THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
125 
and thus get for the values for the K and Na ions, 
B k = 3-16, B Na = 175. 
The complete series of hydration numbers is then as follows* :— 
Brci = 3'33, B NaCI = 2'8, B C1 = 3’5, B K = o'16, B Na = 175. 
With the aid of the numbers for the separate ions the radions are calculated from 
the expression 
r = T 1 (l+B/r 2/3 )-\ 
taking the values for l given by Kohlrausch in his 1900 paper and above set out. 
The values so obtained are set out in the following tables 
Table XIII.—Values of Badions and Ionic Volumes in KC1 Solutions. 
p. 
1 log h. 
r K- 
r ci- 
r K 3 x 10 6 . 
r cl 3 x 10 6 . 
lv. 
0 
oc 
0-01546 
0-01528 
3-692 
3-569 
7-261 
1 
1-7418 
0-01463 
0-01437 
3-128 
2-968 
6-096 
2 
1-5382 
0-01417 
0-01387 
2-843 
2-671 
5-514 
3 
1-4178 
0-01380 
0-01348 
2-627 
2-448 
5-075 
4 
1-3315 
0-01348 
0-01314 
2-448 
2-268 
4-716 
6 
1-2081 
0-01293 
0-01256 
2-163 
1-981 
4-144 
Normal 
1-1542 
0-01266 
0-01227 
2-029 
1-852 
3-881 
Table XIV.—Values of Radions and Ionic Volumes in NaCl Solutions. 
P. 
1 log h. 
,- Na- 
?’ci* 
r Na 3 x 10 3 . 
? d 3 x 10 6 . 
l. 
0 
OC 
0-02296 
0-01528 
12-107 
3-569 
15-676 
1 
1-6714 
0-02214 
0-01422 
10-848 
2-876 
13-724 
2 
1-4678 
0-02167 
0-01365 
10-177 
2-545 
12-722 
3 
1-3474 
0-02129 
0-01321 
9-648 
2-303 
11-951 
4 
1-2611 
0-02095 
0-01282 
9-198 
2-137 
11-335 
Normal 
1-1573 
0-02047 
0-01229 
8-578 
1 • 852 
10-430 
6 
1-1377 
0-02041 
0-01218 
8-506 
1-806 
10-312 
In the above tables the values of the radions are given in ionic units as before 
defined. Expressed in the same unit the volume of an ion would be §7tt 3 . But we 
shall save trouble, with a gain of convenience, if we take the volume of the ions as 
r 3 xlO b . Our unit of ionic volume is therefore the volume of an ion whose radius 
measured in ionic units is 0*01. The volumes of the ions so calculated are also set 
* These numbers can only be regarded as approximately fixed. The existence of the discrepancies 
above indicated in the values of the Hittorf numbers introduces considerable uncertainty. This, 
however, is not of much consequence in the consideration of dilute solutions, since the magnitude of the 
radion is primarily fixed by the mobility at infinite dilution, and the hydration number affects only the 
rate of change of magnitude with dilution, which is small. 
