813 The Theory of the Small Ion in Gases. 



facts. To a large extent the choice amongst formulae with 

 different numerical coefficients is still sub judice. But as 

 regards Mr. "Wellisch \s calculated effect of electric attraction 

 in increasing the ordinary viscous resistance, experiment is 

 against him. His formula for the mobility of an ion would 

 tnke the same form as (^9) in my Phil. Mag. paper of last 

 September, namely w=A'T i /(l + C / /T), where A' and C are 

 parameters characteristic of each gas. For air at 0° 0. with 

 T = 273 Mr. Wellisch finds 07273 = 3-70, whereas I have 

 calculated f»om the experiments of Phillips that for the 

 positive ion in air 0' = 509*6, and for the negative 333*3; so 

 that 07273 has the values 1*86 and 1*22, which are markedly 

 different from the theoretical 3*70 of Mr. Wellisch. From 

 the appeal to experiment it appears that Mr. Wellisch has 

 obtained by calculation too large an effect of electric attraction 

 in increasing ordinary viscous resistance. I think the addi- 

 tional resistance needed is supplied by the viscosity of electric 

 origin which I have attempted to calculate. General consi- 

 derations make the existence of such a resistance probable. 

 The motion of electricity through metallic conductors gene- 

 rates heat, ths charo-ing and dischargino- of condensers heats 

 their dielectric; hence it is probable that the motion of an 

 electric charge amongst the molecules of a gas produces heat 

 in them through the motion of electricity whether analogous 

 to that in a conductor or to that in a condenser. There is little 

 doubt then as to the existence of a viscous resistance of electric 

 origin to the motion of an ion in a gas. The order of its mag- 

 nitude in comparison with that of the mechanical resistance it 

 is desirable to ascertain. J tried to do so by appeal to the broad 

 facts of experiment with the aid of the best estimates of mole- 

 cular diameters. With 2*38 X 10 -8 cm. for the diameter of a 

 molecule of air in (10) of my paper it w^as found that the 

 frictional resistance of electric origin was 7*6 times that of 

 mechanical origin. With 2 - 86xl0~ 8 for that diameter as 

 given on p. 26 of the Phil. Mag. for Jan., the resistance of 

 electric origin is 4*9 times that of mechanical. These esti- 

 mates are very dependent on those of molecular diameters; 

 and there is also the uncertainty about numerical coefficients 

 in the kinetic theory. 



Mr. Wellisch thinks it would be well to get an idea of the 

 order of its magnitude from independent considerations. It 

 seems to me that the attempt to clo so would involve the in- 

 troduction of some hypothesis as to the details of the dissi- 

 pative actions inside a molecule wdien an electron passes close 

 to it, which we are hardly yet ready to make profitably. 

 Probably the careful discussion of experiments such as w r e 

 owe to Mr. Wellisch, Mr. Phillips, Dr. Franck, and many 

 others will prove more fruitful. 



