Faraday to George Biddell Airy   20 February 1854

Royal Institution | 20 Feby, 1854

My dear Sir

It has occurred to me that perhaps the fact (described in p 2 of the Evening notice¹) that many successive shocks could be obtained from one charge of the wire by quick tapping touches, has directed your mind to the condition of length²; for there is an effect of length of wire in that case, though almost insensible, as the results with 100 miles of wire in air described at p.3³, shew. The effect is of this kind. With a given wire, length opposes resistance to conduction:- so when the static electricity, employed in sustaining the induction in the wire, is discharged by touching one end, the resistance of the length of wire has to be overcome and so time is required[.] If the wire is touched for discharge at both ends at once, which was the case in several of our experiments at the wharf⁴, then the resistance is only one fourth; for the double wire may then be considered as a wire of double mass and only half length. Supposing the induction to be entirely accumulated in the 100 plates of Gutta percha referred to in my last letter⁵, & that they were at one end of 50 miles of air wire, at the other end of which the electricity was to be discharged by successive taps, then I believe that the resistance would be the same as that with the 100 miles of water wire charged & discharged at one end only, & the effects the same. On the assumption that the conducting power of metal wires is directly as the sectional area & inversely as their length, a mile of copper wire of the 1/112 of an inch in diameter should offer the same resistance; and a few feet of wet thread should produce the same result:- which from numerous familiar experiments with ordinarily charged Leyden batteries I have no doubt it would do.

But though such an effect in relation to time is due to length of wire, that cause is almost insensible here, for the experiments which you saw with Bain’s⁶ printing telegraph (p.9 of the notice⁷) shewed that with 750 miles of air wire or even 1500 miles the retardation was scarcely sensible; while with the induction or underground wire it was 1 and 2 seconds.

This long time I believe to be due to that conduction which every insulator shews more or less and which therefore follows upon every act of induction; as I have shewn in my old researches, see paragraphs 1323, 1324⁸ & the other paragraphs there referred to. As soon as the 100 miles of water wire are charged inductively, the two electric states begin to travel through the gutta percha between the two surfaces; and hence the leaking of electricity which always occurs. There is as true a conduction through the Gutta percha of 1/10 of an inch thick as through the copper wire 100 miles long; but the amount is so different that the conduction of Gutta percha is almost infinitely small when compared with that of copper. Nevertheless this act of conduction causes that the electricity leaves in part the surfaces of the wire & opposed water, & penetrates the gutta percha; so that the particles of Gutta percha next the wire become positively charged & those next the water negatively charged (the wire being first charged Positive). This charge occupies time; and at the wharf Mr Statham⁹ was continually occupying time for contact with the battery, to charge, as he said, the wire fully. Then when the wire is discharged it requires the time again for the return of the Electricity from the Gutta percha and it is this time which enabled me to divide the charge into as many as 40 distinct portions[.]

My thoughts are so familiar with these considerations, which flow as natural consequences from principles long since published, that I am apt to consider them as of little importance and not worth pointing out. Your notes¹⁰ make me think that perhaps I have been too brief and ought to have enlarged more upon the principles of insulation and conduction and the many beautiful conditions & effects that flow from them[.]

I am My dear Sir | Very Truly Yours | M. Faraday

Geo B. Airy Esq | &c &c &c