Electrons with Molecules of a Gas. 509 



at a millimetre pressure will depend on the distribution of 

 the velocity of agitation, which is much greater than the 

 velocity in the direction of: the electric force. When an 

 electron travels a distance of one centimetre in the direction 

 of the electric force the total length of its trajectory is u/W 

 approximately, and the total number of: collisions it makes 

 with molecules is ufWl, where I is the mean free path of the 

 electron. It: a be the number of molecules ionized by an 

 electron in moving a distance of one centimetre in the 

 direction of the force, the ratio of the number of collisions in 

 which ionization takes place to the total number of collisions 

 is («W/)/w. 



In order to find an average value of the velocity V of the 

 electron required to ionize a molecule the quantity (a\Vl)/u 

 may be equated to the ratio of the number of collisions 

 in which the velocity exceeds V to the total number of 

 collisions. Assuming the velocities of the electrons to be 

 distributed according to Maxwell's law it is easy to show* 

 that the latter ratio is 



3 V' 2 



6\" 



It is convenient to represent the velocity V in terms of the 

 potential P in volts required to give this velocity to a particle 

 with an atomic charge. The value of P in terms of V is 



given by the relation — 2 =27xP, and the equation to 

 determine P becomes u ° 



*m -—/, . 8ixP\ 



'"■( 



i+ 



2k 



The values of P thus obtained are 23*7, 26,2$, 29 volts 

 from the experiments with the smaller forces in which the 

 values of Z/jj were 40, 50, 70, 90 respectively. 



It might seem that this method of finding the potential 

 P would be inaccurate, as the errors of several experimental 

 determinations would be involved. But the values of P as 

 given by the above formula are only slightly affected by 

 large errors in the values of a, /, and W, and the quantity k 

 is the only factor which need be known accurately. The 

 principal error in the calculation is probably due to taking 

 Maxwell's law as giving the distribution of the velocities 

 of electrons acted on by an electric force. It should 

 be remembered that the potentials P thus found are average 

 values, and with the definition of a collision that has 

 * Phil. Mao-. (6) vol. xxvii. p. l>69 (1914). 



