The potential of an electrified sphere is equal to the quantity of electricity with which the sphere is charged, divided by the radius of the sphere. Now the minute cloud particles, which go to make up a drop of rain, may be taken to be very small spheres; and if v represent the potential of each one, q the quantity of electricity with which it is charged, and r the radius of the sphere, we have v = q/r. Suppose 1,000 of these cloud particles to unite into one; the quantity of electricity in the drop, thus formed, will be 1,000q; and the radius, which increases in the ratio of the cube root of the volume, will be 10r. Therefore the potential of the new sphere will be 1000q/10r, or 100q/r; that is to say, it will be 100 times as great as the potential of each of the cloud particles which compose it. When a million of cloud particles are blended into a single drop, the same process will show that the potential has been increased ten thousandfold; and when a drop is produced by the agglomeration of a million of millions of cloud particles, the potential of the drop will be a hundred million times as great as that of the individual particles.[16]
FOOTNOTES:
[1] “Il y a des grands seigneurs dont il ne faut approcher qu’avec d’extrêmes précautions. Le tonnerre est de ce nombre.”—Dict. Philos. art. Foudre.
[2] Electricité Statique, ii., 561.
[3] Deschanel’s Natural Philosophy, Sixth Edition, p. 641.
[4] Fragments of Science, Fifth Edition, p. 311.
[5] Lecture on Thunderstorms, Nature, vol. xxii., p. 341.
[6] Third Series, vol. v., p. 161.
[7] Phil. Trans. Royal Society, 1834, vol. cxxv., pp. 583-591.
[8] In experiments with a Leyden jar, Feddersen has shown that the duration of the discharge is increased, not only by increasing the striking distance, but also by increasing the size of the jar. Now, a flash of lightning may be regarded as the discharge of a Leyden jar of immense size, with an enormous striking distance; and therefore we should expect that the duration of the discharge should be greatly prolonged. See American Journal of Science and Arts, Third Series, vol. i., p. 15.
[9] See original paper by Swan, Trans. Royal Society, Edinburgh, 1849, vol. xvi., pp. 581-603; also, a second paper, ib. 1861, vol. xxii., pp. 33-39.
[10] Nature, vol. xxviii., p. 54.
[11] See, however, an attempt to account for this phenomenon in De Larive’s Treatise on Electricity, London, 1853-8, vol. iii., pp. 199, 200; and another, quite recently, by Mr. Spottiswoode, in a Lecture on the Electrical Discharge, delivered before the British Association at York, in September, 1881, and published by Longmans, London, p. 42. See also, for recent evidence regarding the phenomenon itself, Scott’s Elementary Meteorology, pp. 175-8.
[12] See Jamin, “Cours de Physique,” i., 480-1; Tomlinson, “The Thunderstorm,” Third Edition, pp. 95-103; “Thunderstorms,” a Lecture by Professor Tait, Nature, vol. xxii., p. 356.
[13] Professor Tait, On Thunderstorms, Nature, vol. xxii., pp. 436-7.
[15] See Tomlinson, The Thunderstorm, pp. 87-9.
[16] See Tait on Thunderstorms, Nature, vol. xxii., p. 436.