of Radioactive Products present in the Atmosphere. 831 

 of the air in equilibrium, 



4z7ruk — - — 



is the number of particles of radium A deposited on the wire 

 per cm. per second, or that of radium A or radium C break- 

 ing up per second on each cm. of the wire in equilibrium, 

 provided that there has been do recombination between the 

 particles and the negative ions present in air. AVe have 

 thus come to the same result as had already been arrived at 

 in Art. 7, equation (B). 



(12) In the actual case some of the particles do not reach 

 the wire, as they are neutralized on their way to it by uniting 

 with the negative ions present in air. 



It will not be convenient to solve equation (A) by intro- 

 ducing the correction due to the recombination. Firstly, 

 the production of ions is not uniform. It is extremely intense 

 near the wire on which the active deposits are already col- 

 lected. Secondly, the negative ions are, as soon as they are 

 produced, set in motion, the path of which is represented by 

 the equation 



-2fxk(6 r -6) + icz = const. 



The problem is complicated since the recombination takes 

 place while the particles of radium A and the negative ions 

 are both in motion. 



An approximate solution can, however, be obtained from 

 the consideration described in Art. 11. Let ~Na,+ be the 

 number of the particles of radium A per cubic centimetre of 

 the atmosphere in equilibrium when there is no electric field. 

 Then, on the assumption that they can be treated as ordinary 

 gaseous ions, we have 



^~ t + =X e N e -\ a Na, + -«nNA, + =0, 



where a is the coefficient of recombination, and n the number 

 of the negative ions present in each cubic centimetre of air. 

 If q is the rate at which the negative ions are produced, 



n — \ / — . Therefore, 



V ex. 



A ' + ~X L +*n ~ \ A + y/^Tg * 

 According to the investigations of Rutherford and others*, 



* Rutherford and Cooke, Arner. Phys. Soc. Dec. 1902. McLennan, 

 Phvs. Rev. iv. (1003). McClelland, Phil. Mag. July 3904. Wright, 

 Fhil. Mag. July 1909. 



