}>U the Motion of Positive Ions in a (/as. G13 



smaller than the potential between the electrodes which is 

 required to oive an effect arising from this cause which can 

 he easily detected experimentally. The order of: that potential 

 mav be found it' we supfH:)se that the mean free path of a 

 positive ion is a quarter of that of a negative ion ; so that in 

 going through a centimetre of air at a millimetre pressure a 

 positive ion would make 60 colhsions. Taking, for example, 

 the case in which a force of 700 volts per centimetre is 

 applied, the value of y3 is '14 when the pressure is 1 millimetre; 

 so that on the average only 14 new ions are generated as 

 the result of some GOOO collisions. Let it be supposed that 

 the new ions are generated at the collisions that terminate 

 the 14 longest paths. In general, out of N paths of mean 

 length I the number 3/ which exceed the distance x is given 

 by the formula 



?/ = Ne 



Hence the fourteen longest paths when N = 6000 and 

 /= gL exceed *102 centimetre, so that new ions are generated 

 when the velocity corresponds to a fall of potential of about 

 70 volts. 



A similar investigation shows that new ions may be pro- 

 duced in hydrogen when the fall of potential is about 20 or 

 30 volts. The voltages obtained by this method would be 

 somewhat smaller if the number of collisions per centimetre 

 is taken from the tables given by Mayer [loc. cit.), since the 

 lenjTth of the free path of a molecule in air at 1 millimetre 

 pressure deduced from experiments on viscosity is less than 

 ^J centimetre. 



10. The tables show that the currents in the gas increase 

 very rapidly for small increases in the distance a when the 

 plates are far apart. When the plates were separated by 

 one millimetre more than the largest distances given in the 

 tables, the force X being maintained at the same value, a 

 current was usually obtained which continued after the light 

 from the external source ceased to act and a glow was seen 

 in the space between the ele.trodes. From the values of 

 a and )3 which have been found it is easy to calculate the 

 distance u for the given forces and pressures at which a 

 continuous discharge might be expected, since the value 

 of n then becomes infinite. This condition is satisfied 

 when the quantity a — /Se^""^)'^, the denominator in the ex- 

 pression for n, vanishes, so that the required distiince a' 



IS equal to --. 



Fhil. Mag. S. tJ. Vol. 0. No 35. Sor. 11)03. 2 S 



