suggestion. It is abundantly evident that, in proportion as alternate currents become studied, the quantity we have called the "coefficient of self-induction" of a wire will be one that will be seen to be of equal importance with ohmic resistance, and it would be convenient to have one short word for 10o absolute units of self-induction. Following the precedents which cause us now to select as the names of our practical units the names of distinguished discoverers, might we not venture to appropriate for this purpose the name of our President, and call it a "hughes"? And, if he will not disclaim having a fresh little unit christened after him, we shall not only be the gainers by a convenient word, but we shall add a link of association between it and a presidential address which must ever stand high in interest amongst the number of those which have been delivered within these walls.

Mr. DESMOND G. FITZGERALD: The observations that have been made in the discussion on Professor Hughes's very valuable paper have confirmed me very strongly in the notion that more especially the variable period which precedes the normal current is deserving of further study and greater observation than it has hitherto obtained. The "extra-current" period which follows upon the breaking of the circuit is perhaps better understood. I am confirmed in this view by the continued use of the expression, "the induction of a current on itself," in reference to the former period. I think it can be shown that electro-magnetic induction precedes the passage of a current, and that this expression, which is old, ought also to be considered as obsolete. Another important point is, I think, that these effects-said to be due to self-induction or electro-magnetic inertia-are probably solely dependent upon the electro-magnetic capacity of the conductor, or, rather, of the circuit; and we have no reason, so far as I know, to consider that any other cause is in action. In the Electrical Review of August 18th, 1870, I gave the result of an investigation into the magnetic polarity of a conductor conveying a current. This polarity may be quite familiar to some, but I have reason to believe that it is by no means familiar to everybody; and therefore, with your permission, Mr. President, I will draw the diagram I then gave.

Every conductor conveying a current is found to possess in greater or less degree, according to the nature of the conductor, as well as the magnitude of the current, the polarity here represented. Now, if I were to state that the soft iron core of an electromagnet becomes magnetised by the passage of a current through the coils, I should probably not be contradicted by anybody here. Mr. Preece has made such a statement this evening, and I do not suppose that anyone was disposed to contradict him. But I say that there is reason to think that the production of the magnetism in the conductor, and in the electro-magnet surrounded by its coils, precedes the passage of the current; and if this be the case, it points to an extremely interesting and neglected field of research. When we pass a current through the coils of an electro-magnet we virtually insert a magnet within the coils of that electro-magnet, the polarity of the magnet being such that the current it would induce would oppose the passage of a current such as would generate the magnetism. There seems, therefore, clearly to be, during this period which precedes the normal passage of a current, some short period of time during which there is an absence of current. The question then arises, Is the battery at work during this period? If so, we have this extraordinary thing to consider and to observe: we have a battery at work, and yet we have no indication by the galvanometer of the passage of any current through the circuit. It is familiar to most of you, no doubt, that in a circuit of great electro-magnetic inertia there is no sign of the passage of a current for an appreciable periodappreciable even by the eye-after the completion of the circuit.

It is during this interesting period, apparently, that magnetism is born. We are present at the birth of magnetism when we depress a key to complete a circuit of great electro-magnetic inertia; and I feel sure that Professor Hughes, who has already so strong a grip of the physics of magnetism, will still further enlighten us if he pursues this clue. If, on the other hand, the battery is, as we might suppose, idle during this period when no current is visible in the circuit, then arises the interesting question, which I have myself never been able to satisfactorily answer, Whence is the energy derived-the very considerable quantity of energy-which becomes stored up as electro-magnetic energy in a circuit, say, including a great number of electro-magnets? I myself am inclined to hold, with most people, that during the period which precedes the normal passage of the current the battery is idle, or nearly so. Now there is apparently no available source of energy other than the battery; but whence, I say, is derived the work which is stored up as electro-magnetic energy? This is a most interesting problem, and one which I should be glad to see satisfactorily solved. Possibly some portion of the energy existing as heat in the circuit may disappear; and in this variable period which precedes the passage of the normal current we might, if we could devise instruments sufficiently sensitive, observe the production of cold, as in the period which follows upon the interruption of the normal current we might observe a more than corresponding development of heat.

I had a great deal more to say, particularly as to the instantaneous passage of the current of static charge, the molecular theory of conduction, and the production-which I investigated in 1868-of an elementary magnet by the rotation of a static charge; but as time is so limited, and as I have had to interrupt the order of my notes, I think I will defer any further observations until another opportunity.

Professor SILVANUS P. THOMPSON: I have, Sir, a few remarks to make, some of them of a theoretical nature, together with some deductions of a more practical kind. I have seldom heard with greater pleasure any scientific paper read than the paper

which Professor Hughes gave us as his presidential address. The enormous amount of detail in the experiments he explained, especially of detail requiring thought to understand, is something very remarkable indeed. It has occurred to me that there is one point on which we ought to be a little more clear in arguing about Professor Hughes's experiments. It is this—that we should take into account, in considering this question of the apparent resistance offered by conductors possessing self-induction, the rate at which the current is being made to vary. I have looked rather carefully through Professor Hughes's paper, and I am rather hoping that he will have something presently to say to us in further explanation of this point. He mentions particularly that the rate of interruption of the current by the clock microphone might be anything between (if I remember rightly) 10 and 100 per second. I want to know, if I am not inquiring too closely into the secrets of the experimenting-room, at which of these speeds the particular experimental results were obtained that are plotted out in the various curves shown in the paper. Further, was any difference observed in the case where a high speed of interruption was used, compared with that where a low speed of interruption was used? I ask the question because the practical points that I wish to bring out from the theoretical ones depend upon the rate at which these variations of the current take place or are made to succeed one another. I am not going, by any means, to say that Professor Hughes's mode of experimenting is not perfect; indeed, it is seldom, I think, that a more perfect instrument of its kind has ever been produced to a scientific audience; but I should like to know what would happen if, instead of using the clock microphone—which produces interruptions of a somewhat irregular kind, impossible easily to express in an adequate mathematical form-something more like a musical tone were introduced by a harmonic interruptor. I mean by this something which would send electric undulations of a truly harmonic character, having a definite known period-say, for instance, exactly 100 waves a second, or exactly 400 waves a second-corresponding to some recognisable musical note. I n inclined to think, if Professor Hughes does not mind my

making a suggestion to him, that in some of the cases in which he does not get a really complete balance and silence in the telephone, he would be much more likely to obtain such a result if the interruption that was going on was a simple harmonic one, and did not consist of clicks, short and sharp, or more or less prolonged, according to the elasticity of the spring that makes them by hopping from one tooth of the wheel to the next. The way in which I want to treat this matter is to take the case where a pure musical note creates the variations of the current, so that the varying electromotive force thrown into the circuit should be represented mathematically by some such formula as

where E, represents the electromotive force at the lapse of a certain time (t), E, the maximum electromotive force, and the angle that corresponds, on the circle of reference, to the time that has elapsed since the origin, and therefore equal to 2 π n t, where ʼn is the number of vibrations per second. Were there no selfinduction, we should, of course, write for the current at the

where R is the number of ohms of resistance.

But if there is self-induction as well as resistance in the circuit, then the expression for the current must no longer be written in that simple way. Ohm's law, we may say, is no longer adequate, except in a modified sense, because the self-induction comes in and alters the fluctuations of the current and makes them lag behind those of the electromotive force, retarding them in phase and diminishing them in amplitude. I will not go through the stages whereby the equation is obtained, but it is well known, at any rate to those who work with alternate-current machines, as well as to those who have worked on the problem of the transmission of harmonic interruptions-that is to say, of musical notes-by telephone.

What we have to write is this