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In Arts. 336 to 339 we find a most ingenious method of determining by experiment the effect of the floor, walls and ceiling of a room, and of other surrounding objects, in increasing the apparent capacity of a conductor placed in a given position in the room. The method consists in measuring the capacities of two conductors of the same shape but of different dimensions, the centre of each being at the given point in the room. If the experiment had been made with the conductors at an infinite distance from all other bodies their capacities would have been in the ratio of their corresponding dimensions, but the effect of surrounding objects is to make their capacities vary in a higher ratio than that of their dimensions, and from the measured ratio of the two capacities, the correction for the effect of surrounding objects on the capacity of any small body may be calculated.
Cavendish also verified by experiment what he had already proved theoretically, that the capacity of two condensers is not sensibly altered when they are placed near to each other or far apart.
But besides this series of experiments on electric capacity, another course of experiments on electric resistance was going on between 1773 and 1781, the knowledge of which seems never to have been communicated to the world.
In his paper on the Torpedo in the Philosophical Transactions for 1776 (Art. 398) he alludes to "some experiments of which I “propose shortly to lay an account before this Society,” but he never followed up this proposal by divulging the method by which he obtained the results which he proceeds to state—“that iron “wire conducts about 400 million times better than rain or dis"tilled water*,” and that “sea water, or a solution of one part of “salt in 30 of water conducts 100 times, and a saturated solution “ of sea-salt about 720 times better than rain water."
Such was the reputation of Cavendish for scientific accuracy, that these bare statements seem to have been accepted at once, and soon found their way into the general stock of scientific information, although no one, as far as I can make out, has ever conjectured by what method Cavendish actually obtained them, more than forty years before the invention of the galvanometer, the only instrument by which any one else has ever been able to compare electric resistances.
* This is equivalent to saying that iron wire conducts 555,555 times better than saturated solution of sea salt. A comparison of the experiments of Matthiessen on iron with those of Kohlrausch on solutions of sodium chloride at 18°C. would make the ratio 451,390. The resistance of iron increases and that of the solution diminishes as the temperature rises, and at a temperature of about 11°C, the ratio of the resistances would agree with that given by Cavendish.
We learn from the manuscripts now first published, that Cavendish was his own galvanometer. In order to compare the intensity of currents he caused them to pass through his own body, and by comparing the intensity of the sensations he felt in his wrist and elbows, he estimated which of the two shocks was the more powerful.
As Cavendish does not appear to have prepared an account of these experiments in the manner in which he usually wrote out what he intended to publish, it may be well to describe them here, as we collect them from different parts of his Journals.
The conductors to be compared were for the most part solutions of common_salt of known strength or of other substances. These solutions were placed in glass tubes, more than a yard long, bent near one end. The tubes had been previously calibrated by means of mercury.
Two wires were run into the tube, probably through holes in corks at each end, to serve as electrodes. The length of the effective column of the liquid could be altered by sliding the wire in the straight part of the tube.
In order to send electric discharges of equal quantity and equal electromotive force through two different tubes Cavendish chose six jars of nearly equal capacity from “ Nairne's last battery.” The two tubes to be compared were placed so that the wires run into their bent ends communicated with the outside of this battery of six jars. The wires run into the straight ends of the tubes were fastened to two separately insulated pieces of tinfoil. The six jars were then all charged at once by the same conductor till the gauge electrometer indicated the proper degree of electrification. The conductor was then removed, so that the six jars remained with their inside coatings insulated from each other and equally charged.
Cavendish then taking two pieces of metal, one in each hand, touched with one the tinfoil belonging to one of the tubes to be compared, and then with the other touched the knob of jar No. 1, so as to receive a shock, the charge passing through his body and the first tube.
He next laid one of the metals on the tinfoil of the second tube, and then touching with the other the knob of jar No. 2, he received a second shock, the discharge passing through his body and the second tube.
In this way he took six shocks, making them pass alternately through the first and the second tube, and proceeded to record his impression whether the intensity of the shock through the second tube was greater or less than that of the shock through the first, and concluded that the tube which gave the greater shock had the smaller resistance.
He then adjusted the wire in one of the tubes so as to make the resistance more nearly equal to that of the other, and repeated the experiment, always recording his impression of the result, till he found that one adjustment made the shock of the second tube sensibly greater than that of the first, and that another adjustment made it sensibly less.
From the result of the whole series of experiments he judged what adjustment would make the two shocks exactly equal.
Instead of using six jars only, he seems latterly to have used the whole battery, electrifying one row to a given degree and then communicating this charge to the whole battery, and taking the discharge of one row at a time through the tubes alternately. He seems to have found some advantage in thus using a discharge of greater quantity and smaller electromotive force.
The accuracy which Cavendish attained in the discrimination of the intensity of shocks is truly marvellous, whether we judge by the consistency of his results with each other, or whether we compare them with the latest results obtained with the aid of the galvanometer, and with all the precautions which experience has shown to be necessary in measuring the resistance of electrolytes.
One of the most important investigations which Cavendish made in this way was to find, as he expressed it, “what power of the velocity the resistance is proportional to *.”
Cavendish means by "resistance” the whole force which resists the current, and by “velocity" the strength of the current through unit of area of the section of the conductor.
(In modern language the word resistance is used in a different sense, and is measured by the force which resists a current of unit strength.)
By four different series of experiments on the same solution in wide and in narrow tubes, Cavendish found that the resistance (in his sense) varied as the
1:08, 1:03, 0.976, and 1.00 power of the velocity.
This is the same as saying that the resistance in the modern sense) varies as the
0:08, 0:03, – 0·024 power of the strength of the current in the first three sets of experiments, and in the fourth set that it does not vary at all.
This result, obtained by Cavendish in January, 1781, is an anticipation of the law of electric resistance discovered independently by Ohm and published by him in 1827. It was not till long after the latter date that the importance of Ohm's law was fully appreciated, and that the measurement of electric resistance became a recognised branch of research. The exactness of the proportionality between the electromotive force and the current in the same conductor seems, however, to have been admitted, rather because nothing else could account for the consistency of the measurements of resistance obtained by different methods, than on the evidence of any direct experiments.
Some doubts, however, having been suggested with respect to the mathematical accuracy of Ohm's law, the subject was taken up by the British Association in 1874, and the experiments of Professor Chrystal, by which the exactness of the law, as it relates to metallic conductors, was tested by currents of every degree of
* Arts. 574, 573, 629, 686.
intensity, are contained in the Report of the British Association for 1876.
The laws of the strength of currents in multiple and divided circuits are accurately stated by Cavendish in Arts. 417, 597, 598.
Cavendish applied the same method of experiment to compare the resistance of the same liquid at different temperatures*, and he found that "salt in 69 [of water] conducts 1.97 times better in heat of 105 than in that of 581." He also found that “the proportion of the resistance of saturated solution and salt in 999 to each other seems not much altered by varying heat from 50 to 95."
Kohlrausch, who has made a most extensive series of experiments on the resistance of electrolytes, gives results from which it appears that the ratio of the resistances of salt in 69 at 105° F. and at 58% F. would be 1.59. He also finds that the temperature coefficient for solutions of salt alters very little with the strength. See Note 33.
Cavendish also tested the resistance of solutions of salt of strengths varying from saturation to one in 20000 of distilled water, and arrived at the result, which Kohlrausch has shown to be nearly accurate, that for weak solutions the product of the resistance into the percentage of salt is nearly constant.
Of all substances, that for which different observers have given the most different measures of resistance is pure water.
It has been found indeed that the presence of the minutest trace of impurity in water diminishes its resistance enormously. Thus Kohlrausch found that it was necessary to use water quite freshly distilled in platinum vessels, for if placed in a glass vessel it rapidly diminished in resistance by dissolving a minute quantity of the glass, and a few minutes exposure to the air of the laboratory, by impregnating the water with a trace of tobacco smoke, was found sufficient to spoil it for a determination of resistance. Kohlrausch indeed estimates that the electric conductivity which he obseryed in the purest water he could obtain might be accounted for by the presence of no more than one ten millionth part of hydrochloric acid, a quantity which no chemical analysis
# Art. 691.