While much work still remains to be done, a promising beginning has already been made in determining the origin and relation of the radio-elements. We have seen that the connection between polonium, radio-tellurium, and radio-lead with radium has already been established. Radium itself is now added to the list, and it is probable that actinium will soon follow.

While the experiments undoubtedly show that there is a definite relation between the amount of uranium and radium present in the ordinary radio-active minerals, Danne^[358] has recently called attention to a very interesting apparent exception. Considerable quantities of radium were found in certain deposits in the neighbourhood of Issy-l’Evêque in the Saône-Loire district, although no trace of uranium was present. The active matter is found in pyromorphite (phosphate of lead), in clays containing lead, and in pegmatite, but the radium is usually present in greater quantities in the former. The pyromorphite is found in veins of the quartz and felspar rocks. The veins are always wet owing to the presence of a number of springs in the neighbourhood. The content of uranium in the pyromorphite varies considerably, but Danne considers that about a centigram of radium is present per ton. It seems probable that the radium found in this locality has been deposited from water flowing through it, possibly in past times. The presence of radium is not surprising, since crystals of autunite have been found about 40 miles distant, and probably there are deposits containing uranium in that region. This result is of interest, as suggesting that radium may be removed with water and deposited by physical or chemical action some distance away.

It will be shown in the next chapter that radium has been found very widely distributed over the surface of the earth, but generally in very small quantities.

263. Does the radio-activity of radium depend upon its concentration? We have seen that the radio-active constant λ of any product is independent of the concentration of the product. This result has been established over a very wide range for some substances, and especially for the radium emanation. No certain difference in the rate of decay of the emanation has been observed, although the amount present in unit volume of the air has been varied a millionfold.

It has been suggested by J. J. Thomson^[359] that the rate of disintegration of radium may be influenced by its own radiations. This, at first sight, appears very probable, for a small mass of a pure radium compound is subjected to an intense bombardment by the radiations arising from it, and the radiations are of such a character that they might be expected to produce a breaking up of the atoms of matter which they traverse. If this be the case, the radio-activity of a given quantity of radium should be a function of its concentration, and should be greater in the solid state than when disseminated through a large mass of matter.

The writer has made an experiment to examine this question. Two glass tubes were taken, in one of which was placed a few milligrams of pure radium bromide in a state of radio-active equilibrium, and in the other a solution of barium chloride. The two tubes were connected near the top by a short cross tube, and the open ends sealed off. The activity of the radium in the solid state was tested immediately after its introduction by placing it in a definite position near an electroscope made of thin metal of the type shown in Fig. 12. The increased rate of discharge of the electroscope due to the β and γ rays from the radium was observed. When a lead plate 6 mms. in thickness was placed between the radium and the electroscope, the rate of discharge observed was due to the γ rays alone. By slightly tilting the apparatus, the barium solution flowed into the radium tube and dissolved the radium. The tube was well shaken, so as to distribute the radium uniformly throughout the solution. No appreciable change of the activity measured by the γ rays was observed over the period of one month. The activity measured by the β and γ rays was somewhat reduced, but this was not due to a decrease of the radio-activity, but to an increased absorption of the β rays in their passage through the solution. The volume of the solution was at least 1000 times greater than that of the solid radium bromide, and, in consequence, the radium was subjected to the action of a much weaker radiation. I think we may conclude from this experiment that the radiations emitted by radium have little if any influence in causing the disintegration of the radium atoms.

Voller^[360] recently published some experiments which appeared to show that the life of radium varied enormously with its concentration. In his experiments, solutions of radium bromide of known strengths were evaporated down in a platinum vessel 1·2 sq. cms. in area, and their activity tested from time to time. The activity of the radium, so deposited, at first showed the normal rise to be expected on account of the production of the emanation, but after reaching a maximum, it rapidly decayed. For a weight of 10^-6 mgrs. of radium bromide, the activity for example, practically disappeared in 26 days after reaching its maximum. The time taken for the activity to disappear increased rapidly with the amount of radium present. In another set of experiments, he states that the activity observed on the vessel was not proportional to the amount of radium present. For example, the activity only increased 24 times for a millionfold increase of the radium present, from 10^-9 mgrs. to 10^-3 mgrs.

These results, however, have not been confirmed by later experiments made by Eve. He found that, over the range examined, the activity was directly proportional to the amount of radium present, within the limits of experimental error. The following table illustrates the results obtained. The radium was evaporated down in platinum vessels 4·9 sq. cms. in area.

For an increase of one-thousandfold of the quantity of radium, the activity increased 800 times, while Voller states that the activity, in his experiments, only increased 3 to 4 times.

In the experiments of Eve, the activity was measured by observing the increased rate of discharge of a gold-leaf electroscope when the platinum vessel containing the active deposit was placed inside the electroscope. The activity of 10^-8 mgrs. was too small to be measured with accuracy in the electroscope employed, while 10^-3 mgrs. gave too rapid a rate of discharge. On the other hand, the method of measurement employed by Voller was unsuitable for the measurement of very weak radio-activity.

Eve also found that a small quantity of radium kept in a closed vessel did not lose its activity with time. A silvered glass vessel contained a gold-leaf system, such as is shown in Fig. 12. A solution containing 10^-6 mgrs. of radium bromide was evaporated over the bottom of the vessel of area 76 sq. cms. The activity, after reaching a maximum, has remained constant over the 100 days during which observations have so far been made.

These experiments of Eve, as far as they go, show that the activity of radium is proportional to the amount of radium present, and that radium, kept in a closed vessel, shows no signs of decreasing in activity. On the other hand, I think there is no doubt that a very small quantity of radium deposited on a plate and left in the open air does lose its activity fairly rapidly. This loss of activity has nothing whatever to do with the shortness of life of the radium itself, but is due to the escape of the radium from the plate into the surrounding gas. Suppose, for example, that a solution containing 10^-9 mgrs. of radium bromide is evaporated in a vessel of one sq. cm. in area. This amount of radium is far too small to form even a layer of molecular thickness. It seems likely that, during the process of evaporation, the radium would tend to collect in small masses and be deposited on the surface of the vessel. These would very readily be removed by slow currents of air and so escape from the plate. The disappearance of such minute amounts of radium is to be expected, and would probably occur with all kinds of matter present in such minute amount. Such an effect has nothing to do with an alteration of the life of radium and must not be confused with it.

The result that the total radiation from a given quantity of radium depends only on the quantity of radium and not on the degree of its concentration is of great importance, for it allows us to determine with accuracy the content of radium in minerals and in soils in which the radium exists in a very diffused state.

264. Constancy of the radiations. The early observations on uranium and thorium had shown that their radio-activity remained constant over the period of several years during which they were examined. The possibility of separating from uranium and thorium the active products Ur X and Th X respectively, the activity of which decayed with the time, seemed at first sight to contradict this. Further observation, however, showed that the total radio-activity of these bodies was not altered by the chemical processes, for it was found that the uranium and thorium from which the active products were removed, spontaneously regained their radio-activity. At any time after removal of the active product, the sum total of the radio-activity of the separated product together with that of the substance from which it has been separated is always equal to that of the original compound before separation. In cases where active products, like Ur X and the radium emanation, decay with time according to an exponential law, this follows at once from the experimental results. If I₁ is the activity of the product at any time t after separation, and I₀ the initial value, we know that

where λ is the same constant as before. It thus follows that I₁ + I₂ = I₀, which is an expression of the above result. The same is also true whatever the law of decay of activity of the separated product (see section 200). For example, the activity of Th X after separation from thorium at first increases with the time. At the same time, the activity of the residual thorium compound at first decreases, and at such a rate that the sum of the activities of the thorium and its separated product is always equal to that of the original thorium.

This apparent constancy of the total radiation follows from the general result that the radio-active processes cannot in any way be changed by the action of known forces. It may be recalled that the constant of decay of the activity of a radio-active product has a definite fixed value under all conditions. It is independent of the concentration of the active matter, of the pressure, and of the nature of the gas in which the substance is placed, and it is not affected by wide ranges of temperature. The only observed exception is the product radium C. Its value of λ increases with temperature to some extent at about 1000° C., but at 1200° C. returns nearly to the normal value. In the same way, it has not been found possible to alter the rate of production of active matter from the radio-elements. In addition, there is not a single well-authenticated case where radio-activity has been altered or destroyed in any active body or created in an inactive element.

Certain cases have been observed, which at first sight seem to indicate a destruction of radio-activity. For example, the excited radio-activity is removed from a platinum wire when heated above a red heat. It has been shown, however, by Miss Gates (section 187) that the radio-activity is not destroyed, but is deposited in unaltered amount on the colder bodies surrounding it. Thorium oxide has been shown to lose to a large extent its power of emanating by ignition to a white heat. But a close examination shows that the emanation is still being produced at the same rate, but is occluded in the compound.

The total radio-activity of a given mass of a radio-element, measured by the peculiar radiations emitted, is a quantity which can neither be increased nor diminished, although it may be manifested in a series of products which are capable of separation from the radio-element. The term “conservation of radio-activity” is thus a convenient expression of the facts known at the present time. It is quite possible, however, that further experiments at very high or very low temperatures may show that the radio-activity does vary.

Although no difference has been observed in the radio-activity of uranium over an interval of five years, it has been shown (section 261) that on theoretical grounds the radio-activity of a given quantity of a radio-element should decrease with the time. The change will, however, be so slow in uranium, that probably millions of years must elapse before a measurable change can take place, while the total radio-activity of a given quantity of matter left to itself should thus decrease, but it ought to be constant for a constant mass of the radio-element. It has already been pointed out (section 238) that the activity of radium, measured by the α and β rays, will probably increase for several hundred years after its separation. This is due to the appearance of fresh products in the radium. Ultimately, however, the activity must decrease according to an exponential law with the time, falling to half value in about 1300 years.

The conservation of radio-activity applies not only to the radiations taken as a whole, but also to each specific type of radiation. If the emanation is removed from a radium compound, the amount of β radiation of the radium at once commences to decrease, but this is compensated by the appearance of β rays in the radiations from the vessel in which the separated emanation is stored. At any time the sum total of the β radiations from the radium and the emanation vessel is always the same as that from the radium compound before the emanation was removed.

Similar results have also been found to hold for the γ rays. This was tested by the writer in the following way. The emanation from some solid radium bromide was released by heat, and condensed in a small glass tube which was then sealed off. The radium so treated, and the emanation tube, were placed together under an electroscope, with a screen of lead 1 cm. thick interposed in order to let through only the γ rays. The experiments were continued over three weeks, but the sum total of the γ rays from the radium and the emanation tube was, over the whole interval, equal to that of the original radium. During this period the amount of γ rays from the radium at first decreased to only a few per cent. of the original value, and then slowly increased again, until at the end of the three weeks it had nearly regained its original value, before the emanation was removed. At the same time the amount of γ rays from the emanation tube rose from zero to a maximum and then slowly decreased again at the same rate as the decay of the activity of the emanation in the tube. This result shows that the amount of γ rays from radium was a constant quantity over the interval of observation, although the amount of γ rays from the radium and emanation tube had passed through a cycle of changes.

There is one interesting possibility in this connection that should be borne in mind. The rays from the active substances carry off energy in a very concentrated form, and this energy is dissipated by the absorption of the rays in matter. The rays might be expected to cause a disintegration of the atoms of inactive matter on which they fall and thus give rise to a kind of radio-activity. This effect has been looked for by several observers. Ramsay and W. T. Cooke^[361] state that they have noticed such an action, using about a decigram of radium as a source of radiation. The radium, sealed in a glass vessel, was surrounded by an external glass tube and exposed to the action of the β and γ rays of radium for several weeks. The inside and outside of the glass tube were found to be active, and the active matter was removed by solution in water. The radio-activity observed was very minute, corresponding to only about 1 milligram of uranium. The writer has, at various times, tried experiments of this character but with negative results. The greatest care is necessary in such experiments to ensure that the radio-activity is not due to other causes besides the rays from the radium. This care is especially necessary in laboratories where considerable quantities of the radium emanation have been allowed to escape into the air. The surface of every substance becomes coated with the slow transformation products of radium, viz. radium D, E, and F. The activity communicated in this way to originally inactive matter is often considerable. This infection by the radium emanation extends throughout the whole laboratory, on account of the distribution of the emanation by convection and diffusion. For example, Eve^[362] found that every substance which he examined in the laboratory of the writer showed much greater activity than the normal. In this case the radium had been in use in the building for about two years.

265. Loss of weight of the radio-elements. Since the radio-elements are continually throwing off α particles atomic in size, an active substance, enclosed in a vessel sufficiently thin to allow the α particles to escape, must gradually lose in weight. This loss of weight will be small under ordinary conditions, since the greater proportion of the α rays produced are absorbed in the mass of the substance. If a very thin layer of a radium compound were spread on a very thin sheet of substance, which did not appreciably absorb the α particles, a loss of weight due to the expulsion of α particles might be detectable. Since e/m = 6 × 10³ for the α particle and e = 1·1 × 10^-20 electromagnetic units and 2·5 × 10¹¹ α particles are expelled per second per gram of radium, the proportion of the mass expelled is 4·8 × 10^-13 per second and 10^-5 per year. There is one condition, however, under which the radium should lose in weight fairly rapidly. If a current of air is slowly passed over a radium solution, the emanation produced would be removed as fast as it was formed. Since the atom of the emanation has a mass probably not much smaller than the radium atom, the fraction of the mass removed per year should be nearly equal to the fraction of the radium which changes per year, i.e. one gram of radium should diminish in weight about half a milligram (section 261) per year.

If it is supposed that the β particles have weight, the loss of weight due to their expulsion is very small compared with that due to the emission of α particles. The writer has shown (section 253) that about 7 × 10¹⁰ β particles are projected per second from 1 gram of radium. The consequent loss of weight would only be about 10^-9 grams per year.

Except under very special experimental conditions, it would thus be difficult to detect the loss of weight of radium due to the expulsion of β particles from its mass. There is, however, a possibility that radium might change in weight even though none of the radio-active products were allowed to escape. For example, if the view is taken that gravitation is the result of forces having their origin in the atom, it is possible that, if the atom were disintegrated, the weight of the parts might not be equal to that of the original atom.

A large number of experiments have been made to see if radium preparations, kept in a sealed tube, alter in weight. With the small quantities of radium available to the experimenter, no difference of weight of radium preparations with time has yet been established with certainty. Heydweiller stated that he had observed a loss of weight of radium and Dorn also obtained a slight indication of change in weight. These results have not, however, been confirmed. Forch, later, was unable to observe any appreciable change.

J. J. Thomson^[363] has made experiments to see if the ratio of weight to mass for radium is the same as for inactive matter. We have seen in section 48 that a charge in motion possesses an apparent mass which is constant for slow speeds but increases as the speed of light is approached. Now radium emits some electrons at a velocity comparable with the velocity of light, and presumably these electrons were in rapid motion in the atom before their expulsion. It might thus be possible that the ratio for radium would differ from that for ordinary matter. The pendulum method was used, and the radium was enclosed in a small light tube suspended by a silk fibre. Within the limit of experimental error the ratio of weight to mass was found to be the same as for ordinary matter, so that we may conclude that the number of electrons moving with a velocity approaching that of light is small compared with the total number present.

266. Total emission of energy from the radio-element. It has been shown that 1 gram of radium emits energy at the rate of 100 gram-calories per hour or 876,000 gram-calories per year. If 1 gram of radium in radio-active equilibrium be set apart, its radio-activity and consequent heat emission is given at a time t by

Now on the estimate of the life of radium given in section 261 the value of λ is ¹⁄₁₈₅₀ when 1 year is taken as the unit of time. The total heat emission from 1 gram of radium during its life is thus 1·6 × 10⁹ gram-calories. The heat emitted in the union of hydrogen and oxygen to form 1 gram of water is about 4 × 10³ gram-calories, and in this reaction more heat is given out for equal weights than in any other chemical reaction known. It is thus seen that the total energy emitted from 1 gram of radium during its changes is about one million times greater than in any known molecular change. That matter is able, under special conditions, to emit an enormous amount of energy, is well exemplified by the case of the radium emanation. Calculations of the amount of this energy have already been given in section 249.

Since the other radio-elements only differ from radium in the slowness of their change, the total heat emission from uranium and thorium must be of a similar high order of magnitude. There is thus reason to believe that there is an enormous store of latent energy resident in the atoms of the radio-elements. This store of energy could not have been recognized if the atoms had not been undergoing a slow process of disintegration. The energy emitted in radio-active changes is derived from the internal energy of the atoms. The emission of this energy does not disobey the law of the conservation of energy, for it is only necessary to suppose that, when the radio-active changes have ceased, the energy stored up in the atoms of the final products is less than that of the original atoms of the radio-elements. The difference between the energy originally possessed by the matter which has undergone the change, and the final inactive products which arise, is a measure of the total amount of energy released.

There seems to be every reason to suppose that the atomic energy of all the elements is of a similar high order of magnitude. With the exception of their high atomic weights, the radio-elements do not possess any special chemical characteristics which differentiate them from the inactive elements. The existence of a latent store of energy in the atoms is a necessary consequence of the modern view developed by J. J. Thomson, Larmor, and Lorentz, of regarding the atom as a complicated structure consisting of charged parts in rapid oscillatory or orbital motion in regard to one another. The energy may be partly kinetic and partly potential, but the mere concentration of the charged particles, which probably constitute the atom, in itself implies a large store of energy in the atom, in comparison with which the energy emitted during the changes of radium is insignificant.

The existence of this store of latent energy does not ordinarily manifest itself, since the atoms cannot be broken up into simpler forms by the physical or chemical agencies at our disposal. Its existence at once explains the failure of chemistry to transform the atoms, and also accounts for the rate of change of the radio-active processes being independent of all external agencies. It has not so far been found possible to alter in any way the rate of emission of energy from the radio-elements. If it should ever be found possible to control at will the rate of disintegration of the radio-elements, an enormous amount of energy could be obtained from a small quantity of matter.

267. Production of helium from radium and the radium emanation. Since the final products, resulting from a disintegration of the radio-elements, are not radio-active, they should in the course of geologic ages collect in some quantity, and should always be found associated with the radio-elements. Now the inactive products resulting from the radio-active changes are the α particles expelled at each stage, and the final inactive product or products which remain, when the process of disintegration can no longer be traced by the property of radio-activity.

Pitchblende, in which the radio-elements are mostly found, contains in small quantity a large proportion of all the known elements. In searching for a possible disintegration product common to all the radio-elements, the presence of helium in the radio-active minerals is noteworthy; for helium is only found in the radio-active minerals, and is an invariable companion of the radio-elements. Moreover, the presence in minerals of a light, inert gas like helium had always been a matter of surprise. The production by radium and thorium of the radio-active emanations, which behave like chemically inert gases of the helium-argon family, suggested the possibility that one of the final inactive products of the disintegration of the radio-elements might prove to be a chemically inert gas. The later discovery of the material nature of the α rays added weight to the suggestion; for the measurement of the ratio e/m of the α particle indicated that if the α particle consisted of any known kind of matter, it must either be hydrogen or helium. For these reasons, it was suggested in 1902 by Rutherford and Soddy^[364] that helium might be a product of the disintegration of the radio-elements.

Sir William Ramsay and Mr Soddy in 1903 undertook an investigation of the radium emanation, with the purpose of seeing if it were possible to obtain any spectroscopic evidence of the presence of a new substance. First of all, they exposed the emanation to very drastic treatment (section 158), and confirmed and extended the results previously noted by Rutherford and Soddy that the emanation behaved like a chemically inert gas, and in this respect possessed properties analogous to the gases of the helium-argon group.

On obtaining 30 milligrams of pure radium bromide (prepared about three months previously) Ramsay and Soddy^[365] examined the gases, liberated by solution of the radium bromide in water, for the presence of helium. A considerable quantity of hydrogen and oxygen was released by the solution (see section 124). The hydrogen and oxygen were removed by passing the liberated gases over a red-hot spiral of partially oxidized copper-wire and the resulting water vapour was absorbed in a phosphorus pentoxide tube.

The gas was then passed into a small vacuum tube which was in connection with a small U tube. By placing the U tube in liquid air, most of the emanation present was condensed, and also most of the CO₂ present in the gas. On examining the spectrum of the gas in the vacuum tube, the characteristic line D₃ of helium was observed.

This experiment was repeated with 30 milligrams of radium bromide about four months old, lent for the purpose by the writer. The emanation and CO₂ were removed by passing them through a U tube immersed in liquid air. A practically complete spectrum of helium was observed, including the lines of wave-lengths 6677, 5876, 5016, 4972, 4713 and 4472. There were also present three other lines of wave-lengths about 6180, 5695, 5455 which have not yet been identified.

In later experiments, the emanation from 50 milligrams of the radium bromide was conveyed with oxygen into a small U tube, cooled in liquid air, in which the emanation was condensed. Fresh oxygen was added, and the U tube again pumped out. The small vacuum tube, connected with the U tube, showed at first no helium lines when the liquid air was removed. The spectrum obtained was a new one, and Ramsay and Soddy considered it to be probably that of the emanation itself. After allowing the emanation tube to stand for four days, the helium spectrum appeared with all the characteristic lines, and in addition, three new lines present in the helium obtained by solution of the radium. These results have since been confirmed. The experiments, which have led to such striking and important results, were by no means easy of performance, for the quantity of helium and of emanation released from 50 mgrs. of radium bromide is extremely small. It was necessary, in all cases, to remove almost completely the other gases, which were present in sufficient quantity to mask the spectrum of the substance under examination. The success of the experiments has been largely due to the application, to this investigation, of the refined methods of gas analysis, previously employed by Sir William Ramsay with so much skill in the separation of the rare gases xenon and krypton, which exist in minute proportions in the atmosphere. The fact that the helium spectrum was not present at first, but appeared after the emanation had remained in the tube for some days, shows that the helium must have been produced from the emanation. The emanation cannot be helium itself, for, in the first place, helium is not radio-active, and in the second place, the helium spectrum was not present at first, when the quantity of emanation in the tube was at its maximum. Moreover, the diffusion experiments, already discussed, point to the conclusion that the emanation is of high molecular weight. There can thus be no doubt that the helium is derived from the emanation of radium in consequence of changes of some kind occurring in it.

These results were confirmed later by other observers. Curie and Dewar^[366] performed the following experiment: A weight of about ·42 gr. of radium bromide was placed in a quartz tube, and the tube exhausted until no further gas came off. The radium was then heated to fusion, about 2·6 c.c. of gas being liberated in the process. The tube was then sealed, and some weeks afterwards the spectrum of the gas liberated in the tube by the radium was examined by Deslandres and found to give the entire spectrum of helium. The gas, liberated during the initial heating of the radium, was collected and found to contain a large amount of emanation, although the gas had been passed through two tubes immersed in liquid air. The tube containing these gases was very luminous and rapidly turned violet, while more than half of the gases was absorbed. The spectrum of the phosphorescent light was found to be discontinuous, consisting of three nitrogen bands. No sign of the helium spectrum was observed, although helium must have been present.

Himstedt and Meyer^[367] placed 50 mgrs. of radium bromide in a U tube connected with a small vacuum tube. The tube was carefully exhausted and then sealed off. The spectrum of hydrogen and carbon dioxide alone was observed for three months, but after four months the red, yellow, green and blue lines of the helium spectrum were visible. The slow appearance of the helium spectrum was probably due to the presence in the tube of a considerable quantity of hydrogen. In another experiment, some radium sulphate which had been heated to a bright red heat in a quartz tube was connected with a small vacuum tube. After three weeks, some of the lines of helium were clearly seen, and increased in brightness with time.

268. Connection between helium and the α particles. The appearance of helium in a tube containing the radium emanation may indicate either that the helium is one of the final products, which appear at the end of the series of radio-active changes, or that the helium is in reality the expelled α particle. The evidence at present points to the latter as being the more probable explanation. In the first place, the emanation diffuses like a gas of heavy molecular weight, and it appears probable that after the expulsion of a few α particles, the atomic weight of the final product is comparable with that of the emanation. On the other hand, the value of e/m determined for the projected α particle points to the conclusion that, if it consists of any known kind of matter, it is either hydrogen or helium.

It may be possible to settle the question by accurate measurements of the volume of gas in a tube, filled originally with the radium emanation. Since the emanation itself, and two of the rapidly changing products which result from it, emit α particles, the final volume of the α particles, if they can exist in the gaseous state, would be three times the volume of the emanation. Ramsay and Soddy (section 172) have made experiments of this kind, but the results obtained were very contradictory, depending upon the kind of glass employed. In one case, the volume of the residual gases shrank almost to zero, in another the initial volume increased to about ten times its initial value. In the latter experiment a brilliant spectrum of helium was observed in the residual gas. This difference of behaviour is probably due to different degrees of absorption of helium by the glass tubes.

If the α particles are helium atoms, we may expect that a large proportion of the helium, which is produced in a tube containing the radium emanation, will be buried in the wall of the glass tube; for the α particles are projected with sufficient velocity to penetrate some distance into the glass. This helium may either remain in the glass, or in some cases rapidly diffuse out again. In any case, a fraction of the helium would be liberated when an intense electric discharge is passed through the tube. Ramsay and Soddy have in some instances observed that a slight amount of helium is liberated on heating the walls of the tube in which the emanation had been stored for some time.

The volume of helium produced per year by 1 gram of radium can easily be calculated on the assumption that the α particle is in reality a helium atom.

It has been shown that 2·5 × 10¹¹ α particles are projected per second from 1 gram of radium. Since there are 3·6 × 10¹⁹ molecules in one cubic centimetre of any gas at standard pressure and temperature, the volume of the α particles released per second is 7 × 10^-9 c.c. and per year 0·24 c.c. It has already been pointed out that, on this hypothesis, the volume of helium released by the emanation is three times the volume of the latter. The amount of helium to be obtained from the emanation released from 1 gram of radium in radio-active equilibrium is thus about 3 cubic mms.

Ramsay and Soddy have tried to estimate experimentally the probable volume of helium produced per second by one gram of radium. The helium, obtained from 50 mgrs. of radium bromide, which had been kept in solution in a closed vessel for 60 days, was introduced into a vacuum tube. Another similar tube was placed in series with it, and the amount of the helium in the latter adjusted until on passing a discharge through the two tubes in series the helium lines in each tube were of about the same brightness. In this way they calculated that the amount of helium present was 0·1 cubic mm. On this estimate, the amount of helium produced per year per gram of radium is about 20 cubic mms. We have seen that the calculated amount is about 240 cubic mms., on the assumption that the α particle is a helium atom. Ramsay and Soddy consider that the presence of argon in one of the tubes may have seriously interfered with the correctness of the estimation. On account of the great uncertainty attaching to estimates of the above character, the value deduced by Ramsay and Soddy does not exclude the probability that the calculated volume may be of the right order of magnitude.

In order to explain the presence of helium in radium on ordinary chemical lines, it has been suggested that radium is not a true element, but a molecular compound of helium with some substance known or unknown. The helium compound gradually breaks down, giving rise to the helium observed. It is at once obvious that this postulated helium compound is of a character entirely different from that of any other compound previously observed in chemistry. Weight for weight, it emits during its change an amount of energy at least one million times greater than any molecular compound known (see section 249). In addition, it must be supposed that the rate of breaking up of the helium compound is independent of great ranges of temperature—a result never before observed in any molecular change. The helium compound in its breaking up must give rise to the peculiar radiations and also pass through the successive radio-active changes observed in radium.

Thus in order to explain the production of helium and radio-activity on this view, a unique kind of molecule must be postulated—a molecule, in fact, which is endowed with every single property which on the disintegration theory is ascribed to the atom of the radio-elements. On the other hand, radium as far as it has been examined, has fulfilled every test required for an element. It has a well-marked and characteristic spectrum, and there is no reason to suppose that it is not an element in the ordinarily accepted sense of the term.

On the theory that the radio-elements are undergoing atomic disintegration, the helium must be considered to be a constituent of the radium atom, or, in other words, the radium atom is built up of parts, one of which, at least, is the atom of helium. The theory that the heavy atoms are all built up of some simple fundamental unit of matter or protyle has been advanced at various times by many prominent chemists and physicists. Prout’s hypothesis that all elements are built up out of hydrogen is an example of this point of view of regarding the subject.

On the disintegration theory, the changes occurring in the radio-atoms involve an actual transformation of the atoms through successive changes. This change is so slow in uranium and thorium that at least a million years would be required before the amount of change could be measured by the balance. In radium it is a million times faster, but even in this case it is doubtful whether any appreciable change would have been observed by ordinary chemical methods for many years had not the possibility of such a change been suggested from other lines of evidence.

The similarity of the α particles from the different radio-elements indicates that they consist of expelled particles of the same kind. On this view, helium should be produced by each of the radio-elements. Its presence in minerals containing thorium, for example in monazite sand and the Ceylon mineral described by Ramsay, indicates that helium may be a product of thorium as well as of radium. Strutt^[368] has recently suggested that most of the helium observed in radio-active minerals may be a decomposition product of thorium rather than of uranium and radium; for he finds that minerals rich in helium always contain thorium, while many uranium minerals nearly free from thorium contain little helium. The evidence in support of this view is, however, not altogether satisfactory, for some of the uranium minerals in question are secondary uranium minerals (see Appendix B), deposited by the action of water or other agencies at a comparatively late date, and are also, in many cases, highly emanating, and consequently could not be expected to retain more than a fraction of the helium produced in them.

Taking the view that the α particles are projected helium atoms, we must regard the atoms of the radio-elements as compounds of some known or unknown substance with helium. These compounds break up spontaneously, and at a very slow rate even in the case of radium. The disintegration takes place in successive stages, and at most of the stages a helium atom is projected with great velocity. This disintegration is accompanied by an enormous emission of energy. The liberation of such a large amount of energy in the radio-active changes at once explains the constancy of the rate of change under the action of any of the physical and chemical agencies at our command. On this view, uranium, thorium and radium are in reality compounds of helium. The helium, however, is held in such strong combination that the compound cannot be broken up by chemical or physical forces, and, in consequence, these bodies behave as chemical elements in the ordinary accepted chemical sense.

It appears not unlikely that many of the so-called chemical elements may prove to be compounds of helium, or, in other words, that the helium atom is one of the secondary units with which the heavier atoms are built up. In this connection it is of interest to note that many of the elements differ in their atomic weight by four—the atomic weight of helium.

If the α particle is a helium atom, at least three α particles must be expelled from uranium (238·5) to reduce its atomic weight to that of radium (225). It is known that five α particles are expelled from radium during its successive transformations. This would make the atomic weight of the final residue 225 – 20 = 205. This is very nearly the atomic weight of lead, 206·5. I have, for some time, considered it probable that lead is the end or final product of radium. The same suggestion has recently been made by Boltwood^[369]. This point of view is supported by the fact that lead is always found in small quantity in all uranium minerals, and that the relative proportions of lead and helium in the radio-active minerals are about the same as would be expected if lead and helium were both decomposition products of radium. Dr Boltwood has drawn my attention to the fact that the proportion of lead in many radio-active minerals varies with the content of helium. A mineral rich in helium in nearly all cases contains more lead than a mineral poor in helium. This cannot be considered, at present, more than a speculation, but the facts as they stand are very suggestive.

269. Age of radio-active minerals. Helium is only found in the radio-active minerals, and this fact, taken in conjunction with the liberation of helium by radium, indicates that the helium must have been produced as a result of the transformation of radium and the other radio-active substances contained in the minerals. Now in a mineral about half the helium is, in many cases, released by heat and the residue by solution. It seems probable that the helium produced throughout the mass of the mineral is mechanically imprisoned in it. Moss^[370] found that, by grinding pitchblende in vacuo, helium is evolved, apparently showing that the helium exists in cavities of the mineral. Travers^[371] has suggested that, since helium is liberated on heating, the effect may be due to the heat generated by grinding. The escape of the helium from the heated mineral is probably connected with the fact observed by Jaquerod^[372] that helium passes through the walls of a quartz tube, heated above 500° C. The substance of the mineral probably possesses a similar property. Travers considers that helium is present in the mineral in a state of supersaturated solid solution, but the facts are equally well explained by assuming that the helium is mechanically imprisoned in the mass of the mineral.

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.

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:—

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

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)μM²/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