The most remarkable exception is common salt itself, the solution of which was one in 29, and therefore in 1116 there were 37.2 parts of salt. Now the equivalent of NaCl is 585, which is very much. greater.

Besides this the conductivity of a solution of salt in 29 of water would be much less in comparison with that of the other solutions than would appear from Cavendish's results, whereas if we assume that the molecular strength of the salt solution was really the same as that of the other solutions, the numbers do not differ much from those given by Kohlrausch.

The following table shows the results obtained by Cavendish and by Kohlrausch.

The theory of the electric resistance of electrolytes has been put on an entirely new footing by M. F. Kohlrausch, who has not only measured the resistance of a large number of solutions of different strengths and at different temperatures, but has discovered that the conductivity of a dilute solution of any electrolyte in water is the sum of two quantities, which we may call the specific conductivities of the components of the electrolyte, multiplied by the number of electro-chemical equivalents of the electrolyte in unit of volume of the solution. (Since the components of an electrolyte are not themselves electrolytes, it is manifest that they can have no actual conductivity, but the number to which we may give that name is such that when any two ions are actually combined into an electrolyte, the conductivity of the electrolyte depends on the sum of their respective numbers.)

Kohlrausch has also calculated the actual average velocity in millimetres per second with which the components are carried through the solution under an electromotive force of one volt per millimetre; and on the hypothesis that the components are charged with the electricity which travels with them, he has calculated the force in kilogrammes weight which must act on a milligramme of the component in order to make its average velocity in the solution one millimetre per second.

It appears to me that the simplest measure of the specific conductivity of an ion is the time during which we must suppose the electric force to act upon it so as to generate twice its actual average velocity. If we suppose that all the molecules of the ion are acted on by the electromotive force, but that each of them is brought to rest by

a collision with a molecule of the opposite kind n times in a second, then
the average velocity will be half that which the force can communicate
to the molecule in the nth part of a second.

According to the theory of Clausius, it is only a small proportion,
say 1/p, of the molecules, which, at any given instant, are dissociated
from molecules of the other kind, so as to be free to move under the
action of the electromotive force, so that we must suppose each of the
free molecules to continue free for a time pT; but since the proportion
of free molecules to combined ones is quite unknown, the only definite
result we can obtain from Kohlrausch's data is a certain very small
time T, such that if the electromotive force acted on the molecules of
the component during the time T, it would impress on them a velocity
twice their actual average velocity.

Since the time 7 is very small, it is more convenient to speak of
the molecule being brought to rest n times in a second, and to cal-
culate n.

On the Ratio of the Charge of a Globe to that of a Circle of the same

Diameter.

The true value of this ratio is = 1.570796....

Cavendish has given several different values as the results of his
experiments.

In the account of his experiments, which represents his most matured
conclusions, he states this ratio as 1:57 (Art. 237).

All the other values, however, either as stated by Cavendish or
as deducible from his experiments, are lower than this.

In Art. 281 the charge of the globe of 12.1 inches diameter being 1,
that of a circle 18.5 inches diameter is given as 992. The ratio of the
charge of a globe to that of a circle of equal diameter as deduced from
this is 1.542.

In Art. 445 the charge of the globe is compared with that of
a pasteboard circle of 19.4 inches diameter. Cavendish gives the actual
observations but does not deduce any numerical result from them, which
shows that he did not attach much weight to them. As they seem to
be the earliest measurements of the kind, I have endeavoured to in-
terpret the observations by assuming that the positive and negative
separations were equal when the observations are qualified in the same
words by Cavendish.

I thus find 14.2 or 14.3 for the charge of the globe, and 15-2 for
that of the circle, and from these we deduce for the ratio of the charge
of a globe to that of a circle of equal diameter 1·5054.

In Art. 456 the ratio as deduced by Cavendish from the observations
on the globe and the tin circle of 18.5 inches diameter is 1.56.

From the numerical data given in the same article, the ratio would
be 1.554.

Cavendish evidently thought the result given here of some value, for
he quotes it in the foot-note to Art. 473.

Another set of observations is recorded in Art. 478, from which we
deduce the ratio 1.561.

It appears by a comparison of Arts. 506 and 581 that Cavendish, at
the date of the latter article (which is doubtful), supposed the ratio to be
1.5. (See foot-note to Art. 581.)

At Art. 648 the ratio is stated as 1.54.

At Art. 654 measures are given from which we deduce 1.542 and
1.37.

The numbers in Art. 682 are the same as those in Art. 281.

ALPHABETICAL INDEX.

The references are to the Articles.