Ir] IONIZATION THEORY OF GASES 55 
occasionally produced by collision when the negative ion moves 
freely between two points differmg in potential by 10 volts. If 
the difference be about V = 20 volts, fresh ions are produced at 
each collision'. 
Now the energy W, acquired by an ion of charge e moving 
freely between two points at a difference of potential V, is given by 
W = Ve. 
Taking V=20 volts=2% E.s. units, and e=3°4x 10-%, the 
300 
energy W required to produce an ion by collision of the negative 
ion is given by 
Wee 2730x 1lOm ergs: 
The velocity w acquired by the ion of mass m just before a 
collision is given by 
and D> R= 
Now < = 1°86 x 10’ electromagnetic units for the electron at 
slow speeds (section 76). 
Taking V = 20 volts, 
m = 2°7 x 10° ems. per sec. 
This is a velocity very great compared with the velocity of 
agitation of the molecules of the gas. 
The negative ions alone are able to produce ions by collision 
in a weak electric field. The positive ion, whose mass is at least 
1000 times greater than the electron, does not acquire a sufficient 
velocity to produce ions by collision until an electric field is applied 
nearly sufficient to cause a spark through the gas. 
An estimate of the energy required to produce an ion by X rays 
has been made by Rutherford and M°Clung. The energy of the 
rays was measured by their heating effect, and the total number of 
ions produced determined. On the assumption that all the energy 
of the rays is used up in producing ions, it was found that V=175 
' Some difference of opinion has been expressed as to the value of V required 
to produce ions at each collision. ‘Townsend considers it to be about 20 volts; 
Langevin 60 volts and Stark about 50 volts. 
