Electromagnetic Theory, Vol. 1 (1893) — part 29 of 31

to and fro too quickly for practical observation. Take, then, a long india-rubber cord, suspended from a height, as is some- times done by lecturers. The speed of transmission of pulses may be made small enough to allow the disturbances to be conveniently watched. Then, if the cord hang vertically at rest to begin with, and its lower end be momentarily jerked, bringing it immediately back to its original position, a hump is generated, which runs along to the fixed end. It is not much changed in transit, and is reflected back, and re-reflected many times. But we only want to consider the passage of a hump one way. Properly speaking, then, we should have so long a cord that reflection is (by frictional loss) insignificant. Per- haps a very long cord laid upon a surface of ice would be more suitable for the purpose. But if the " fixed end " be movable transversely, and its motion be resisted by a force proportional to its velocity, their constant ratio may have such a value given to it (depending upon the mass and tension of the cord), that the arriving disturbances do not produce any reflected waves, but are»absorbed by the terminal resistance. The cord then behaves as if it were infinitely long. This is theory, of course, but I dare say a sufficiently good practical imitation could be got by means of a terminal block sliding upon a wire with friction. An imperfect cancellation of the reflection is easily got.

Disregarding the slow change of type and the attenuation, so that there is undistorted propagation of a hump, or of a succession of humps making a train of waves going one way only, this case is analogous to the transmission of waves along a uniform circuit of no resistance. The two constants L and S in the electrical case are replaced by another two, viz., the density (linear, or mass divided by length) and tension of the cord. Thus, large permittance, that is, small elastance, means small tension, or a slack cord ; and large inductance means a massive cord. If I said a " heavy " cord, it might be thought that its weight was concerned in the matter in question, but it is not, save as a disturbing factor. The transverse displace- ment of the cord may be compared with the transverse voltage in the electrical circuit. Other comparisons (theoretically better) may be made, but this is perhaps the most convenient if the motion of humps be actually watched.

THEORY OF PLANE ELECTROMAGNETIC WAVES. 431

Now to imitate the action of the resistance (assumed to be constant) of an electrical circuit, the transverse motion of the cord must be frictionally resisted, and the frictionality (or coefficient of friction) should be constant. That is, the frictional force should be proportional to the transverse velocity. The motion of the cord is frictionally resisted, both internally and externally. It is very unlikely that this should give rise to a constant frictionality, but there is a similarity insofar as the waves sent along the cord do attenuate and are distorted as they progress.

But the friction is not anything like enough in the case of a cord in air to imitate the submarine cable ; besides that, the mass is too great, and likewise the tension. Even to copy telephonic waves going along very long copper wires of low resistance, we should increase the friction in the mechanical analogue if we desire to have an equal amount of attenuation in a wave length. The cord should, therefore, be in a viscous medium, and the viscous resistance to the cord's motion should be so great as to produce a marked attenuation during the transit of a hump, though it should not be so great as to prevent its distinct propagation as a hump, without great dis- tortion of shape and spreading out. Under these circumstances we may exemplify low-resistance, long-distance, overland tele- phony, where the inductance is relatively large and the permittance relatively small.

But to imitate a submarine- cable we should have a slack cord of small mass in a highly viscous medium. We can then send a hump only a little way along it as a hump, for it becomes greatly distorted and diffused. Consequently, if we compared the displacements at a great distance along the cord with those impressed upon it at the free end, we should find a state of things quite different from what occurs in the case of an india-rubber cord in air. The main features of the originated disturbances might be recognised, unless the attenuation were too great, but they would be out of all proportion. In particular, there is a tendency to obliterate small humps, or ripples whilst the big ones persist. The propagation is of the sluggish kind characteristic of diffusion, quite unlike that of purely elastic waves. If the slack cord could have no mass at all, we should then imitate a submarine cable wholly without inductance.

432 ELECTROMAGNETIC THEORY. CH. IV.

Under these circumstances we could convert the diffusive waves to something like elastic waves by giving mass to the cord. Without changing either its tension or the frictionality, we could, by a continuous increase of density, cause the nature of propagation to pass continuously from the sluggish, diffusive kind to the elastic kind with approximate preservation of form of waves. We might also do the same by -increasing the tension and reducing the frictionality, keeping the density small (like, by reducing the permittance and the resistance in an electrical circuit, bringing the inductance into impor- tance). But these are not immediately in question. By increasing the mass, or equivalently the inertia of the cord, we impart momentum to the waves, which allows them to be carried forward, in spite of the little tension, against the resistance of the surrounding medium.

So it is in the electrical case. By increasing the inductance we impart momentum to the waves, and that carries them on. This statement is independent of the particular mechanical analogy that may be employed for illustration. It is probably representative of the actual dynamics of the matter, associating L with inertia, and LC with momentum. The soundness of this dynamical explanation (made by me some years since in asserting and proving the fact concerned) was endorsed by Lord Kelvin. And I am proud to add, for the benefit of those who may excuse themselves from understanding me by the plea that I am a Schopenhauer (!), that Lord Kelvin expressed his appreciation of the very practical way in which I had reduced my theory to practice.

Many other dynamical arrangements might be alluded to, exemplifying the power of inertial momentum to overcome frictional resistance, but it is not easy to get a good one exhibiting elastic waves plainly.

To illustrate the nature, and to emphasise the possible magnitude of the effect, suppose we have the power of continuously increasing the inductance of an Atlantic cable from a small quantity up to a very large one, without altering its resistance or permittance, and without introducing any other actions than those to be controlled by resistance, permittance, and inductance. Starting with L = 0, and making, say, 1,000 waves per second \t one end, there will be 1,000

THEORY OP PLANE ELECTROMAQNBTIC WAVES. 433

waves per second of workable magnitude only in a small part of the cable near the sending end ; the amplitude will attenuate to insignificance, not exactly in the shore-end, but before 100 miles is traversed. But let waves of the same size (which will need greater battery power to produce) be kept up at the sending end whilst L is continuously increased all along the cable. The region of practical waves will continuously extend itself right through the cable, by a partial conversion to elastic waves, with little attenuation in transit. With very big inductance the waves would reach the distant end nearly in full size. Even then they could be doubled in size by the reflection, though there would be no useful purpose served by that. The amount of inductance required, however, to produce these results would be out of all reason. Nevertheless, the illustration serves its purpose in showing the action of self- induction, which is, as before stated, wholly beneficial, as it increases the amplitude and lessens the distortion. Some remarks on increasing inductance will come later.

Self-induction combined with Leaks. The Bridge System of Mr. A. W. Heaviside, and suggested Distortionless Circuit.

§ 216. In the meantime, some few remarks on self-induction combined with leakage should come in here. Self-induction came in with the telephone. That was, originally, a mere house-to-house affair. At any rate, lines were only a few miles long. So condenser action was out of practical question then. On the other hand, the frequency of the currents concerned is very great, and that makes inertia important. So the theory of telephones is a magnetic affair when the lines are short enough, just as if they were lines in a laboratory.

But the telephone soon got beyond that, and it became necessary, with the use of longer and longer lines and under- ground lines, to examine the influence of their permittance in conjunction with their inductance. In hardly any case of telephony can we ignore the self-induction, and take the permittance alone. The resistance would need to be so large that the lines would be wholly unsuitable for telephony, except for mere local lines. So permittance and inductance usually

pp

434 ELECTROMAGNETIC THEORY. CH. IV.

go together in considering telephony, and if one of them is ignorable it is the permittance rather than the inductance.

Following the telephone came exchanges. But there was an exchange before telephones. My brother, Mr. A. W. Heaviside, had an intercommunication exchange at Newcastle, using alphabetical indicators, whereof the manipulation resembled that of the hurdy-gurdy. These were beautiful instruments mechanically ; but, of course, the telephone soon stopped their manufacture. The exchange referred to was then turned into a telephone exchange. Now, in certain cases it was needed to have many instruments in one circuit, with local intercommu- nication ; a sort of family arrangement, so to speak ; for example, a number of coal pits and colliery offices belonging to one firm. The custom was to set all the intermediates in sequence (otherwise, but perhaps not so well, called in series) In the circuit. Why was this done? Simply because they knew no better. It was the custom to do so in the telegraphs generally, being an obvious arrangement — not so much in England, though, as elsewhere. But when this was done with telephones, or with call-instruments replacing them, it was found that the intermediates had a very deleterious influence, which very soon set a limit to the admissible number of inter- mediates on a circuit and to the length of the circuit, especially when underground wires were included. My brother, who took up the telephone with ardour from the first (making the first one made in England, I believe), found by experiment that it was quite unnecessary to put the instruments in sequence according to old practice, and that an immense improvement was made by taking them out of the circuit, and putting them across it, as shunts or bridges. Like lamps in parallel, in fact. It seems very easy and obvious now. But it is not so easy to conceive the state of mind of old stagers. Anyhow, the pro- position to put the instruments in bridge was pooh-poohed at first, not being understood. As, however, it was demonstrably a wonderful improvement it was adopted, first at Newcastle, and then elsewhere, and became known as the Bridge System.

When this system was brought to my knowledge, and I was asked for theoretical explanation, it presented itself in a double aspect. First of all, there was the complete removal from the circuit of intermediate impedance in big lumps. This was

THEORY OP PLANE ELECTROMAGNETIC WAVES. 435

manifestly the main reason of the increase in working distance possible, and why a far greater number of intermediates co^ld be put on. For they were not put in the circuit, but on it, st> to speak.

The other aspect of the matter was this. Considering that the bridge system consists electrically of a circuit with a number of leaks on it, and bearing in mind my old investigations concern- ing leaks, I inquired whether the intermediates were not ac- tually beneficial to through communication, independently of the previous effect. Was not the articulation better, not merely than if the intermediates were in series in the circuit, but better than if the shunts or bridges were removed altogether, leaving insulation ? My brother's answer was Yes, certainly, in certain cases, b*ut doubtful in others. It appeared, however, to be only a minor effect, of not much importance compared with the major one. Besides, the bridges caused a weakening of the intensity of the speech received when many bridges were passed. To pre- vent this weakening becoming inconveniently great, the inter- mediate call-instruments in bridge were purposely made to have considerable resistance and inductance, far more than would be needed or desirable for their natural use. This tended to prevent the currents passing along the line from entering the shunts, and especially so as regards the currents of high frequency, and allowed them to be transmitted in greater magnitude.

It will be observed here that the expediting effect of leakage considered before (§§ 213, 214) is merely incidental, and is, in fact, partly destroyed by the large impedance of the bridges, in order to mitigate the attenuative evil. The shunts are inductive shunts, intentionally very much inductive. Now, my proposed leaks (§214) for submarine cables were non- inductive, and intentionally so, though it may be remarked that it would make very little difference with the slow signalling of Atlantic cables if they were inductive. On the other hand, a recent proposal of Prof. Silvanus Thompson is to use induc- tive shunts on cables. The arrangement is electrically as in the bridge system, but the object is different. This point will be returned to.

The investigation of this bridge system of telephony suggested to me the distortionless circuit, as I have before acknowledged

FP2

436 ELECTROMAGNETIC THEORY. CH. IV.

("Electrical Papers," Vol. II., p. 402). It may be of interest to state how it came about, since it is not presented to one by the above-described experiences with the bridge system. The ques- tion was, What was the effect of a bridge, or of a succession of bridges, when the self-induction of the line was not negligible ? Now the influence of the bridges can be very readily stated for steady currents, of course. There is no difficulty, either, in finding the full formulae required to express the voltage and current and their variations in any part of the system when the inductance and permittance are operative, as well as a set of leaks, when one knows how to do it. But the general formulae thus obtained are altogether too complicated to be readily interpretable. I was, therefore, led to examine the effect produced by a leak on a wave passing it of the" elastic type. This implies that the resistance of the line is sufficiently low for waves of the frequency concerned to retain that type approximately. (Ln should be greater than R.) Now this was comparatively an easy problem, and the result was to show that a leak (or conductance in bridge) had the opposite effect on a wave passing it along the line to that of a resistance inserted in the circuit at the same place, in this sense : — A resistance in the circuit reflects the charge positively and the current negatively, or increases the charge and reduces the current behind the resistance. On the other hand, a leak reflects the current positively and the charge negatively, or in- creases the current and reduces the charge behind the leak. (See also §§ 197, 209.) A resistance and a leak together at the same place therefore tend to counteract one another in producing a reflected wave, leaving only an at- tenuating effect on the transmitted wave. This led to the distortionless circuit. For although the compensation of the resistance in the circuit and the conductance across it is im- perfect when they are finite, it becomes perfect when they are infinitely small. They may then be a part of the circuit itself, namely, the resistance a part of the resistance of the line, and the conductance a part of the leakage. We now have perfect compensation with this one, or any number of successive resist- ances and leaks of the same kind, provided their ratio is pro- perly chosen. This occurs when R and K, the resistance and conductance per unit length of circuit, of the line and of the

THEORY OF PLANE ELECTROMAGNETIC WAVES. 437

leakage respectively, are taken in the same ratio as the two other constants, L and S. Or, when L/R = S/K, indicating equality of the electric and magnetic time-constants. There is now an undistorted transmission of any kind of signals. And since every circuit has R, L, and S, it follows that it can be made distortionless by the addition of leakage alone of a certain amount, or distortionless to the extent permitted by the ap- proximate constancy of R, L, and S. (See " Electrical Papers," Vol. II., pp. 119 to 168, for detailed theory of the distortionless circuit.)

In § 213 we saw that even in the electrostatic theory leakage would allow us to signal as fast as we liked provided we could do it with an infinitesimal current. This was not because the circuit was made distortionless, but on account of the infinitely rapid charge and discharge. Now the inclusion of the in- fluence of self-induction shows that we can do the same with a finite leakage conductance, and have finite distortionless sig- nals, due to waves of the purely elastic type. Given R and S then, if L should be so small that the introduction of K of the proper amount to reach the distortionless condition should produce unreasonable attenuation, then one way of curing this would be to increase L. For then a smaller amount of leakage will serve. The bigger L, the smaller need K be, and when it is very big, then very little K is needed. This brings us round to the case at the end of § 215, where we had elastic waves with little attenuation on an Atlantic cable got without any leakage, and since we see now that very little leakage is needed to bring about the distortionless condition, we conclude that it is approximately distortionless without the leakage.

Evidence in Favour of Self-induction. Condition of First-Class Telephony. Importance of the Magnetic Reactance.

§ 217. Let us now ask what is the evidence in favour of the beneficial action of self-induction. There was plenty in 1887; it is overwhelming now. But there are two sorts of evidence, the theoretical and the experiential. The two are not funda- mentally different, however ; only the former is more indirect than the latter. We have certain electrical laws established, mainly by laboratory work followed by mathematical inves-

138 BLBCTROMAGi^ExiC THEORY. CH. IV.

tigation, and there is no reason whatever to suppose that they do not hold good out of doors as well as inside. The important thing is to correctly recognise the prevailing conditions and determine their results. Now, if you can be pretty sure that you have done this, and have confidence in your investigations, then you may consider that you prove a thing, even though there may be no direct evidence. Discoveries are frequently made in this way. " A foundation of experimental fact there must be ; but upon this a great structure of theoretical de- duction can be based, all rigidly connected together by pure reasoning, and all necessarily as true as the premises, provided no mistake is made. To guard against the possibility of mis- take and oversight, especially oversight, all conclusions must sooner or later be brought to the test of experiment ; and if disagreeing therewith, the theory itself must be re-examined, and the flaw discovered, or else the theory must be abandoned." (Oliver Lodge.) But to convince other people is quite another matter. They may not be competent to understand the evidence. Or they may be fully competent, but not have suffi- cient acquaintance with the subject ; or not have time to examine it ; or not have the energy ; or have no interest in it. Then, as Elijah said to the priests of Baal, you must " Call him louder!"

Now, the foundation of fact is the experimental facts of elec- tricity and the laws deduced therefrom, though these laws are sometimes more comprehensive than the facts upon which they are based. But there was, in 1887, a certain amount of direct evidence as well, quite enough to make the theoretical con- clusions practically certain, by the confirmation they afforded. Assuming the electrostatic theory to be true in telephony (for which, however, there waa never any sufficient warrant) we can calculate its consequences. They indicate that the product RSJ2 of the total resistance and the total permittance limits the distance I through which telephony is possible. How big it may be is questionable, on account of the very complicated nature of the problem when the human is taken in as a part of the mechanism. We cannot say certainly beforehand how much distortion is permissible before the human will fail to recognise certain sounds as speech. But the electrostatic theory shows such very considerable distortion even when

THEORY OP PLANE ELECTROMAGNETIC WAVES. 439

RSI2 is as low as 5,000 or 7,000 ohms x microfarads, that it is scarcely credible that any sort of telephony could be prac- ticable if it were much bigger, as 10,000 for example. Perhaps 5,000 might be taken as the practical limit for rough purposes. But experience showed that good telephony was got up to 10,000 and higher, in this country with circuits including underground cables, as well as in America, where long-distance telephony had already made a good beginning. Manifestly the electrostatic theory was erroneous by direct as well as indirect evidence. Now the inclusion of the influence of self-induction in the theory explained these results (and also the failure of iron wires and the success of copper) and pointed out how to improve upon them, viz., by directing us to lower R and increase L in order to increase the value of RS£2 possible. So there was sufficient direct evidence then to satisfy anyone com- petent to judge who considered it fairly without being pre- judiced by the law of the squares. Since that time, the amount of this direct evidence has been greatly multiplied, and RS£2 has got up to 50,000, which may be about ten times as great as the probable value under purely electrostatic con- ditions. But there is nothing critical about 50,000. It might be 500,000 if the circuit were long enough. We may need to reduce R when we increase Z, but not in proportion to the inverse square of Z, or anything like it.

Any long circuit may be made approximately distortionless if the magnetic side of the phenomena can be made important, and without the inconvenience of the leakage needed to remove the distortion, which leakage, however, is essential when the magnetic side cannot be made important. The useful guide in considering telephony is the size of the quantity R/Ln, the ratio of the resistance to the reactance, the two terms appear- ing in (R2 + L2tt2)*, the impedance of unit length of circuit, apart from the permittance.

The term " reactance " was lately proposed in France, and seems to me to be a practical word. It may be generalised to signify the value of Lrc, positive or negative, of any combina- tion of coils and condensers, L being then the effective induct- ance. When L and the reactance are positive, the magnetic side prevails and the current lags ; and when it is negative, the electric side prevails and the current leads.

440 ELECTROMAGNETIC THEORY. CH. IV.

At present, however, R and L are as before. Now the ratio R/L/7& may be very large. If so, the influence of L is small, and we shall have something like the electrostatic theory, provided the range of n be such as to make the ratio always large. But this state of things is quite unsuitable for long- distance telephony. The most suitable state is when R/Lw- is a proper fraction throughout the whole range of n ; that is, when R is less than the smallest value of Im. We shall then have approximately distortionless propagation of the type

as may be seen by examining the solution for simply periodic waves, and observing that when R/Lw- is small we have nearly the same attenuation in a given distance at all frequencies (not too low), so that there is little distortion, and the element of frequency tends to disappear altogether, and we reduce the formula to the above type.

Practice shows, however, that this state of things is unneces- sarily good for commercial telephony, which admits of a considerable amount of distortion. Then R/Lw, is not less than 1 throughout the whole range of n, but is greater at the low frequencies and less at the higher.* For example, if the lowest value of n be 625, and L = 20 (centim. per centim., usual units), the least value of IM is 12,500. If also the resistance is 5 ohms per kilometre, then R is 50,000. The value of R/L» is then 4 at the lowest frequency, and 2, 1, J, £, J at the five successive octaves, the last being at n= 20,000. Here we have an excellent state of things from n= 2,500 up to 20,000, and only at the low frequencies does R prevail over Lra. If R be halved, or L be doubled (for it is indifferent which is done), then R/Lra is less than 1 from » = 1,250 upwards. Divide n by 2?r to obtain £he frequency. This 2?r has nothing to do with the ridiculous 4?r which the B.A. Committee want to consecrate. The significant point in calcu- lations of this kind is the position of n in the scale of frequency which produces equality of R and Tun. When it is low we have good quality ; when high, then relatively bad. Perhaps the American electricians may be able from their extended

• See my " Electrical Papers " for details ; especially App. C, p. 339, Vol. II.

THEORY OP PLANE ELECTROMAGNETIC WAVES. 441

experience to give practical information on this and other points concerned in telephony, and construct an empirical formula of a sound character for determining the limiting dis- tance roughly in terms of the electrical data, with given kinds of instruments for transmission and reception. It should be understood that the above remarks do not apply to short lines, at least in general. We may, indeed, so arrange matters that the above type is still preserved (with R/Lw, less than 1) by practical annihilation of reflected waves, but otherwise serious modification may be needed. And with very short lines we may apply a purely magnetic theory, of course.

Various Ways, good and bad, of increasing the Inductance of Circuits.

§ 218. Supposing, now, that practicians have come to discard the supposed limitations so persistently asserted by official electricians in England, and to open their eyes to the part played by self-induction, they will naturally recognise the wide possibilities that are suggested in future developments, and want to know whether such possibilities can be converted into actualities, and whether the conversion is practicable. For myself, I am not much concerned in this part of the question. It is for practicians to find out practical ways of doing things that theory proves to be possible, or not to find them if they should be impracticable. Nevertheless, since I am responsible for these views concerning the parts played by self-induction and leakage, I add a few remarks on the applicational side.

The ideal is the distortionless circuit, requiring both self- induction and leakage. If we utilise the present existent inductance only, then the needed leakage may be too great by far in many cases. On the other hand, if the existent induct- ance is big enough to make R/Lw. small, in the sense described in § 217, we do not want the leakage particularly, or not at all practically, it may be. It is clear, then, that we should aim at making L/R, the magnetic time- constant, as big as possible.

Now, here is one way of doing it. If, a few years ago, an old practitioner was asked to put up a long-distance telephone circuit, he, being under the belief that R should be high, or at least that it need not be small, and that L should be as small as

442 ELECTROMAGNETIC THEORY. x CH. IV.

possible, in order to prevent the deleterious action of self- induction, would probably carry out his principles by putting up a circuit, several hundred miles long, consisting of a pair of fine wires, put quite close together. Or, if he was free from the error as regards R, he would use larger wires. But still close together, for that makes L the smallest. Also, he would not consider this to be bad as regards S, the permittance, being under the belief that the permittance of the circuit of two wires was just one half that of either with respect to the earth, so that their proximity did no harm in increasing condenser action, whilst it destroyed the deleterious self-induction. Now, such a circuit might do very well for local telephony, but for the purpose required there could not be a worse arrangement. The supposed case is not an extravagant one, since it involves the carrying out of official views thoroughly. The cure would be quite easy. Increase the inductance by separating the wires as widely as possible or convenient. If necessary, reduce R as well. The permittance will also be reduced in about the same ratio as the inductance is increased. By this simple process L may be largely multiplied, say from 2 to 20 (cm. per cm.), a tenfold magnification, without separating the wires so much as to require a double line of poles. This way of doing it is the secret of the success of the long-distance telephony which arose in America when iron was discarded. L is made important, and R is kept low. But although L increases very fast on initial separation of wires, it does not continue to increase fast on further separation, so that practical limitations are soon set to the process. The above example shows how a very bad line may be turned into a very good one by increasing the inductance. Another way is suggested, but only to be immediately rejected. It is, nevertheless, instructive to study failures. We can increase L to any extent by using finer and finer wires. This would be admirable if it were all. But, unfortunately, this process alters R, and faster still ; so that R/L increases instead of diminishing. Consider, for simplicity, merely a wire with a concentric tube for return. Then R/L is nearly propor- tional to RS. Now Lord Kelvin gave a formula long ago, showing that this quantity was made a minimum when the radii of the tube and wire bore a certain ratio. Then L/R is a maximum, approximately, and on decreasing the radius of

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THEORY OF PLANE ELECTROMAGNETIC WAVES. 443

the wire it falls off, ultimately very rapidly, which is the reverse of what is wanted.

A third way must also be immediately rejected. By using iron wires we can increase L largely with steady currents. But then the skin effect, or imperfect penetration, becomes important with telephonic currents in iron wires. It does two things, both harmful. It lowers L and increases R. So we do not get the large increase of L suggested at first, but only a comparatively small one with currents of great frequency, and we do get a lot of extra resistance that should particularly be avoided. Iron wires are failures for long-distance telephony, as was found long ago.

The case of copper-coated iron or steel wires is doubtful. Such wires were used in America, and it was said that they were successful for long-distance telephony. But here, evidently, the copper is very important in giving conductance. As regards the interior iron core, it must be considered very questionable tvhether it can be so good as an amount of copper of the same resistance (steady). It is not well placed for increasing the inductance, and the imperfect penetration will operate injuriously.

If we put the iron outside the copper the iron will be better situated for increasing L for steady currents (which is no good), but will act injuriously with rapidly oscillating currents, and partly prevent the utilisation of the conductance of the copper, if it be thick enough to make the increased L important.

The above considerations show that if iron be introduced to increase the inductance it should not be in the main circuit, but external to it. There are, then, two principal ways sug- gested. First, to load the dielectric itself with finely-divided iron, and plenty of it. This is very attractive from the theoretical point of view, as it results in the production of a strongly magnetic insulator, which is practically homogeneous in bulk, being, therefore, a sort of non-conducting iron of low permeability. In this way L, as compared with the same with- out the iron, may be multiplied greatly. There is a partially counteractive influence, however, due to increased permittance. This plan is interesting, in view of the wave theory. It is like multiplying the p in ether, and lowering the speed of pro- pagation, but at the same time allowing waves to keep up

444 ELECTROMAGNETIC THEORY. CH. IV.

against the resistance of wires they may be running along. But as regards the practicability of this plan I say nothing, except that I have often smiled at this ironic insulator (in more than one sense ironic), and the idea of telephoning through a core resembling a poker with a copper wire run through the middle.

The other way is to put the divided iron outside the working dielectric. Then it had better not be divided into particles, but in the way well known to dynamo and transformer people, cut up so as to facilitate the flux of induction, whilst being electrically non-conducting transversely thereto.