CHAPTER XXXVIII.

ATMOSPHERIC ELECTRICITY.

462. Potential at a Point in the Air.-Experiment shows that in an open space the potential at a point in the air is always different from that of the earth. Two methods may be used to determine the value of this potential.

Let a small insulated sphere, of radius r, be placed at the point in question and connected for a moment with the earth by means of a very fine wire. If V is the value of the potential at this point due to external masses, the potential of the earth being as usual taken as zero, the sphere will acquire a charge, m, of electricity such that the potential of the sphere becomes zero, like that of the earth. The potential at the centre being V +

m

r

m

we have V+ = 0.

r

If the sphere is then placed in a Faraday cylinder (§ 15), we may measure its charge m, and so obtain

D

T

But the simplest method consists in putting at the place in question a point which forms part of an insulated conductor (§ 20). Assuming that the point is perfect, equilibrium cannot exist so long as the point, and therewith the conductor of which it forms part, is at a different potential from that of the air near the point.

FIG. 373.

Saussure used a small electroscope provided with a point (Fig. 373). If the case is at the potential of the ground, the divergence

of the leaves varies with the potential of the air at the end of the point; but the action of the point is too imperfect to allow us to consider that equilibrium is attained.

We have seen how a water-dropping apparatus (§ 81) enables us to realise the effect of a perfect point, and how it assumes the potential of the air at the point where the drops separate from the conductor. The dropping apparatus (Fig. 374) is preferable to a

FIG. 374.

lighted wick, owing to a small difference of potential produced by the combustion, which may amount to half a volt.

The insulated reservoir is connected with an electrometer, the deflection of which measures the potential. By using a mirror and allowing the image to fall on a uniformly moving band of photographic paper, a continuous registration of the indications of the instrument is obtained.

It is thus found that in fine weather the potential anywhere in the open air is always positive; that its value increases with the height of the point above the ground, and almost in direct proportion; but that at the same place rapid and often large variations occur.

The results vary so much that it is difficult to give numerical statements. Above an open plain, for example, the change of potential with height is often between 10 and 1000 volts per metre, but it is sometimes far more.

If, instead of insulating the point, or the arrangement which acts as a point, we connect it with the earth, statical equilibrium cannot be established, and a continuous flow of electricity traverses the conductor. The flow is manifestly equal to the amount given out by the point. It increases with the difference of potential, but it cannot be used to measure this difference, the quantity given off being always so extremely small.

If there is a small break in the conducting wire, the difference of potential at the break may be great enough to produce a succes

sion of sparks. Sparks are sometimes produced in this way between the needle and the quadrants of the electrometer.

463. Distribution of Potential.—At a given instant, the surfaces where the potential has constant and equidistant values above an open plain are equidistant horizontal planes. If the surface of the ground is irregular, the nearest equipotential surfaces follow its undulations, and approach each other over the elevated parts, and the more so the higher and more abrupt these are. Around a house, all parts of which may be regarded as connected with the earth, and therefore at zero potential, the equipotential surfaces are vertical near the walls and follow the contours of the roof, being closer to each other over the ridge; on the other hand, they separate widely from each other in a court surrounded by high walls, or in a street. As we rise, the effects of the inequalities disappear, and it may be assumed that beyond a certain height the equipotential surfaces are horizontal planes.

As the equipotential surfaces tend to become parallel to the surface of the ground the nearer they are to it, the electric force at each point is perpendicular to the surface. And since, in fair weather, the value of the potential increases with the distance, it follows that the electric force is directed towards the earth; its intensity at each point is inversely proportional to the distance between two consecutive equipotential surfaces (§ 33).

464. Negative Electrification of the Earth.-The phenomena observed near the ground are thus the same as they would be near a negatively electrified conductor in equilibrium. It follows from Coulomb's theorem (§ 43), that if F is the value of the force near a conductor, the electric density σ at the corresponding point of the surface is given by the equation

= 9

F 4π

Let us assume that the equipotential surfaces are horizontal, and that the potential increases by I volt per centimetre—that is, in

The electrostatic pressure—or, in other words, the force which would tend to lift a surface of 1 square centimetre placed on the ground-would be

4.4 X 10-7,

10-4 2по2 72π

that is to say, half a millionth of a dyne, a force wholly insufficient to raise the lightest body.

This charge, small as it is, might however be made evident by a method like that of the proof plane: a disc like that of an electrophorus applied to the ground, and then removed by an insulating handle, would show a negative charge when tested by a delicate electroscope.

2r

Let be the radius of the disc; it will take a charge q = πρσ, and since the capacity of a circular disc of radius is this charge will raise it to the potential ro. If we assume

σ =

I

π

and remember that an electrostatic unit of potential is " I 200π equal to 300 volts, the expression for the potential in volts will be r. If the radius were 25 centimetres, this would give a potential of nearly 10 volts.

The measurement of the charge of the disc would give the value of σ, and therefore of F. We deduce from it for the value of the potential at a height h from the ground (§ 32),

V = Fh.

The potential of the air is not, however, always positive, and therefore that of the ground is not always negative; in cloudy weather, especially during rain, and sometimes, though very rarely, with cloudless sky, the potential of the air is negative, and therefore that of the soil positive. This, however, must be regarded as quite exceptional, and there is reason to believe that if at a given moment the sky were clear over the whole surface of the globe, the globe itself would be wholly negative.

465. Position of the Acting Masses.—The measurement of the potential at a point of the air near the ground teaches us nothing as to the situation of the acting electrical masses. An example will make this intelligible. Suppose that a water-dropping collector is placed in a closed room, and that a sphere charged with positive electricity is then introduced; the electrometer will at once show positive potential. Again, instead of bringing in an electrified body, let the positive charge of a Leyden jar, whose outer

coating is connected with the inside of the room, escape by a point, the air of the room will be positively charged, and the electrometer will again indicate a positive electrification, equal, it may be, to that in the former case, although the acting masses are distributed in a totally different manner. As a matter of fact, any observations made near the ground give nothing more than the electrical condition of the ground itself; they tell us, as we have seen, the density of the surface-layer, but furnish no information as to whether this layer is the result of an independent charge, or is due to an external influence-that of the air, for example, which is positively electrified.

It may be observed, however, that if the electrification belongs exclusively to the earth, the potential above an extended plane ought to vary strictly as the distance-in other words, the electric force should be constant. On the other hand, if the mass of the air is itself electrified, the force must vary with the height, and should diminish if the air is positive, and increase if it is negative. We have, however, no data as to the law of the variation of the force.

Experiment seems to show that the mass of air is positive; two water-dropping apparatus set up, one in the open and the other under a wire cage, with large meshes completely closed and in communication with the ground, give in general proportional indications. External charges have no effect on the second apparatus ; the potential is due solely to the electricity of the air within the cage, and this may be regarded as being at each instant only a specimen of the outer air.

If the air has really an independent charge, the incessant variations of potential at a given point are explicable as due to the displacement of masses of air more or less electrified, and we might infer the distance of those masses from the extent of the surface of the ground over which the variations of potential at the same moment are proportional.

466. Origin of Atmospheric Electricity. The question naturally suggests itself: What is the origin of the electricity of the air and the ground? A very seductive hypothesis is that which ascribes the electricity to the evaporation of water; the vapour being supposed to carry positive electricity with it, leaving negative electricity in the water and on the ground. Unfortunately none of the experiments made with a view of confirming this hypothesis have given it any conclusive support; on the contrary, the fact that rain is usually negatively electrified appears to contradict it.