Of course, it is not intended here to convey the idea that the molecules are spheres like shot or cricket-balls; they undoubtedly have a structure of their own. And no pronouncement is made as to the divisibility or non-divisibility of the molecules. All that is alleged is that if the division be carried to a minuteness near to or beyond that of the dimensions of the structure, portions of the substance will be obtained which have not the physical properties of the substance in bulk.
The recent interesting researches of chemists and physicists into phenomena which seem to demonstrate the disintegration, not merely of molecules, but even of the atomic structure of matter, attracted Lord Kelvin's attention in his last years, and suo more he endeavoured to frame dynamical explanations of electronic (or, as he preferred to call it, "electrionic") action. But though keenly interested in all kinds of research, he turned again and again to the older theories of light, and his dynamical representations of the ether and of crystals, with renewed vigour and enthusiasm.
CHAPTER XV
SPEED OF TELEGRAPH SIGNALLING—LAYING OF SUBMARINE CABLES—TELEGRAPH INSTRUMENTS—NAVIGATIONAL INSTRUMENTS, COMPASS AND SOUNDING MACHINE
Theory of Signalling
When the question of laying an Atlantic cable began to be debated in the middle of the nineteenth century, Professor Thomson undertook the discussion of the theory of signalling through such a cable. It was not generally understood by practical telegraphists that the conditions of working would be very different from those to which they were accustomed on land lines, and that the instruments employed on such lines would be useless for a cable. Such a cable consists of a copper conductor separated from the sea-water by a coating of gutta-percha; it forms an elongated Leyden jar of very great capacity, which, when a battery is connected to one end of the conducting core, is gradually charged up, first at that end, and later and later at greater distances from it, and then is gradually discharged again when the battery is withdrawn and the end of the conductor connected to earth. Here, again, an application of Fourier's analysis solved the problem, which, with certain modifications, and on the supposition that the working is slow, is essentially the same problem as the diffusion of heat along a conducting bar, or the diffusion of a salt solution along a column of water. The signals are retarded (and this was one of the results of the investigation) in such a manner "that the time required to reach a stated fraction of the maximum strength of current at the remote end," when a given potential difference is applied at the other, or home end, is proportional to the product of the capacity and resistance of the cable, each taken per unit of the length, and also proportional to the square of the length of cable. In other words, the retardation is proportional to the product of the resistance of the copper conductor and the total capacity of the cable. This gave a practical rule of great importance for guidance in the manufacture of submarine cables. The conductor should have the highest conductivity obtainable, and should therefore be of pure copper; the insulating covering should, while forming a nearly absolutely non-conducting sheath, have as low a specific inductive capacity as possible. The first of these conditions ran counter to some views that had been put forward, to the effect that it was only necessary to have the internal conductor highly conducting on its surface; and some controversy on the subject ensued. The inverse square law, as it was called, was vehemently called in question, from a mistaken interpretation of some experiments that were made to test it. For if the potential at the home end be regularly altered, according to the simple harmonic law, so that the number of periods of oscillation in a second is n, the changes of potential are propagated with velocity 2√(πn⁄cr), where c and r are the capacity and resistance of the cable, each taken per unit length. In this case, for a long cable, there is a velocity of propagation independent of the length; and this fact seems to have misled the experimenters. Thomson's view prevailed, and the result was the establishment, first by Thomas Bolton & Sons, Stoke-on-Trent, of mills for the manufacture of high conductivity copper, which is now a great industry.
The Fourier mathematics of the conduction of heat along a bar suffices to solve the problem, so long as the signalling is so slow as not to bring into play electromagnetic induction to any serious extent. For rapid signalling in which very quick changes of current are concerned the electromotive forces due to the growth or dying out of the current would be serious, and the theory of diffusion would not apply. But ordinary cable working is quite slow enough to enable such electromotive forces to be disregarded.