Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/339

between the molecules) as abscissæ, and $k/\mathrm {N}$ as ordinates, he is able to obtain the specific molecular conductivity for infinite dilution. When the values for $u$ and $v$ are worked out for these ideal solutions, it is found that the velocity of any given ion is independent of the nature of the salt of which it forms part, and hence Kohlrausch assigns numbers to various ions which represent their specific ionic velocity.

From a table of these numbers we can at once deduce the conductivity of any given salt solution, and the agreement of the values so obtained with those experimentally observed, furnishes the first confirmation of Kohlrausch’s theory. He calculates the conductivity of various salt solutions of strength $0.1$ gramme equivalent per litre, and then experimentally determines it for solutions of that strength. Some of his results are as follows:—

⁠Name of salt.⁠ ⁠Molecular conductivity⁠
calculated from the
ionic velocities.  Molecular conductivity 
observed. KCl 1060 1047 NH₄Cl 1040 1035 NaCl 0860 0865 1/2BaCl₂ 0840 0861 1/2ZnCl2₂ 0780 0768 KI 1070 1069 KNO₃ 1000 0983 AgNO₃ 0900 0886 KC₂H₃O₂ 0780 0784 HCl 3260 3244 KOH 1950 1986 NaOH 1750 1700

The tabulated numbers are $k/m\times 10^{8}$ where $k$ is the conductivity in terms of that of mercury, and $m$ is the number of gramme equivalents of salt per litre. The general agreement is very remarkable, though several exceptions show that the law is not of universal application; for instance, acetic acid should give 2980, while the observed number is 43.

The next confirmation of the theory was given by Dr. Oliver Lodge (‘B. A. Report,’ 1886), who actually observed the velocity of the hydrogen ion as it travelled along a glass tube and discolourized a solution of phenol-phthallein as it went. The tube contained a jelly in which was dissolved a little phenol-phthallein and common salt, with just enough soda to bring out the colour. The tube joined two vessels filled with sulphuric acid, and when a current was passed between them the hydrogen travelled with it, and liberated HCl as it went along the tube. This decolourized the phenol-phthallein, and could thus be traced. The velocity per unit potential gradient came out as $.0029$, $.0026$, and $.0024$ centim. per second, while Kohlrausch’s theoretical number was $.0030$.

This agreement is striking evidence in favour of Kohlrausch’s theory and leads us