Uieory of Electrolytic Dissociation. 285 



Dr. Larmor has pointed out to the writer, there is reason to 

 believe that the gaseous laws would fail at much smaller 

 concentrations in solutions o£ electrolytes than in those of 

 non-electrolytes, If, as is most likely, the forces between the 

 dissolved molecules are electrical in nature, the effect of two 

 non-ionized bipolar molecules on each other will be analogous 

 to that between two short magnets : the force will vary 

 inversely as the fourth power of the distance. On the other 

 hand, with two isolated charged ions, the force will be that 

 between two small electrified bodies, and will vary as the 

 inverse square of the distance. Thus, beyond a certain 

 minute range, the inter-molecular forces will rapidly become 

 insensible, and solutions of non-electrolytes will then conform 

 to the gaseous laws. Electrified ions, however, will produce 

 sensible effects on each other at ranges much beyond these 

 inter-molecular spheres of action, and, even at great dilution, 

 will diverge from the ideal conditions. Such divergence 

 will certainly change the quantity of work done on dilution, 

 and thus affect the osmotic properties. It is not clear, how- 

 ever, that it will also diminish the migratory freedom neces- 

 sary for electrolysis : the inter-ionic forces will, on the 

 average, be equal in all directions, and may not influence 

 the mobility of the ions under an electromotive force. As a 

 conclusion, then, it follows if we accept the dissociation theory 

 that, in those solutions which are known to be fully ionized 

 at great dilutions, the limiting values of the osmotic pro- 

 perties and of the electrical conductivity should indicate the 

 same number of ions to the molecule ; when the concen- 

 tration increases and the ionization of such solutions ceases 

 to be complete, it is possible, but not necessary, that, through- 

 out a small range, the two methods should give identical 

 values for the coefficient of ionization; the concentration at 

 which such identity ceases should probably indicate the 

 point at which inter-ionic forces begin to prevent further 

 conformity with the gaseous laws ; and finally, for the case 

 of solutions in which complete ionization is not shown by 

 the equivalent conductivity, we cannot assume that any exact 

 relation between the two lines of research will be found. 



We must now see how far the experimental facts bear our 

 these theoretical conclusions. The equivalent conductivity 

 of electrolytes reaches a definite limit at a dilution which can 

 only be experimentally examined with accuracy in solutions 

 of simple salts, such as potassium chloride, which contain 

 two monovalent ions. In these cases alone, then, can we look 

 for the verification of the ideal relations. At the present 

 time, the best known of the osmotic properties is the depression 



