Note to Page 20.
On the High Potential of a Flash of Lightning.
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]