tube should be earth connected. When the bulb or spark gap is 2 or 3 meters from the electroscope and the air velocity is diminished, a considerable time will elapse before any of the ions can reach the electroscope and these will be but a small percentage of the number originally present.

As the first ions arriving are swept into the chamber of the electroscope the leaf begins to move and its rate of fall increases and finally reaches a constant value which is maintained until a short time after the X-rays (or spark) is stopped, following which the rate of leak slowly reduces to zero. The apparent slowness of the leaf in starting and stopping is largely due to the effect of friction between the air and the inner surface of the tube. This appreciably diminishes the velocity of the air in that region, so that on starting, ions passing through the central portion of the tube arrive first. After the rays are stopped, ions near the surface trail along behind, gradually decreasing in number as recombination and diffusion proceed. The effect will of course vary with the length, diameter and material of the tube and the velocity of the air. It will later be shown that this irregular distribution of ions in the tube may affect the value obtained for the recombination constant. For high velocity and a short length of tube the leaf starts at once with a uniform rate of deflection and stops abruptly. Using a spark gap 2 meters from the electroscope and a slow air current, a relatively large rate of leak was observed after 35 seconds had elapsed between the stoppage of the spark and the arrival of the first ions in the chamber.

The rapidity with which gaseous ions diffuse may be well illustrated by inserting a compact bundle of tiny, thin-walled metal tubes inside the tube near the slit. These should be soldered together and make good contact with the inner surface of the tube. Diffusion takes place so rapidly, as the ions pass through the tubes, that with the same air velocity and ionizing source, the number of ions reaching the electroscope is enormously diminished.

The effect of water vapor or dust particles

where N and n are the number of ions present in the gas at the beginning and end of time t, respectively. This law has also been verified for gases exposed to X-rays by McClung3 also by McClelland using arcs and flames as the ionizing agents.

The method most generally employed when large quantities of the gas are available has been to pass the ionized gas through an earthed metal tube with constant velocity and measure the saturation currents at different points along the tube by means of an electrometer. A gas meter was used to measure the velocity through the tube as already intimated.

The deflection of the electrometer indicates the number of ions in a certain portion of the tube at a given instant. The fall of the gold leaf of an electroscope is, however, an integrating process like that of the gas meter and continues over a considerable time for each reading.

If the ionizing agent or the velocity of the ions themselves should undergo slight changes, the rate of fall of the gold leaf would give a good indication of the average number of ions passing at a given time. The sensibility of the electroscope will also remain fairly constant over long intervals and is readily tested.

In the course of some work involving the use of X-rays and y-rays from radium salt, it 1 Rutherford, Phil. Mag., V., 44, p. 422, 1897. 2 Rutherford, Phil. Mag., V., 47, p. 142, 1899. McClung, Phil. Mag., VI., 3, p. 283, 1902. McClelland, Phil. Mag., V., 46, p. 29, 1898.

was necessary to measure their relative ionizing effects at a given point in air. This was accomplished by sucking the ionized air from the vicinity of the given point through a metal tube into the chamber of an electroscope placed at some distance, as shown in Fig. 1. By noting the rate of deflection of the gold leaf for different air velocities curves corresponding to decay curves were plotted, using ionization in divisions per minute as ordinates and the times of passage of the ions through the tube as abscissæ. By continuing these curves back to zero time an approximation was obtained of the relative ionization originally present. A more exact estimate was made by obtaining the recombination constants for the two ionizing agents and, assuming the square law, calculating the original ionization when the ionization after a given time was known. This work suggested a further study of the recombination constants by this method, using various ionizers, and an examination of the recombination constants for ions produced by "hard" X-rays or the more penetrating v-rays aз compared with these values for the softer and less penetrating radiations.

Before using the electroscope as an indicator of the number of ions present at any instant, it was necessary to determine the deflection to which the gold leaf must be charged in order to obtain saturation conditions for the maximum velocity utilized. This was found by passing the ionized gas through the chamber of the electroscope to be used, then through the chamber of a second electroscope of high sensibility in close proximity to the one to be tested. The gold leaf of the latter was then charged to a potential sufficient to give no leak in the auxiliary electroscope. For lower potentials ions escaped into the second electroscope and the rate of leak of the first did not give a true indication of the number of ions passing into it. When the potential to which the leaf is charged is considerably lower than that necessary for saturation the decay curves obtained may show a maximum point, since there may be a critical velocity at which a maximum number of ions

will give up their charges to the electroscope. At such a velocity the gain in the number entering the chamber will be counterbalanced by the number escaping without giving up their charges.

The order of experiment was then as follows: Determine the saturation potential necessary for a given position of an ionizing agent at the maximum velocity to be used. Obtain the natural leak of the electroscope when the ionizing agent was present, but with no current passing through the tube. Obtain rates of deflection of the leaf in divisions per minute for each of as large a number of different velocities as time and the capacity of the suction pump would permit. The leaf was charged to a given deflection and allowed to leak over the same number of divisions for each reading. The mean of several observations was taken at each velocity. Successive times for the flow of .5 cubic foot of gas through the meter at a given velocity were also recorded. These values were then plotted using ionization in divisions per minute as ordinates and cubic feet per minute as abscissæ. From the smooth curve thus obtained a number of points were chosen and the time of decay of the ionization to these given amounts calculated from the rates of flow. Two of the ionization values were then selected as representing N and n in the formula

where t was the difference between the calculated times of decay for the values chosen. Thus assuming the recombination law, a the recombination constant was calculated in arbitrary units. Using this value for a, a number of values for n were computed and compared with the experimental values. The ionizing agent was then placed at different distances from the electroscope and similar decay curves plotted as a series of checks and with the purpose of obtaining a better idea of the part played by diffusion. This was repeated for brass tubes of different diameters, using X-rays, Y-rays, electric sparks and black

1

Curves A and A, are plotted, using the calculated and observed times, respectively, for ions to pass 121.4 cm. through a brass tube of 5.4 cm. diameter. Curves B, B1; C, C1; D, D, are plotted, using calculated and observed times for ions to pass 246 cm., 109 cm., and 25.4 cm., respectively, through a brass tube 2.95 cm. in diameter. For a brass tube 1.12 cm. in diameter, with the spark gap placed 226. cm. from the electroscope, for rates of flow greater than .25 cu. ft. per min. the difference between the calculated and observed times was less than .1 sec.

Sample decay curves are shown in Fig. 4. Observed times of passage of the ions through the tube were used as abscissæ rather than the times calculated by means of the meter from the rate of flow. Experimental conditions under which these curves were obtained are recorded in Table II.

The radium salt used in these experiments was contained in tiny aluminum tubes .7 mm. thick and approximately 2 cm. long. These were sealed into thin glass tubes to prevent leakage of radium emanation, and when used inside the brass tube were suspended at its axis by silk threads. The uranium cylinder referred to under H in Table II. was a hollow paper tube 5 cm. long and 2.9 cm. in diameter, with a coating of black oxide of uranium glued on the inside. This cylinder was suspended in the middle of the tube. The a

Thickness of Lead Over

.0097

An attempt was made to see if the recombination constant was a function of the quality of a given radiation. X- or y-rays were shot through the slit, first bare, then covered by foils or sheets of lead. A series of decay curves were thus obtained and the recombination constants calculated. Values were obtained with the slit bare at the beginning and end of the series to check the constancy of the sensibility of the gold leaf. The slit was covered at all times by a mica sheet .03 mm. thick.

TABLE V

Vel. in Exp. Ioniza- Calc. Ioniza- RecomTube in Cm. tion in Divs. tion in Divs. bination

by assuming the square law. The effect of diffusion at the lower velocities is well shown by the way in which the observed values fall below the corresponding calculated results. The values used in each experiment for calculating the recombination constant are marked by an asterisk.

In Table IV. the observed and calculated values are given for X-rays as an ionizing agent at a distance 27.7 cm. from the electroscope for an air current through a brass tube 2.95 cm. in diameter, using the arrangement of Fig. 1.