212 PROCEEDINGS OP THE AMERICAN ACADEMY. 



The at least approximate validity of the simple Kohlrausch equation 

 under such widely different conditions, is a fact that must receive atten- 

 tion in any theoretical explanation of the phenomenon. The fact seems 

 somewhat remarkable when it is considered how great the change is in 

 the state of the solvent, which has been raised from near its melting point 

 to not very far below its critical point, and when it is considered that the 

 dissociation has decreased in the 0.1 normal solutions from about 84 per 

 cent at 18° to 60 per cent at 306° (see Section XV). The equation 

 cannot, however, retain its validity as the dissociation tendency ap- 

 proaches zero ; for then with increasing concentration the calculated 

 values of A would soon become negative : it must, if it is to apply 

 generally, be modified by multiplying the cube-root of the concentration 

 by some function of A which does not vary much as long as A/A is large, 

 in a manner similar to that which has been proposed by Barmwater. 



The fact that the van't Hoff equation does not express satisfactorily 

 the results with many salts even at 18° (see KC1 in Table X) has led 

 to the suggestion by Storch and Bancroft that a general expression of 

 the form A — A= KA"C" _1 be employed, the exponent n being different 

 with each salt. Our results show that in order to attain agreement it would 

 be necessary to vary the value of n also with the temperature. Thus it 

 was found that by putting ?i=1.6, the results with sodium chloride at 

 306° are expressed with a mean deviation of only 0.15 per cent, but the 

 use of this same exponent with the results at 18° gives rise to a mean 

 deviation of 0.69 per cent, while as shown in the above tables, the van't 

 Hoff function, with n = 1.5, applies well at 18°, but fails at 306°. The 

 fact that even at the highest temperature the exponent required has risen 

 only to 1.6 shows that the results do not correspond much more closely 

 with the Mass-Action Law, which requires the exponent 2, than they do 

 at the ordinary temperature. 



In view of the foregoing considerations there is at present no more 

 reliable means of deriving the conductivity A for zero concentration from 

 our results at the higher temperatures than by the application of the 

 Kohlrausch equation. We have therefore determined from our plots the 

 intercept of the straight line representing this equation with the axis along 

 which the conductivity values are laid off ; and it is these values of A 

 which are recorded within parentheses in Table VIII. For the sake of 

 uniformity, the A values at 18° were derived in the same way from the 

 data of Kohlrausch and Maltby ; they are about 1.2 per cent larger than 

 those deduced by these investigators. 



