The expressions inductive power, and dielectric constant, are used as synonymous with specific inductive capacity.

§ 2. Variation with Time.-It was soon found that for solid dielectrics the time for which the experiment lasted had a marked influence on the value obtained for σ.

If, in Chapter VI. § 2 (i.), we interpose a plate of ebonite I between the two condenser plates A and B, we have initially a certain inductive action of the plate A on B; this being indicated by the divergence of the needle of the electrometer E.

But we shall observe that this action gradually gets less, as the plate I gradually yields to the electric strain. There is a slow separation of electricities on I similar to the practically instantaneous separation that occurs in a conducting plate. In fact, with time the ebonite plate I acts more or less as a conducting plate; and then, like a conducting plate, it screens B from the action of A to a greater or less degree (see Chapter X. § 17).

Or again we can, by waiting, charge a Leyden jar from a source of constant potential with a larger charge than it would receive in the first instance; the specific inductive capacity of the glass appearing to increase with time. As explained in Chapter VI. § 10, there is

a penetration of the charge, and we find residual charges.

The true specific inductive capacity would be that obtained before any such action on the dielectric had taken place.

§3. Cavendish's Method.-Cavendish determined, with a degree of accuracy that is surprising when we consider the apparatus that was at his dis

posal, the value of σ for various dielectrics.

His general method was as follows. condensers constructed with glass and tin-foil.

He

prepared a series of These he employed

as arbitrary standards, with which he compared condensers in which

various other dielectrics were used. In this way he obtained the inductive capacity of these materials as compared with that of the standard glass. Then he determined the ratio borne by the inductive capacity of this glass to that of air, and so obtained finally the specific inductive capacity (see definition) of the dielectrics employed.

In fig. i. D represents in section the condenser in which the dielectric was the substance whose specific inductive capacity was desired. G represents one or more standard condensers. The upper plates of both were charged from the same source, and therefore to the same potential; and the under plates were put to earth or were at zero potential. If the charges upon the upper plates were + a and + b respectively, then those upon the lower plates would be (very nearly) a and b respectively; the charges on the upper plates exceeding those on the lower by negligible 'free' charges.

When the condensers were charged, matters were arranged as in fig. ii. It is not difficult to see that if a and b were equal, then the charges a and

b would (very nearly) neutralise one another. The wire connecting these plates communicated with a delicate electroscope; and thus

To Electrometer

G

Earth.

it could be seen

whether there was neutralisation or no.

Standard condensers were

grouped together until such neutralisation was observed. When this was the case the capacity of G was equal to that of D. For, by our formula,

(a=K' (V-Vo)

b=K (V-Vo)

where K' and K were the capacities of the two condensers D and G respectively. And since (V-Vo) was the same for both, it followed that a could only equal b if K'= K. Then, from a knowledge of the dimensions of the two condensers, Cavendish determined the ratio of the two inductive capacities, or the ratio that would have existed between the charges a and b had the condensers been similar in all respects save in the nature of the dielectric

In somewhat the same manner he compared the capacities of these standards with that of a large sphere 'isolated' (see Chapter V. § 8 &c.) in the middle of the room. From this comparison he was able to calculate what would have been the capacitics of the standards had

air been their dielectric, and thus he finally found the ratio that the charge a would have borne to that of an exactly similar condenser having air as the dielectric.

$4. Faraday's Method.-(a) The figures represent, complete and in section, the apparatus used by Faraday; this being a condenser of a convenient and symmetrical form. The outer coating consisted of a hollow brass sphere P Q, that was always put to earth. The inner coating was a brass globe C. This could be charged by means of the knob B connected with it. of shellac serving to insulate the wire connecting B and C.

A represents a layer

Further, the space between PQ and C was air-tight; by means of a tap any gas could be introduced, and PQ could be pulled apart so as to admit of the introduction of various dielectrics into the space between C and PQ.

(b) The potentials of B at different times could be compared (not measured in absolute units) by touching B with an insulated ball of a certain size, communicating this charge to a torsion balance (see Chapter IV. § 12 (i.)), and observing the torsions needed in the different cases to keep the needle deflected at constant angle.

Note.--As this method of comparing potentials is obsolete, we merely state that they can be so compared; we do not go further into the matter.

(c) For his experiments it was necessary to have two such condensers that were of exactly equal capacities when filled with air.

To test whether this were the case, he charged the one and measured the potential of its knob B. He then connected this knob B with the knob B' of the uncharged condenser; thus causing the charge to be divided between the two condensers. He then measured the potential of B again. If the jars were of equal capacity the new potential should be half the old. In fact. in mathematical symbols we have

if the capacities are equal (see Chapter VI. § 4).

(d) Having provided himself with two similar condensers, he filled one with the substance whose specific inductive capacity was required. (For convenience he only half filled it, and calculated accordingly.) He then charged the other, or air-condenser, and observed the potential v of its inside coating. The knob B was then connected with the knob of the condenser which had been filled with the dielectric in question and had been left uncharged. The new potential v' of the compound condenser was then measured. As before stated, the outside coatings were to earth. Let K be the capacity of the air condenser, and ☛ K that of the similar condenser filled with the dielectric in question, where is the required specific inductive capacity.

Then we have

σ

§ 5. Modern Methods. -For the reason given in § 2, methods have been devised to obviate the errors due to penetration of charge. These methods employ rapidly alternating + and charges, this reversal of charge occurring even as often as 12,000 times per second in some of Gordon's experiments. The condensers

thus never remain charged for more than a fraction of a second ; and the charge has, so to speak, no time to penetrate into the body of the dielectric.

Let us suppose that, when this reversal of charge takes place with a certain rapidity, the value of is measured; and let us further suppose that, on increasing the rapidity of reversal, no change is made in this value of obtained. When this is the case it may fairly be said that errors due to penetration of charge have been obviated.

σ

Gordon's experiments.-Mr. Gordon has made a series of elaborate experiments on the specific inductive capacities of various solid dielectrics, in which the principle of rapid reversal of charge was employed.

As it is not possible to give in a brief space a satisfactory account of the apparatus and methods employed, the reader is referred to Gordon's 'Physical Treatise on Electricity and Magnetism,' where he will find a full description given. It may, however, be mentioned that there are two considerations which may modify considerably the value of the results obtained; the first objection is of undoubted weight, the second is possibly without foundation.

(i.) In calculations concerning the circular brass plates which formed the plates of the condensers, no allowance was made for the variations in distribution which occur within a considerable distance of their edges. These condenser-plates should have been provided with guard-rings (see Chapter X § 32).

(ii.) Further, it may reasonably be asked whether, with these rapid reversals of charge, the conditions are truly statical. Whether, in fact, we are obtaining what we desired, viz. the true electrostatical specific inductive capacity of the dielectric. It is assumed that these extraordinarily rapid swingings to and fro of electrical charges leave the theory of the condenser unaltered. If this be really the case, it must be because the rapidity with which statical electric equilibrium is attained immeasurably transcends the rapidity of the reversals.