By using the iron wire as a shunt and increasing the discharge so as to obtain a shock of easily remembered intensity, Cavendish was enabled to compare the wire with a column 5.1 inches long of saturated solution of salt.

By this experiment the resistance of saturated solution of salt is 355400 times that of iron.

By the statements in Art. 398, that the resistance of rain-water is 400,000,000 times that of iron wire, and 720 times that of a saturated solution of sea-salt, the resistance of saturated solution would be 555555 times that of iron wire.

It is true that this result given by Cavendish does not agree with the only experiment he has recorded, but we must remember that it is the only result which he published, and therefore he must have thought it the best he had.

By Kohlrausch's experiments on salt solutions combined with Matthiessen's on metals, the resistance of saturated solution of salt is 451390 times that of annealed iron, when both are at 18°C. The ratio of the resistances would agree with that given by Cavendish at a temperature of about 11°C.

The coincidence with the best modern measurements is remarkable.

NOTE 33, ART. 619.

Conductivity of Solutions of Salt.

According to the measurements of Kohlrausch

the electric con

ductivity k, of saturated solution of sodium chloride, the conductivity of mercury at 0° C. being taken as unity, is given by the equation

10% 1259 (1+0.0308t+ 0.000146).

=

When the temperature is near 18o C., we may use the equation

10% 2015+45·1 (t - 18).

Saturated solution at 18° contains according to Kohlrausch 26-4 Cavendish's saturated solution contained

per cent. of salt.

of salt, which is equivalent to 26.45 per cent.

1

3.78

Kohlrausch finds that saturated solution of salt is one of the best standard substances for the comparison of the resistance of other electrolytes. Its conductivity seems to be sensibly the same, whether it is made with chemically pure salt or with the ordinary salt of comThe temperature coefficient is also smaller than that of many other electrolytes.

merce.

* Wiedemann's Annalen Bd. vi. (1879) p. 51.

For other solutions of sodium chloride he finds that at 18°

where p is the proportion, by weight, of the salt to the whole solution.

For the particular solutions examined by Cavendish we have

The substances mentioned by Cavendish are easily identified, with the exception of "calc. S. S. A." and "f. alk. D." The weights of the quantities furnish no indication, for they are so large as to show that a dilute solution was used. The letters A and D probably indicate the bottles in which the solutions were kept.

The expression f. alk. or fixed alkali occurs in several parts of Cavendish's writings, especially in the manuscripts lithographed by Mr Vernon Harcourt in the Report of the British Association for 1839. It certainly means pearl ashes or carbonate of potash. The full title seems to have been alkali fixum vegetabile, as distinguished from alkali fixum fossile, which is sodic carbonate, and other writers seem to have used the expression fixed alkali for either of these, but Cavendish always uses the expression as a synonym for pearl ashes, and distinguishes potassic hydrate by the name of "sope leys."

The conductivity as determined by Cavendish agrees much better with potassic carbonate than with potassic hydrate, the conductivity of which is much greater.

It seems likely that calc. S. S. was sodic carbonate, and the conductivity would agree very well with this explanation, only it is difficult to find among the names in use at the time any which could be written in this form. Mr Maine has suggested Calcined Salsola Soda. The burnt seaweed from the shores of the Mediterranean, from which soda was often extracted was, I believe, called salsola, but I doubt whether the word soda was then in use.

The weights of the other substances are, when reduced to pennyweights, not very far from the equivalent numbers now received, hydrogen being taken as the unit.

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 58.5, 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 calculate 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 π = 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
15. (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.