If an ordinary clothes-line, say twenty feet long, receives a wave-impulse from the hand at one end, the motion will proceed to the other end as a series of waves. If a rope twice as heavy is used, a larger part of the original impulse will be received at the remote end than in the first experiment. Of course, there comes a limit to the thickness of the rope which may be thus employed; we must not choose a ship’s cable for instance, but the rope most effective in results is much heavier than one would suppose before trial. Lord Rayleigh, in his treatise on the theory of sound, has shown that according to Lagrange it is unnecessary to thicken a cord when we wish to add to its weight; as an alternative we may fasten weights upon it at due intervals, the whole having less mass than if we used a heavy rope of equal effectiveness. Just what intervals are best will depend upon the thickness and rigidity of the cord, upon its length, the amount and kind of wave committed to it, as shown by Professor Michael I. Pupin of Columbia University, New York, who extended the mathematical problem dealth with by Lagrange and Lord Rayleigh. In the singular efficiency of transmission thus studied he saw a principle which, by analogy, he believed to hold true in the electrical field as in mechanics. This principle he has illustrated in his paper published in the Proceedings of the American Institute of Electrical Engineers, 1900, page 215. In A of the accompanying figure, derived from that paper, is a tuning fork, C, with its handle rigidly fixed. To one of its prongs is attached a flexible inextensible cord, bd. Let the fork vibrate steadily by any suitable means. The motion of the cord will be a wave motion, as in B. The attenuation of the wave as it dies down is represented in C. Experiments show that, other things being equal, increased density of the string will diminish attenuation, because a larger mass requires a smaller velocity in order to store up a given quantity of kinetic energy, and smaller velocity brings with it a smaller frictional loss. Moreover, as the string is increased in density, its wave-length is shortened. [Illustration: Prof. Pupin’s diagram explaining his system of long distance telephony.]