384 Reports on Special Researches 



penetrating radiation apparatus, and ionization chamber of the radioactive-content 

 apparatus respectively. H, I, J, and L are the corresponding potentiometer systems, V 

 is the voltmeter, and E is an earthed connection. The keys Ki and h serve to connect A 

 to the potentiometer, A'2 and k-i serve for B and so on. The reversing switches, ki, ki, kz, ki, 

 enable the electroscopes to be charged with either sign of electricity. Since the electroscope 

 A requires, as we shall see, the 150- volt range on the voltmeter, it must be separated there- 

 from by a separate switch S. The operation of the system will be clear from the figure, and 

 it will not be necessary to describe it in greater detail. The electroscope systems are 

 suspended from gunbals and each is provided with a small glow lamp and switch for use at 

 night, and a spirit-level of convenient sensitivity. It is possible by means of the levels to 

 guide the instruments by hand so that they are sufficiently vertical when readings of the 

 electroscopes are made. 



The method which is usually employed for measuring the conductivity of the air is 

 that due to Gerdien. In this method air is drawn by a fan through the space between two 

 concentric cylmders, the central member of which is charged and connected to an electro- 

 scope. The theory of the instrument shows that so long as the velocity of the air-current 

 is large enough to insure that the central cylinder is unable to extract from the air all of the 

 ions which it attracts as the air passes through, the rate of loss of charge by the cylinder is 

 independent of the air velocity. It depends only upon the conductivity contributed by the 

 ions of sign opposite to the charge on the central cylinder. Under these conditions, treating 

 the apparatus as portions of length I of two mfinitely long concentric cylinders of internal 

 and external radii r, and r,, respectively, Gerdien deduced the expression^ 



L2log ra/rO T V2 



for the unipolar conductivity X corresponding to the particular sign of ions involved. In 

 this formula Ci is the capacity of the whole apparatus, including the electroscope, and T 

 is the time taken for the potential of the central cylinder to fall from Vi to V2. This 

 formula is inaccurate in that it neglects the finite extent of the cyUnders and more particu- 

 larly the influence of the rod supporting the central cylinder. If, however, the quantity 

 1/2 log {ra/rt), which here corresponds to the capacity of the concentric cylinders under the 

 above assumptions, be replaced by the measured capacity C2 of the concentric cylinders, 

 including the portion of the supporting-rod which is exposed to the air-current, the formula 

 becomes exact^ in the form 



4^XC, = ^log|l (3) 



For since the rate of supply of electricity to the apparatus as a result of the conductivity 

 of the air is 4irXC2V,^ we have 



_C',^ = 47rXCo7 (4) 



dt 



which integrates to (3). 



In the work on the Carnegie the potential drops are small, and the differential form (4) 

 is the more convenient one for use. A formula allowing for leakage during the experiment 

 can most conveniently be deduced as follows. 



Suppose that the fall in potential of the insulated system in the small time t is 5F, 

 corresponding to 6 divisions alteration in deflection of the electroscope. Suppose, also, that 

 the alteration of deflection in the same tim e, as a result of leakage, with no air-flow, is e. 



'Terr. May., vol. 10. pp. 69-71, 190) '^See W. F. G. Swann. Terr. Mag., vol. 19, pp. 81-8S, 1914. 



