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experiments have been made on the subject (see Das Leitvermögen der Elektrolyte).

By combining the results thus obtained with the sum of the velocities, as determined from the conductivities, Kohlrausch calculated the absolute velocities of different ions under stated conditions. Thus, in the case of the solution of potassium chloride considered above, Hittorf’s experiments show us that the ratio of the velocity of the anion to that of the cation in this solution is .51 : .49. The absolute velocity of the potassium ion under unit potential gradient is therefore 0.000567 cm. per sec., and that of the chlorine ion 0.000592 cm. per sec. Similar calculations can be made for solutions of other concentrations, and of different substances.

Table IX. shows Kohlrausch’s values for the ionic velocities of three chlorides of alkali metals at 18° C, calculated for a potential gradient of 1 volt per cm.; the numbers are in terms of a unit equal to 10−6 cm. per sec.:—

Table IX.
  KCl NaCl LiCl
m u + v u v u + v u v u + v u v
 0 1350 660 690 1140 450 690 1050 360 690
 0.0001 1335 654 681 1129 448 681 1037 356 681
 .001 1313 643 670 1110 440 670 1013 343 670
 .01 1263 619 644 1059 415 644 962 318 644
 .03 1218 597 621 1013 390 623 917 298 619
 .1 1153 564 589 952 360 592 853 259 594
 .3 1088 531 557 876 324 552 774 217 557
 1.0 1011 491 520 765 278 487 651 169 482
 3.0 911 442 469 582 206 376 463 115 348
 5.0       438 153 285 334 80 254
10.0             117 25 92

These numbers show clearly that there is an increase in ionic velocity as the dilution proceeds. Moreover, if we compare the values for the chlorine ion obtained from observations on these three different salts, we see that as the concentrations diminish the velocity of the chlorine ion becomes the same in all of them. A similar relation appears in other cases, and, in general, we may say that at great dilution the velocity of an ion is independent of the nature of the other ion present. This introduces the conception of specific ionic velocities, for which some values at 18° C. are given by Kohlrausch in Table X.:—

Table X.
K 66 × 10−5 cms. per sec. Cl 69 × 10−5 cms. per sec.
Na 45 I 69
Li 36 NO3 64
NH4 66 OH 162
H 320 C2H3O2 36
Ag 57 C3H5O2 33

Having obtained these numbers we can deduce the conductivity of the dilute solution of any salt, and the comparison of the calculated with the observed values furnished the first confirmation of Kohlrausch’s theory. Some exceptions, however, are known. Thus acetic acid and ammonia give solutions of much lower conductivity than is indicated by the sum of the specific ionic velocities of their ions as determined from other compounds. An attempt to find in Kohlrausch’s theory some explanation of this discrepancy shows that it could be due to one of two causes. Either the velocities of the ions must be much less in these solutions than in others, or else only a fractional part of the number of molecules present can be actively concerned in conveying the current. We shall return to this point later.

Friction on the Ions.—It is interesting to calculate the magnitude of the forces required to drive the ions with a certain velocity. If we have a potential gradient of 1 volt per centimetre the electric force is 108 in C.G.S. units. The charge of electricity on 1 gram-equivalent of any ion is 1/.0001036 = 9653 units, hence the mechanical force acting on this mass is 9653×108 dynes. This, let us say, produces a velocity u; then the force required to produce unit velocity is PA = 9.653×1011/u dynes = 9.84×105/u kilograms-weight. If the ion have an equivalent weight A, the force producing unit velocity when acting on 1 gram is P1 = 9.84×105/Au kilograms-weight. Thus the aggregate force required to drive 1 gram of potassium ions with a velocity of 1 centimetre per second through a very dilute solution must be equal to the weight of 38 million kilograms.

Table XI.
Kilograms-weight. Kilograms-weight.
  PA P1   PA P1
K 15×108  38×106 Cl 14 108 40×106
Na 22 ”  95 ” I 14 ” 11 ”
Li 27 ” 390 ” NO3 15 ” 25 ”
NH4 15 ”  83 ” OH  5.4 ” 32 ”
H  3.1 ” 310 ” C2H8O2 27 ” 46 ”
Ag 17 ”  16 ” C3H5O2 30 ” 41 ”

Since the ions move with uniform velocity, the frictional resistances brought into play must be equal and opposite to the driving forces, and therefore these numbers also represent the ionic friction coefficients in very dilute solutions at 18° C.

Direct Measurement of Ionic Velocities.—Sir Oliver Lodge was the first to directly measure the velocity of an ion (B.A. Report, 1886, p. 389). In a horizontal glass tube connecting two vessels filled with dilute sulphuric acid he placed a solution of sodium chloride in solid agar-agar jelly. This solid solution was made alkaline with a trace of caustic soda in order to bring out the red colour of a little phenol-phthalein added as indicator. An electric current was then passed from one vessel to the other. The hydrogen ions from the anode vessel of acid were thus carried along the tube, and, as they travelled, decolourized the phenol-phthalein. By this method the velocity of the hydrogen ion through a jelly solution under a known potential gradient was observed to about 0.0026 cm. per sec, a number of the same order as that required by Kohlrausch’s theory. Direct determinations of the velocities of a few other ions have been made by W. C. D. Whetham (Phil. Trans. vol. 184, A, p. 337; vol. 186, A, p. 507; Phil. Mag., October 1894). Two solutions having one ion in common, of equivalent concentrations, different densities, different colours, and nearly equal specific resistances, were placed one over the other in a vertical glass tube. In one case, for example, decinormal solutions of potassium carbonate and potassium bichromate were used. The colour of the latter is due to the presence of the bichromate group, Cr2O7. When a current was passed across the junction, the anions CO3 and Cr2O7 travelled in the direction opposite to that of the current, and their velocity could be determined by measuring the rate at which the colour boundary moved. Similar experiments were made with alcoholic solutions of cobalt salts, in which the velocities of the ions were found to be much less than in water. The behaviour of agar jelly was then investigated, and the velocity of an ion through a solid jelly was shown to be very little less than in an ordinary liquid solution. The velocities could therefore be measured by tracing the change in colour of an indicator or the formation of a precipitate. Thus decinormal jelly solutions of barium chloride and sodium chloride, the latter containing a trace of sodium sulphate, were placed in contact. Under the influence of an electromotive force the barium ions moved up the tube, disclosing their presence by the trace of insoluble barium sulphate formed. Again, a measurement of the velocity of the hydrogen ion, when travelling through the solution of an acetate, showed that its velocity was then only about the one-fortieth part of that found during its passage through chlorides. From this, as from the measurements on alcohol solutions, it is clear that where the equivalent conductivities are very low the effective velocities of the ions are reduced in the same proportion.

Another series of direct measurements has been made by Orme Masson (Phil. Trans. vol. 192, A, p. 331). He placed the gelatine solution of a salt, potassium chloride, for example, in a horizontal glass tube, and found the rate of migration of the potassium and chlorine ions by observing the speed at which they were replaced when a coloured anion, say, the Cr2O7 from a solution of potassium bichromate, entered the tube at one end, and a coloured cation, say, the Cu from copper sulphate, at the other. The coloured ions are specifically slower than the colourless ions which they follow, and in this case it follows that the coloured solution has a