Hence the new potential will be (from Chapter X.)

New potential = 10,000 x (old potential).

Besides this we shall in general have the charge tending to pass to the outside of a cloud as a whole, and this would still further decrease the capacity and increase the potential.

When the flash passes, the drops will, as a ruie, more readily coalesce, there being no longer the electrostatic 'repulsion' between them. This may be one cause of the sudden fall of rain observed to follow a powerful flash.

§ 5. Potential at a Point in the Atmosphere. Observations on the phenomena of thunder-storms are occasional; and are, as a rule, of necessity very inexact.

There are, however, daily observations of a far more exact nature that are made, viz. observations of potential that exist between the earth and points in the atmosphere at different heights above the earth.

(a) Before discussing this matter we will, even at the risk of repeating somewhat, examine what is meant by the potential at a point in the atmosphere.

We have, in Chapter V. §§ 2 and 3, given some explanation of what is meant by 'potential' and how it is measured. The reader must wait until he has read Chapter X. to understand fully what is given in a general way in Chapter V.; he can then turn back to the present chapter and read it again. But the passages referred to are sufficient to show that we measure the potential at a point in the atmosphere by seeing how much work it takes to raise + unit electricity from our arbitrary zero of potential, the earth, up to the point in question.

(b) A small conductor, elevated above the earth, is at the

potential of the region where it is situated when it has no charge on it; since it would require the same work to bring the + unit up to the body from the earth as it would to bring the + unit up to the same place before the conductor was put there.

(c) If an earth-connected conductor be situated at a region A in the atmosphere that is at a different potential from the earth, a charge of opposite sign to this potential will be induced on the conductor, as explained in earlier chapters (see Chapter VI. § 2 (ii.), &c.). If this charge can escape, as it will off a point, or still better off a flame, this convectional escape can only cease when the region is reduced to the zero potential of the earth. The charge induced on the conductor will indicate by its magnitude the potential of the region at A.

(d) If a conductor be situated at A, and be connected with an insulated conductor situated elsewhere, e.g., nearer the surface of the earth where there is a different potential, induction will take place somewhat as in the last case, a charge being induced of opposite sign to the potential at A.

If this charge can escape, as by means of a flame, this convectional escape will take place until the whole conductor is at the potential of the region at A; for there cannot be equilibrium until this is the case. But it must be noticed that, if the conductor be large enough, this escape may sensibly alter the original potential of the region A.

Notes. The above reasoning is of a general nature. It can however be shown, by reasoning somewhat beyond this Course, that—

(i.) When there is a charge on the surface of a conductor, this means that the conductor is at a different potential from the region surrounding it; and conversely.

(ii.) That any such charge is urged normally outward from the conductor. (iii.) That when there is no such charge, this means that the conductor is at the same potential as the region surrounding it; and conversely.

§ 6. Methods of Measuring the Potential at a Point in the Atmosphere.

(i.) One method, formerly used, was based upon (c) of the last section.

A ball was elevated into the region in question; was temporarily connected with earth; was again insulated; was lowered;

and finally the charge induced (of opposite sign to the potential in question) was examined.

(ii.) But the best method is as follows.

E represents a quadrant electrometer (see Chapter X. § 33, for full description and complete figure). One pair of quadrants is put to earth, and from the other pair is raised a wire ending in a flame or slow-match at the point A, whose potential is required. Thus we have an insulated conductor consisting of the slowmatch, wire, and pair of quadrants. As explained in (d) of the last section, there will be a convectional discharge by means of the slow

match until the end of this latter is uncharged, and is, therefore, at the potential of the region A (see last section (b)). When this is the case, then the wire and the pair of quadrants with which it is connected will all be at the potential of the region A. The needle of the electrometer will then indicate by its deflexion the difference of this potential from the zero potential of the other pair of quadrants.

(iii.) Or we may employ the dropping of water to carry off the induced charge, and so to reduce the conductor to the potential of the region where the water breaks into drops.

If with the pair of quadrants there be connected an insulated tank, and if a pipe from this reach to A, and if there the water fall away in drops, we shall attain the desired end just as well as we did by the use of a flame or slow-match.

§ 7. Results of Observations. Some results arrived at by such observations are here given. In ordinary circumstances the potential of the atmosphere under a cloudless sky is +; and it

increases as we move higher from the earth. There are variations during the day, and these are fairly regular for all cloudless days.

Clouds may be charged to a + or - potential; and hence, when clouds pass, the points in the atmosphere which lie between them and the earth will also have a + or potential respectively. Whatever the potential of the atmosphere, there will be found on the exposed surface of the earth a charge of opposite sign, the potential of the earth being of course zero.

§ 8. Sheet-Lightning and other Phenomena.—With respect to the Aurora Borealis, references to papers on this subject will be found in the Preface, p. viii.

Sheet-lightning may, in some cases, be a true brush or glow discharge. In other cases this name is wrongly given to the visible reflection of a spark discharge that itself occurs out of sight.

Forked-lightning.-The lightning-spark is nearly always zigzag in its course. It is supposed that a greater resistance is created in the direct line of a spark, and thus the discharge is diverted along the line of least resistance to one side or the other. In very rare cases the discharge is straight; so that we conclude the crookedness of the usual path to be due in some way to the air through which it passes.

Globe-lightning.-There is one form of discharge of which the explanation is at present very imperfect. It is now sufficiently well established that sometimes a globe form of discharge is seen. This appears like a fiery globe moving slowly, or even at times resting stationary. Its movements are sometimes very erratic. It appears at times to follow conductors; it is said to break through non-conducting structures such as walls; and all accounts agree that it ultimately disappears with a powerful detonation. Planté has produced on a small scale similar appearances by aid of a voltaic battery, which gave him large quantities of electricity and a high difference of potential; but it is not certain that there is a true connection between the two phenomena.

Some believe this 'globe' form to be a kind of Leyden jar highly charged; but this explanation does not appear to make matters clearer.

No doubt in some cases the phenomenon was really a heated aerolite; but in other cases its nature seems undoubtedly to have been that of an electric discharge.

CHAPTER IX.

SPECIFIC INDUCTIVE CAPACITIES.

§ 1. Definition. We stated in Chapter VI. § 4 (iv.) that the charge of a condenser depended, cæteris paribus, on the nature of the substance that was between the two plates; or, in usual language, on the nature of the dielectric.

We propose in this chapter to discuss at some length the relative efficiencies of different substances as dielectrics.

If we have two condensers of exactly similar construction, one having air as the dielectric and the other having some other substance A as its dielectric, we shall find that for any given difference of potential between the plates the two condensers have unequal charges. Further, we shall find that the ratio between the two charges is constant, whatever the form of the condensers and difference of potential between the plates, provided that all conditions are the same for the two condensers.

Thus we have for the substance A a constant number representing its efficiency as a dielectric as compared with air. We call this number the specific inductive capacity of the substance A, and usually denote it by the symbol .

Or we define as follows.

The specific inductive capacity of a substance A

=

Capacity of the condenser when
A is the dielectric

Capacity of the condenser when
air is the dielectric

We here give a table of the specific inductive capacities of a few substances.

These results must, however, be regarded as approximate only.