The accounts of Cavendish's death differ to some extent in their details, but otherwise are very similar. It appears that he requested his servant, "as he had something particular to engage his thoughts, and did not wish to be disturbed by any one," to leave him and not to return until a certain hour. When the servant came back, at the time appointed, he found his master dead. This was on February 24, 1810, after an illness of only two or three days.
It is mainly on account of his researches in electricity that the biography of Cavendish finds a place in this volume. These investigations took place between the years 1760 and 1783, and, as already stated, were all conducted in the stables attached to his father's house in Marlborough Street. It was by these experiments that electricity was first brought within the domain of measurement, and many of the numerical results obtained far exceeded in accuracy those of any other observer until the instruments of Sir W. Thomson rendered many electrical measurements a comparatively easy matter. The near agreement of Cavendish's results with those of the best modern electricians has made them a perpetual monument to the genius of their author. It was at the request of Sir W. Thomson, Mr. Charles Tomlinson, and others, that Cavendish's electrical researches might be given to the public, that the Duke of Devonshire, in 1874, entrusted the manuscripts to the care of the late Professor Clerk Maxwell. They had previously been in the hands of Sir William Snow Harris, who reported upon them, but after his death, in 1867, the report could not be found. The papers, with an introduction and a number of very valuable notes by the editor, were published by the Cambridge University Press, just before the death of Clerk Maxwell, in 1879. Sir W. Thomson quotes the following illustration of the accuracy of Cavendish's work:—"I find already that the capacity of a disc was determined experimentally by Cavendish as 1/1·57 of that of a sphere of the same radius. Now we have capacity of disc = (2/π)a = a/1·571!"
Cavendish adopted Franklin's theory of electricity, treating it as an incompressible fluid pervading all bodies, and admitting of displacement only in a closed circuit, unless, indeed, the disturbance might extend to infinity. This fluid he supposed, with Franklin, to be self-repulsive, but to attract matter, while matter devoid of electricity, and therefore in the highest possible condition of negative electrification, he supposed, with Æpinus, to be, like electricity, self-repulsive. One of Cavendish's earliest experiments was the determination of the precise law according to which electrical action varies with the distance between the charges. Franklin had shown that there was no sensible amount of electricity on the interior of a deep hollow vessel, however its exterior surface might be charged. Cavendish mounted a sphere of 12·1 inches in diameter, so that it could be completely enclosed (except where its insulating support passed through) within two hemispheres of 13·3 inches diameter, which were carried by hinged frames, and could thus be allowed to close completely over the sphere, or opened and removed altogether from its neighbourhood. A piece of wire passed through one of the hemispheres so as to touch the inner sphere, but could be removed at pleasure by means of a silk string. The hemispheres being closed with the globe within them, and the wire inserted so as to make communication between the inner and outer spheres, the whole apparatus was electrified by a wire from a charged Leyden jar. This wire was then removed by means of a silken string and "the same motion of the hand which drew away the wire by which the hemispheres were electrified, immediately after that was done, drew out the wire which made the communication between the hemispheres and the inner globe, and, immediately after that was drawn out, separated the hemispheres from each other," and applied the electrometer to the inner globe. "It was also contrived so that the electricity of the hemispheres and of the wire by which they were electrified was discharged as soon as they were separated from each other.... The inner globe and hemispheres were also both coated with tinfoil to make them the more perfect conductors of electricity." The electrometer consisted of a pair of pith-balls; but, though the experiment was several times repeated, they shewed no signs of electrification. From this it was clear that, as there could have been no communication between the globe and hemispheres when the connecting wire was withdrawn, there must have been no electrification on the globe while the hemispheres, though themselves highly charged, surrounded it. To test the delicacy of the experiment, a charge was given to the globe less than one-sixtieth of that previously given to the hemispheres, and this was readily detected by the electrometer. From the result Cavendish inferred that there is no reason to think the inner globe to be at all charged during the experiment. "Hence it follows that the electric attraction and repulsion must be inversely as the square of the distance, and that, when a globe is positively electrified, the redundant fluid in it is lodged entirely on its surface." This conclusion Cavendish showed to be a mathematical consequence of the absence of electrification from the inner sphere; for, were the law otherwise, the inner sphere must be electrified positively or negatively, according as the inverse power were higher or lower than the second, and that the accuracy of the experiment showed the law must lie between the 2 1/50 and the 1 49/50 power of the distance. With his torsion-balance, Coulomb obtained the same law, but Cavendish's method is much easier to carry out, and admits of much greater accuracy than that of Coulomb. Cavendish's experiment was repeated by Dr. MacAlister, under the superintendence of Clerk Maxwell, in the Cavendish Laboratory, the absence of electrification being tested by Thomson's quadrant electrometer, and it was shown that the deviation from the law of inverse squares could not exceed one in 72,000.
The distinction between electrical charge or quantity of electricity and "degree of electrification" was first clearly made by Cavendish. The latter phrase was subsequently replaced by intensity, but electric intensity is now used in another sense. Cavendish's phrase, degree of electrification, corresponds precisely with our notion of electric potential, and is measured by the work done on a unit of electricity by the electric forces in removing it from the point in question to the earth or to infinity. Along with this notion Cavendish introduced the further conception of the amount of electricity required to raise a conductor to a given degree of electrification, that is, the capacity of the conductor. In modern language, the capacity of a conductor is defined as "the number of units of electricity required to raise it to unit potential;" and this definition is in precise accordance with the notion of Cavendish, who may be regarded as the founder of the mathematical theory of electricity. Finding that the capacities of similar conductors are proportional to their linear dimensions, he adopted a sphere of one inch diameter as the unit of capacity, and when he speaks of a capacity of so many "inches of electricity," he means a capacity so many times that of his one-inch sphere, or equal to that of a sphere whose diameter is so many inches. The modern unit of capacity in the electro-static system is that of a sphere of one centimetre radius, and the capacity of any sphere is numerically equal to its radius expressed in centimetres. Cavendish determined the capacities of nearly all the pieces of apparatus he employed. For this purpose he prepared plates of glass, coated on each side with circles of tinfoil, and arranged in three sets of three, each plate of a set having the same capacity, but each set having three times the capacity of the preceding. There was also a tenth plate, having a capacity equal to the whole of the largest set. The capacity of the ten plates was thus sixty-six times that of one of the smallest set. With these as standards of comparison, he measured the capacities of his other apparatus, and, when possible, modified his conductors so as to make them equal to one of his standards. His large Leyden battery he found to have a capacity of about 321,000 "inches of electricity," so that it was equivalent to a sphere more than five miles in diameter. One of his instruments employed in the measurement of capacities was a "trial plate," consisting of a sheet of metal, with a second sheet which could be made to slide upon it and to lie entirely on the top of the larger plate, or to rest with any portion of its area extending over the edge of the former. This was a conductor whose capacity could be varied at will within certain limits. Finding the capacity of two plates of tinfoil on glass much greater than his calculations led him to expect, Cavendish compared them with two equal plates having air between, and found their capacity very much to exceed that of the air condenser. The same was the case, though in a less degree, with condensers having shellac or bee's-wax for their dielectrics, and thus Cavendish not only discovered the property to which Faraday afterwards gave the name of "specific inductive capacity," but determined its measure in these dielectrics. He also discovered that the apparent capacity of a Leyden jar increases at first for some time after it has been charged—a phenomenon connected with the so-called residual charge of the Leyden jar. Another feature on which he laid some stress, and which was brought to his notice by the comparison of his coated panes, was the creeping of electricity over the surface of the glass beyond the edge of the tinfoil, which had the same effect on the capacity as an increase in the dimensions of the tinfoil. The electricity appeared to spread to a distance of 0·07 inch all round the tinfoil on glass plates whose thickness was 0·21 inch, and 0·09 inch in the case of plates 0·08 inch thick.
His paper on the torpedo was read before the Royal Society in 1776. The experiments were undertaken in order to determine whether the phenomena observed by Mr. John Walsh in connection with the torpedo could be so far imitated by electricity as to justify the conclusion that the shock of the torpedo is an electric discharge. For this purpose Cavendish constructed a wooden torpedo with electrical organs, consisting of a pewter plate on each side, covered with leather. The plates were connected with a charged Leyden battery, by means of wires carried in glass tubes, and thus the battery was discharged through the water in which the torpedo was immersed, and which was rendered of about the same degree of saltness as the sea. Cavendish compared the shock given through the water with that given by the model fish in air, and found the difference much greater than in the case of the real torpedo, but, by increasing the capacity of the battery and diminishing the potential to which it was charged, this discrepancy was diminished, and it was found to be very much less in the case of a second model having a leather, instead of a wooden, body, so that the body of the fish itself offered less resistance to the discharge. One of the chief difficulties lay in the fact that no one had succeeded in obtaining a visible spark from the discharge of the torpedo, which will not pass through the smallest thickness of air. Cavendish accounted for this by supposing the quantity of electricity discharged to be very great, and its potential very small, and showed that the more the charge was increased and the potential diminished in his model, the more closely did it imitate the behaviour of the torpedo.
But the main interest in this paper lies in the indications which it gives that Cavendish was aware of the laws which regulate the flow of electricity through multiple conductors, and in the comparisons of electrical resistance which are introduced. It had been formerly believed that electricity would always select the shortest or best path, and that the whole of the discharge would take place along that route. Franklin seems to have assumed this in the passage quoted[4] respecting the discharge of the lightning down the uninsulated conductor instead of through the building. The truth, however, is that, when a number of paths are open to an electric current, it will divide itself between them in the inverse ratios of their resistances, or directly as their conductivities, so that, however great the resistance of one of the conductors, some portion, though it may be a very small fraction, of the discharge will take place through it. But this law does not hold in the case of insulators like the air, through which electricity passes only by disruptive discharges, and which completely prevent its passage unless the electro-motive force is sufficient to break through their substance. In the case of the lightning-conductor, however, its resistance is generally so small in comparison with that of the building it is used to protect, that Franklin's conclusion is practically correct.
In his paper on the torpedo Cavendish stated that some experiments had shown that iron wire conducted 400,000,000 times better than rain or distilled water, sea-water 100 times, and saturated solution of sea-salt about 720 times, better than rain-water. Maxwell pointed out that this comparison of iron wire with sea-water would agree almost precisely with the measurements of Matthiesen and Kohlrausch at 11°C. The records of the experiments which led to these results were found among Cavendish's unpublished papers, and the experiments also showed that the conductivity of saline solutions was very nearly proportional to the percentage of salt contained, when this was not very large—a result also obtained long afterwards by Kohlrausch. In making these measurements Cavendish was his own galvanometer. The solutions were contained in glass tubes more than three feet long, and a wire inserted to different distances into the solution; thus the discharge could be made to pass through any length of the liquid column less than that of the tube itself. From the Leyden battery of forty-nine jars, six jars of nearly equal capacity were selected and charged together, and the charge of one jar only was employed for each shock. The discharge passed through the column of liquid contained in the tube, from a wire inserted at the further end, until it reached the sliding wire, when nearly the whole current betook itself to the wire on account of its smaller resistance, and thence passed through the galvanometer, which was Cavendish himself. Two tubes were generally compared together, and the jars discharged alternately through the tubes, and the tube which gave the greatest shock was assumed to possess the least resistance. The wires were then adjusted till the shocks were nearly equal, and positions determined which made the first tube possess a greater and then a less resistance than the second. From these positions the length of the column of liquid was estimated which would make the resistances of the two tubes exactly equal. But the result which has the greatest theoretical interest was obtained by discharging the Leyden jars through wide and narrow tubes containing the same solutions. By these experiments Cavendish found that the resistances of the conductors were independent of the strengths of the currents flowing in them; that is to say, he established Ohm's law for electrolytes in a form which carried with it its full explanation. This was in January, 1781. Ohm's law was first formally stated in 1827. The physical fact which is expressed by it is that the ratio of the electro-motive force to the current produced is the same for the same conductor, otherwise under the same physical conditions, however great or small that electro-motive force may be.
Cavendish devoted considerable attention to the subject of heat, especially thermometry. In many of his investigations on latent and specific heat he worked on the same lines as Black, and at about the same time; but it is difficult to determine the exact date of some of Cavendish's work, as he frequently did not publish it for a long time after its completion, and most of Black's results were made public only to his lecture audience. Cavendish, however, improved upon Black in his mode of stating some of his results. The heat, for instance, which is absorbed by a body in passing from the solid to the liquid, or from the liquid to the gaseous, condition, Black called "latent heat," and supposed it to become latent within the substance, ready to reveal itself when the body returned to its original condition. This heat Cavendish spoke of as being destroyed or generated, and this is in accordance with what we now know respecting the nature of heat, for when a body passes from the solid to the liquid, or from the liquid or solid to the gaseous, condition, a certain amount of work has to be done, and a corresponding amount of heat is used up in the doing of it. When the body returns to its original condition, the heat is restored, as when a heavy body falls to the ground, or a bent spring returns to its original form. Cavendish's determination of the so-called latent heat of steam was very slightly in error.