June 11, 1909] 



SCIENCE 



921 



tion of the ionic size whieli lias been made 

 on these lines assumes the ions as charged, 

 the molecules as uncharged conducting 

 spheres, and, taking the radius of the mole- 

 cules as 10~* centimeters, reaches the con- 

 clusion that the radius of the ion can not 

 exceed three times this value. 



To account for the change of mobility- 

 associated with alteration of the pressure 

 or temperature conditions, it is supposed 

 that the clusters of molecules forming the 

 ions consist of fewer members at low pres- 

 sures and at high temperatures than under 

 ordinary circumstances. As the tempera- 

 ture rises, for instance, the ion may be 

 imagined as shedding one by one its com- 

 ponent molecules. The mobility, however, 

 varies continuously and not by jumps; it 

 may, therefore, be considered, in addition, 

 that a cluster at any temperature does not 

 always consist of the same number of 

 molecules. In the numerous collisions, to 

 which an ion as a constituent of a gas is 

 subjected, a molecule of the cluster may be 

 lost at one, to be gained at another impact, 

 the cluster acting on the whole as if it con- 

 tained the average number of members; it 

 is this average number which, from this 

 point of view, must be taken as decreasing 

 continuously with rise of temperature. 



From a consideration of the slow move- 

 ment of the ions in an electric field com- 

 pared with that which it is assumed a single 

 charged molecule would have in the same 

 circumstances, it is possible, with the aid 

 of the principles of the kinetic theory, to 

 make an estimate of the number of mole- 

 cules which go to make an ion. The argu- 

 ment is given in Mr. Phillips's paper on 

 "Ionic Velocities in Air at Different Tem- 

 peratures,"* and he calculates from his re- 

 sults that the positive ion at — 179° C. 

 consists, on the average, of about four and 

 a half molecules (4.63), while at -f 138° 

 * Phillips, Proc. B. B., A, 78, p. 167, 1906. 



C. the average number is only about one 

 and a half (1.52). For the negative ion 

 slightly smaller figures are obtained. 



Such an idea of the small ion, based, 

 either on the direct argument in its re- 

 stricted form already noted, or on the cal- 

 culation just mentioned, can not be con- 

 sidered satisfactory, and it is now shown 

 to be unnecessary by two workers at op- 

 posite sides of the world, Mr. Wellisch at 

 Cambridge and Mr. William Sutherland 

 at Melbourne. 



In this connection it is interesting to 

 recall another physical problem which ap- 

 parently also required for its explanation 

 a shrinkage of the molecules with rise of 

 temperature, that of the relation between 

 the temperature and the viscosity of a gas. 

 The solution of the problem was finally 

 reached in 1893 by Mr. Sutherland, from 

 a consideration of the influence of molecu- 

 lar force in bringing about collisions which 

 would otherwise not occur, the investiga- 

 tion being published in his paper on "The 

 Viscosity of Gases and Molecular Force.'" 

 The result of mutual attraction, only sen- 

 sible at small distances, is to make the 

 molecules, considered forceless, behave as 

 if they had a diameter greater than the 

 true value. As the molecular force is less 

 effective in causing collisions the greater 

 the velocity with which two molecules ap- 

 proach each other, the apparent diameter 

 to which it gives rise is less the higher the 

 temperature. It is now shown by the 

 writers I have mentioned that there is a 

 similar effect due to the ionic charge. 

 Owing to the influence of the electrical at- 

 traction, collisions between ions and mole- 

 cules take place which would otherwise be 

 avoided, and consequently the ions act as 

 molecules of greater than the normal size, 

 the apparent diameter decreasing as the 

 temperature rises. 



For the movement of an ion through 

 ° Sutherland, Phil. Mag., 36, p. 507, 1893. 



