1903.] 



and the Mechanical Friction of the Solvent. 



345 



(6.) Other Formula}. — Among the former attempts to derive an empirical 

 formula from the behaviour in ordinary temperatures, which does not 

 k i>fiori lose its significance as the conductivity or the fluidity 

 approaches zero, that of Slotte, <f> = 4> (1 +bt)", must be given the 

 first place. This has recently assumed a greater importance on account 

 of the extensive work of Thorpe and Rodger. Here, in the case of 

 the fluidity, the condition that d^jdt = where <f> = is fulfilled, for 

 here everywhere n>l. For the conductivity, however, nothing is 

 gained, since in the case of the acids n<\, and there dKjdt = oo for 

 k = ; there is, therefore, no object in recalculating our results 

 according to this formula. However, in a former paper I have given 

 the preference to Slotte's formula in a remark concerning fluidity. 

 To try to bring the coefficients of this formula into a relationship with 

 those of the quadratic formula was indeed not allowable. 



(7.) Experimental Indications. — The attempt to draw conclusions in 

 regard to the region near the zero value from the course of the 

 phenomenon in the region where the fluidity &c. have values of 

 considerable magnitude, would have, of course, very little prospect of 

 success. But perhaps the attempt to follow the fluidity of water or 

 the conductivity of dilute solutions down to lower temperatures would 

 be more successful than we think, if made in closed vessels of small 

 dimensions. 



Up to the present time we are acquainted only with phenomena 

 from which uncertain conclusions from analogy can be drawn. The 

 idea may be pretty certainly held as probable, that the viscosity and 

 the electrical resistance finally increase more slowly than the quadratic 

 formula extrapolated would indicate. In regard to viscosity, I 

 remember the investigations of Tammann on the freezing of over- 

 cooled liquids, and Ostwald's observations on salol. The phenomenon 

 of the gradual solidification of alcohol at low temperatures also leads 

 to the same conclusion. 



Numerous observations of the same kind in regard to electrical 

 behaviour are also recorded. The very slow increase of the conduc- 

 tivity of glass with increasing temperature is well known. A quanti- 

 tative determination of this has been made by Messrs. Bousfield and 

 Lowry. But how far a heterogeneous mixture like glass can be 

 considered parallel to a dilute ionised solution is doubtful. In the 

 same way, experiments such as those of Lehmann on the electrolysis 



introduction of errors is without much weight ; it is, at any rate, practically the 

 same case as that of the gas formula. This is written, making use of the absolute 

 zero, vp = const. (t + t), where t = 273, although it is certain that the result 

 v — for t = — 1 is false, so that the formula must assume another form before 

 v approaches its zero value. The constant of the gas formula loses its significance 

 at the point where the gas passes into the liquid state. The same is true for the 

 temperature constant of the fluidity, which we have introduced, when it passes 

 out of the liquid state. 



