Passing now by analogy from motion of matter to motion of electricity, we can, speaking figuratively, state that vibratory motion of electricity will be transmitted from one end of a conducting wire to the other the more efficiently the heavier and the less compressible that electricity is, or, dropping now our figurative mode of speech, we can say that, other things being equal, the higher the kinetic and the elastic reaction of the moving electricity the more efficiently will the energy of its vibratory motion be transmitted over the wire. But that means that the inductance of the wire should be made as large and its capacity as small as possible. That much was perfectly obvious in Thomson’s and Kirchhoff’s work, some twenty years before Vaschy and Heaviside took up the mathematical theory of telephonic transmission. These two celebrated mathematicians, however, deserve much credit for their enthusiastic backing of inductance among the sceptical telephone engineers, who, at that time, knew little of the mathematical theory and of the general principle of transmission of vibratory motions. A coil of wire wound around an iron core is the first picture in our mind when we hear inductance mentioned. Hence, if inductance increases the efficiency of transmission in a telephone transmission-line, and you cannot introduce it into the line in large amounts in any other way, then one would certainly suggest putting a lot of coils into the telephone-line and examining the results of this haphazard guess. Vaschy tried this guess, and failed. The late Mr. Pickernell, chief engineer of the long-distance department of the American Telephone and Telegraph Company, also tried it, and he also failed. It was obvious that, as Heaviside expressed it, experiment gave no encouragement with regard to inductance introduced in this way. I tried it and found that experiment offered very much encouragement to inductance introduced this way; I succeeded, because I did not guess; I was guided by the mathematical solution of the generalized La Grangian problem. What does this solution say when applied to electrical motions in a wire? It says this: Place your inductance coils into your telephone-line at such distances apart that for all vibratory motions of electricity which it is desirable to transmit there shall be several coils per wave-length. In telephonic transmission of speech that means one coil every four or five miles on overhead wires, and one coil in about every one to two miles in a telephone cable. For these wave-lengths, the wire possessing discreet lumps of inductance in the form of inductance-coils acts like a wire with uniformly distributed inductance. Such a wire transmits efficiently according to the general physical principle described above. In order to illustrate this by a mechanical analogy, we can say that a light silk cord stretched between two fixed points and carrying at equidistant points heavy bird-shot will act like a