Section 197, It Has Been Shown That

$$ Q = \frac {nλ1} {λ1 − λ2} (e^{–λ2 t} - e^{–λ_1 t}) $$ .... (4).

The value of Q{t} passes through a maximum Q{T} at the time T when

$$ \frac {λ2} {λ1} − e^{-(λ1–λ2) T} $$ .

The maximum activity I{T} is proportional to Q{T} and

$$ \frac {It} {IT} = \frac {Qt} {QT} = \frac {e^{–λ2 t} - e^{–λ1 t}} {e^{–λ2 T} − e^{–λ1 T}} $$ .

It will be shown later that the variation with time of the activity, imparted to a body by a short exposure, is expressed by an equation of the above form. It thus remains to fix the values of λ₁, λ₂. Since the above equation is symmetrical with regard to λ₁, λ₂, it is not possible to settle from the agreement of the theoretical and experimental curve which value of λ refers to the first change. The curve of variation of activity with time is unaltered if the values of λ₁ and λ₂ are interchanged.

It is found experimentally that the activity 5 or 6 hours after removal decays very approximately according to an exponential law with the time, falling to half value in 11 hours. This is the normal rate of decay of thorium for all times of exposure, provided measurements are not begun until several hours after the removal of the active body from the emanation.

This fixes the value of the constants of one of the changes. Let us assume for the moment that this gives the value of λ₁.

Then λ₁ = 1·75 × 10⁻⁵ (sec)⁻¹.

Since the maximum activity is reached after an interval T = 220 minutes (see Fig. 65), substituting the values of λ₁ and T in the equation, the value of λ₂ comes out to be

λ₂ = 2·08 × 10⁻⁴ (sec)⁻¹.

This value of λ₂ corresponds to a change in which half the matter is transformed in 55 minutes.

Substituting now the values of λ₁, λ₂, T, the equation reduces to

$$ \frac {It} {IT} = 1\cdot37 (e^{–λ2 t} − e^{–λ2 t}) $$ .

The agreement between the results of the theoretical equation and the observed values is shown in the following table:

Time in Theoretical Observed value minutes value of of I{t}/I{T} I{t}/I{T}

15 ·22 ·23

30 ·38 ·37

60 ·64 ·63

120 ·90 ·91

220 1·00 1·00

305 ·97 ·96

After 5 hours the activity decreased nearly exponentially with the time, falling to half value in 11 hours.

It is thus seen that the curve of rise of activity for a short exposure is explained very satisfactorily on the supposition that two changes occur in the deposited matter, of which the first is a rayless change.

Further data are required in order to fix which of the time constants of the changes refers to the first change. In order to settle this point, it is necessary to isolate one of the products of the changes and to examine the variation of its activity with time. If, for example, a product can be separated whose activity decays to half value in 55 minutes, it would show that the second change is the more rapid of the two. Now Pegram has examined the radio-active products obtained by electrolysis of thorium solutions. The rates of decay of the active products depended upon conditions, but he found that, in several cases, rapidly decaying products were obtained whose activity fell to half value in about 1 hour. Allowing for the probability that the product examined was not completely isolated by the electrolysis, but contained also a trace of the other product, this result would indicate that the last change which gives rise to rays is the more rapid of the two.

This point is very clearly brought out by some recent experiments of Miss Slater, who has made a detailed examination of the effect of temperature on the active deposit of thorium.

A platinum wire was made active by exposure for a long interval to the thorium emanation, and then heated for a few minutes to any desired temperature by means of the electric current. The wire, while being heated, was surrounded by a lead cylinder in order that any matter driven off from it should be collected on its surface. The decay of activity both of the wire and of the lead cylinder was then tested separately. After heating to a dull red heat, no sensible diminution of the activity was observed at first, but the rate of decay of the activity on the wire was found to be more rapid than the normal. The activity of the lead cylinder was small at first but increased to a maximum after about 4 hours and then decayed at the normal rate with the time.

These results are to be expected if some thorium A is volatilized from the wire; for the rise of activity on the lead cylinder is very similar to that observed on a wire exposed for a short time in the presence of the thorium emanation, i.e., under the condition that only thorium A is initially present.

On heating the wire above 700° C. the activity was found to be reduced, showing that some thorium B had also been removed. By heating for a few minutes at about 1000° C. nearly all the thorium A was driven off. The activity on the wire then decayed exponentially with the time, falling to half value in about 1 hour. After heating for a minute at about 1200° C. all the activity was removed. These results show that thorium A is more volatile than B, and that the product which gives out rays, viz. thorium B, has a period of about 55 minutes.

Another series of experiments was made, in which an active aluminium disc was placed in an exhausted tube, and exposed to the cathode ray discharge. Under these conditions, a part of the activity of the disc was removed. When the disc was made the anode, the loss of activity was usually 20 to 60 per cent. for half-an-hour’s exposure. If the disc was made the cathode, the loss was much greater, amounting to about 90 per cent. in 10 minutes. Part of the active matter removed from the disc was collected on a second disc placed near it. This second disc on removal lost its activity at a far more rapid rate than the normal. The rate of decay on the first disc was also altered, the activity sometimes even increasing after removal. These results indicate that, in this case, the apparent volatility of the products is reversed. Thorium B is driven off from the disc more readily than thorium A. The rates of decay obtained under different conditions were satisfactorily explained by supposing that the surfaces of the discs after exposure to the discharge were coated with different proportions of thorium A and B.

The escape of thorium B from the disc under the influence of the discharge seems rather to be the result of an action similar to the well-known “sputtering” of electrodes than to a direct influence of temperature.

The results obtained by von Lerch on the electrolysis of a solution of the active deposit also admit of a similar interpretation. Products were obtained on the electrodes of different rates of decay, losing half their activity in times varying from about 1 hour to 5 hours. This variation is due to the admixture of the two products in different proportions. The evidence, as a whole, thus strongly supports the conclusion that the active deposit from thorium undergoes two successive transformations as follows:

(1) A “rayless” change for which λ₁ = 1·75 × 10⁻⁵, i.e., in which half the matter is transformed in 11 hours;

(2) A second change giving rise to α, β and γ rays, for which λ₂ = 2·08 × 10⁻⁴, i.e., in which half the matter is transformed in 55 minutes.

It is, at first sight, a somewhat unexpected result that the final rate of decay of the active deposit from thorium gives the rate of change not of the last product itself, but of the preceding product, which does not give rise to rays at all.

A similar peculiarity is observed in the decay of the excited activity of actinium, which is discussed in section 212.

For a long exposure in the presence of a constant supply of thorium emanation, the equation expressing the variation of activity with time is found from equation (8), section 198,

$$ \frac {It} {I₀} = \frac {Q} {Q₀} = \frac {λ2} {λ2 - λ1} e^{–λ1 t} − \frac {λ1} {λ1 − λ2} e^{–λ_2 t} $$

$$ = \frac {λ2 e^{–λ1 t}} {λ2 - λ1} (1 − \cdot083 e^{−1\cdot90 × 10^{−4} t} ) $$ .

About 5 hours after removal the second term in the brackets becomes very small, and the activity after that time will decay nearly according to an exponential law with the time, falling to half value in 11 hours. For any time of exposure T, the activity at time t after the removal (see equation 11, section 199) is given by

$$ \frac {It} {I₀} = \frac {Q} {QT} = \frac {ae^{–λ2 t} - be^{–λ1 t}} {a − b} $$,

where I₀ is the initial value of the activity, immediately after removal, and

$$ a = \frac {1 − e^{–λ2 T}} {λ2} $$,

$$ b = \frac {1 − e^{–λ1 T}} {λ1} $$,

By variation of T the curves of variation of activity for any time of exposure can be accurately deduced from the equation, when the values of the two constants λ₁, λ₂ are substituted. Miss Brooks has examined the decay curves of excited activity for thorium for different times of exposure and has observed a substantial agreement between experiment and theory.

The results are shown graphically in Fig. 78. The maximum value of the activity is, for each time of exposure, taken as 100. The theoretical and observed values are shown in the Figure.

=208. Analysis of the decay and recovery curves of Th X.= The peculiarities of the initial portions of the decay and recovery curves of Th X and thorium respectively (Curves A and B, Fig. 47, p. 221), will now be considered. It was shown that when the Th X was removed from the thorium by precipitation with ammonia, the radiation increased about 15 per cent. during the first day, passed through a maximum, and then fell off according to an exponential law, decreasing to half value in four days. At the same time the activity of the separated hydroxide decreased for the first day, passed through a minimum, and then slowly increased again, rising to its original value after the lapse of about one month.

When a thorium compound is in a state of radio-active equilibrium, the series of changes in which Th X, the emanation, and thorium A and B are produced, go on simultaneously. Since a state of equilibrium has been reached for each of these products, the amount of each product changing in unit time is equal to the amount of that product supplied from the preceding change in unit time. Now the matter Th X is soluble in ammonia, while thorium A and B are not. The Th X is thus removed from the thorium by precipitation with ammonia, but A and B are left behind with the thorium. Since the active deposit is produced from the emanation, which in turn arises from Th X, on the removal of the parent matter Th X, the radiation due to this active deposit will decay, since the rate of production of fresh matter no longer balances its own rate of change. Disregarding the initial irregularity in the decay curve of the active deposit, its activity will have decayed to half value in about 11 hours, and to one quarter value at the end of 22 hours. As soon, however, as the Th X has been separated, new Th X is produced in the thorium compound. The activity of this new Th X is not, however, sufficient to compensate at first for the loss of activity due to the change in the active deposit, so that, as a whole, the activity will at first decrease, then pass through a minimum, then increase again.

The correctness of this point of view has been tested by Rutherford and Soddy as follows: If the precipitated thorium hydroxide after the removal of Th X is put through a series of precipitations with ammonia at short intervals, the Th X is removed almost as fast as it is formed, and, at the same time, the activity of thorium B in the thorium decays.

The following table indicates the results obtained. A portion of the precipitated hydroxide was removed after each series of precipitations and its activity tested in the usual way.

Activity of hydroxide per cent.

After 1 precipitation 46

After 3 precipitations at 39 intervals of 24 hours

After 3 more precipitations at 22 intervals of 24 hours and 3 at intervals of 8 hours

After 3 more each of 8 hours 24

After 6 more each of 4 hours 25

The differences in the last three numbers are not significant, for it is difficult to make accurate comparisons of the activity of thorium compounds which have been precipitated under slightly different conditions. It is thus seen that as a result of successive precipitations, the activity is reduced to a minimum of about 25 per cent. The recovery curve of the activity of this 23 times precipitated hydroxide is shown in Fig. 79. The initial drop in the curve is quite absent, and the curve, starting from the minimum, is practically identical with the curve shown in Fig. 48, which gives the recovery curve of thorium hydroxide after the first two days. This residual activity—about 25 per cent. of the maximum—is non-separable from the thorium by any chemical process that has been tried.

The initial rise of activity of Th X, after it has been separated, will now be considered. In all cases it was found that the activity of the separated Th X had increased about 15 per cent. at the end of 24 hours, and then steadily decayed, falling to half value in about four days.

This peculiarity of the Th X curve follows, of necessity, from the considerations already advanced to explain the drop in the recovery curve. As soon as the Th X is separated, it at once produces from itself the emanation, and this in turn produces thorium A and B. The activity due to B at first more than compensates for the decay of activity of the Th X itself. The total activity thus increases to a maximum, and then slowly decays to zero according to an exponential law with the time. The curve expressing the variation of the activity of the separated Th X with time can be deduced from the theory of successive changes already considered in chapter IX. In the present case there are four successive changes occurring at the same time, viz. the change of Th X into the emanation, of the emanation into thorium A, of A into B, and of B into an inactive product. Since, however, the change of the emanation into thorium A (about half changed in one minute) is far more rapid than the changes occurring in Th X or thorium A and B, for the purposes of calculation it may be assumed without serious error that the Th X changes at once into the active deposit. The 55 minute change will also be disregarded for the same reason.

Let λ₁ and λ₂ be the constants of decay of activity of Th X and of thorium A respectively. Since the activity of Th X and of thorium A falls to half value in 4 days and 11 hours respectively, the value of λ₁ = ·0072 and of λ₂ = ·063, where 1 hour is taken as the unit of time.

The problem reduces to the following: Given the matter A (thorium X) all of one kind, which changes into B (thorium B), find the activity of A and B together at any subsequent time. This corresponds to Case I. (section 197). The amount Q of B at any time T is given by

$$ Q = \frac {λ1 n₀} {λ1 − λ2} (e^{–λ2 t} - e^{–λ_1 t}) $$,

and the activity I at any time of the two together is proportional to λ₁P + Kλ₂Q, where K is the ratio of the ionization of B compared with that of A.

Then

$$ \frac {It} {I₀} = \frac {λ1 P + Kλ2 Q} {λ1 n₀} $$

$$ = e^{–λ1 t} (1 + \frac {Kλ2} {λ2 − λ1} (1 − e^{-(λ2 − λ1) t})) $$,

where I₀ is the initial activity due to n₀ particles of Th X.

By comparison of this equation with the curve of variation of the activity of Th X with time, shown in Fig. 47, it is found that K is almost ·44. It must be remembered that the activity of the emanation and Th X are included together, so that the activity of thorium B is about half of the activity of the two preceding products.

The calculated values of I{t}/I₀ for different values of t_ are shown in the second column of the following table, and the observed values in the third column.

Time Theoretical Observed value value

0 1·00 1·00

·25 days 1·09 —

·5 „ 1·16 —

1 „ 1·15 1·17

1·5 „ 1·11 —

2 „ 1·04 —

3 „ ·875 ·88

4 „ ·75 ·72

6 „ ·53 ·53

9 „ ·315 ·295

13 „ ·157 ·152

The theoretical and observed values thus agree within the limit of error in the measurements. The theoretical curve is shown in Curve A, Fig. 80 (with the observed points marked, for comparison). The curve B shows the theoretical curve of the decay of the activity of Th X and the emanation, supposing there is no further change into the active deposit. Curve C shows the difference curve between the curves A and B, i.e. the proportion of the activity at different times due to the active deposit. The activity due to the latter thus rises to a maximum about two days after removal of the Th X, and then decays with the time at the same rate as the Th X itself, i.e. the activity falls to half value every four days. When t exceeds four days, the term

$$ e^{-(λ2 − λ1) t} $$

in the theoretical equation is very small.

The equation of decay after this time is therefore expressed by

$$ \frac {It} {I₀} = (1 + \frac {Kλ2} {λ2 − λ1}) e^{–λ_1 t} $$,

i.e. the activity decays according to an exponential law with the time.

=209. Radiations from Thorium products.= It has been shown in the last section that the activity of thorium, by successive precipitations with ammonia, is reduced to a limiting value of almost 25 per cent. of the initial activity. This “non-separable activity” consists of α rays, the β and γ rays being altogether absent. According to the disintegration theory, this is an expression of the fact that the initial break-up of the thorium atom is accompanied only by the expulsion of α particles. We have seen in section 156 that the thorium emanation also gives out only α rays. In the active deposit, thorium A gives out no rays, while thorium B emits all three types of rays.

Some hours after separation, Th X gives out α, β, and γ rays, but the appearance of β and γ rays is probably due to the thorium B associated with it. The β and γ ray activity of Th X is much reduced if a current of air is continuously aspirated through a solution of Th X to remove the emanation. It seems likely that if the emanation could be removed as fast as it was formed, so as to prevent the formation of thorium B in its mass, Th X itself would give out only α rays: but, on account of the rapid rate of change of the thorium emanation, it is difficult to realize this experimentally.

=210. Transformation products of Thorium.= The transformation products of thorium and the rays emitted by them are graphically shown below (Fig. 81).

A table of the transformation products of thorium is shown below, with some of their physical and chemical properties.

Product Time to be λ (sec)⁻¹ Radiations Physical and half chemical transformed properties

Thorium α rays Insoluble in ammonia

Th. X 4 days 2·00 × α rays Soluble in 10⁻⁶ ammonia

Emanation 54 secs. 1·28 × α rays Inert gas, 10⁻² condenses −120° C.

Thorium A 11 hours 1·75 × no rays Soluble in 10⁻⁵ strong acids. Volatile at a white heat. B can be separated from A by electrolysis and by difference of volatility.

Thorium B 55 mins. 2·1 × α, β, γ rays Same 10⁻⁴

? — — — -

=211. Transformation products of Actinium.= It has previously been pointed out (sections 17 and 18) that the actinium of Debierne and the emanium of Giesel contain the same radio-active constituent. Both give out a short-lived emanation which imparts activity to the surface of bodies. Recently, thanks to Dr Giesel of Braunschweig, preparations of “emanium” have been placed on the market, and most of the investigations that are described later have been made with this substance.

Actinium X. Actinium and thorium are very closely allied in radio-active properties. Both emit an emanation which is rapidly transformed, but the rate of change of the actinium emanation is still more rapid than that of thorium, the activity decreasing to half value in 3·7 seconds. Miss Brooks has analysed the active deposit from the emanation of actinium, and has shown that two successive changes occur in it, very similar in character to those observed in the active deposit of thorium. It thus seemed probable, from analogy, that an intermediate product, corresponding to Th X in thorium, would be found in actinium. Recent work has verified this supposition. Giesel and Godlewski independently observed that a very active substance could be separated from “emanium,” very similar in chemical and physical properties to Th X in thorium. This product will, from analogy, be called “actinium X.” The same method, which was used by Rutherford and Soddy to separate Th X from thorium, is also effective in separating actinium X from actinium. After precipitation of the active solution with ammonia, actinium X is left behind in the filtrate. After evaporation and ignition, a very active residue remains. At the same time, the precipitated actinium loses a large proportion of its activity.

Giesel observed the separation of an active product, using a fluorescent screen to detect the radiations. A very complete examination of the product actinium X has been made by Godlewski in the laboratory of the writer.

After separation of actinium X, the activity, whether measured by the α or β rays, increases about 15 per cent. during the first day, and afterwards decays exponentially with the time, falling to half value in 10·2 days. The activity of the separated actinium was small at first but steadily increased with the time, reaching a practical maximum after an interval of sixty days. After the first day, the decay and recovery curves of activity are complementary to one another. The curves of rise and decay are shown graphically in Fig. 82, curves I and II respectively.

Godlewski observed that a solution of actinium, freed from actinium X, gave out very little emanation, while a solution of actinium X gave off the emanation in large quantity. The amount of emanation from the solution was measured by observing the activity produced in a testing vessel, similar to that shown in Fig. 51, when a constant current of air was passed through the solution. The emanating power of actinium X decreased exponentially with the time at the same rate as that at which the actinium X lost its activity. At the same time the actinium solution increased in emanating power, reaching its original value after about 60 days. The behaviour of actinium and thorium is thus quite analogous, and the explanation advanced to explain the decay and recovery curves of thorium applies equally well to the corresponding curves of actinium.

The actinium X is produced at a constant rate from the parent matter actinium, and is transformed according to an exponential law with the time. The constant of change λ = ·068 (day)⁻¹, and this value is characteristic of the product actinium X. As in the case of thorium, the above experiments show that the emanation does not arise from actinium itself but from actinium X. The emanation in turn breaks up and gives rise to an active deposit on the surface of bodies.

=212. Analysis of the active deposit from the emanation.= Debierne observed that the excited activity produced by actinium decayed to half value in about 41 minutes. Miss Brooks showed that the curves of decay of the excited activity after removal depended upon the duration of exposure to the emanation. The curves for different times of exposure have already been shown in Fig. 69.

Bronson, using the direct deflection method described in section 69, accurately determined the activity curve corresponding to a short exposure to the actinium emanation. The curve obtained is shown in Fig. 83.

This curve is similar in shape to the corresponding curve obtained for the active deposit from thorium, and is explained in a similar way. The activity I{t} at any time t_ is given by

$$ \frac {It} {IT} = \frac {e^{–λ2 t} − e^{–λ1 t}} {e^{–λ2 T} − e^{–λ1 T}} $$,

where λ₁ and λ₂ are two constants, and I{T} the maximum activity reached after an interval T. After 20 minutes the activity decreased exponentially with the time, falling to half value in 35·7 minutes. This gives the value λ₁ = ·0194 (min.)⁻¹. By comparison with the curve, the value of λ₂ was found to be ·317 (min.)⁻¹. This corresponds to a change in which half the matter is transformed in 2·15 minutes. Exactly as in the analogous curve for thorium, it can be shown that the matter initially deposited undergoes two changes, the first of which is a rayless one. The same difficulty arises in fixing which of the values of λ refers to the first change. An experiment made by Miss Brooks (loc. cit._) shows that the rayless product has the slower period of transformation. The active deposit of actinium was dissolved off a platinum wire and then electrolysed. The anode was found to be active, and the activity fell off exponentially with the time, decreasing to half value in about 1·5 minutes. Allowing for the difficulty of accurately measuring such a rapid rate of decay, this result indicates that the product which gives out rays has the rapid period of 2·15 minutes. The analysis of the active deposit of actinium thus leads to the following conclusions:

(1) The matter initially deposited from the emanation, called actinium A, does not give out rays, and is half transformed in 35·7 minutes.

(2) A changes into B, which is half transformed in 2·15 minutes, and gives out both α and β (and probably γ) rays.

Godlewski found that the active deposit of actinium was very easily volatilized. Heating for several minutes at a temperature of 100° C. was sufficient to drive off most of the active matter. The active deposit is readily soluble in ammonia and in strong acids.

=213. Radiations from actinium and its products.= Actinium in radio-active equilibrium gives out α, β, and γ rays. Godlewski found several points of distinction between the β and γ rays of actinium and of radium. The β rays of actinium appear to be homogeneous, for the activity measured by an electroscope was found to fall off accurately according to an exponential law with the thickness of matter traversed. The β rays were half absorbed in a thickness of 0·21 mm. of aluminium. This indicates that the β particles are all projected from actinium with the same velocity. In this respect actinium behaves very differently from radium, for the latter gives out β particles whose velocities vary over a wide range.

After the β rays were absorbed, another type of more penetrating rays was observed, which probably corresponds to the γ rays from the other radio-elements. The γ rays of actinium were, however, far less penetrating than those from radium. The activity due to these rays was reduced to one-half after passing through 1·9 mms. of lead, while the thickness of lead required in order to absorb half the γ rays of radium is about 9 mms.

The active deposit gave out α and β (and probably γ) rays. It was difficult to decide definitely whether actinium X gave out β as well as α rays. When the actinium X was heated to a red heat, the β activity was temporarily reduced to about half its initial value. This decrease was probably due to the removal of the active deposit, which, we have seen, is readily volatilized by heat. If the β ray activity cannot be further reduced, this would point to the conclusion that actinium X, as well as actinium B, gives out β rays, but the evidence so far obtained is not conclusive.

The ease with which the active deposit is volatilized by heat offers a very simple explanation of the initial peculiarities of the decay and recovery curves (Fig. 82) of actinium X. The activity of actinium X rises at first, but there is no corresponding decrease in the activity of the actinium left behind. It has been shown that the active deposit is soluble in ammonia, and, in consequence, is removed with the actinium X. The products actinium A and B and actinium X, immediately after separation, are in radio-active equilibrium and we should not therefore expect to find any increase of activity after removal, such as is observed in the case of thorium, where thorium A and B are not removed with thorium X. However, in heating the actinium X to drive off the ammonium salts, some of the active deposit is volatilized. After cooling, the amount of the active deposit increases to nearly its old value and there is a corresponding increase of the activity.

=214. Products of Actinium.= There is one very interesting point of distinction between the radio-active behaviour of thorium and actinium. The latter after removal of actinium X, shows only about 5 per cent. of the original activity, while thorium, after removal of Th X, always shows a residual activity of about 25 per cent. of the maximum value. This very small residual activity indicates that actinium, if completely freed from all its products, would not give out rays at all, in other words, the first change in actinium is a rayless one.

The radio-active products of actinium are shown graphically in Fig. 84. Some of their chemical and physical properties are tabulated below.

Products Time to be Rays Some Physical and half Chemical properties transformed

Actinium ? No rays Insoluble in ammonia

Actinium X 10·2 days α, (β and γ) Soluble in ammonia

Emanation 3·9 secs. α rays Behaves as a gas

Actinium A 35·7 mins. No rays Soluble in ammonia and strong acids.

Actinium B 2·15 mins. α, β and γ Volatilized at 100°C. B can be separated from A by electrolysis

Footnote 296:

Soddy, Trans. Chem. Soc. 81, p. 460, 1902.

Footnote 297:

Rutherford and Grier, Phil. Mag. Sept. 1902.

Footnote 298:

Becquerel, C. R. 131, p. 137, 1900.

Footnote 299:

Meyer and Schweidler, Wien Ber. Dec. 1, 1904.

Footnote 300:

Meyer and Schweidler, Wien Ber. 113, July, 1904.

Footnote 301:

Rutherford, Phil. Trans. A. 204, pp. 169–219, 1904.

Footnote 302:

Pegram, Phys. Rev. p. 424, December, 1903.

Footnote 303:

Miss Slater, Phil. Mag. 1905.

Footnote 304:

von Lerch, Ann. de d.] Phys. November, 1903.

Footnote 305:

The ‘rayless change’ certainly does not give out α rays, and special experiments showed that no appreciable amount of β rays were present. On the other hand, the second change gives out all three types of rays.

Footnote 306:

Miss Brooks, Phil. Mag. Sept. 1904.

Footnote 307:

Rutherford and Soddy, Trans. Chem. Soc. 81, p. 837, 1902. Phil. Mag. Nov. 1902.

Footnote 308:

Miss Brooks, Phil. Mag. Sept. 1904.

Footnote 309:

Rutherford, Phil. Trans. A. p. 169, 1904.

Footnote 310:

Giesel, Ber. d. D. Chem. Ges. p. 775, 1905.

Footnote 311:

Godlewski, Nature, p. 294, Jan. 19, 1905.

Footnote 312:

Debierne, C. R. 138, p. 411, 1904.

Footnote 313:

Miss Brooks, Phil. Mag. Sept. 1904.