Negative Ions at Low Pressures. 327 



The value o£ x which makes this expression equal to K is. 

 given by the equation 



_ tf(l-*,/K) 



x ~ (l-^/A-O * 



The number of particles which have a mobility not less" 

 than K is the same as the number of electrons which travel a 

 distance x without uniting with a molecule, and by the 

 preceding expression is equal to 



Ne ■*(i-ife 1 /A 1 )5r 



If we take as a measure of the mobility of the negative 

 particles a mobility such that half the particles have- 

 mobilities greater and half less than this value, then K must 

 make this expression equal to N/2, and therefore 



d(l-k 2 /K) V 



(l-ki/kj) x/, v a~ ' 



or 



-ir = 693 a • v -• 



Since XkijV is the ratio of the speed parallel to x to the 

 total speed of the electron, it is never greater than unity, so 

 that K will not differ appreciably from h 2 until n\ is com- 

 parable with d. When nX is large compared with d, and 

 X/cj smaller than V, K will increase with X,and in this case 

 the mobility of the negative ion will increase with the electric 

 force. 



We have supposed that there was a flash of ionization at 

 the beginning of the interval T. If, however, the ionization 

 is continuous over this time and if q electrons are produced 

 per second, the number reaching the plate will, if T is less 

 than djLX, be equal to 



«^0 



»T-d/yfe,X 



v o 

 or 



!(•-*«- V>_, r *(i-fc)) («) 



where 



v^Y/^XnX^-kJk,). 



If T is greater than d/k 2 X y then all the ions emitted from 



