V. S. Titov.

RADIOACTIVE EMANATION

IN THE WATERS AND GASES OF THE THERMAL SPRINGS

OF THE VILLAGE OF NOVAYA BELOKURIKHA

IN ALTAI

Tomsk.

Type-lithography of the Siberian Association of Printing Business, corner of Dvoryanskaya St. and Yamsk. Lane, own building.

1913.

Printed by order of the Director of the Tomsk Technological Institute,
Emperor Nicholas II.

Radioactive Emanation in the Waters and Gases of the Thermal Springs of the Village of Novaya Belokurikha in Altai

CONTENTS

Radioactive Emanation in the Waters and Gases of the Thermal Springs of the Village of Novaya Belokurikha in Altai

V. S. Titov.

The village of Novaya Belokurikha is situated at the northern spurs of the Tomsk Altai, 63 versts from the town of Biisk, at \(54{.}9^\circ\) E. from Pulkovo and \(52{.}6^\circ\) N, at an elevation of 251 meters above sea level, in a locality where the steppe sharply changes into mountains—by a small river of the same name as the village.

Above the village the little river appears as a rapid stream, flowing through a narrow valley often obstructed by enormous boulders. But at the village itself the river cuts through the last ridge of hills and at once loses its mountainous character. At this place, on the right bank, there are two wells with wooden casings, into which warm water collects. One of the wells is under a wooden shed, and the other under the open sky. The first has about 4 square arshins of cross-section and is about 1 sazhen deep, so that its bottom is scarcely lower than the bottom of the river flowing nearby; the other is about \(2\frac{1}{2}\) square arshins in cross-section and up to \(\frac{1}{2}\) arshin deep. The bottom of this second well is very clogged, and from the well there is sometimes a faint smell of hydrogen sulfide. Both wells adjoin closely a small wooden building, where baths are prepared for patients arriving here. In what follows, we shall call the larger well well No. 1, and the smaller—well No. 2.

Along the very bank of the little river (the right one), downstream from the wells for 50 paces, one can everywhere find warm water seeping through a layer of clay and gravel. In addition, outlets of warm water can be established at several points on the bottom of the river opposite the wells and below; at these points the water at the bottom is warm, and the release of gas bubbles is noticeable, as it is from the bottom of both wells.

I have repeatedly had occasion to collect these gases rising from the bottom of the wells, and I can report that from one square meter of the water surface in the well, on average, in 1 hour one can collect up to 110 liters of gas present at atmospheric pressure.

The portions of gases which I collected never smelled of hydrogen sulfide, and in general had no odor. They exerted no noticeable action on metals. The chemical nature of these gases has been investigated by absolutely no one. Nevertheless, one may think that these gases consist chiefly of carbon dioxide.

According to my observations, the water of well No. 1 always had a temperature of 31.6° C, while in the second well the temperature fluctuated from 31.4° C to 31.6° C. The water from well No. 1 is pleasant to the taste and is constantly used for drinking and for preparing food. From this alone one may conclude how insignificant the quantity of mineral substances dissolved in it must be. On this matter Prof. Lemann (“Scientific Sketch of the Tomsk Region,” Tomsk, 1898) reports the following: “The only more or less detailed analysis acquainting us with the chemical composition of the Belokurikha springs was made back in 1869. According to the data of this analysis, the water has a specific gravity of 1.0012, a weakly alkaline reaction, and contains 0.033% of solid salts.” Taking into consideration so insignificant a content of mineral salts, Prof. Lemann ranks the Belokurikha springs “among the completely indifferent thermal springs.”

Nevertheless, the Belokurikha waters enjoy, among the population of Tomsk Province—especially in the Barnaul and Biisk districts—a reputation as healing waters, and during June and July up to 100 baths a day are given to visiting patients at these waters.

I had the opportunity to study the waters and gases of the Belokurikha thermal springs for their content of radioactive emanations during July 1907 and from June 14 to July 13, 1908. In organizing my first trip to Belokurikha, Prof. A. I. Efimov rendered me substantial assistance. I consider it my duty to express here my deep gratitude to him. In 1908 the Council of the Tomsk Technological Institute honored me with a travel assignment to investigate the radioactivity of certain Altai thermal springs and granted me 300 rubles for this purpose. This gave me the opportunity, in addition to investigations in the village of Novaya Belokurikha, to carry out corresponding observations on the waters and gases of the Rakhmanov springs in the Arasan Valley (I defer the description of the results of these latter observations to a more convenient time). I permit myself to offer here my deep gratitude to the Council of the Tomsk Technological Institute. On both of my trips to the village of Novaya Belokurikha I was accompanied by the student V. P. Markov. He was interested in the work no less than I myself, and rendered me numerous services in organizing and conducting the observations, not only in the village of Novaya Belokurikha but also in Tomsk. I consider it my pleasant duty here as well to express to V. P. Markov my deep gratitude.

Chapter I.

Decay of the radioactive emanation contained in the waters and gases of the thermal springs of the village of N. Belokurikha.

§ 1. Ionization of the air produced by water from well No. 1, and changes in this ionization with time.

Wishing to know to what extent the waters of the Belokurikha springs are capable of making electrically conductive the air blown through them, I employed the method first proposed by Himstedt (Ann. d. Physik, Bd. 12, 1903, p. 107 and Bd. 13, 1904, p. 573), of circulating, through the water under investigation, air enclosed within a certain closed circuit. I carried out this method in a manner close to that in which it is described by H. Mache (Wiener Berichte, Bd. 113, 1904, p. 1329 and Bd. 114, 1905, Hefte III, IV, V) and very close to the way this method is described by Prof. A. P. Sokolov in his article “Radioactivity of certain Russian mineral waters, muds, and soils” (Journal of the Russian Physico-Chemical Society, physical section, vol. 37, 1905, p. 101). My closed circuit consisted of the well-known Elster–Geitel bell with an electroscope and discharger (from the firm Günter-Tegetmeyer; this apparatus is described by Elster and Geitel in Phys. Zeitschr., 1904, p. 321 and Zeitschrift f. Instrumentenkunde, 24, 1904, p. 193), a rubber pump bulb, a glass bottle of capacity 8.4 liters, a Drechsel bottle with beads and sulfuric acid, a tower with calcium chloride, a glass tube with clean cotton wool, and, finally, again the bell. The capacity of the bell was 8.555 liters, with a height of 35 centimeters and a diameter of 17.5 centimeters. The dimensions of the pump bulb were such that after 120 strokes of the pump all the air in the circuit could make one circulation. In what follows we shall call the leakage current the quantity

\[ \frac{\Delta v \times \text{capacity of the electroscope}}{\Delta t}, \]

where \(\Delta v\) is the change in potential of the charged electroscope during the time \(\Delta t\). If the circulation in the circuit was carried out in the absence of the water or gas under investigation, then the leakage current observed after circulation we shall call the natural leakage current and denote by \(i_N\). If, however, the circulation of air took place through the water or gas under investigation, then the leakage current observed after circulation we shall call the total leakage current and denote by \(i\). We shall further take the capacity of our electroscope, when it stands under the bell connected to earth, as a special unit of capacity, and one hour as the unit of time. Under these conditions, the natural leakage current in my experiments in Belokurikha in the summer of 1907,

fluctuated within the limits \(3.9—3.4 \dfrac{\text{volt}\times\text{capacity}}{\text{hour}}\), while the saturation current exceeded these limits many times over. Here, for example, is the observation of July 4.

At \(2^{h}40^{m}p\), circulation of air in the circuit was begun through 6.09 liters of water, just taken from well No. 1. (The place of observation was 100 paces from the well.) The circulation continued for 23 minutes, after which the bell was isolated from the rest of the circuit, and observation of the saturation current was begun. With the aid of a stopwatch, the time of fall of the right leaf of the electroscope from the 16th to the 9th division of the scale was observed, which approximately corresponds to a fall of potential of 62.2 volts.

The following Table I presents several data from this observation of the saturation current. From this table it is seen that, 25 min. after the start of circulation, the saturation current exceeds the natural leakage current by a factor of 883; that the magnitude \(i\) increases, reaching a maximum approximately \(2\frac{1}{2}\) hours after the start of circulation, and then slowly falls. The ratio \(i/i_{N}\) at the maximum is equal to 1237. The maximum increase of \(i\) amounts to 40% of that value of \(i\) which occurred immediately after the end of circulation.

Table I.

The very same picture was repeated in another experiment carried out by me (begun on July 8) with the circulation of air through a new portion of water from well No. 1. The current \(i\), of correspondingly the same magnitude as in the first experiment, during the first hours after the circulation (this time during 3 hours) increased to a maximum (this time to 46% of its initial value), in order then to fall slowly. Such results from my two experiments on measuring the current \(i\) in air passed through water from well No. 1 make probable the supposition that the water under investigation contains in solution a radioactive gas similar to, and perhaps identical with, radium emanation; that this gas, in a closed circuit containing water and air, is distributed between the water and the air up to a certain stationary state in accordance with the laws of Dalton and Henry, exactly as has been proved for true radium emanation by Himstedt and R. v. Traubenberg (Phys. Zeitschr., 5, 1904, p. 210, and 6, 1905, p. 820). In view of such a supposition, the study of the change in the difference \(i-i_N\) as a function of time is of great interest. For this purpose I continued the observations, begun on July 8, through July 17 inclusive. The conditions under which these observations were made did not favor their accuracy. First, there was the danger that the tightness of the bell jar might have suffered from the jolting during transport of the apparatus; secondly, I could set up my bell jar for observations only at a window, and moreover one facing south, and therefore, although the window, insofar as was possible in the living quarters, was kept closed, the instrument was heated by the sun’s rays. Such heating could intensify the leakage of gases from under the bell jar. Indeed, until July 14 I observed that during the day the decrease of the discharge current took place noticeably faster than during the night; but from July 14 on this phenomenon appeared much less sharply. Precisely from July 14 the weather became, and for a long time remained, overcast, whereas before the 14th there had been clear sunny days. There was yet another circumstance which could complicate the elucidation of the connection between \(i-i_N\) and \(t\). The fact is that only from July 13 did the current \(i\) weaken so much that it became the “saturation current.” (I am convinced of this by comparing my observations with the observations of Prof. A. P. Sokolov on the decay of the electrical conductivity of gas from the source “Narzan” in Table I of his article “The Radioactivity of Certain Russian Mineral Waters, Muds, and Soils,” p. 1. The bell jar and electrometer used by Prof. A. P. Sokolov were almost identical with mine), and the connection between \(i-i_N\) and \(t\), of course, will vary depending on the change in the conditions of formation of the current \(i\). Therefore, in what follows I consider only those measurements of the current \(i\) which were made after 7 o’clock in the evening on July 13.

As was already said above, the time of fall of the right leaf of the electroscope from 16 to 9 divisions of the scale was observed with the aid of a stopwatch; moreover, each time three determinations of this time were made, one after another. The decay of the electrical conductivity proceeded comparatively so slowly, and the three successive measurements took place so quickly, that during this time the decay of the electrical conductivity, of course, could not in any way be noticed. From the three successive measurements of the time of fall of the leaf from 16 to 9 divisions, the mean was taken and referred to the mean instant between the beginning of the first observation and the end of the third. With the aid of the mean value thus obtained for the time of fall of the leaf, the current of discharge \(i\) was calculated for the mean instant; moreover, the electrostatic capacity of the electroscope under the conditions of the experiment was taken as 1; \(\Delta v\), the diminution of potential corresponding to the above-mentioned fall of the leaf, was taken as equal to 21991 certain units of potential, and the time was expressed in seconds. The difference \(i-i_N\) we shall henceforth denote by \(J_t\), where \(t\) denotes the instant to which the current \(i\) refers. The complex \((J_t,t)\) we shall call an “observed point.” We have at our disposal 17 observed points, where \(i_N\), in the above-mentioned units of potential, will be represented by the number 0.3, the first value of the current \(i\) by the number 143.6, and the last (17th) by the number 62.9. Since, in determining \(i\), the greatest possible error may reach 5% of the measured quantity, it is clear that the quantity \(i_N\) in our case is lost in the errors of observation, and it may quite well be neglected. From the 17 observed points I formed 11 pairs \((1\text{—}7,\,2\text{—}8,\,3\text{—}9,\,4\text{—}10,\,5\text{—}11,\,6\text{—}12,\,7\text{—}13,\,8\text{—}14,\,9\text{—}15,\,10\text{—}16,\,11\text{—}17)\) and for each pair, respectively, from the equality

\[ J_{t'}=J_t e^{-\lambda(t'-t)} \]

we calculate the quantity \(\lg(e^{-\lambda})\). The results of these calculations proved to be the following:

\[ \begin{array}{ccc} -0.00414 & -0.00382 & -0.00432\\ 450 & 401 & 378\\ 406 & 393 & 375,\\ 411 & 374 & \end{array} \]

whence the mean will be \(-0.00401\). The greatest deviation of the separate values of \(\lg(e^{-\lambda})\) from the mean is 12%. But if, in determining the quantity \(J_t\), the greatest possible error can reach 5%, then by the formula

\[ \frac{10\% \cdot \lg e}{\lg\left(\dfrac{J_{t'}}{J_t}\right)}, \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (1) \]

representing the greatest possible error for \(lg(e^{-\lambda})\); such an error may reach an excess of \(20\%\). Hence it follows that all 11 values of \(log(e^{-\lambda})\) may be regarded as differing from one another only owing to random errors of observation, and that for each pair of observed points \(lg(e^{-\lambda})\) there is a constant quantity equal to

\[ -0.00401 + 0.00005, \]

where \(+0.00005\) represents the probable error of the mean result of computing \(lg(e^{-\lambda})\). But in that case, for every point observed by us, the following relation is valid, within the limits of the errors of observation:

\[ J_t : e^{-\lambda} = \mathrm{constans}, \]

where \(\lambda\), computed from the condition \(lg(e^{-\lambda})=-0.00401\), will be equal to \(0.00923\ \frac{1}{\text{hour}}\). Taking as the origin of time the moment at which circulation began, and denoting the above-derived constant (constans) by \(J_0\), we then obtain the equality

\[ J_t = J_0 e^{-\lambda t}\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \tag{2} \]

The quantity \(J_0\) can be found from any one of our “points of observation.” I computed \(J_0\) from each of these points, took the mean, and obtained the number \(466.6\). Taking \(J_t\) and \(t\) as variables, we may regard equality (2) as the equation of a certain curve. All the points observed by us will deviate from this curve only as a consequence of errors of observation. In order to present more clearly all the deviations of the observed points from the curve with equation (2) and with the constants \(\lambda\) and \(J_0\) found above, I computed, from equality (2), \(J_{120}, J_{130}, \ldots, J_{220}\), plotted 11 points on a diagram, laying off time in hours along the axis of abscissas and the quantities \(J_{120}\), etc., along the axis of ordinates, and through these points drew the curve. From this curve I determined 17 ordinates for all those \(t\) for which there are “observed points.” The quantities \(J_t\) obtained in this way I compared with those actually found.

The results of such a comparison are contained in the following Table II, and Diagram 1 shows the curve

\[ J_t = 466.6\, e^{-0.00923\,t} \]

and all the “observed points.”

Diagram 1.

Horizontal axis: hours.

Table II.

Thus, the quantities $J_t$ observed by us, in their changes with time, undoubtedly follow the simple exponential law, as every simple radioactive transformation should, as does the corresponding change in the electrical conductivity of the gas that absorbs those radiations which accompany radioactive transformation. In this way, beyond any doubt, beneath our bell jar we have a radioactive gas, and one close in its properties to the emanation of radium. Indeed, for our case the quantity $\theta$, determined by the equality $\theta=\dfrac{ln\,2}{\lambda}$ and representing the time during which $J_t$ decreases to $1/2$ of its value, proves to be equal to 3.13 days (from $\lambda=0.00923\,\dfrac{1}{\text{hour}}$), whereas for radium emanation the most probable value for $\theta$ is considered to be the value found by Rümelin (Phys. Zeitschr., 8, 1907, p. 803), equal to 3.75 days (with $\lambda=0.00788$). Since there can be no doubt that, from our bell jar, during the prolonged observation of the currents, the radioactive gas could have escaped outward, it must be assumed that the number we obtained for $\lambda$ exceeds the true value of $\lambda$, while the number found for $\theta$ is less than the true one. The fact is that a slow leakage of radioactive gas, provided only that the conditions of leakage do not change, does not mask the exponential law of decay of activity, but only increases $\lambda$, correspondingly decreasing $\theta$. Such a property of small leaks of radioactive gases was established, for example, by Prof. A. P. Sokolov, who observed the decay of the activity of gas from the “Narzan” spring, and it becomes entirely understandable if one admits,

that the quantity of radioactive gas escaping in the time element \(\Delta t\) is proportional to \(\Delta t\) and to the quantity of all the gas present at the moment \(t\) in our reservoir. Thus there arises the supposition that the radioactive gas which can be extracted from the water we are investigating is radium emanation, the same radioactive gas that was discovered by Dorn and studied by P. Curie, Rutherford, Soddy, and others. To verify this supposition it would have been necessary to observe the decay of true radium emanation with the same instrument and under the same conditions under which the observations of changes in \(i\) with time were made. But since I did not have radium salts at hand, I decided to carry out the above-mentioned comparison with radium emanation after returning to Tomsk, bringing there a portion of water from well No. 1. This water proved to be so “strong” in its content of radioactive emanation that the points \(i\) produced by this emanation could conveniently be observed even 10–14 days after taking the portion of water from well No. 1.

§ 2. Ionization in the gas collected over well No. 2, and the change of this ionization with time.

Wishing to know how sharply expressed were the radioactive properties of the gases rising from the bottom of wells No. 1 and No. 2, we (V. P. Markov and I) collected under water, in a wooden bucket, the gas given off over well No. 2, in an amount of approximately 16 liters, and then, through driers and a tube with clean cotton wool, drew this gas under our bell, which had been carefully brought for this purpose to well No. 2. We began to draw the gas under the bell at \(4^{h}45^{m}p\) (July 19), and at \(5^{h}35^{m}p\) we were already at the place of our regular work and began observations of the discharge current, observing with the aid of a stopwatch the time of fall of the right leaf of the electroscope from 16 to 9 divisions of the scale. These observations continued for more than 8 days (until July 28); below, in Table III, several of the first observations are given.

Table III.

From this table it is evident that the first observation gives, for \(i\), a value 11975 times greater than the current of natural dissipation \((i_N=3.4)\), while the maximum dissipation current, observed approximately \(2\frac{1}{2}\) hours later, exceeds \(i_N\) by 14970 times. Thus we have an increase of the dissipation current up to a certain maximum, occurring approximately \(3\frac{1}{2}\) hours from the start of suction and exceeding the initially measured current \(i\) by 25% of its value—and then a slow fall. Studying this slow fall, I established, from VII. 21.—\(7^{h}50^{m}a\) to VII. 28.—\(7^{h}53^{m}a\), 40 points of observation \((J_t,t)\), in exactly the same way as I did this in the corresponding observations in air blown through water; only \(\Delta v\), the fall of potential corresponding to the fall of the leaf from division 16 to division 9, I estimated this time as 1000 arbitrary units of potential. But there is one essential difference in the conditions of observation of the attenuation of the currents \(i\) before—with water—and now—with gas: now, for all 40 “points of observation,” the currents \(i\) were far from saturation.

Strictly speaking, the matter was not so much one of saturation as of the fact that, during the whole series of observations, one and the same fraction \(\alpha\) of the ions present at the given moment was always expended for the formation of the current \(i\). In the case of a saturated current \(\alpha=1\); for an unsaturated one, \(\alpha<1\). Far from the point of saturation and over a certain interval of time, the quantity \(\alpha\), at constant initial potential \(v\) and constant \(\Delta v\), could change so insignificantly that this change could neither obscure the actual law of attenuation of the presumed radioactive emanation nor appreciably alter the constant \(\lambda\). This supposition, as will be seen below, proved to be correct. Forming from the 40 observed points 30 pairs \((1—11,\ 2—12,\ldots,\ 30—40)\) and calculating for each pair the corres-

respectively to the equality \(J_t' = J_t e^{-\lambda(t'-t)}\), I obtained, on the average, the value \(\log(e^{-\lambda})\),

\[ -0.003891 \pm 0.000044, \]

where the greatest deviation from the mean amounted to 18%, whereas the maximum possible, calculated by formula (1), was 30% too high. The value \(J_0\), calculated as the mean from all 40 observed points according to the equality

\[ J_t = J_0 e^{-\lambda t}, \]

proved to be equal to 206.8. In the following Table IV one may see how much the observed points depart from the curve

\[ J_t = 206.8 e^{-0.008959 t}, \]

which, together with all the observed points, is shown in diagram No. 2. Examining the table, we see that the maximum deviation of the calculated and observed values of \(J_t\) is 4.5%, whereas the errors in the determination of \(i\) could reach 5% and even 6%. Thus, the simple exponential law of decay of the quantities \(J_t\) is fully confirmed.

Table IV.

Diagram 2.

Already at the first glance at Diagram No. 2 one may notice that the observed points are arranged in separate clusters. Proceeding along the curve in the direction of increasing times, we pass through four clusters, each of 6 points; then two separate points, then again two clusters of 6 points each and, finally, one point. It turns out that each cluster corresponds to a particular day: the first cluster is the observations of July 21, then July 22, 23, and 24; on the 25th only two observations were made in all: one in the morning and one in the evening. Further on we have clusters for July 26 and 27, and one observation on July 28. All the clusters possess the following properties: the first points of each cluster are always situated above the curve, and moreover considerably higher than all the other points of the cluster. The second property, most sharply expressed in clusters 1, 4, and 5, consists in the fact that the first half of the cluster lies above the curve, and the second below. These properties of our clusters indicate that during the day the dying away of the discharge current proceeded more rapidly than during the night. Thus the clusters illustrate the phenomenon which, in the preceding paragraph on page 5, I noted in describing the observations on the decay current in the period from July 8 to 13 inclusive, when the weather was fine with sunny days. In the period from July 21 to 28 our bell jar stood in the same window as before, but during that time the weather was changeable, more often overcast, owing to which the phenomenon of the more rapid daytime than nighttime decay of the current \(i\), although noticeable quite definitely, was nevertheless less sharp than it had been in the period July 8–13.

§ 3. Comparison of the constants of decay of the ionization in air blown through water from well No. 1, and in gas collected over well No. 2.

Of great interest to us is the comparison of the constants \(\log(e^{-\lambda})\), \(\lambda\), and \(\theta\), obtained by us in studying the emanation contained in the water of well No. 1, and the emanation contained in the gas which we collected over well No. 2. The following Table V contains these constants for both cases. In the third horizontal line of the table it is shown to what extent the probable errors of the mean results permit the corresponding constants to be brought together.

Table V.

From this table it is evident that the differences of the corresponding constants, although very small, nevertheless all lie within the limits of the probable errors of the mean result; moreover, \(\theta\) for the emanation in the gas is greater than \(\theta\) for the emanation in the water. This circumstance, however, cannot at all testify to a difference in the nature of the one and the other emanation, since, in studying the decay of the emanation in the gas, we used unsaturated currents, as a result of which \(\theta\) must have turned out somewhat larger than it actually is, and \(\lambda\) smaller. Thus it must be considered that the emanation found by us in the water of well No. 1 and the emanation found in the gas collected over well No. 2 represent one and the same emanation.

§ 4. Comparison of the constants of decay of ionization in air blown through water from well No. 1 with the same constants for radium emanation.

On August 3, at 7 o’clock in the morning, a glass bottle of \(1/4\) vedro was filled with water from well No. 1, corked with a stopper and Mendeleev cement, and taken to Tomsk, where, beginning on August 13, I studied the change in the discharge currents under the Elster–Geitel bell jar after circulation of air in a closed circuit through the portion of water that had been brought. Previously all possible measures were taken to eliminate errors in the airtightness of the bell jar. The circuit was arranged in exactly the same way as in Belokurikha. The natural discharge before introducing the water under investigation into the circuit was such that the right leaf fell from 18 to 17 divisions of the scale in the course of 69 minutes. When all observations of the currents \(i\) had been completed and it was again possible to measure the natural discharge, it turned out that the leaf fell through the same interval in the course of 72 minutes. For the calculation of \(i_N\) I took the mean of 72 and 69. The room in which the circuit and the bell jar were set up was well protected from the sun’s rays and, in general, from all fluctuations of temperature. In exactly the same way as in Belokurikha, 32 observation points \((J_t, t)\) were established; only now it was no longer possible to neglect the current \(i_N\), since the observed fall of the leaf was not from 16 to 9, but from 18 to 17 divisions of the scale, and the corresponding fall of potential was estimated at 50,000 units of potential (in volts this is 8.1). The electrical capacitance of the charged system under the bell jar was, as before, taken equal to 1. Under these conditions \(i_N\) proved equal to 11.8; the first observed current \(i_1\) was represented by the number 268, the maximum observed (after \(4^{\mathrm h} 28^{\mathrm m}\) from the beginning of circulation) by the number 342.5, and the last observed, \(i_{32}\), by the number 81.2. All currents \(i\) were saturation currents. From the last 23 points \((J_t, t)\) I arbitrarily took 5 points (Nos. 10, 14, 18, 26, 28), formed from them all possible groups of combinations by 2, and for each group, according to the formula

\[ J_{t'} = J_t e^{-\lambda(t' - t)} \]

compute the value \(\log(e^{-\lambda})\). Ten results of these computations gave, on average,

\[ -0.003507 \pm 0.000041, \]

where \(\pm 0.000041\) is the probable error of the mean result. The greatest deviation from the mean result reached 15%, whereas the maximum possible error in computing \(\log(e^{-\lambda})\), if the possible maximum error in determining \(i\) is estimated at 5%, could reach even 40%. The constant \(J_0\), computed from the five above-mentioned points according to the equality

\[ J_t = J_0 e^{-\lambda t} \]

proved to be equal to 296 for \(\lambda\) equal to \(0.003075 \pm 0.000095\ \frac{1}{\text{hour}}\). In the following Table VI one can see how far the observed points depart from the curve

\[ J_t = 296 \cdot e^{-0.003075 t}, \]

which, together with all the observed points, is shown in Diagram No. 3.

Table VI.

V. O. Titov.

Diagram 3.

Examining the table, we see that for the last 23 points the difference between the observed and calculated \(J\) nowhere exceeds \(2.5\%\), and, consequently, the last 23 points fully follow the simple exponential law, whereas the first points do not follow such a law. Before discussing the causes of this latter circumstance, we shall compare the constants \(\lambda\) and \(\theta\) obtained by us with those for radium emanation. As was already noted earlier, the most probable values of these latter constants are considered to be those found by Rümelin (loc. cit.), \(\lambda = 0.00788 \frac{1}{\text{hour}}\) and \(\theta = 3.75\) days. Meanwhile, from the observation just described we obtained

\[ \theta = 3.58 \pm 0.04 \text{ days and } \lambda = 0.008075 \pm 0.000095 \ \frac{1}{\text{hour}}. \]

Assuming that the number 3.75 has been determined with the same probable error as the number 3.58, we arrive at the conclusion that the difference between the constants now found and the corresponding constants of Rümelin lies outside the limits of the probable errors of the mean result. The same follows when my constants are compared with the constants found for radium emanation by Rutherford ($\theta = 3.71$ days and $\lambda = 0.00779$). I do not know whether I can explain such a discrepancy by leakage from the bell jar of the emanation I studied, since I do not know whether I achieved, or did not achieve, complete tightness of the bell jar. But even if the question of tightness is decided in the affirmative, the deviation of my constants from the constants given for radium emanation by Rutherford and Rümelin does not yet speak against the supposition that the emanation I studied is precisely the emanation of radium, since, when the radioactive constant is determined by observations of the ionization caused in the atmosphere of a closed vessel by radiations $\alpha$, $\beta$, $\gamma$ that are very complex in composition, it is difficult, in place of an apparent value depending on the method of investigation and in particular on the vessel containing the radioactive body, to obtain the true value of the constant. Thus, the question occupying us can be resolved by comparing the constants found by us only with such values of the constants of radium emanation as were found with the same (or, better still, the very same) specimen of the bell jar of Elster and Geitel. Such measurements of the constants of radium emanation were made by R. Schenk (Richard Schenk, Radioactive Eigenschaften der Luft, des Bodens und des Wassers in und um Halle, Jahrbuch d. Radioaktivität, Bd. 2, 1905, p. 19), and he found for $\lambda$ the number $0.008072 \ \frac{1}{\text{hour}}$; this number fully coincides with that found by me. It was found by Schenk, as also by me, only after known efforts to eliminate errors in the tightness of the bell jar.

Thus it must be considered established that the emanation found in the water of spring No. 1, and consequently also the emanation found in the gas collected over spring No. 2, after the lapse of a known time from the beginning of the gradual penetration of these emanations under the bell jar, die away in it in exactly the same way and with the same constants as radium emanation after it has come into radioactive equilibrium with the products of its decay. Thus, the supposition of the identity of the emanation found by us and the emanation of radium is made still more probable. For the final clarification of the question of the nature of the emanations studied, I deemed it necessary to make observations of the phenomena of induced activity, making use for this purpose of my stay in the village of Belokurikha in the summer of 1908.

V. S. Titov.

Chapter II.

Radioactive induction produced by the emanation under investigation.

§ 1. Schmidt’s “normal” electroscope and the observed decay of the radioactive induction of radium emanation.

In 1905 H. W. Schmidt described (Phys. Zeitschr., 6, 1905, p. 561) an electroscope constructed by him with an aluminum leaf, with a discharge conductor enclosed in a chamber separate from the leaf, and with a microscope for reading the indications of the electroscope. This simple instrument (briefly described in Russian by Prof. Klossovsky in his Course of Meteorology), with proper selection of the leaf (the leaf must not give the Cri-Cri phenomenon, Ebert, Phys. Zeitschr., 6, p. 642) and proper graduation (see H. W. Schmidt, Phys. Zeitschr., 7, p. 157), and especially after K. Kurz (Phys. Zeitschr., 7, p. 375) provided the aluminum leaf with a quartz fiber, proves to be a very convenient electrometer and in this capacity was used by Schmidt in his extensive investigation of the disintegration of radium A, B and C (H. W. Schmidt, “Ueber den Zerfall von Radium A, B und C,” Ann. d. Physik, Bd. 21, 1906, p. 609). In this work, among other things, the following question of interest to us is solved. A certain solid body \(Z\), during a time \(\vartheta\), which in what follows we shall call the time of activation, remained in an atmosphere of radium emanation, and then was removed as quickly as possible from this atmosphere and placed in that chamber of the above-mentioned Schmidt electroscope which contains the discharge conductor. This chamber we shall subsequently call the “space of the discharge conductor” and denote by \(R\). The question is: what will be the discharge current caused in this space by the activated body, and how will this current vary with time? If it is assumed that in the atmosphere of emanation only \(RaA\) has deposited on our body \(Z\), while \(RaB\) and \(RaC\) could appear on this body only as a result of the decay of radium A deposited on \(Z\), then, guided by the well-known theory of Rutherford and Soddy on the decay of radioactive atoms, the amount of radium A which will still remain on our body \(Z\) in the space \(R\) after a time \(t\) following the cessation of activation may be represented as follows:

\[ A = qe^{-\lambda_1 t}\left(1 - e^{-\lambda_1 \vartheta}\right), \ldots \ldots \ldots (3) \]

where \(A\) denotes the number of atoms of radium A at the moment of time \(t\), \(\lambda_1\)—the transformation constant of radium A, and \(q\) denotes the number of atoms of \(RaA\) which would be present on the body \(Z\) at the moment of cessation of activation, i.e. at \(t=0\), if \(\vartheta\), the time of activation, had continued up to the moment of establishment of radioactive equilibrium between the ema-

radium and radium \(A\), from which moment on the quantities of atoms of radium \(A\) and of radium emanation subsequently change in such a way that they remain strictly proportional. Denoting by \(\lambda_2,\lambda_3\) the corresponding constants of transformation of \(RaB\) and \(RaC\), and by \(B\) and \(C\) the corresponding quantities of atoms of these substances on body \(Z\) at the same moment of time \(t\) for which equality (3) was written, we may write two other equalities:

\[ B=q\left[\frac{\lambda_2}{\lambda_2-\lambda_1}\cdot e^{-\lambda_1 t}(1-e^{-\lambda_1\vartheta}) +\frac{\lambda_1}{\lambda_1-\lambda_2}\cdot e^{-\lambda_2 t}(1-e^{-\lambda_2\vartheta})\right]\ .\ .\ (4) \]

\[ \begin{aligned} C=q\Bigg[& \frac{\lambda_2\lambda_3}{(\lambda_1-\lambda_2)(\lambda_1-\lambda_3)}\cdot e^{-\lambda_1t}(1-e^{-\lambda_1\vartheta})+\\ &+\frac{\lambda_3\lambda_1}{(\lambda_2-\lambda_3)(\lambda_2-\lambda_1)}\cdot e^{-\lambda_2t}(1-e^{-\lambda_2\vartheta})+\\ &+\frac{\lambda_1\lambda_2}{(\lambda_3-\lambda_1)(\lambda_3-\lambda_2)}\cdot e^{-\lambda_3t}(1-e^{-\lambda_3\vartheta})\Bigg]\ .\ .\ .\ .\ .\ (5) \end{aligned} \]

Now, for brevity, let us rewrite all three equalities in the following form:

\[ A=q\cdot a,\quad B=q\cdot b,\quad C=q\cdot c, \]

where the meanings of \(a,b,c\) are easy to understand from the equalities (3), (4), and (5) considered.

The ionization that will be produced in the space of scattering by \(RaA\), \(RaB\), and \(RaC\) will be composed of the actions of each of these substances separately—actions proportional to the quantities \(A\), \(B\), and \(C\). But because these substances ionize the air by radiations differing not only quantitatively but also qualitatively, the factors of proportionality between \(A\), \(B\), and \(C\) and the ionizations \(J_1,J_2,J_3\) caused by them will be different for all three bodies, and will depend, moreover, on the form and size of the scattering space. Denoting these factors by \(k_1,k_2,k_3\), and the total ionization in the space \(R\) at some moment of time by \(J\), we have the equality

\[ J=k_1A+k_2B+k_3C, \]

or

\[ J=qk_2(k''a+b+k'c), \]

where

\[ k''=\frac{k_1}{k_2}\quad\text{and}\quad k'=\frac{k_3}{k_2}. \]

Observing \(J\) for a whole series of moments of time \(t\), and knowing \(a,b,c\) for the corresponding \(t\) from the known constants \(\lambda_1,\lambda_2,\lambda_3\) and \(\vartheta\), as is shown by equalities (3), (4), and (5), one can find the values of the quantities \(k''\) and \(k'\) for the given specimen of Schmidt’s electroscope. For this ex-

of the specimen that Schmidt used in his above-mentioned work, and which below we shall call the “normal” specimen, it turned out that \(k'' = 6.0\) and \(k' = 8.0\). From these \(k'\) and \(k''\) one can calculate the quotient

\[ \frac{J}{qk_2} \]

for any moment \(t\) and for any time \(\vartheta\). H. W. Schmidt carried out these calculations for \(\vartheta = 1, 5, 15, 30, 60, 90, 120, 150\) and \(\infty\) minutes, and for 24 different moments \(t\), beginning with 0 and ending with 240 minutes. The results of these calculations, in the form of mantissas of three-place logarithms, are presented by Schmidt in Table 11 on p. 662 of Ann. d. Physik, Bd. 21, 1906, in his above-mentioned work. The dimensions of the scattering chamber of the “normal” specimen for which this table was compiled are as follows: diameter 7.2 cm, height 7.5 cm, diameter of the scatterer 0.5 cm, its height 4.5 cm. When the scatterer chamber is made smaller, \(k'\) remains constant, while \(k''\) increases, approaching \(k'\), i.e. 8.0. When this chamber is enlarged, both \(k'\) and \(k''\) decrease. How large these changes in \(k'\) and \(k''\) are when the scatterer chamber is changed is not known to me precisely, but in any case they should not be large.

Suppose that, with the aid of the “normal” specimen, we make a series of measurements of the scattering current \(J_t\), caused by a body \(Z\) previously activated for \(\vartheta\) minutes in an atmosphere containing radium emanation. Let the concentration of the emanation be such that the quantity \(q\), defined above, has the value \(q_1\). Then, another time, suppose that we activate our body \(Z\) for the very same time \(\vartheta\), also in an atmosphere of radium emanation, but already at another concentration—one for which the quantity \(q\) has the value \(q_2\). Then, placing body \(Z\) in the scattering chamber, we make a series of measurements of the scattering current \(j_t\), and at the same moments, reckoning as the initial moment the moment at which activation ceased. Then it is clear that for every pair of corresponding moments in the two series of observations the quantities \(J_t\) and \(j_t\) must be related as \(q_1\) and \(q_2\), so that

\[ \frac{J_t}{j_t} = \text{constans} \]

or

\[ \lg J_t - \lg j_t = \text{constans}. \]

From this it is perfectly clear in what way, using the “normal” specimen of Schmidt’s electroscope, one can decide the question whether the radioactive induction that may be produced by the water and gas of the thermal springs under investigation is the radioactive induction of radium, or a more complex phenomenon, or even an entirely different phenomenon.

§ 2. Study of the induced activity of the emanation under investigation by means of Schmidt’s electroscope at short activation times.

I had one specimen of a Schmidt electroscope from Sprindler—Hoyer (in Göttingen). The total surface area of the discharge space in this specimen was 253.7 cm², and the volume 274.6 cm³. (Diameter 7.2 cm, height 6.85 cm; diameter of the discharger 1.15 cm, height of the discharger 4.2 cm), whereas for the standard specimen the corresponding values were 258.7 cm² and 304.6 cm³. In view of such close agreement in the dimensions of the discharge space in mine and in the standard specimen, it is entirely possible to apply also to my specimen of Schmidt’s electroscope the data in Table 11 of the above-mentioned work by Schmidt on the decay of radium \(A\), \(B\), and \(C\).

For the study of the phenomena of induced activity by means of Schmidt’s electroscope, it is very important to know the relative significance of the divisions of the scale of this instrument. Strictly speaking, in this respect the scale should be studied anew after each transportation of the apparatus. But in the “travel” regime in which I had to work in the village of N. Belokurikha, I found it possible to use that calibration of the scale which I had made after my return to Tomsk, [by Schmidt’s method, with the aid of the saturation current produced by a grain of radium salt sealed into a glass tube (H. W. Schmidt, Ueber die Eichung und Gebrauch von Blattelektrometern, Ph. Z., 7, 1906, p. 157)]—all the more so because, over a rather extensive interval of the scale, the difference between the results of my calibration and the data of the table sent to me by Spiendler-Hoyer was small, as is seen from the following Table VII.

Table VII.

From this table it is evident that in the interval 3.0—10.0 there are no differences exceeding 3.33%, and in the interval 2.0—10.0 there are no differences exceeding 4.7%. Owing to the fact that the electroscope had to be charged with an ebonite rod, it was impossible to avoid large variations in the initial potentials of the electroscope; and in such a case there are inevitable, though small, yet perceptible variations in the value of the scale divisions, which could lead to variations also in the relative values of the scale intervals. Moreover, in a certain interval of the scale there was sometimes observed the phenomenon called by Ebert (Phys. Zeitschrift, 6, 1905, p. 642) the Cri-Cri phenomenon: in its motion the leaf would begin to slow its course, then speed it up again. Sometimes this entire phenomenon proceeded rather slowly, and sometimes so rapidly that a small jump was noticed in the motion of the leaf.

The walls of the discharge chamber themselves served me as the body \(Z\). The emanation under investigation was blown into the discharge chamber, remained there for a time \(\theta\), and was then quickly blown out. By \(T\) I shall denote the time elapsed from the moment of taking the water under investigation from the well to the beginning of activation; in the case of gases, by \(T\) I shall denote the time from the beginning of gas collection to the beginning of activation. Since the gas was collected comparatively slowly, \(T\) in this case could not be less than \(1^{h} 24^{m}\) (observation of June 25). In the case of water, however, I could vary \(T\), beginning from \(40^{sec}\). Here it was of interest to take \(T\) as small as possible, since in this way one could hope to catch traces of some rapidly decaying emanation, if such existed in the waters under investigation and could produce the phenomenon of radioactive induction.

Here are the results of the first observation of the decay of the induced activity of air passed through water from well No. 1. The observation was made on June 23 in the courtyard of the bath building, in a half-covered room. Thanks to the proximity to the well (the well was twenty paces from the observation site), it was possible to make \(T\) equal to only \(40^{sec}\). The duration of the activation \(\theta\) was equal to \(12^{min}\). All stages of this observation and the calculation of the observational results are presented in the following Table VIII, divided into 15 columns.

In column 1 is indicated the No. of the individual observation; in column 2 is indicated the moment, read by the chronometer, at which the fiber of the leaf passed ...

of the electroscope through the pressures of the scale indicated in the third column. In column 4 are indicated the intervals whose times of passage by the filament of the leaf are indicated in column 6, and in the fifth column are indicated the values \(v\) of these intervals in volts. In column 7 are given the mean moments of passage of the filament of the leaf through the corresponding interval; in the 8th is indicated the current of complete discharge \(i\), in millivolts per second at a capacity of the electroscope equal to 1; in the 9th, the quantities \(J_t=i-i_N\), where \(i_N\) is the current of the natural discharge, expressed in the same units as \(i\). In the 10th column is given the time elapsed from the moment of cessation of activation to the corresponding mean moment; in column 11 are given \(\lg_{10} J_t\); in the 12th, the corresponding \(\lg_{10} j_t\), taken from the table on page 622 of Annalen der Physik, Bd. 21, the characteristic being put equal to zero. In column 13 are indicated the differences \(\lg_{10} J_t-\lg_{10} j_t\). In column 14 the quantities \(\lg_{10} J_t\) have been reduced to \(\lg j_t\) by means of the mean value of the differences contained in column 13. These reduced logarithms we shall denote by \(\lg J'_t\). In column 15 are indicated the differences \(\lg J'_t-\lg j_t\).

In the above-mentioned table 11 on p. 622 of Ann. d. Physik, Bd. 21, there are no data for \(\vartheta=12^{\min}\). In this case I proceeded as follows. I found numbers corresponding to the logarithms given for \(\vartheta=5^{\min}\) and \(\vartheta=15^{\min}\); from these numbers I interpolated numbers for the case \(\vartheta=12^{\min}\). From the logarithms of these numbers found by interpolation and from the corresponding times a curve was drawn, by means of which the numbers of column 12 were found. In this way I proceeded each time when \(\vartheta\) was not contained in Schmidt’s table.

If the error of measurement of the quantity \(i\) can reach \(5\%\), then the maximum possible error in determining \(\lg J_t\), calculated by the formula

\[ \frac{5\%\,\lg_{10} e}{\lg_{10} J_t}, \]

can in the present case also reach \(5\%\). Meanwhile the differences indicated in the 15th column of Table VIII nowhere exceed \(1.5\%\) of the logarithm of the observed quantity \(J_t\). Hence it may be concluded that the numbers of column 13 turned out to differ among themselves only as a consequence of random errors of observation, and that the decay of the induced activity observed by us fully follows the laws of decay of tem—

Table VIII.

of the induced activity of solid bodies produced by radium emanation. This is clearly represented in Diagram No. 4, in which along the abscissa axis are plotted the times elapsed from the moment activation ceased, in minutes, and along the ordinate axis are plotted \(\lg j_t\), corresponding to the moments 0, 2, 5, 8, 10, 12, 15, 18, 20, and 25 minutes. From the points thus obtained, the decay curve of the induced activity of the radium emanation for \(\theta = 12\) minutes was drawn, and then the points \((\lg J_t', t)\) were marked with crosses, the values \(\lg J_t'\) being taken from column 14 of Table VIII. We see that the crosses everywhere lie on the curve.

Diagram 4.

In the following Table IX I report the results of observations of the decay of the induced activity of gas collected over well No. 2. This observation was made on June 25 in the courtyard of the bath building, in the same room as the above-mentioned observation of June 23. In the present case \(T = 1^{\mathrm h} 24^{\mathrm{min}}\), \(\theta = 10^{\mathrm m} 23^{\mathrm{sec}}\), \(i_N = 0.9\) millivolt per second, with the capacitance taken as 1. This time I do not give the information with which columns 2–9 in Table VIII were filled.

Table IX.

As is evident from this table, the greatest value of the difference \(\lg j_t - \lg J_t'\) amounts to \(1.4\%\) of the corresponding value of \(\lg J_t\) (No. 1). Meanwhile, the maximum possible error in determining \(\lg J_t\) will be \(1.5\%\), assuming that the maximum possible error in determining \(i\) is \(5\%\). It follows from this that the decay of the induced activity observed by us follows exactly the laws of decay of the induced activity of radium emanation. This is clearly shown by Diagram No. 5, constructed in exactly the same way as the preceding Diagram No. 4. Here too we see that the observed points (marked by circles) follow well the curve representing the decay of the induced activity of radium emanation.

Diagram 5.

The following Table X presents the results of observations of the induced activity of the gas collected above well No. 2, but with a different activation time, namely: at \(\vartheta = 30\frac{1}{4}\) minutes, \(T\) about 2 hours, \(i_N = 2.0\) millivolts per second (taking the capacitance of the electroscope as 1.). The observation was made on June 27 in the evening in a half-closed room.

Table X.

The greatest value of the difference \(\log j_t - \lg J'_t\) in Table X is (No. 17) \(1\%\) of the magnitude \(\lg J_t\), while, with a possible \(5\%\) error in the determination of \(i\), the error in \(\lg J_t\) may reach \(2\%\). Consequently, from Table X it must also be concluded that the decay of the induced activity observed by us fully follows the law of decay of the induced activity of radium emanation. This is clearly represented by Diagram 6, constructed in exactly the same way as Diagrams 4 and 5.

Diagram 6.

§ 3. Study of the induced activity of the emanation under investigation with the aid of the Elster and Geitel bell jar at long activation times and independently of the calibration of the electrometer needle.

In addition to the observations described above, made with Schmidt’s electroscope, I have two further observations of the decay of the induced activity of the emanation under investigation. This time I used the Elster-Geitel bell jar and electroscope, with the inner surface of the bell jar serving as body \(Z\). The time \(\vartheta\) in one case was \(5 \tfrac{1}{2}\) hours, and in the other 7 hours. Owing to the long activation time, the large portions of water and gas, and the large surface of body \(Z\), the discharge currents \(i\) proved so strong that the study of their decay with time could be made independently

from the calibration of the electrometer scale: both in the study of the decay of the emanation and now, the fall of the leaf (to the right) was always observed in one and the same interval of the scale (from division 17 to division 10, which interval corresponded to a fall of potential of 61.06 volts). Despite the enormous difference in the dimensions of the space of the discharger beneath the bell jar (surface \(2987\ \mathrm{cm}^2\), volume \(8555\ \mathrm{cm}^3\)) and the corresponding space in the “normal” electrometer, the decay of the discharge current of the induced activity under the bell jar, in the observations described, agreed very well with the data of Schmidt’s table. It should be noted that in these observations the bell jar, during activation, was insulated and charged to a negative potential of 800 volts (approximately).

The following Table XI presents the results of observations on the decay of the activity induced by blowing air through water from well No. 1. The observation was made on June 25; \(T = 16\) minutes, \(t = 5\frac{1}{2}\) hours, \(i_{\mathrm{N}} = 4.8\) millivolts per second at capacity 1. The quantities \(J_t\), \(j_t\), and \(J'_t\) have the same meaning as before.

Table XI.

The maximum possible error in determining $\lg J_t$ is 1.5% of this quantity. Meanwhile the greatest value of the difference $\lg j_t - \lg J_t'$ is only 1.2%. Consequently, the decay of the induced activity observed by us proceeds in exactly the same way as the decay of the induced activity of radium emanation for the same activation time. This is clearly shown by Diagram 7: we see that the observed points (marked with crosses) follow well the curve representing the decay of the induced activity of radium emanation.

Diagram 7.

The following Table XII presents the results of observations on the decay of the activity induced by the gas collected over well No. 2. The observation was made on June 26, $T$ about 3 hours,

\[ i_N = 9.0 \frac{\text{Millivolt} \div \text{capacity } 1}{\sec}, \qquad \vartheta = 7 \text{ hours}. \]

Table XII.

The first measurement of the discharge current entered in Table XII was made only 71.5 minutes after the cessation of activation, since only from this moment did the currents $i$ become saturation currents. The greatest possible error in $\log J_t$ reaches 1.2% of this quantity, whereas the greatest value of the difference $\lg j-\lg J'_t$ amounts to only 0.8% of the quantity $\lg J_t$. Consequently, this time too the decay of the induced activity observed by us proceeds in exactly the same way as the decay of the induced activity of radium emanation. This is clearly shown by diagram 8; we see that the observed points (marked by crosses) follow well the curve representing the decay of the induced activity of radium emanation.

Diagram 8.

Chapter III. Measurement of the quantity of emanation contained in the gases and waters under investigation.

§ 1. The methods of Mache and Schmidt for measuring the quantity of emanation.

Let \(J_0\) represent the magnitude of the saturation current produced in the space of the condenser \(R\) by radium emanation immediately after its introduction into this space. Of course, \(J_0\) is the difference \(i_0 - i_N\), where \(i_N\) is the current of natural saturation, and \(i_0\) is the current of full saturation at the very same moment to which \(J_0\) refers. Let \(y\) denote the quantity of the introduced emanation. Then we may write the equality

\[ y = K \cdot J_0, \]

where \(K\) is, for the given condenser space, a constant quantity and denotes the amount of emanation necessary to excite

in this space a saturation current of 1 unit of current. The variability of the factor \(K'\) when the shape and size of the discharging space \(R\) are changed arises from the fact that not all radiations accompanying the transformation of the emanation into radium \(A\) are absorbed by the air in the space \(R\); rather, part of them is absorbed by the walls of this space and has no influence on the formation of the current \(i_0\). This absorbed part of the radiation changes depending on changes in the shape and size of the space \(R\), and therefore, for one and the same quantity of emanation \(y\), different values of \(J_0\) will correspond in different “discharging spaces.” Let us suppose that we have succeeded in eliminating the absorption of radiation by the walls of the space \(R\). In such a case, as a measure of the emanation introduced into \(R\), we would obtain another value, \(J'_0\), greater than \(J_0\). W. Duane showed what relation exists between \(J_0\) and \(J'_0\) in the case when the discharging space has the form of a cylinder. (William Duane. Sur l’ionisation de l’air en présence de l’émanation du radium, Journal de Physique, (4), t. IV, 1905, p. 605). It turns out that

\[ J'_0 = J_0 \cdot \frac{1}{1 - 0.52 \cdot \frac{s}{v}}, \]

where \(s\) is the surface area and \(v\) the volume of the discharging space. The multiplier

\[ \frac{1}{1 - 0.52 \cdot \frac{s}{v}} \]

we shall denote by \(D\). For our Elster–Geitel bell jar, \(D = 1.22\), and for our Schmidt electroscope, \(D = 1.94\). Denoting by \(K\) the factor of proportionality between \(J'_0\) and \(y\), we obtain the equality

\[ y = K \cdot D \cdot J_0 \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (6) \]

The magnitude \(K\) denotes the quantity of radium emanation that must be introduced into the given space \(R\) in order to excite in it a current equal to \(1/D\) units. It is clear that, when the dimensions of the space \(R\) are varied, provided only that its cylindrical form is preserved, the product \(J_0D\), for one and the same value of \(y\), must always remain constant. The magnitude \(K\) may be approximately calculated from the following data given by H. Mache in his already cited article Ueber die Radioaktivität der Gasteiner Thermen (Wiener Berichte, Bd. 113, Abth. IIa, 1904, s. 1329). According to Mache’s calculation, the amount of emanation that excites a current of \(564 \cdot 10^{-3}\) electrostatic units is equal to \(12 \times 10^{-7}\ \mathrm{mm}^3\). Hence, for \(K\) one obtains approximately:

\[ K = 2.13 \times 10^{-6}\ \frac{\mathrm{mm}^3}{\text{el.-st. unit of current}} . \]

In any case, even if \(K\) is not yet known with sufficient accuracy, it is an absolutely constant quantity. Thus the measurement of \(y\) is reduced to the measurement of \(J_0\), in units independent of the method and the instrument

measurements, such as, for example, electrostatic units of current.

As is known, the discharge current produced by radium emanation after its introduction into the space of the discharger begins to increase rapidly. Its magnitude at the moment \(t\), taking the moment of introduction as the zero moment, we shall denote by \(J_t\). Since it is very difficult to measure directly the current of complete discharge \(i_0\), the quantity \(J_0\) has to be calculated from several values of \(J_t\). This not only avoids the difficulties of measuring \(i_0\), but also improves the accuracy of determining \(J_0\). During a short interval of time \(t\) after the introduction of the radium emanation into the discharger space, its quantity, owing to the slowness of its radioactive transformation, does not have time to decrease so much that this decrease would be measurable. In that case the quantity \(J_t\) may be represented as the following function of time:

\[ J_t = J_0 + Bf(t), \ldots \ldots \ldots \ldots \ldots \ldots (7) \]

where \(Bf(t)\) will denote the discharge current produced already only by the activity induced by the radium emanation on the walls of the discharger space. Duane, in the work cited above, found the form of the function \(Bf(t)\), using for this purpose the formula given by P. Curie and Danne for the decay of the induced activity of radium emanation (C. R. 1904, t. 138, p. 685), and introducing here constants depending on the dimensions of the cylindrical space of the discharger. By observing a series of quantities \(J_{t_1}, J_{t_2}, \ldots\), one can with sufficient accuracy find both the constants and \(J_0\). Somewhat earlier than the appearance of the above-mentioned work by Duane, H. Mache (l. c.), proceeding from the same consideration—that the term \(Bf(t)\) in equation (7) depends exclusively on the appearance of induced activity, while the ionization produced by the emanation remains constant—proposed the following graphical method for determining \(J_0\).

For some time after introduction into the space of the discharger, as in Duane’s method, a series of quantities \(J_{t_1}, J_{t_2}, \ldots, J_{t_n}\) is observed; then, as quickly as possible after determining the quantity \(J_{t_n}\), the space of the discharger is opened, strongly ventilated, and closed again, after which one proceeds as quickly as possible to observe the decay of the induced activity. Let \(\tau_0\) denote the moment of opening the space \(R\), and let \(J'_{\tau_1}, J'_{\tau_2}, \ldots, J'_{\tau_m}\) be the series of discharge currents caused by the decaying induced activity. The times \(t_1, t_2, \ldots, t_n, \tau_0, \tau_1, \ldots, \tau_m\) are counted from the moment when the emanation is introduced into the space of the discharger. Observations made before the moment \(\tau_0\) allow one to form \(n\) points with coordinates \((J_t, t)\), and observations made after \(\tau_0\) allow one to form \(m\) points with coordinates \((J'_\tau, \tau)\). Through the first \(n\) points one draws the curve of increase of the discharge currents up to the opening of the chamber, and through the second \(m\) points one draws the curve of decay of the induced activity. Then both curves are extrapolated to the moment \(\tau_0\). The difference \(J_{\tau_0} - J'_{\tau_0}\) will represent the desired \(J_0\). The success of applying this method of Mache depends on how...

the curves of increase and decay of the current are determined. But the most critical point of the method is the extrapolation of the curves, since the course of the curve between the given points in general still does not characterize its course outside these points, especially in the case of the decay curve of the induced activity of radium emanation. This curve, as is known, changes its character twice: the rapid fall in the first 15 minutes after the cessation of activation is replaced by an almost constant ordinate for approximately 20 minutes, and then by a new fall, though not so rapid as the first. Nevertheless, in one respect Mache’s method has an advantage over Duane’s method. Duane’s method is applicable only when the introduction of the emanation into the space of the decomposer is accomplished so rapidly that the initial moment of this introduction may, without appreciable error, be taken as the moment of the introduction itself. Otherwise the function \(Bf(t)\) will be quite different from that indicated by Duane, and in such a case the use of this method loses its meaning. Meanwhile, Mache’s method does not depend on special assumptions concerning the form of the function \(Bf(t)\) and does not lose its meaning even when the introduction of the emanation into the space of the decomposer takes place slowly, as, for example, occurs in the study of the radioactivity of waters by the method of circulation in a closed circuit. Only after a comparatively long circulation (from 20 to 30 minutes) of the air of the circuit through the water under investigation is the emanation gradually introduced into the space of the decomposer, for example, under the bell of Elster–Geitel. Only in the study of the radioactivity of gases does the circulation method make it possible rapidly to introduce the emanation under investigation under the bell. In this case, into the closed circuit containing the “space of the decomposer,” the rubber-bulb pump, and the drying tubes, there is introduced the vessel with the gas under investigation, which, owing to the circulation, is rapidly distributed throughout the entire circuit, and the more rapidly the closer the volume of the decomposer space is to the volume of the rubber-bulb pump producing the circulation: two or three strokes of the pump, and the introduction of the emanation into the decomposer space is complete. In 1905 H. W. Schmidt (Phys. Zeitschr., 6, p. 561) showed how, in the case of waters as well, the introduction of the emanation into the decomposer space could be made so rapid that, in determining \(J_0\), one could use Duane’s rational method. The essence of Schmidt’s method is as follows: into a vessel \(F\), provided with two stopcocks, as shown in the figure, the water under investigation is poured so that its level is below the inner opening \(a\) of the lower stopcock \(K_1\), after which the stopcocks \(K_1\) and \(K_2\) and the neck \(B\) are closed, and the liquid in the vessel is subjected to vigorous shaking. As a result of the shaking, after only \(1/2\) minute equilibrium is established in the distribution of the emanation between the air occupying—

volume \(V\), and the water, occupying a volume \(W\). Thus above the water there is obtained an emanation-containing gas in the amount \(V\ \mathrm{cm}^3\). This gas, by means of the stopcocks \(K_1\) and \(K_2\), is introduced into one circuit with the space of the electroscope and the pump–bulb. Thus, in Schmidt’s method the water under investigation remains outside the circuit in which the air circulates. Thanks to this it proved possible to remove from the circuit the desiccants and the tube with water: Schmidt’s preliminary experiments showed that, despite prolonged and vigorous shaking of vessel \(A\) with distilled water, the subsequent blowing of air from \(V\) into the space of the electroscope produced there no noticeable increase in the natural leakage current, and consequently caused neither deterioration of the insulation nor any ionization.

Schmidt carried out these experiments also with warm water, the temperature of which reached \(50^\circ\mathrm{C}\), and the results were the same. But Schmidt did not make experiments with aqueous solutions of salts and with water in which gases are dissolved in greater than usual quantity, as is very often the case with many ground and juvenile waters. Meanwhile one may suppose that gases liberated during bubbling will prove to be ionized, just as the gases liberated during the electrolysis of acids and alkalis prove to be ionized (Townsend, Phil. Mag., (5), 45, 125 and 149, 1898), and in certain chemical reactions (Bloch, Recherches sur la conductibilité électrique de l’air produite par le phosphore et sur les gaz récemment préparés, Annales de chimie et de physique, (8), t. 4, 1905, p. 25).

A similar hypothesis was expressed by Prof. A. P. Sokolov in his work, already cited more than once above, “Radioactivity of Certain Russian Mineral Waters, Muds, and Soils,” concerning the gases released from liquid carbonic acid when the pressure is lowered.

If ions analogous to Bloch’s ion-dust particles are produced in this process, then, of course, they will scarcely be destroyed even when desiccants and cotton wool are introduced into the circuit, and consequently they will inevitably raise the estimate of the content of radioactive emanation in the water under investigation. But it is possible that there exist ions with properties, so to speak, intermediate between Bloch’s ions and ordinary rapidly recombining ions. In such a case, the introduction of desiccants and cotton wool into the circuit may produce in the circuit an ionization that can simulate the decay of thorium emanation and, to a greater or lesser extent, obscure the corresponding increase in the values of \(J_t\) for radium emanation during the first 2–3 hours after the emanation has been introduced into the space of the electroscope. The possibility of the occurrence of this “parasitic,” in Prof. A. P. Sokolov’s expression, ionization, arising from causes having nothing in common with radioactivity, must be borne in mind each time one wishes to determine the radioactivity of some water by the method of ionization of air in close contact with the water, or when one wishes to establish the nature of an undoubtedly existing radioactive emanation.

only from the changes in the quantities \(J_t\) during the first time after the emanation has been introduced into the discharge chamber, or when it is desired to estimate the quantity of emanation contained in the water under examination, the nature of which is already known.

In any case, the aim which Schmidt set himself—to introduce the emanation into the discharge chamber as rapidly as possible, so that the time spent on this operation could, without appreciable error, be taken as one instant—was achieved, and the more so because the rubber bulb pump can be taken to have approximately the same dimensions as the discharge chamber, while the volume \(V\) can be made considerably larger than this chamber \(R\). In this way it becomes possible to determine \(J_0\) rationally, calculating it from \(J_t\), using the dependence indicated by Duane. For this same purpose H. W. Schmidt, starting from equations (3), (4), and (5), representing the course of the radioactive process in \(RaA\), \(RaB\), and \(RaC\), and with the aid of the constants \(k''\) and \(k'\) indicated on p. 32, calculated, for a “normal” specimen of his electroscope, the ratios \(J_0/J_1\) for times \(0\), \(1/2\), \(1\), \(1 \frac{1}{2}\), \(2\), \(3\), etc., up to 15 minutes, counting as the zero moment the moment of introduction of the emanation into the discharge chamber. The results of these calculations by Schmidt are contained in Table III of his article Über eine einfache Methode zur Messung des Emanationsgehalts von Flüssigkeiten in Phys. Zeitsch., 6, 1905, p. 561. We shall call the quantities \(J_0/J_1\) contained in this table Schmidt’s multipliers.

§ 2. Measurement of the quantity \(\dfrac{x}{v}\) for gases by the method of Mache and Duane—Schmidt.

To measure the quantity of emanation in the gas collected above well No. 2, a closed circuit was assembled from the discharge chamber, the volume of which chamber we shall denote by \(R\), from the rubber bulb pump, from the reservoir in which the gas under examination is contained at atmospheric pressure, from the system of dryers, and again the discharge chamber. The volume of the portion of gas taken for examination we shall denote by \(V\), and the volume of the pump together with the dryers and connecting tubes by \(V'\). Thus the volume of the entire circuit will be \(V + V' + R\). For brevity we shall denote this sum by \(U\). Let the quantity of emanation in a liter of the gas under examination, at atmospheric pressure and at the mean temperature of the observations, be denoted by \(x\), and let \(y\), as above, denote the quantity of emanation introduced, after circulation, into the discharge chamber. Then the quantity of emanation introduced into the circuit is represented by \(\dfrac{xV}{1000}\), and for \(y\) we have the equation

\[ y = x \cdot \frac{V}{1000} \cdot \frac{R}{U}. \]

whence, substituting for \(y\) its value from equation (6), we obtain

\[ x = K . D J_0 \frac{1000}{V} \cdot \frac{U}{R}. \]

Here it is assumed that \(U, V, V'\), and \(R\) are expressed in \(\mathrm{cm}^3\), and \(x\) and \(y\) in \(\mathrm{mm}^3\).

\(J_0\) was determined twice by the method of Mache and three times by the method of Duane-Schmidt. In the first case I used an Elster-Geitel bell, and in the second a Schmidt electroscope. In order to measure \(J_0\) in electrostatic units (C. G. S.), it is necessary to know the capacities of the electroscopes used and to calibrate their scales. How the scale of the Schmidt electroscope was calibrated has already been reported (p. 23). The scale of the Elster-Geitel electroscope, however, was calibrated in the following manner. Gas collected over spring No. 2 was introduced under the bell, and after the emanation had reached radioactive equilibrium with its decay products, and the leakage currents had become saturated, the times required for the leaf to pass through various intervals of the scale were determined over a long period of time (about 5 days). From such (very numerous) observations the relative values of the intervals of the scale were established. For their absolute evaluation it remained to determine the value in volts of some one interval. Such was the interval between divisions 13 and 10 of the scale. By comparison of the electroscope under study with an electroscope of the same type, but one that had never yet been used, this interval was evaluated at 27.1 volts. The same value of this interval was obtained also after the return to Tomsk, with the aid of a battery of small accumulators. As for the capacities of the electroscopes, comparison with a Harm’s condenser showed them to be exactly those indicated by the firms that had manufactured these electroscopes: 12.5 cm for the electroscope under the Elster-Geitel bell and 6.1 cm for the Schmidt electroscope. The following Table XIII presents the data relating to two measurements of the quantity \(J_0\) by the method of Mache. The quantities \(t_1, t_n, \tau_0, \tau_1, \tau_n, n, m, J_{\tau_0}, J'_{\tau_0}, J_0, K, x\), and \(V\) have the same meaning that was assigned to them above in the present and preceding paragraphs; moreover, \(J_{\tau_0}\), \(J'_{\tau_0}\), and \(J_0\) in columns 9, 10, and 11 are in millivolts per second at electroscope capacity 1, but in computing the quantity \(x/K\) (column 13) \(J_0\) is already expressed in electrostatic units of current, for which purpose the numbers in column 11 are multiplied by 12.5 (the capacity of the electroscope in cm) and divided by \(300 \times 1000\).

Table XIII.

Table XIV.

The above Table XIV presents data relating to three measurements of the quantities \(J_0\) and \(x/R\) by the method of Duane and Schmidt, while Table XV presents the entire course of the measurements and calculations of the value \(J_0\) for 27. VI. 08. The table is compiled exactly as indicated by Schmidt (Phys. Zeitschr., 7, 1906, p. 209). I reproduce it here for convenience in my further exposition. The table is divided into 12 columns. Column 2 contains the moments, read from the chronometer, at which the thread of the leaf passes through the divisions of the scale indicated in column 3. Column 4 gives those intervals of the scale for which the time of passage by the thread of the leaf is reported in column 6. Column 5 gives the values of the intervals in volts, and column 7 gives the mean moment at which the thread passes through these intervals. Column 8 contains the values \(i_t\) in millivolts per second; column 9, the values \(J_t = i_t - i_N\); column 10, the moments \(t\), counted from the moment of introducing the emanation into the space of the scatterer; column 11, the Schmidt multipliers \(J_0/J_t\) corresponding to these moments; and column 12, the products of the found \(J_t\) by the corresponding Schmidt multipliers, i.e. \(J_0\). It is clear that, in the absence of observational errors, all the numbers in column 12 should be identical. From the numbers found in column 12 the mean \((422.4 \pm 1.1)\) has been taken, and this is entered in the 4th column of Table XIV.

Table XV.

If, from all five values of the quantity \(x/K\) found by us (two from Table XIII and three from Table XIV), we take the mean, then we obtain \(78.6\times 10^{-3}\) electrostatic units. The greatest deviation from this mean calculation of \(x/K\) is only \(4\%\). If one takes into account that the quantities \(x/K\) were measured by entirely different methods, and with entirely different instruments, and under entirely different conditions of observation [in the observations with Elster and Geitel’s bell about 4.5 liters of gas were introduced into the vessel, whereas in the observations with Schmidt’s electroscope 1.7 and 0.138 liters; in the first case the experiment lasted about 45 min, and in the second about 6 min; in the first case a fall of potential of 62 volts was observed, and in the second 17–29 volts, etc.], then the agreement of the obtained measurement results should be noted, especially in view of the communication made at the 41st general meeting of the American Chemical Society in Boston (December 28–31, 1909) by Merle Randall [abstracted in Chemiker Zeitung, No. 34, 1910]. This scientist wished, by means of the ionization current, to measure the quantity of radium emanation which occurs per 1 gr. of uranium in uranium salt obtained from pitchblende. For this purpose he used various methods of measurement and various electroscopes. It turned out that the ionization currents thereby obtained, which could have been considered a measure of the above-mentioned quantity of emanation, varied greatly both depending on the method of the electroscope employed (usually each type of electroscope placed on the market corresponds to only one method of measurement), and on the total quantity of salt which, when dissolved, releases radium emanation. Depending on the method and the electroscope employed, these variations lay between \(2.36\times 10^{-12}\) amp. (\(708.7\times 10^{-3}\) electrostatic units) for Boltwood’s electroscope and \(4.80\times 10^{-12}\) amp. (\(1441.5\times 10^{-3}\) electrostatic units) for Schmidt’s electroscope. From this Randall draws the conclusion that “the assumption of many European scientists” that the result of measuring the quantity of radium emanation by ionization current will not depend on the method and electroscope employed, if only the ionization current is expressed in amperes or electrostatic units of current, is incorrect. The above-reported results of measuring the quantities \(x/K\) are in complete discord with such a conclusion. The small difference obtained among the five found values of the quantity \(x/K\) cannot in any way be ascribed either to the great difference in the instruments used for the measurement, or to the great difference in the methods of measuring the quantity \(J_0\), or to the great difference in the quantities of emanation introduced into the vessel, since in Table XIV there is a value of \(x/K\) (June 27) which differs from the result of the observation of June 23 by only \(0.6\%\). Nevertheless, the quan—

…tions in the values of the quantity \(\frac{x}{K}\) in Table XIV cannot be ascribed to accidental errors of observation. In that case it must be admitted that either the amount of emanation per one liter of the gas under investigation was different on the different days of observation; or that the number of ions present in the space of the condenser could be greater than corresponded to the emanation introduced, and thus a phenomenon of “parasitic” ionization occurred, the magnitude of this “parasitic” ionization being able to be at times greater, at times smaller, and in general having to decrease with time until complete disappearance. Since, in the measurements with Elster and Geitel’s bell jar, dryers and a tube with cotton wool were introduced into the circuit, it may be thought that in this case there was no parasitic ionization at all. It could have disappeared here also for the reason that the observations of the quantities \(J_t\) were begun only 8–9 minutes after the introduction of the emanation under the bell jar. Since no dryers or cotton wool were introduced into the circuit with Schmidt’s electroscope, and observations of the quantities \(J_t\) were begun much earlier (at the latest 4 m 56 sec. after the introduction of the emanation), then, according to the hypothesis set forth above concerning “parasitic” ionization, it is to be expected that the results of the measurements made by Schmidt’s method will be greater than the results of the measurements made with Elster and Geitel’s bell jar. That this is indeed so is shown by Table XIV. The same hypothesis explains why the result of the observation of 27.VI is much closer to the number 77 than the result of the observation of 25.VI: for on 27.VI the measurements of the quantity \(J_t\) were begun only 4 m 56 sec. after the introduction of the emanation, whereas on 25.VI these measurements were begun after only 2 m 58 sec.; as a consequence, the “parasitic” ionization must have made itself felt more strongly in the observation of 25.VI. But how, then, is one to explain that the result of the observation of 1.VII is closer to 77 than the result of the observation of 25.VI? For on 1.VII the measurement of the quantity \(J_t\) was begun only 55 sec. after the introduction of the emanation. But this time the observation continued considerably longer than before, namely 5 m 07.5 sec., whereas earlier it was about 1 m 20 sec. In 5 m 07.5 sec. the parasitic ionization, large at first, could have died away. That this was in fact so is seen by considering those 11 values of \(J_0\) from which the number 123.3 was obtained as the mean. Table XVI presents to us, for each of the three observations made by Schmidt’s method, the data which, for the observation of 27.VI, are contained in columns 10 and 12 of Table XV. In columns 3, 6, and 9 of Table XVI are given the differences between the mean value \(J_0\) and the corresponding values \(J_0\) calculated from \(J_t\) at different times \(t\).

Table XVI.

Examining this table, we see that the character of the change in the numbers \(J_0\) in column 8 is not at all the same as for the numbers in columns 2 and 5; in column 8 a one-sided change in the values \(J_0\) is clearly expressed, namely their decrease. The observation of 1.VII was completed 5-odd minutes after the introduction of the emanation, approximately at the time when the observation of 27.VI was begun. In this latter observation a systematic decrease in the values \(J_0\) is no longer noticeable. It should also have been noticed in the observation of 25.VI. If from column 8 we take only the first five values of \(J_0\), the mean will be 126.8, corresponding to which for \(x/K\) we obtain \(81.4 \times 10^{-3}\); and if we take the last five values of \(J_0\), the mean will be 119.5, and for \(x/K\) we have \(76.7 \times 10^{-3}\). Thus all the data of Table XVI are in complete agreement with the hypothesis of “parasitic” ionization, disappearing 5–6 minutes after the introduction of the gas under investigation into the discharge space. It should also be noted that in all five cases of change in \(x/K\) the gas was introduced into the space—

the amount of decay approximately at one and the same time after the beginning of its collection, on average after 1 h. 20 m.

Since in the literature there have been indications confirming Ebert’s opinion that, after a decrease in barometric pressure, the emission of radioactive emanations from the earth’s crust becomes more abundant [e.g., J. Jaufmann, Meteorologische Zeitschrift, 1905, p. 102], I made readings on the aneroid during the whole period of work in the village of Novaya Belokurikha at 8 o’clock in the morning, 1 o’clock in the afternoon, and 9 o’clock in the evening. During the period 22.VI—2.VII slow fluctuations of the barometer were observed within the limits of 29.25—28.91 English inches. The fluctuations observed by me in the value \(x/K\) cannot be placed in any connection with the above-mentioned fluctuations of barometric pressure.

§ 3. Measurement of the value \(x/K\) for the water under investigation by the Mache method.

We now pass to the description of measurements of the quantity of radium emanation contained in 1 liter of water from wells No. 1 and No. 2, by the Mache method. Let \(w\) denote, in cm\(^3\), the quantity of the tested water introduced into the circuit, and let \(U\), \(R\), \(x\), \(y\) have, mutatis mutandis, the same meaning that was assigned to them in the preceding paragraphs. The quantity of emanation that we introduced with the water into our circuit is

\[ \frac{xw}{1000}. \]

When (after circulation) equilibrium is established in the distribution of the emanation between the air and the water, then in \(w\) cm\(^3\) of water there will be contained as much emanation as is contained in \(a \cdot w\) cm\(^3\) of air, where \(a\) denotes the so-called absorption coefficient of radium emanation in water. Hence, for the density of the emanation in the air of the circuit, we obtain the expression

\[ \frac{xw}{1000} : U - (1-\alpha)w; \]

for \(y\) the equality

\[ y = x \cdot \frac{w}{1000} \cdot \frac{R}{U-(1-\alpha)w}, \]

and for \(x\)

\[ x = K \cdot D \cdot J_0 \cdot \frac{1000}{w} \cdot \frac{U-(1-\alpha)w}{R}. \]

Since the water under investigation contains very few dissolved salts, for \(\alpha\) in our case one may take the same value as for distilled water. R. Hoffmann, as reported by M. Kofler (Phys. Z., 9, 1908, p. 6), found for distilled water at 20°C the value 0.28 for \(\alpha\), while M. Kofler found the value 0.27. At 40° by

for \(R. Hoffmann\) for \(\alpha\) we already have the value 0.16. Since our water, during circulation, had a temperature of about \(25^\circ\text{C}\), we shall take for it \(\alpha\) equal to 0.25. It should be noted here, incidentally, that for those values of \(U\) and \(w\) which occurred in our measurements, even a considerable error in determining \(x\), for example if for \(\alpha\) instead of \(1/4\) we had taken \(1/3\), could have changed the result of the measurement by no more than 1.1%.

The following table, XVII, presents data relating to measurements of the quantities \(J^0\) and \(x/K\) by the method of Mache. The heading \(T\) contains the time elapsed from the moment the water was taken from the wells to the beginning of circulation. All the other headings have the same meaning as the corresponding headings of Table XIII, with the exception of one, which was not in Table XIII and the meaning of which is indicated in Table XVII itself. In all the measurements the quantity \(U\) was one and the same and was equal to \(13956\ \mathrm{cm}^3\).

Table XVII.

§ 4. Measurement of the value \(x/K\) for the water from well No. 1 by Schmidt’s method. Taking into account the description of Schmidt’s method given in § 1 of the present chapter, we shall find that the quantity of emanation introduced into the cylinder will be represented by

\[ \frac{w}{1000}\cdot \frac{xV}{V+a w}, \]

where \(w\), \(x\), \(a\) have the same meaning as above, and \(V\) denotes, according to § 1, the volume of air above the water in vessel \(F\). In that case, for \(y\) and \(x\) we shall obtain the following equalities:

\[ y=\frac{w}{1000}\cdot \frac{xV}{V+aV}\cdot \frac{R}{V+V'+R}, \]

\[ x=KDJ_0\cdot \frac{1000}{w}\cdot \frac{V+V'+R}{R}\left(1+a\cdot \frac{w}{V}\right), \]

where \(V'\) and \(R\) have the same meaning as in § 2.

In the case of the measurements described, \(R=274.5\ \mathrm{cm}^3\), \(V'=204.1\ \mathrm{cm}^3\), and \(w+V=1700\ \mathrm{cm}^3\) (the volume of vessel \(F\)). The following Table XVIII presents the data relating to all the measurements of the value \(x/K\) that I made by Schmidt’s method for the water from well No. 1, \(T\) having the same meaning as in Table XVII.

Considering Table XVIII, we see that on 23.VI, 8.VII, and 12.VII there were obtained for \(x/K\) the same values as by Mache’s method with Elster-Geitel’s bell. But whereas in Table XVII all 7 values of \(x/K\) agree very well with one another, in Table XVIII this agreement is absent: the values of \(x/K\) vary here from 24.4 to 16.9. In general, Schmidt’s method and apparatus give, for \(x/K\), larger values than Mache’s method and Elster-Geitel’s apparatus. But this circumstance, already observed by us in measuring \(x/K\) for gases, is expressed more sharply here. Considering the conditions of those observations reported in Table XVIII which gave values of \(x/K\) greater than \(17.4\times 10^{-3}\), and when the duration of shaking was no more than 2 minutes, we find, first, that these observations were begun very soon after the introduction of the emanation into the space of the disperser, whereas from consideration of Table XIV we concluded that the supposed parasitic ionization, which increases the values found for \(x/K\), disappears no earlier than 5–6 minutes after the introduction of the emanation into the space of the disperser. Further, considering Table XVIII, we see that in all cases when more than 17.4 was obtained for \(x/K\), and when the shaking lasted no more than 2 minutes, a decrease in the values of \(J_0\) is noted in the “remarks” column. This decrease at first proceeds rapidly, and then slowly. Thus the hypothesis of parasitic ionization stated in § 2 applies also in the present case. But here we supplement it with the following two further propositions.

V. S. Tytov.

Table XVIII.

1. The parasitic ionization, expressed in the measurement of the quantities \(x/K\), is, in the case of waters, much more abrupt than in the case of gases. Whereas in the former case the greatest discrepancy between the values of \(x/K\) found by the methods of Mache and Schmidt reaches 32%, in the case of gases the maximum observed discrepancy amounts to only 6% of the value of \(x/K\) found by Mache’s method.

2. The more vigorous and prolonged the shaking of the air and of the water under investigation, the more persistently the parasitic ionization is retained; moreover, the stage of its rapid decrease is, in this case, almost absent.

Turning attention to observation 23.VI, we find that here parasitic ionization is absent despite the fact that observation of the quantities \(J_t\) was begun very soon after the introduction of the emanation into the space of the discharger (31 sec after the beginning of activation). This absence of “parasitic” ionization in the indicated observation may have to be ascribed to the fact that here the shaking of the water and air was brief and weak. In any case, it by no means follows from the hypothesis set out above concerning “parasitic” ionization that this phenomenon must always occur in the first 5–6 minutes after the introduction of the emanation into the space of the discharger.

Conclusion

In conclusion, I permit myself to summarize the results of my present work in the following propositions.

1. In both the waters and the gases of the thermal springs of the village of Novaya Belokurikha, the presence of radium emanation has been fully established.

2. No other emanations, for example thorium emanation, were found in these thermal springs.

3. Schmidt’s method and apparatus (Phys. Zeitschr., 6, 1905, p. 561; 7, 1906, p. 209) can give, for both the gas and the water of the above-named thermal springs, the same values of the quantity \(x/K\) as Mache’s method and the Elster–Geitel apparatus.

4. Depending on the conditions of observation, Schmidt’s method may give for the quantity \(x/K\) values exceeding the corresponding values found by Mache.

5. From this it is by no means possible to draw the conclusion that the saturation current of ionization cannot be a measure of the quantity of emanation—a measure independent of the instrument and method of measurement and of the portion of emanation taken for measurement.

6. A possible explanation of the discrepancy between the results of measuring the quantity \(x/K\) by Schmidt’s method and by Mache’s may be provided by the hypothesis of “parasitic” ionization, occurring in the scattering space and disappearing no earlier than 5–6 minutes after the introduction of emanation into it. When measuring the quantity \(x/K\) in waters, the parasitic ionization remains all the more persistent the more vigorous and prolonged was the shaking of the water and air under investigation.

7. The question of the causes of the occurrence and the nature of the phenomenon of “parasitic” ionization requires special laboratory investigation.

8. The most probable value of the quantity \(x/K\) for the gases I investigated is \(77.1 \times 10^{-3}\) electrostatic units, and for the waters \(17.2 \times 10^{-3}\) of the same units. Hence, for \(a\), the coefficient of absorption of radium emanation in the waters of the thermal springs of the village of Novaya Belokurikha, we obtain the number 0.22.

Moscow, January, 1911.