L. The Irregularities in the Radiation from Radioactive Bodies. By Hans Geiger, Ph.D., John Harling Fellow, University of Manchester [Communicated by Professor E. Rutherford, F.R.S.]. In all experiments in which the ionization currents due to two radioactive substances are balanced against each other by means of an electrometer, it is not found possible to obtain an exact balance. The needle of the electrometer always moves quite irregularly over a certain number of divisions on the scale. This effect cannot be eliminated, no matter how much care is taken in the adjustment. Bronson [citation redacted], who was troubled by this effect in the use of his steady 540 [header] deflexion electrometer, suggests that the effect may be due to an exceedingly small and rapid change in the ionization itself. E. v. Schweidler [citation redacted] has in a special paper drawn attention to the fact, that according to the disintegration theory certain irregularities in the radiation from radioactive substances are to be expected. He calculates from the laws of probability that these irregularities should under certain conditions be within the limits of measurement. K. W. F. Kohlrausch [citation redacted] made some experiments to test the accuracy of the theory of v. Schweidler. A discussion of his results will be given later. In the course of some experiments, my attention was attracted by the impossibility of obtaining a steady balance of two opposite ionization currents due to the [alpha] rays. A few experiments will now be described which I have made to test the cause and the magnitude of these irregularities. It was of importance first to prove whether the effect was due to a real variation of the intensity of the radiation or to some secondary effect which might be eliminated. For this purpose, the following experiment was made : — Two ionization vessels, A and B, were arranged as shown in fig. 1. Between [figure redacted] them, and insulated from them by the ebonite plugs e, c and the guard-rings g and h, was fixed a piece of aluminium foil D, which was connected with an electrometer of the Dolezalek [header] 541 type. The vessels A and B were closed at E and F by aluminium foil and connected with the opposite poles of a battery of 400 volts, the middle point o£ which was earthed. A narrow pencil of [alpha] rays was sent through both vessels from the point R, and as in practice the vessel B was somewhat larger than A it was easy to balance the two opposite ionization currents. Now in this case any effect of the irregularities of the radiation itself was eliminated, since each [alpha] particle contributed equally to the ionization currents both in A and B. The experiment, however, did not show an entire absence of the oscillations of the electrometer needle, but the effect was undoubtedly smaller than when the ionization currents of the same intensity were produced from two different sources at R and U, R producing ions only in A and U only in B. The two curves given in fig. 2 correspond to the movement [figure redacted] of the needle of the electrometer over a time of 4*5 minutes. Curve I. shows the effect due to one source of rays, Curve II. the effect of two separate sources. The intensity of the radiation was the same for both curves. The small oscillating effect shown in Curve I. was probably due to the irregular thickness of the aluminium foil D. Some of the particles were stopped in the leaf and could not produce ionization in B, while other particles passed through the small holes, thus producing a stronger ionization in B than in A. The general arrangement used for the further experiments is shown in fig. 3. E is the electrometer of which one pair of quadrants was earthed and the other pair connected with two ionization vessels A and B. The outsides of the vessels were charged up to + 200 and —200 volts respectively. The radiation from suitable radioactive substances was allowed to pass into the vessels through two openings which were covered with [footer] 542 [header] aluminium foil in order to avoid possible disturbances from air-currents. By means of a screw S the distance of the radioactive matter U from the vessel B could be varied and a balance obtained between the ionization currents in A and B. When the balance was obtained as closely as possible.. [figure redacted] the needle of the electrometer showed small oscillations which were observed over a definite time, generally five minutes. With this arrangement, a comparison was made between the irregularities of the ionization currents produced by [alpha] particles with those produced by a current of the same intensity due to [beta] particles. Two wires which had been exposed to the radium emanation were placed at R and U quite close up to the vessels A and B (fig. 3). The ionization in this case is almost entirely due to [alpha] particles. The oscillations of the needle over a space of five minutes are shown in the Curves I. and II. of fig. 4. The intensity of the radiation was for Curve I. 340 and for Curve II. 1100 divisions per minute on the electrometer-scale, where one division corresponds to the calculated ionization produced b} about 22 [alpha] particles. The Curves III. and IV. of the same figure were obtained under the same conditions except that the ionization in the cylinders A and B was produced by [beta] particles. For this purpose a little glass tube containing about 5 ing. EaBr 2 was brought near to the vessels and its distance adjusted till the ionization in both cylinders was equal and of the same [header] 543 intensity as in the case of the [alpha] particles. The Curves III. and IT. correspond to I. and II. respectively as regards the intensity of the ionization currents. The Curve III. shows [figure redacted] no oscillations at all, while IY. shows oscillations but comparatively to a very slight extent. The fact that hardly any observable oscillations occurred in the case of [beta] radiation shows, independently of any theory, that the effect observed with [alpha] radiation is really due to the irregular nature of the [alpha] radiation, and not to a secondary effect. The difference in the shape of the curves is to be expected from simple theoretical considerations. It is known that the absolute average error in a large number of observations for two events P and Q is given by [figure redacted] where N is the number of observations and p and q are the probabilities for the events P and Q respectively. If we apply this formula to radioactive changes, taking N as the number of atoms present, the number of atoms breaking up during a given time [tau] ([tau] being small compared [footer] 544 [header] with the period of the substance) is given by [formula redacted], the number of atoms still unchanged after the time r is given by [formula redacted]. From this it follows that the probability of a single atom breaking up during the time [tau] is [lambda][tau], while the probability that the same atom will exist after that time is [formula redacted]. Hence the absolute average error is [formula redacted] or, neglecting the square of [lambda][tau] compared with [lambda][tau] itself, the error is [formula redacted] where Z is the number of atoms disintegrating during the time [tau]. This result was first deduced by E. v. Schweidler (loc. cit.) in a similar manner. According to the simple radioactive theory, the average number of atoms breaking up during the time [tau] is given by [formula redacted] The actual number observed may show a deviation from this, or an average error equal to the square root of the number of atoms breaking up during the time [tau]. The absolute average error increases therefore with the number of atoms breaking up, i. e. with the intensity of the radiation ; while the relative error [formula redacted] decreases. The movement of the needle of the electrometer registers the absolute error. The correctness of this theoretical conclusion may be tested as follows : — Rutherford has shown that one [alpha] particle from radium itself produces 80,000 ions in its path of 3*5 cms. in air at atmospheric pressure ; while Durack has found that each of the swifter [beta] particles from radium expelled at a speed approaching that of light makes a new pair of ions in every 6 cms. of air at 1 mm. pressure. Consequently, in the cylinders A and B which were about 12 cms. in length one [beta] particle will produce at atmospheric pressure 4 x 760 or about 3000 ions. Therefore, in order to produce the same ionization current with [beta] particles, about 25 times as many [beta] particles as [alpha] particles are necessary. Hence the average error in the number of [beta] particles shot out is [formula redacted] The average error measured by the electrometer is [formula redacted] as one [beta] particle produces only an effect 1/25 of that produced [header] 545 by one [alpha] particle. Therefore the error measured in the ease of [beta] particles, on the same electrometer and under the above-mentioned conditions, should be about one-fifth of that observed for [alpha] particles giving the same intensity of ionization. The smallness of the irregularities in Curves III. and IV. (fig. 4) compared with those shown in Curves I. and II. is thus to be expected. A special series of measurements has been made to show how the average error depends upon the intensity of the radiation. At the points R and U (fig. 3) two wires were placed which were made intensely active by exposure to the radium emanation. While the activity was decaying, the oscillations of the needle were observed at intervals, and curves were drawn showing the oscillations as accurately as possible over intervals of 5 1/2 minutes. From these curves the average error was determined by counting the divisions passed over by the electrometer needle during the attempted balance, and dividing that number by the number of swings observed during the same time. The average error was also calculated theoretically. An example may be given. Experimental Determination of the Error. The data are taken from Curve II. (fig. 4). The number of divisions passed over in 5 1/2 minutes, counting the maximum divergence both positive and negative, was 380 and the number of oscillations during that time was 64. Hence the average magnitude of one oscillation was [formula redacted] divisions, and the average deviation or the error ±2*95 divisions. Theoretical Determination of the Error. The error is given by [formula redacted] where Z is the number of atoms breaking up during the time [tau]. This number gives also the number of [alpha] particles shot into the vessel during the time [tau]. The time r is in this case the average time of swing, being 5*8 sec. as an average taken from all the curves. The intensity of the radiation of one wire was 1100 divisions per minute, and therefore, as one division corresponds to the ionization produced by about 22 [alpha] particles, the number of particles shot into the vessel is 2*4 x 10 4 per minute, and therefore the number shot into both vessels in 5*8 sec. is [formula redacted] The square root of this is 68. The average error taken over 546 [header] 5*8 sec. is thus ±68 [alpha] particles or transformed into divisions [formula redacted] divisions. The figures in the following table are all calculated in the same way as indicated in the above example. The difference between the theoretical and experimental error is about 15 per cent. Intensity of the radiation. Absolute error determined. Theoretically. Experimentally. [table redacted] The agreement is better than one would expect considering the conditions of the experiment and the uncertainty of the data from which the number of [alpha] particles is deduced. A slight correction ought also to be made since the electrometer needle was not quite dead-beat. The agreement between theory and experiment is quite as close if the error is determined by measuring the magnitude of the oscillations of the electrometer-needle for any convenient time, for example, each half minute, instead of the time of swing of the electrometer, viz. 5'8 seconds. Kohlrausch (loc. cit.) did not find a numerical agreement between the theory and his experiments, but this seems to be due to an incorrect use of the formula, since on calculating the error as above from his data, quite a close agreement (10 per cent.) is obtained for saturation currents. If the current is not saturated, as was the case in some of Kohlrausch's experiments, the above formula cannot be applied. For if the current is only half saturated, half of the ions produced from each [alpha] particle are lost by recombination ; consequently each [alpha] particle produces only one half of its effect under ordinary conditions of saturation. Taking this fact into consideration, a close agreement between theory and experiment was also found by calculating the data given by Kohlrausch for non-saturated currents. [header] 547 The agreement between theory and experiment in Kohlrausch's paper seems to me to be of special interest, for the method used by him differs from the method employed in this paper, while the intensity of the radiation in his experiments was nearly twenty times greater than the strongest used in mine. I have to thank Professor Rutherford for the kind interest he has taken during the progress of this research. Physical Laboratory, University of Manchester. Note added March 12, 1908. — Since the above was communicated a paper has been published by E. Meyer and E. Regener in the Verhandlungen der deutschen physikalischen Gesellschaft, No. 1, 1908. The authors also find, using a different method to the writer, that the error increases with the square root of the intensity of the radiation. Further, they state that by measuring the error e and the saturation current i the charge of an ion may be determined. But the calculation involves the number of ions produced by an [alpha] particle, and this number was determined by Rutherford under the assumption that the charge of an [alpha] particle is identical with the charge of an ion. This, however, is still an unsettled question. I may add here that the number of [alpha] particles emitted per sec. from a given substance can be determined directly by simply measuring the error e and the saturation current i. For the error e in E.S.U. is given by [formula redacted] where N is the number of ions produced by one [alpha] particle, e the charge of an ion, and Z the number of particles emitted per sec, while the saturation current is given in E.S.U. by [formula redacted] By division we get Z as function of e and i only. The agreement between the errors determined by theory and by experiment indicates that the calculated number of [alpha] particles emitted per sec. from a radioactive body of known activity is of the right order of magnitude.