallest unit of matter was obtained in 1897 by J. J. Thomson in his classic research on the nature of the cathode rays produced by an electric discharge in a vacuum tube. We have seen that Sir William Crookes, who was the first to demonstrate the remarkable properties of these rays, had suggested that they consisted of streams of projected charged matter and represented—as he termed it—a new or “fourth state of matter.”

J. J. Thomson showed by two distinct methods (section 50), that the cathode rays consisted of a stream of negatively charged particles projected with great velocity. The particles behaved as if their mass was only about ¹⁄₁₀₀₀ of the mass of the atom of hydrogen, which is the lightest atom known. These corpuscles, as they were termed by Thomson, were found at a later date to be produced from a glowing carbon filament and from a zinc plate exposed to the action of ultra-violet light. They acted as isolated units of negative electricity, and, as we have seen, may be identified with the electrons studied mathematically by Larmor and Lorentz. Not only were these electrons produced by the action of light, heat, and the electric discharge, but similar bodies were also found to be emitted spontaneously from the radio-elements with a velocity far greater than that observed for the electrons in a vacuum tube.

The electrons produced in these various ways were all found to carry a negative charge, and to be apparently identical; for the ratio _e_/_m_ of the charge of the electron to its mass was in all cases the same within the limits of experimental error. Since electrons, produced from different kinds of matter and under different conditions, were in all cases identical, it seemed probable that they were a constituent part of all matter. J. J. Thomson suggested that the atom is built up of a number of these negatively charged electrons combined in some way with corresponding positively charged bodies.

On this view the atoms of the chemical elements differ from one another only in the number and arrangement of the component electrons.

The removal of an electron from the atom in the case of ionization does not appear to affect permanently the stability of the system, for no evidence has so far been obtained to show that the passage of an intense electric discharge through a gas results in a permanent alteration of the structure of the atom. On the other hand, in the case of the radio-active bodies, a positively charged particle of mass about twice that of the hydrogen atom escapes from the heavy radio-atom. This loss appears to result at once in a permanent alteration of the atom, and causes a marked change in its physical and chemical properties. In addition there is no evidence that the process is reversible.

The expulsion of a β particle with great velocity from an atom of radio-active matter also results in a transformation of the atom. For example radium E emits a β particle, and, in consequence, gives rise to a distinct substance radium F (polonium). A case of this kind, where the expulsion of a β particle with great velocity causes a complete rearrangement of the parts of an atom, is probably quite distinct from the process which occurs during ionization, where a slow speed electron escapes from the atom without apparently affecting the stability of the atom left behind.

The only direct experimental evidence of the transformation of matter has been derived from a study of the radio-active bodies. If the disintegration theory, advanced to account for the phenomena of radio-activity, is correct in the main essentials, then the radio-elements are undergoing a spontaneous and continuous process of transformation into other and different kinds of matter. The rate of transformation is slow in uranium and thorium, but is fairly rapid in radium. It has been shown that the fraction of a mass of radium which is transformed per year is about ¹⁄₂₀₀₀ of the total amount present. In the case of uranium and thorium probably a million years would be required to produce a similar amount of change. Thus the process of transformation in uranium and thorium is far too slow to be detected within a reasonable time by the use of the balance or spectroscope, but the radiations which accompany the transformation can easily be detected. Although the process of change is slow it is continuous, and in the course of ages the uranium and thorium present in the earth must be transformed into other types of matter.

Those who have considered the possibility of atoms undergoing a process of transformation have generally thought that the matter as a whole would undergo a progressive change, with a gradual alteration of physical and chemical properties of the whole mass of substance. On the theory of disintegration this is not the case. Only a minute fraction of the matter present breaks up in unit time, and in each of the successive stages through which the disintegrated atoms pass, there is in most cases a marked alteration in the chemical and physical properties of the matter. The transformation of the radio-elements is thus a transformation of a part _per saltum_, and not a progressive change of the whole. At any time after the process of transformation has been in progress there will thus remain a part of the matter which is unchanged, and, mixed with it, the products which have resulted from the transformation of the remainder.

The question naturally arises whether the process of degradation of matter is confined to the radio-elements or is a universal property of matter. It will be shown in chapter XIV that all matter, so far examined, exhibits the property of radio-activity to a slight degree. It is very difficult, however, to make certain that the observed radio-activity is not due to the presence in the matter of a slight trace of a radio-element. If ordinary matter is radio-active, it is certain that its activity is much less than that of uranium, and consequently that its rate of transformation must be excessively slow. There is, however, another possibility to be considered. The changes occurring in the radio-elements would probably never have been detected if the change had not been accompanied by the expulsion of charged particles with great velocity. It does not seem unlikely that an atom may undergo disintegration without projecting a part of its system with sufficient velocity to ionize the gas. In fact, we have seen that, even in the radio-elements, several of the series of changes in both thorium, radium, and actinium are unaccompanied by ionizing rays. The experimental results given in Appendix A strongly support this point of view. It may thus be possible that all matter is undergoing a slow process of transformation, which has so far only been detected in the radio-elements on account of the expulsion of charged particles with great velocity during the change. This process of degradation of matter continuing for ages must reduce the constituents of the earth to the simpler and more stable forms of matter.

The idea that helium is a transformation product of radium suggests the probability that helium is one of the more elementary substances of which the heavier atoms are composed. Sir Norman Lockyer, in his interesting book on “Inorganic Evolution,” has pointed out that the spectra of helium and of hydrogen predominate in the hottest stars. In the cooler stars the more complex types of matter appear. Sir Norman Lockyer has based his theory of evolution of matter on evidence of a spectroscopic examination of the stars, and considers that temperature is the main factor in breaking up matter into its simpler forms. The transformation of matter occurring in the radio-elements is on the other hand spontaneous, and independent of temperature over the range examined.

Footnote 333:

Perrin, _Revue Scientifique_, April 13, 1901.

Footnote 334:

Becquerel, _C. R._ 133, p. 979, 1901.

Footnote 335:

Rutherford and McClung, _Phil. Trans._ A, p. 25, 1901.

Footnote 336:

Rutherford, _Phil. Mag._ Jan. and Feb. 1900.

Footnote 337:

P. Curie, _C. R._ 136, p. 223, 1903.

Footnote 338:

Rutherford, _Phil. Mag._ April, 1903.

Footnote 339:

M. and Mme Curie, _C. R._ 134, p. 85, 1902.

Footnote 340:

Rutherford and Soddy, _Trans. Chem. Soc._ 81, pp. 321, 837, 1902.
_Phil. Mag._ Sept. and Nov. 1902.

Footnote 341:

Rutherford and Soddy, _Phil. Mag._ April, 1903.

Footnote 342:

Rutherford and Soddy, _Phil. Mag._ May, 1903.

Footnote 343:

Rutherford, _Phys. Zeit._ 4, p. 235, 1902. _Phil. Mag._ Feb. 1903.

Footnote 344:

Rutherford, _Phil. Mag._ May, 1903.

Footnote 345:

Curie and Laborde, _C. R._ 136, p. 673, 1903.

Footnote 346:

J. J. Thomson, _Nature_, p. 601, 1903.

Footnote 347:

Crookes, _C. R._ 128, p. 176, 1899.

Footnote 348:

F. Re, _C. R._ p. 136, p. 1393, 1903.

Footnote 349:

Richarz and Schenck, _Berl. Ber._ p. 1102, 1903. Schenck, _Berl. Ber._
p. 37, 1904.

Footnote 350:

Armstrong and Lowry, _Proc. Roy. Soc._ 1903. _Chem. News_, 88, p. 89,
1903.

Footnote 351:

Rutherford and Soddy, _Phil. Mag._ May, 1903.

Footnote 352:

Boltwood, _Nature_, May 25, p. 80, 1904. _Phil. Mag._ April, 1905.

Footnote 353:

McCoy, _Ber. d. D. Chem. Ges._ No. 11, p. 2641, 1904.

Footnote 354:

Strutt, _Nature_, March 17 and July 7, 1904. _Proc. Roy. Soc._ March
2, 1905.

Footnote 355:

Strutt, _Proc. Roy. Soc._ March 2, 1905.

Footnote 356:

Soddy, _Nature_, May 12, 1904; Jan. 19, 1905.

Footnote 357:

Whetham, _Nature_, May 5, 1904; Jan. 26, 1905.

Footnote 358:

Danne, _C. R._ Jan. 23, 1905.

Footnote 359:

J. J. Thomson, _Nature_, April 30, p. 601, 1903.

Footnote 360:

Voller, _Phys. Zeit._ 5, No. 24, p. 781, 1904.

Footnote 361:

Ramsay and Cooke, _Nature_, Aug. 11, 1904.

Footnote 362:

Eve, _Nature_, March 16, 1905.

Footnote 363:

J. J. Thomson, International Electrical Congress, St Louis, Sept.
1904.

Footnote 364:

Rutherford and Soddy, _Phil. Mag._ p. 582, 1902; pp. 453 and 579,
1903.

Footnote 365:

Ramsay and Soddy, _Nature_, July 16, p. 246, 1903. _Proc. Roy. Soc._
72, p. 204, 1903; 73, p. 346, 1904.

Footnote 366:

Curie and Dewar, _C. R._ 138, p. 190, 1904. _Chem. News_, 89, p. 85,
1904.

Footnote 367:

Himstedt and Meyer, _Ann. d. Phys._ 15, p. 184, 1904.

Footnote 368:

Strutt, _Proc. Roy. Soc._ March 2, 1905.

Footnote 369:

Boltwood, _Phil. Mag._ April, 1905.

Footnote 370:

Moss, _Trans. Roy. Soc. Dublin_, 1904.

Footnote 371:

Travers, _Nature_, p. 248, Jan. 12, 1905.

Footnote 372:

Jaquerod, _C. R._ p. 789, 1904.

Footnote 373:

Ramsay and Travers, _Zeitsch. Physik. Chem._ 25, p. 568, 1898.

Footnote 374:

Ramsay, _Nature_, April 7, 1904.

Footnote 375:

Lodge, _Nature_, June 11, p. 129, 1903.

Footnote 376:

Larmor, _Aether and Matter_, p. 233.

Footnote 377:

J. J. Thomson, _Phil. Mag._ p. 681, Dec. 1903.

Footnote 378:

Lord Kelvin, _Phil. Mag._ Oct. 1904.

Footnote 379:

Thomson, _Phil. Mag._ March, 1904.

Footnote 380:

Rutherford and Soddy, _Phil. Mag._ May, 1903.

Footnote 381:

See Strutt and Joly, _Nature_, Oct. 15, 1903.

Footnote 382:

Strutt, _Phil. Mag._ June, 1903.

Footnote 383:

Elster and Geitel, _Phys. Zeit._ 4, No. 19, p. 522, 1903. _Chem.
News_, July 17, p. 30, 1903.