and Two New Types of Viscosity. 7 



varying inversely as the fourth power o£ the distance. But 

 present purposes will be served i£ in (7) we replace 77 by #, 

 and put c=0, obtaining 677116a for the resistance due to 

 induced viscosity. 



3. The Theoretical Equation for Molecular 

 Specific C 'onductivity. 



P Let h be the mass of the atom of hydrogen. In a solution 

 of n gram-molecules per cm. 3 of a . solute whose molecule 

 yields ?i x positive and n 2 negative ions of valencies iq and v 2 , 

 and whose degree of ionization is i, we have q 1 — inn 1 /h ions 

 of the one sort, and q 2 =inn. 2 /h ions of the other. For the 

 steady motion of an ion of each sort we must equate the 

 electric driving force to the whole resistance. Consider a 

 positive ion of radius cq moving with velocity it 1; and a 

 negative of radius a 2 moving with velocity u 2 . The relative 

 velocity of the positive ion and its nearest negative neighbours 

 is u x — u. 2 . Their mean distance apart to take the place of q~i 

 in (4) we may estimate in the following way : — Imagine the 

 in(n 1 + n 2 )/h ions uniformly distributed so that each receives 

 for domain {in(ni-\-n 2 )/h}~ 1 cm. 3 , then the distance of an ion 

 from its nearest neighbours of opposite sign is {in(?i 1 + n 2 )/h \~^t 

 and our £ is to be multiplied by v 1 v 2 , and by jq 2 or v 2 . Thus 

 for the resistance to the motion of each ion due to the 

 viscosity J over the area \in(ni + n^)/h\~* belonging to the 

 ion is this area multiplied by ^(u 1 — u 2 y/{in(n l + n 2 )/h}~^ or 

 %(ui — u 2 ) {infa -f n 2 )/h}~*. 



Then we have the resistances given in (7) and after (7), and 

 for the motion of a positive and a negative ion we have the 

 equations 



VxedE/dx = v^v^i u^ — //.^{ind^-}- n 2 )} 5 -\-67ru 1 v{ 2 6 1 a 1 



-f ^iru 1 7ja 1 ( 1 + c a{ 2 ), I 



c ' 

 —v 2 ed^ijdx — — v 1 v 2 2 ^{u 1 —u 2 ){in(9ii + n 2 )}~^ + 67ru 2 v 2 2 2 a 2 | 



+ 6iru 2 r,a 2 (1 + c. a 2 2 ). J 



An additional factor iq or v 2 goes with f because the viscous 

 effect on ve is v times that on e. 



Now the electric current across each cm. 2 section of the 

 solution is ein(niy^u 1 — n 2 v 2 u 2 jlh^ and to express this more 

 ■compactly let us put in (5) A = A/77 and 



1/A r= 6wa 1 ^{C , y 1 V/4wK 1 « 1 8 ZA + 1/(1 + C/0! 8 ) /«% (8) 



So) 



