﻿Nature of the Large Ions in the Air. 523 



where n 2 is the number of air molecules per cubic centimetre, 

 and M the mutual potential energy at collision o£ ion and 

 molecule due to the ionic charge. In the case of the large 

 ion, on account of its size, M will no doubt be very small 

 compared with m 2 v 2 , and the last factor in the above expression 

 will be neglected in this discussion as probably differing 

 little from unity. 



Let _ s 1 _ nil 



then with well known substitutions the expression for the 

 reciprocal of the mobility may be written 



1 



Pop 



8N f 



t't ois oerj 



(! + *)» Vy(l+y), 



where N is the number of air molecules per cubic centi- 

 metre and p the density of air under standard conditions, 

 7] the viscosity at the temperature t° C, and p the air pressure. 

 The modification of this formula so that it may include 

 the effect of the persistence of velocities after collision is 

 doubtless a small one, and may be neglected for the present 

 purpose. 



The diameter of the ion as calculated by the preceding- 

 expression does not vary greatly for moderate changes in 

 the density, so, in view of the lack of any knowledge of the 

 core, limits to the diameter of the ion according to this 

 method of estimation are set out in Table II. for various 

 values of the mobility, by assuming firstly that the ion is all 

 water, and secondly that the density of the whole is 2*5, 

 this figure being considered as possibly the value of the 

 density of the core. 



If the resistance to the motion of the transition layer is 

 not negligible compared with that offered to the motion of the 

 ion as a whole, then the diameter of the liquid part of the 

 drop corresponding to any mobility will be less than that 

 given in the table, and the mass greater than that indicated 

 by the diameter. 



The calculation has been made from the following data : — 



JV==1-29x10 10 e.s.u. 5 s 2 = 2-9x 10" 8 (diam. of air molecule), 

 ?/ 20 =l-80xlO- 4 3 m 2 =4-7xl0" 2a (mass „ „ ), 



p = <M)01293, volume of ion= sirfe-V, 



p=l-0132xl0 6 . 



