Messrs Laby and Carse, On a relation, etc. 289 



found that the temperature variation of the conductivity and 

 viscosity of water can be expressed by one formula and repre- 

 sented by one curve. Kohlrausch's conductivity -temperature 

 curves for aqueous solutions of sodium acetate and sodium 

 valerate (the only two substances, whose anions are common to 

 his and this paper), were sensibly the same as the fluidity-tempe- 

 rature curve of water. Thus in these three cases there is ground 

 for supposing that U (the velocity of a given ion under a constant 



force) is proportional to the fluidity ( - ] 



or 

 lit 



U = constant x — . 



When the driving force (F) varies 



F 

 U= constant x — . 



This suggests that the motion of an ion through an electrolyte 

 may be very similar to that of small bodies through a viscous fluid. 

 Sir George Stokes* has shown that the velocity (assumed small) of 

 a sphere moving through a homogeneous viscous medium, when 

 no slipping occurs, is 



F 



v = a > 



07771a 



where F is the driving force, jx the coefficient of viscosity of the 

 medium, and a the radius of the sphere"!". If we assume this law 

 to hold for the motion of an ion in an electrolyte, though for 

 bodies of molecular dimensions the medium is not homogeneous 

 as postulated above, the radius of the ion, assumed spherical, may 

 be calculated. The value thus obtained for the radius is suffi- 

 ciently different from that deducible from the radius of the mole- 

 cule calculated by Jeansj from the kinetic theory of gases to 

 make the applicability of the law to this case doubtful. 



There appeared, however, another way of finding approxi- 



* Camb. Phil. Trans, ix. 58 (1850). 

 t A more general expression is 



F 

 Gir/xa 



/ /3a + 3/A 



where /3 is the coefficient of sliding friction and is infinity for no slipping and 



zero for infinite slipping, and so ^ J- may vary between 1 and |. Wbetham 



11 6 ' p« + 2fx. J 



(Phil. Trans, clxxxi. A 559, 1890) has shown that for the steady flow through a 

 capillary tube there is no slipping, and H. S. Allen (Phil. Map. 323, Sept. 1900) 

 that for small air bubbles rising in water or aniline, " the velocity of the bubble 

 agrees with that deduced from theoretical considerations by Stokes on the assump- 

 tion that no slipping occurs at the boundary." 



X Phil. Mag. Ser. vi. Vol. vm. pp. 692—699 (1904). 



VOL. XIII. PT. V. 20 



