Mobilities of Ions in Air at High Pressures. 487 



the electrode GH. As the range of the alpha rays from 

 polonium is only about 3'8 cm. in air at atmospheric 

 pressure, it will be seen that, at a pressure of about 70 

 atmospheres and higher, the ionized portion of the air 

 between GH and CD was confined to a very thin layer 

 close to the latter plate. 



The experiment consisted in measuring the current between 

 CD and GH with various positive and negative voltages 

 applied to AB at the different pressures. The formula for 

 determining the mobilities which is applicable to the present 

 case is that given by Rutherford * and Child f. 



Expressed in electrostatic units the mobility of an ion is 



given by 



73 • 



^ = ^ — qv2* cm * a seconc ' P er 300 volts a cm., . (1) 



where i is the current between CD and GH in e.s.u. per 

 square cm. cross-section, d the distance in cm. between GH 

 and CD, and V the potential difference between them in 

 electrostatic units. 



Expressed in practical electromagnetic units, 



k = 3200 — * vr L / cm. a second per volt a cm., . (2) 



where d is in cm., V is in volts, and i is in electrostatic units, 

 and is the current per square cm. cross-section between CD 

 and GH. 



As d was 1 cm. in the apparatus used by us the relation 

 (2) reduces to 



3200. tt./ 

 ^ ~ ~~3V2— W 



From equation (3) it will be seen that for a selected 

 pressure the current i should be proportional to V 2 . 



At all the pressures used this law of proportionality 

 between i and V 2 was tested by giving different values to V, 

 and in all cases it was found to hold. One of the different 

 sets of readings obtained at a pressure of 145"35 atmo- 

 spheres will serve to illustrate this point. The voltages 

 applied, together with their squares and the corresponding 

 currents per square cm. cross-section, are given in Table I. 

 They are represented graphically in fig. 2, and it is clear 

 from the diagram that the relation between i and V 2 is a 

 linear one. 



* Rutherford, Phys. Review, vol. xiii. (6) p. 321 (1901). 

 t Child, Phys. Review, vol. xii. (3) p. 187 (1901). 



