From Immigrant to Inventor

by Michael Pupin

A string without weight is stretched like a violin string between two fixed points; at equidistant intervals along this string are attached equal weights, say bird-shot. The problem is, how will this string, loaded with weights, vibrate when disturbed by an impulse? La Grange found a beautiful solution for this historic problem, and the solution marks the beginning of an epoch in the history of mathematical physics. This solution enabled him to analyze mathematically the vibrations of a violin string, one of the famous mathematical problems of the eighteenth century. I made a bold attempt to find a solution for a more general and less hypothetical form of this problem. I supposed that the string itself had weight, and that it, as well as the little weights attached to it, moved through a viscous medium. I felt intuitively what the solution should be, and considered it of much scientific importance. I finally found the most general mathematical solution of this generalized problem, and the beauty of it was that it could be stated in a very simple language. I shall state it later. The solution was exactly what I had expected it to be, and it thrilled me more than any work that I had ever done. I always believed that my training in ground-signalling which the herdsman of Idvor had taught me some twenty years before was responsible for this intuitive guess. Early impressions, particularly those relating to novel scientific facts, are very intense.

I was much encouraged by the thought that I was able to add very substantially to the solution of a historic problem first solved by famous La Grange. In order to communicate some of my joy to Mrs. Pupin, I told her that I was ready to give up mathematical reading for the rest of that summer, and we started on a drive through Switzerland. That is, she drove, while I walked a good part of the time, particularly when the carriage was moving along the zigzag roads going up to a pass, which happens often in Switzerland drives. Making short cuts, I met her every now and then on the up-grade parts of the steep and winding roads, and rode with her on the down-grade. During these walks, being alone, I pondered a great deal about my solution of the generalized La Grangian problem. One day, while climbing up to the Furka pass, it occurred to me that since the motion of electricity through a wire experiences reacting forces similar to those in the motion of the material elements in a stretched string, my generalized solution should be applicable to the motion of electricity, and I was immediately aware that I had made a very important invention. I tried to convince Mrs. Pupin of it, but she said: “I will believe what you say and will gladly congratulate you if you will promise that you will not be absent-minded during the rest of our trip.” I promised, but it was very difficult to live up to the promise. I never told her how often I longed to be back in my modest laboratory in the musty cellar under President Low’s office at Columbia College, and that too in spite of the heavenly beauty of the views which on my walks met me on every turn of the winding roads which lead up to the wonderful passes of Switzerland. I was most anxious to submit my theory to an experimental test. When our tour in Switzerland was finished I had every detail of the proposed experimental tests worked out in my head, and yet my good wife never accused me of being absent-minded. In less than a year from that time I had finished my first rough test, and was preparing for a more elaborate investigation when the discovery of the X-ray was announced, at the very end of 1895, and I, like everybody else, dropped everything and eagerly sought information about this wonderful discovery. It was the work I dropped then which I took up again after my recovery from the breakdown of 1896.

Now what is the invention which occurred to me first on my walk to the Furka pass in Switzerland in the summer of 1894? A bit of scientific history is connected with it, which I shall tell here briefly:

A vibrating motion of electricity at one end of a long wire is propagated along the wire in much the same way as the vibratory motion of a rope or string is propagated from one of its terminals to the other. This propagation of electrical motion from one end of a long conducting wire to the other was first investigated by Professor William Thomson, the late Lord Kelvin, of the University of Glasgow, in 1855, when the first Atlantic cable was projected. He worked out the problem for electrical signalling over a submarine cable, and three years later Kirchhoff, who was one of my teachers in Berlin, worked it out for telegraphic signalling over land-lines stretched over poles. When telephony was invented in 1876, there was, of course, a demand for a mathematical theory of telephonic transmission over long conducting wires. He who understood Thomson’s and Kirchhoff’s work could experience no serious difficulty in working it out. Vaschy, a Frenchman, and Heaviside, an Englishman, were the first to work it out; they did it in the chronological order just indicated, Vaschy leading Heaviside by about two years. They both observed that just as in cable and land-line telegraphy so also in telephony the reduction of the transmitted electrical force was the smaller the larger the so-called inductance of the transmitting wire. Many people believe that this observation was an important discovery; I never thought so, because I believed that Thomson’s and Kirchhoff’s work made that observation obvious. But, however that may be, the observation was made by Vaschy two years before it was made by Heaviside, and neither one nor the other saw in it a special case of a general physical principle, which the Allies appreciated much during the World War in their struggles against the submarines. I shall describe it briefly:

Sound is transmitted through water or through a solid much more efficiently than it is through air. I knew that, when, as herdsman’s assistant in Idvor, I learned the art of signalling through the ground. Now why should water or hard and heavy ground transmit sound better than air does? Idvor’s herdsman did not tell me that, but, having gained the knowledge of the fact very early, I was prepared to seize upon the dynamical explanation as soon as I needed it; and I felt the need of it in Switzerland in the summer of 1894.

Transmission of sound means transmission of vibratory motion from one element of a substance to the contiguous elements. The element which transmits its vibratory energy acts and the elements which receive it react. Each element is capable of exerting three reacting forces. One is against the change of velocity of its motion, that is, against change of momentum. This reaction is called the kinetic reaction, and, as I have pointed out before, it was discovered by Galileo three hundred years ago. The second reaction is against the elastic compression of the receiving element. It is called the elastic reaction, and was discovered by Hook, a contemporary of Newton, two hundred years ago. The third is a frictional reaction, the knowledge of which is very old. There are, therefore, three forms of energy generated in the reacting element of every vibrating body by the work of the acting element. The first reaction results in energy of motion of the mass of the reacting element; the second one results in the energy of its elastic compression; and the third one generates heat. The first and the second are energies of sound vibration and are transmitted again to the contiguous elements, but the third is not a vibratory sound energy and is not transmitted as such; it remains as heat and represents the reduction of sound energy transmitted from any one part to the contiguous parts. It is obvious that this reduction will be, relatively, the smaller the greater the first two reactions are in comparison with the frictional reaction. Heavy, incompressible bodies, like water, metals, or hard solid ground, have incomparably greater kinetic and elastic reactions than air, hence they transmit sound much better than air does. This physical principle did splendid service during the World War in submarine and subterranean detection by sound. The herdsman’s assistants in Idvor, when I was a boy, profited much from it in their signalling through the ground. I am not aware that Vaschy and Heaviside had a clear knowledge of it. If I am correct, then it is quite remarkable that Serb peasants should have been cognizant of a physical principle which was probably unknown to English and French savants, like Vaschy and Heaviside.

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 heavy uniform cord for all vibratory motions the wave-length of which embraces several intervals separating the bird-shot, and will transmit these motions much more efficiently from one end of the cord to the other than if the bird-shot were not there. This simple experiment with bird-shot and a long stretched cord can easily be tried; it is a very inexpensive experiment and will convince you even if you know nothing about the mathematical elements of the problem. This is the simple experiment which I had in my head during my tramping along the zigzag roads in Switzerland in 1894. A professor of physics, who often acted as consulting physicist to telephone companies, had such a loaded cord hung up over his lecture-room table for the purpose of explaining transmission of wave-motion from one end of the cord to the other, but he never inferred anything from it regarding loading a telephone-line with inductance-coils. When I called his attention to it, and joked about it, he blamed his hard luck, implying, I thought, that solving a dynamical problem and building upon the foundation of this solution an electrical invention is a question of luck.

From the simple apparatus, just referred to, to the elaborate electrical demonstrations which would convince stubborn and hard-headed telephone engineers, was a very long pull. The most embarrassing feature in these demonstrations was that I could not afford large expenditures of money to carry them out on actual telephone conductors; besides, it would have been unwise to disclose to interested parties, the owners of long-distance telephone-lines, a theory for which I had not yet obtained a satisfactory experimental proof. I had to invent laboratory apparatus equivalent to telephone lines or cables of great length, which would enable me to do all the experimenting in my laboratory. That required almost as much thought, inventive effort, and mathematical achievement as the solution of the extended La Grangian problem.

The first part of my research I communicated to the American Institute of Electrical Engineers in March, 1899. It dealt only with the mathematical theory of my laboratory apparatus. It spoke a great deal about La Grange, but nothing directly about the invention. In October of that year, a friend of mine, Doctor Cary T. Hutchinson, told me that he suspected that an invention was hidden in that communication. “If you have detected it, others have detected it also, and are by this time in the Patent Office,” said I. “Are you not there yourself?” asked Hutchinson, looking somewhat disturbed, and when he heard that I was not he looked discouraged. When, however, I declared my readiness to undertake to design for some clients of his a telephone cable to operate between New York and Boston, guaranteeing to employ a wire not bigger than in ordinary cables capable of operating satisfactorily over a distance of only twenty miles, Hutchinson grew quite serious, and advised me to apply for a patent before doing anything else. I finally followed his advice, and not any too soon. There were others, besides Hutchinson, who had recognized that in my communication to the American Institute of Electrical Engineers there was hidden an invention for which telephone engineers had been eagerly waiting ever since the birth of the telephone art. This created an interference in the Patent Office which annoyed me, but not nearly so much as I had been annoyed there before. About a year from the date of my application for patent, the American Telephone and Telegraph Company acquired my American patent rights, treating me most generously. It gave me what I asked; my friends thought that I had not asked enough, but to a native of Idvor a dollar looks much bigger than to a native of New York who may be a next-door neighbor to some Morgan or Rockefeller. Besides, the opinion of the highest telephone authority in the world that my solution of the extended La Grangian problem had a very important technical value was much more gratifying to me than all the money in the world.