of knowledge, as it were, brought right to us, and so placed that it can be embodied in our proceedings in order that at any time we may refresh our memory and replenish our minds by going to it, as we now go to a text-book or an encyclopædia.

It is now, I think, three years since at the Boston meeting of this Institute,' I pointed out that impedances were capable of, and had already been employed in many useful applications to electric work, although we did not at that time often make use of the word "impedance." It seems to me that one of the great beauties of practical electrical work is that functions, magnitudes, and apparently disadvantageous phenomena, which seem at first to be prejudicial to good work, can often be utilized and made subservient to good work in other directions. I may instance the polarization, which to the early battery inventors and constructors was such an obstacle, frequently opposing their best attempts at success; yet at the present time the phenomena of polarization having been more fully worked out, we find that it can be made really advantageous, and that by prosecuting researches in such phenomena, the storage battery has been reached; so, taking my own special line of work, it was found in the very early years of telephony that an electro-magnet in a telephonic circuit was a very strong bar to the passage of the telephonic impulses; so much so that one of our members, Mr. F. W. Jones, in devising a remedy for it, said that electro-magnets were opaque to rhythmical or rapidly alternating currents. But with the greater advance of the science in its many industrial applications, and our own improved knowledge and experience, it is found that impedances can actually be made useful, in that two wires can be made use of to transmit three messages at the same time, using the two wires as the direct and return wires of the metallic telephone circuit; while on the Van Rysselberghe plan, each one of the two wires composing that circuit may be severally used for the transmission of telegraphic messages; and this simply by placing impedances, made by properly winding covered wire around the iron, and interposing them between the telephonic circuit and the telegraph circuit proper. Such contrivances are much older however in telegraphy. I believe Mr. Cromwell Fleetwood Varley (now gone from us, but whom England and America delighted to honor,) used impedances in 1870-he called them echocymes-for a similar purpose, that is for working Morse telegraphy and harmonic telegraphy on one and the same wire. In the matter of electric lighting we find that Professor John Hopkinson devised impedances by winding wires, the amount of which could be made adjustable, on closed magnetic circuit laminated iron cores, in order that are lights might be regulated in multiple arc; and ĺ need scarcely call the attention of any one here to the wonderful application in the automatic regulation of lighting by transform

1. "The Industrial Utilization of the Counter Electromotive Force of SelfInduction" TRANSACTIONS, vol. vii., p. 226.

ers, as suggested, I believe, by Mr. Kennedy, but worked out by his successors, Messrs. Zipernowski, Déri and Blathy.

I have mentioned that "impedance" is an extremely modern term, it having been devised and given to us by Mr. Oliver Heaviside, within the last seven years; it is, however, a very graphic and highly suitable term, and I for one am much obliged to Mr. Oliver Heaviside for this favor, and others of the same kind.

Mr. Chairman, I have heard or read, I cannot tell which, at the present time, that the late Lord Derby in one of his addresses to students, defined knowledge as that which a man has so secured that he can produce it at any moment from his own head. Referring once more to the remarks I first made, I would like to say that I agree with Mr. John T. Sprague entirely, in his view that while that definition is no doubt a first class definition when cramming for an examination, it is not such a good definition when applied to the man of science who must use his science to earn his daily bread; and that real knowledge, the knowledge which the practical man carries in his head, is not perhaps the most valuable part of his knowledge. What really constitutes the best part of his outfit, is the knowing where to find what he wants when he wants it; and it seems to me that the paper we have had this evening will be a great aid to many of us in that kind of knowledge. Hereafter when we want to know anything about impedance, so far at least as it has up to the present time been investigated, we shall come to Mr. Kennelly's paper.

The knowledge which we can carry in our heads is, it seems to me, very much like money we carry in our pockets- very useful for making small change at the moment; but not so useful to carry on business with. But the knowledge which we can get hold of when we need it, when we are asked a question about it, or when a question comes up in our business the knowledge that we can have recourse to, and find out what we want-such knowledge is more like money that we have in our bank accounts, that is to say, if we have bank accounts, and any money in them. DR. PUPIN :-Mr. Chairman, I intended to make several remarks on the paper, but since it is so late I feel that I must cut them down and be very brief.

In the first place, it strikes me that Mr. Kennelly has done very good service to practical electrical engineers in making tables to which the electrical engineer can always refer, just as he refers to tables for his resistances, and finds out what will be the impedance of such and such a circuit. It is a very useful thing and it is done in the way in which only Mr. Kennelly can do it. He is well known for his neatness, and for his patience in working out such problems, so that any eulogistic remarks from me would be superfluous.

The other point which struck me as a very good point indeed, is Mr. Kennelly's remark regarding the simplicity of the alterna

ting current theory. I pointed out in a paper read three years ago at the Boston meeting of this Institute,' that the alternating current theory is just as simple as the continuous current theory, it is based on one single law, namely, Ohm's law. But, of course; we have to limit ourselves to instantaneous values of things, and just as we say in a continuous current circuit, that the impressed electromotive force plus the total drop is equal to zero, so we can say in the alternating current circuit that the sum of all the electromotive forces taken with their proper sign plus the total drop is equal to zero. We have therefore one and the same law for both kinds of current. That gives us our fundamental equation or fundamental relation between the quantities which are involved. But since that relation is true for infinitely short intervals of time, its symbolical expression gives us what is called in mathematics a differential equation. The integral relations which will hold true for any interval of time are obtained by the process of integration. Now in finding the integral relation between the current and the other quantities which define the circuit, like self-induction, capacity, resistance, etc., we find that if we want to obtain the current, we have to divide the impressed E. M. F., not by the resistance alone, but by the resistance plus something else, and that something else is composed with the resistance, just the same way as two forces, namely by the parallelogram of forces-two forces wich are at right angles to each other. We have therefore the simple rule that the resistance can be composed with the inductance speed, as Mr. Kennelly calls it, just the same as one force can be composed with another which is at right angles to it. In other words the parallelogram of forces is applicable to this case. If there is a condenser, there is capacity in the circuit, and in finding the integral relation between the current and the time, we find that the behavior of the condenser can be represented graphically in a very simple way by introducing into the parallelogram of forces just mentioned, a third component equal to the capacity speed, this third component to be always subtracted from the component representing inductance speed.

I call this graphic method of representing impedance the application of the parallelogram of forces to the alternating current circuits. Mr. Kennelly prefers to speak of vector quantities and the addition of vectors. But, of course, these graphical methods are incidental results of considerable practical importance. The primary law is Ohm's law in its generalized form, and its applicability to variable currents, variable but stationary. If the flow is not stationary, then Ohm's law even in this generalized form will be applicable to infinitely short lengths only of linear conductors as, for instance, in the case of very long wires and high frequency.

1 ་་ Practical Aspects of the Alternating Current Theory": TRANSACTIONS, vol. vii. p. 204, 1890.

The next point which I wish to discuss very briefly is the so called Ferranti effect. I am, however, somewhat timid about it after the remarks of our Chairman, saying that a great many people had rushed into print about this Ferranti effect.

THE CHAIRMAN:-It was merely the statement that was given

to me.

DR. PUPIN :-Well, the statement then that was given to our Chairman makes me hesitate. I also rushed into print about something like the Ferranti effect. I published a paper in the American Journal of Science and the next paper is now in print about this very thing. The Ferranti effect is a real, existing effect and can be made very strong indeed. Most people have no idea how strong this effect can be made. It is very simple. The Ferranti effect is only a special case of the more general effect which I call the resonance. It could have been foreseen twentyfive years ago from Maxwell's equations deduced at about that period. Maxwell, I think, was the first to show the effect of introducing a condenser capacity into an alternating current circuit, and it is very interesting to observe this circumstance. Maxwell was spending an evening with Sir William Grove who was then engaged in experiments on vacuum tube discharges. He used an induction coil for this purpose, and found that if he put a condenser in parallel with the primary circuit of his induction coil, that he could get very much larger sparks, which meant, of course, that he got a very much larger current through his primary coil, an alternating current generator being used to feed the primary. He could not see why. Maxwell, at that time, was a young man. That was about 1865, if I do not err. Grove knew that Maxwell was a splendid mathematician, and that he also had mastered the science of electricity as very few men had, especially the theoretical part of it, and so he thought he would ask this young man how it was possible to obtain such powerful currents in the primary circuit by adding a condenser. Maxwell who had not had very much experience in experimental electricity at that time, was at a loss. But he spent that night in working over his problem, and the next morning he wrote a letter to Sir William Grove explaining the whole theory of the condenser in multiple connection with a coil. It is wonderful what a genius can do in one night! He pointed out the exact relations between the condenser, the self-induction and the frequency which would give the largest current, and he was the first to do this, so far as I know.

We must always remember that as soon as we add capacity to a circuit we are giving it elasticity. Without capacity the circuit has no elasticity. Take a stiff wire and suspend a weight, say a cylindrical bar, by it. Suppose that this wire has no elasticity. In order to twist this weight, in order to deflect it from its posi

1 April, 1893,

tion of equilibrium, we have to use a force that will twist the weight out of shape. The moment of inertia of the weight, when twisted around, is being changed. That is just what happens in an alternating current circuit which has no appreciable capacity. The electromotive force working on such a circuit produces forced vibrations. But suppose that the stiff wire has elasticity. Then if you give an impulse to the weight, it will swing, and thie period of the swing will depend on the moment of inertia of the weight, and on the elasticity of the wire and on nothing else, provided of course that the frictional resistances are not too large. We can make that weight swing rapidly by making the moment of inertia small or the elasticity large, one of the two, or both. Now the coefficient of self-induction in the circuit, corresponds to the moment of inertia of the swinging weight, and the capacity in the circuit corresponds to the elasticity of the wire, and just as the elasticity of the wire and the moment of inertia of the weight determine the period of the circuit, so the capacity in the circuit, and the self-induction determine the electrical period of the circuit. That is to say if you create a disturbance in the circuit, say by pulling quickly a permanent magnet away from the coil, you will start an electrical disturbance there, and the electricity will swing back and forth, just as a pendulum swings back and forth, the period of that swing depending on the coefficient of self-induction and the capacity of the circuit. The electricity in the circuit will swing back and forth till it is reduced to rest by the ohmic resistance. If you now apply a periodically varying impulse-not a single impulse, but a periodically varying impulse to the torsional pendulum just mentioned, you will make it oscillate, but the oscillation will be forced, if the period of the acting force is different from the natural period of the pendulum. But if the two periods are exactly the same, then the oscillation of the pendulum is a free oscillation, and the force and pendulum are in resonance. Now what is the effect of free oscillation? The effect of free oscillation is to reach a larger swing than the forced oscillation under the action of a force of the same mean intensity. The swing will continually increase, until the work done against the frictional resistances during one half of the swing is exactly equal to the work which the moving force does in that time. If, therefore, the resistance is very small, you see that the swing will increase indefinitely. But what happens to the wire? Resonant swinging means simply this:-The kinetic energy of the swinging weight is periodically reduced to zero, that is, transformed entirely into the potential energy of the elastic forces of the wire and vice versa; so that the larger the swing, the larger will be the maximum elastic force with which the wire reacts; so that the smaller the frictional resistances the larger the elastic reaction. But we must remember that the elastic force in the wire corresponds to our potential difference in the condenser, so that