344 



Dr. Kohlrausch. The Resistance of the Ions [Feb. 17, 



The fact is therefore established that the temperature change of the 

 fluidity of water is nearly the same as that of the conductivity of 

 dissociated aqueous solutions of electrolytes which haye a large tem- 

 perature coefficient. Even if nothing more was known than this fact, 

 the question of a connection between the electrolytic and the 

 mechanical motion in water must be considered a matter for serious 

 discussion. 



(5.) Discussion of the Extrapolation. — Extrapolation of an empirical 

 formula over a wide range can never be considered as necessarily repre- 

 senting the truth. This is especially true in a case like the present, 

 where at low temperatures it is applied to a state of matter other than 

 that for which the formula was originally deduced. It is a priori impos- 

 sible for the formula to hold where its extrapolation gives to the con- 

 ductivity or the fluidity a value zero. Since these quantities are from 

 their very nature positive, negative values are physically impossible. 

 Therefore the cutting of the zero axis by the curve at an acute angle 

 is a priori inadmissible, just as, for example, the assumption is 

 inadmissible that the Joule heating effect is proportional to the current 

 strength, or that the kinetic energy is proportional to the velocity. 

 A quantity from its nature positive can, as it becomes zero, have a 

 finite differential quotient as function of another quantity, only when 

 the other quantity cannot vary beyond the critical point. This can 

 be considered identical with the impossibility of negative values. In 

 reality the conductivity and the fluidity must reach the zero value in 

 a curve which is tangent to the axis of temperature. (Becoming zero 

 through a discontinuous process as in freezing is, of course, something 

 entirely different.) 



Therefore the quadratic formula, in spite of the fact that it shows 

 such a remarkably wide range of applicability, must be replaced by 

 another expression before the zero value is reached. 



The above explanation shows that my view of the " critical tem- 

 perature " of the fluidity and the conductivity of water as derived 

 from the quadratic formula, does not materially differ from that of 

 Messrs. Bousfield and Lowry. This temperature is only a quantity 

 by which one constant of the ordinary formula can be replaced ; but 

 the importance of the constant now introduced is verified, in that now 

 the individualities of the ions, if they do not entirely vanish, at any 

 rate disappear except for small differences. Further, the remarkable 

 fact follows, that approximately the same constant may be intro- 

 duced in the temperature formula of the viscosity of water. This 

 number, entering as a temperature, may therefore be called a funda- 

 mental constant of water, of course with the reservation which follows 

 from the fact that it varies by several degrees in the different cases. * 

 (Of- 3.) 



* The objection that the use of such a constant may be responsible for the 



