and Two New Types of Viscosity, 33 



with the effect of ordinary viscosity. For it the resistance 

 due to induced viscosity in (34) is only one-fifth of the whole 

 resistance. From (34) and (31) we get that 6irrjah/e 2 v in 

 electrostatic units is the same quantity as 0-0097B* in ohm -1 , 

 which becomes 0-00971)3/9 x 10 11 in electrostatic units ; hence 

 we have the equation 



9 x 10 n x 6irrjah/e 2 v=0'0097B^ 



with 



^ = 0-0001035/3 xlO 10 , e = 3xl0- 10 , v=l, Vls = 0'0106, 



so a, the radius of C 5 H n COO, is 2*26 x 10 -8 cm. Now B, 

 the limiting volume of a gram-molecule of hydrogen, is 8'6, 

 so for the radius of the hydrogen molecule we get the value 

 (8-6/112)* x 2-26 xl0- 8 = 0-9(5 xl0~ 8 , which is practically 

 identical with that obtained from the kinetic theory of 

 gases. 



With the coefficient of diffusion we shall proceed in a 

 similar manner, that is we shall first find the radius of a 

 molecule of about the size of C 5 H n OOO, say that of glucose 

 C 6 H 12 6 . For this the value of B used in my paper on 

 diffusion is 134, which is perhaps 10 per cent, too large for 

 the gram-molecular volume of glucose in the solid state, but 

 such an error affects only minutely the ultimate estimate of 

 the radius of the hydrogen molecule. From (27) and (28) 



RTfl(l + 10-5/B*) 



67rrja 



Now at 0° C. KT for 2 grams of hydrogen is 226 x 10 8 , and 

 so at 16° C. the temperature of the diffusion experiments of 

 Ihovert, 



RT = 239 x 10 8 , A=s4A/*=0'0001035 x 10" 20 , and ^ = 0-0111, 



and so a the radius of a molecule of glucose is 3'14 x 10 _s cm., 

 and the radius of the hydrogen molecule is 



(8-6/134)* x 3-14 x 10- 8 = 1-19 x 10~ § . 



The agreement of these two new estimates of molecular size 

 with that from the kinetic theory of gases is as satisfactory 

 as could be expected. It shows that there is no need to 

 adopt the hypothesis of Kohlrausch and other writers that 

 different ions attach to themselves different envelopes of 

 solvent in such solvents as water. It has been proved that 

 the ion in electric conduction and the molecule in diffusion 

 move independently. 



Phil. Mag. S. 6. Vol. 14. No. 79. July 1907. P 



