is greater at first than afterwards, and is greater for highly-charged bodies than for those feebly charged. The law of dissipation of charge therefore resembles Newton's law of cooling, according to which the rate of cooling of a hot body is proportional to the difference of temperature between it and the surrounding objects. If the potential of the body be measured at equal intervals of time it will be found to have diminished in a decreasing geometric series; or the logarithms of the potentials at equal intervals of time will differ by equal amounts. The rate of loss is, however, greater at negatively-electrified surfaces than at positive.

This may be represented by the following equation: -

Vt = Vo€ pt,

where Vo represents the original potential and V the potential after an interval t. Here e stands for the number 2.71828 ... (the base of the natural logarithms), and p stands for the "coefficient of leakage," which depends upon the temperature, pressure, and humidity of the air. The same formula serves for the discharge of a condenser of capacity K through a resistance R; if p is written for 1/KR.

327. Positive and Negative Electrification. The student will not have failed to notice throughout this lesson frequent differences between the behaviour of positive and negative electrification. The striking dissimilarity in the Lichtenberg's figures, the displacement of the perforation-point in Lullin's experiment, the unequal tendency to dissipation at surfaces, the unequal action of heat on positive and negative charges, the remarkable differences in the various forms of brush and glow discharge, are all points that claim attention. Gassiot described the appearance in vacuum tubes as of a force emanating from the negative pole. Crookes's experiments in high vacua show molecules to be violently discharged from the negative electrode, the vanes of a little fly enclosed in such tubes being moved from the side struck by the negative discharge. Holtz found that

when funnel-like partitions were fixed in a vacuum tube the resistance is much less when the open mouths of the funnels face the negative electrode. These matters are yet quite unaccounted for by any existing theory of electricity.

327 a. Roentgen's Rays. In 1895 Roentgen discovered that highly exhausted tubes, such as the Crookes tubes (Art. 321), when stimulated by electric discharges, emit some invisible rays which have very remarkable properties. They excite brilliant fluorescence on such substances as the platinocyanide of barium; they differ from ultra-violet light and other invisible kinds of radiation in being incapable of refraction, of polarization, or of regular reflexion. They pass freely through aluminium, zinc, wood, paper, and flesh, but not through lead, platinum, glass, or bone. They also act on ordinary photographic plates. Hence it is possible by using a fluorescent screen to see, and by using sensitive plates to photograph, the shadows of such things as the bones in the living body, or the bullet in the barrel of a gun. It is found that these rays are given off, inside the Crookes tubes, from the solid surface- the glass or a metal target placed inside on purpose against which the kathode rays are directed. Those substances which have highest atomic weights absorb the Roentgen rays best, or if used as targets emit them best. Hence the target should be of platinum, or uranium, or osmium.

LESSON XXV.- Atmospheric Electricity

328. The phenomena of atmospheric electricity are of two kinds. There are the well-known electrical phenomena of thunderstorms; and there are the phenomena of continual slight electrification in the air, best observed when the weather is fine. The phenomena of the Aurora constitute a third branch of the subject.

329. The Thunderstorm an Electrical Phenomenon. -The detonating sparks drawn from electrical machines and from Leyden jars did not fail to suggest to the early experimenters, Hauksbee, Newton, Wall, Nollet, and Gray, that the lightning flash and the thunderclap were due to electric discharges. In 1749, Benjamin Franklin, observing lightning to possess almost all

the properties observable in electric sparks,* suggested that the electric action of points (Art. 46), which was discovered by him, might be tried on thunderclouds, and so draw from them a charge of electricity. He proposed, therefore, to fix a pointed iron rod to a high tower. Before Franklin could carry his proposal into effect, Dalibard, at Marly-la-ville, near Paris, taking up the hint, erected an iron rod 40 feet high, by which, in 1752, he drew sparks from a passing cloud. Franklin shortly after succeeded in another way. He sent up a kite during the passing of a storm, and found the wetted string to conduct electricity to the earth, and to yield abundance of sparks. These he drew from a key tied to the string, a silk ribbon being interposed between his hand and the key for safety. Leyden jars could be charged, and all other electrical effects produced, by the sparks furnished from the clouds. The proof of the identity was complete. The kite experiment was repeated by Romas, who drew from a metallic string sparks 9 feet long, and by Cavallo, who made many important observations on atmospheric electricity. In 1753 Richmann, of St. Petersburg, who was experimenting with an apparatus resembling that of Dalibard, was struck by a sudden discharge and killed.

330. Theory of Thunderstorms. Solids and liquids cannot be charged throughout their substance; if charged at all the electrification is upon their surface (see Art. 41). But gases and vapours, being composed of myriads

*Franklin enumerates specifically an agreement between electricity and lightning in the following respects: - Giving light; colour of the light; crooked direction; swift motion; being conducted by metals; noise in exploding; conductivity in water and ice; rending imperfect conductors; destroying animals; melting metals; firing inflammable substances; sulphureous smell (due to ozone, as we now know); and he had previously found that needles could be magnetized both by lightning and by the electric spark. He also drew attention to the similarity between the paleblue flame seen during thundery weather playing at the tips of the masts of ships (called by sailors St. Elmo's Fire), and the "glow" discharge at points.

of separate particles, can receive a bodily charge. The air in a room in which an electric machine is worked is found afterwards to be charged. The clouds are usually charged more or less with electricity, derived, probably, from evaporation going on at the earth's surface. The minute particles of water floating in the air become more highly charged. As they fall by gravitation and unite together, the strength of their charges increases. Suppose eight small drops to join into one. That one will have eight times the quantity of electricity distributed over the surface of a single sphere of twice the radius (and, therefore, of twice the capacity, by Art. 272) of the original drops; and its electrical potential will therefore be four times as great. Now a mass of cloud may consist of such charged spheroids, and its potential may gradually rise, therefore, by the coalescence of the drops, and the electrification at the lower surface of the cloud will become greater and greater, the surface of the earth beneath acting as a condensing plate and becoming charged, by influence, with the opposite kind of electrification. Presently the difference of potential becomes so great that the intervening strata of air give way under the strain, and a disruptive discharge takes place at the point where the air offers least resistance. This lightning spark, which may be more than a mile in length, discharges only the electricity that has been accumulating at the surface of the cloud, and the other parts of the cloud will now react upon the discharged portion, producing internal attractions and internal discharges. The internal actions thus set up will account for the usual appearance of a thundercloud, that it is a well-defined flat-bottomed mass of cloud which appears at the top to be boiling or heaving up with continual movements.

331. Lightning and Thunder. Three kinds of lightning have been distinguished by Arago: (i.) The Zig-zag flash or "Forked lightning," of ordinary occurrence. The zig-zag form is probably due either to the

presence of solid particles in the air or to local electrification at certain points, making the crooked path the one of least resistance. (ii.) Sheet lightning, in which whole surfaces are lit up at once, is probably only the reflexion on the clouds of a flash taking place at some other part of the sky. It is often seen on the horizon at night, reflected from a storm too far away to produce audible thunder, and is then known as "summer lightning." (iii.) Globular lightning, in the form of balls of fire, which move slowly along and then burst with a sudden explosion. This form is very rare, but must be admitted as a real phenomenon, though some of the accounts of it are greatly exaggerated. Similar phenomena on a small scale have been produced (though usually accidentally) with electrical apparatus.

The sound of the thunder may vary with the conditions of the lightning spark. The spark heats the air in its path, causing sudden expansion and compression all round, followed by as sudden a rush of air into the partial vacuum thus produced. If the spark be straight and short, the observer will hear but one short sharp clap. If its path be a long one and not straight, he will hear the successive sounds one after the other, with a characteristic rattle, and the echoes from other clouds will come rolling in long afterwards. The lightning-flash itself never lasts more than 15 of a second, but sometimes is oscillatory in character (see Art. 515).

The damage done by a lightning-flash when it strikes an imperfect conductor appears sometimes as a disruptive mechanical disintegration, as when the masonry of a chimney-stack or church-spire is overthrown, and sometimes as an effect of heat, as when bell-wires and objects of metal in the path of the lightning-current are fused. The physiological effects of sudden discharges are discussed in Arts. 255 and 325.

The "return-stroke" experienced by persons in the neighbourhood of a flash is explained in Art. 29.