of Radioactive Products present in the Atmosphere. 827 

 Remembering that r 2 — x 2 + (z—h) 2 and r /2 = x 2 + (~ + Ji) 2 , and 

 writing /> tor -~- 7 we get 



7 2 /,2 



*o*±j(y/l+P*-l\ and sTQ^g-Cx/l+i^+l). 



If r , ?' ', O , and o f are the values of r, ?•', 0, and 0' respec- 

 tively for x=x Q and z = z , then 



cos(0 o -0 o )=--^-- = - — — -. 



Therefore a branch of the curve which passes through a? , r 

 is given by the equation 



and graphically represented by RP . It will be seen that 

 the other branch RiP can be represented by 



*-»-K' ^^ ♦ -) - P a - nA^Ph- 



These curves divide the space into two regions. All the 

 particles within the region RPqRj, such as at S or S 1? reach 

 the point A, i. e. they are caught by the wire, while those 

 outride the region, such as at T or Tj, escape from it. We 

 shall call the region within the surface RP R 1? the " effective 

 region." 



(7) Since XeNe is the number of particles of radium A 

 produced per second per c.c. of air, that produced in an 

 elementary volume ds x ds 2 dl at P will be 



A. E N E ds i ds. 2 dl per second, 



where ds x and ds 2 denote the line-elements of the curves 

 </> = const, and yfr = const, respectively, and I denotes the 

 distance measured in the direction of the wire. 



After an interval of time t, which is taken by these 

 particles to reach the wire, the number will be decreased to 



provided that the recombination of the particles with the 

 negative ions present in the air be disregarded. 



