Inventors at Work, with Chapters on Discovery

by George Iles

CHAPTER XXV
THEORIZING—Continued

Analogies have value . . . Many principles may be reversed with profit . . . The contrary of an old method may be gainful . . . Judgment gives place to measurement, and then passes to new fields.

Analogy as a Guide.

A conviction that has over and over again served the discoverer assures him that like causes underlie effects which seem diverse. When Thomas Young observed the recurrent bands of darkness due to interferences of light, he at once detected a parallel to the beats by which interferences of sound produce silence. He was therefore persuaded that light moves in waves as does sound, that it is not, as Newton supposed, a material emission. A chapter might be filled with examples of the same kind: let one suffice.

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.

Prof. Pupin’s diagram explaining his system of long distance telephony.

Suppose now that we attach a weight, say a ball of beeswax, at the middle point of the string, so as to increase the vibrating mass. This weight will become a source of reflections and less wave energy will reach the farther end of the string than before. Subdivide the beeswax into three equal parts and place them at three equi-distant points along the cord. The efficiency of transmission will be better now than when all the wax was concentrated at a single point. By subdividing still further the efficiency will be yet more improved; but a point is soon reached when further subdivisions produce very slight improvement. This point is reached when the loaded cord vibrates nearly like a uniform cord of the same mass, tension, and frictional resistance; such a cord, bearing 12 small weights of beeswax, is represented as D when at rest, as E when in motion. . . . It is impossible so to load a cord as to make it suitable for waves of all lengths; but if the distribution of the loads satisfies the requirements of a given wave-length, it will also satisfy them for all longer wave-lengths.

A cord of this kind has mechanical analogy with an electrical wave conductor. In a wire transmitting electricity inductance coils may be so placed as to have just the effect of the bits of wax attached to the cord in our illustration; in both cases the waves are transmitted more fully and with less blurring than in an unloaded line. The mathematical law of both cases is the same. It was in ascertaining that law so as to know where to place his inductance coils that Professor Pupin arrived at success. Preceding inventors, missing this law, came only to failure. He constructed an artificial cable of 250 sections, each consisting of a sheet of paraffined paper on both sides of which was a strip of tin-foil, the whole fairly representing a cable 250 miles in length. At each of the 250 joints in the course of this artificial circuit he inserted a twin inductance coil wound on one spool 125 millimetres broad and high, and separated by cardboard ¹⁄₆₄ inch thick. Each coil had 580 turns of No. 20 Brown & Sharpe wire. Just as with the weighted rope this circuit transmitted its current much more efficiently than if the inductance coils had been absent.