of Radioactive Products present in the Atmosphere. 825 



emanation produce atoms of radium A in situ, and these in 

 turn quickly change into atoms of radium B, and so on. 

 Consequently, the distribution of the atoms of radium A 

 must be very nearly uniform, and their number in each c.c. 



will be — — - , if X E and X A are the constants of transformation 

 X A 



of the emanation and of radium A respectively. 



(5) Rutherford* has shown that the carriers of the active 

 deposits of radium and thorium move through a gas under 

 an electric field with a velocity v which is proportional to 

 the intensity F at that point, thus 



t?=*F. 



It was found that k is nearly the same for the carriers of 

 both radium and thorium deposits, and equal to about 1*3 cm. 

 per second for a potential gradient of 1 volt per cm. in air at 

 standard pressure and temperature. 



These particles, in addition to the action of the electric 

 field, may be conveyed by a current of air. 



(6) Starting from the above assumptions, we shall find 

 the number of the particles of radium A deposited on unit 

 length of a wire in unit of time, when it is stretched at a 

 height of h above the ground, and raised to a negative 

 potential — V. 



For convenience of calculation, it is assumed that the wire 

 is infinitely extended with the charge — fju per unit length. 



We shall first consider the case in which a wind of velocity 

 w is blowing horizontally in the direction of 

 a, perpendicular to the length of the wire. 

 Take the axis OX on the section of the surface 

 of the earth by a plane perpendicular to the 

 length of the wire, and OZ on the vertical 

 line passing through A, the position of the 

 wire. Let A' be the image of A with respect 

 to OX, so that 



OA = OA' = h. 



The component-velocities of a particle at 

 point P(#, z) are given by 



dx a 7 /x x \ 



dz n ifz + h z — h\ 



* Rutherford, Phil. Mag. vol. v. p. 103 (1903). See also Franck, 

 Vtrh. d. D. Phys. Ges. Oct. 1909. 



