IN THE | **** *** *-* : --------ºº------ BEFORE THE EXAMINER OF INTERFERENCES. --~~~~#-----—- \ PUPIN HUTIN & LEBLANC ) Wo. 17,196. STONE, ~~e— Subject : Selective Distribution of Electrical Energy. RECORD OF M. L. PUPIN. Ewing, whitMAN & Ewing, 41 Wall St., New York. Attorneys for M. J. Pupin. . . . # º ~~~~}-º-º- . ...’ 5,3 ¥ §§ º: - - NEW YORK, ... --~~ Press of McILRoy & EMMET, 106–108 LIBERTY ST. Jätent Offict, . . . . . . . . . .--> * 7** intr No./ ZZZ 6/Paper No./27. __ . -sº- ... " /,' ſ —S Transportation. #2 (' Library 2-4 7, c. Éa sºa vº- ? ºr 72.2. ~ /#44%, 2Z.e/3/azzo , # -z, žene- 722.7% 7%,72&e aſ Zöe C Cº ~ zºo) tan p. = * * = p: C. £25 ſo; 216 Michael I. Pupin. In his answer to x Q. 283, Mr. Stone proposes to de- termine experimentally the apparent, or, as he calls it, effective, self-induction and capacity of a circuit by measuring the phase. He does not say what experimen- tal method he would employ. Suppose, however, that he has done the experiment successfully. The last formula, just given above, shows that a knowledge of the phase is not sufficient for the calculation of apparent self-induction and capacity unless the apparent resistance os is known. There is nothing in Mr. Stone's exhibits which would enable one to calculate the apparent resist- ance of a selective system, nor did this knowledge exist then, nor does it exist now in the electrical literature, out- side of the formula just given. I fail, therefore, to see in Mr Stone's definition of apparent self-induction and apparent capacity in terms of the phase an intelligible definition. Again, Mr. Stone says that the current in circuit 34 will be greater than in any other circuit when this cir- cuit fulfils the condition f 1 * } T = gº, Va., C. that is, when p;" o's C; = 1 Or * * { 1 2 C. 05 Rºo) -- 1 ( £95 C5 ( * ps C, OI’ 05 – 0. or W ! } 1.--> – ' pº Ms Lºs = 0 º p, C. p. Lº -- ſº ; § 2. An inspection of the formula for I, shows that in this case the apparent impedance (according to my definition, not according to Mr. Stone's) is reduced to the apparent resistance and in this respect the state of the circuit 34 Michael I. Pupin. 217 resembles then the state of a simple circuit, when the simple circuit is in resonance with an impressed simple harmonic electromotive force. It is, however, a super- ficial resemblance only, for whereas, the simple circuit is in resonance with the impressed electromotive force, when its impedance is reduced to ohmic resistance, the complex circuit, like the circuit (34) is far from being in resonance with the impressed electromotive force when its apparent or effective impedance is reduced to the ap- parent resistance. It is evident that Mr. Stone was led astray here by carrying the analogy between a simple circuit and a circuit forming a part of a selective system too far. That } O's - O does not give the maximum for I, for the frequency ps is self-evident. To get this maximum we have to solve the equation for the purpose of finding the value of ps, in terms of the electro-magnetic constants of the system given in Fig. 7 of Stone’s specification. Mr. Stone's fundamental formula is therefore incorrect. The same applies to Messrs. Hutin & Leblanc's formulae. Let us assume, however, for the sake of argument that os = 0 expresses the condition of resonance in circuit 34, in the sense that the current in this circuit is then a maximum for frequency ps. Will the current I, be then greater in this branch than in any other branchº That is to say, will I, be greater than, say It, in other words, will - M. < JM. 4/p;" L'A + R’.” Wp, dº-E of O5 4/p.” L’.” + R’.” 218 Michael I. Pupin. * Not necessarily. In fact, I, may easily be much smaller than I. But if that be so, then Mr. Stone's directions, even under the assumption just made, fail to secure selectivity. Suppose, however, that o; = 0 does actually secure selectivity in circuit 34 for frequency ps, and that or = 0 o'e - 0 os = 0 or = 0 os = 0 or = 0 secures selectivity in circuits 30, 31, 32, 33. ... 36 respec- tively for frequencies p, ps. . . .p. respectively, the ques- tion arises now :-How much assistance would an electri- cian (desirous of putting a system like the one in Fig. 7 of Stone’s specification into practical operation) obtain from these seven equations? That which he has at his disposal is a certain number of impressed simple harmonic electromotive forces of given frequencies, and, in addi- tion to that a certain number of coils and condensers. These he has to adjust in such a way as to satisfy the seven equations. The numerical values for these quanti- ties cannot be calculated from these seven simultaneous equations, for we encounter equations of a higher de- gree than we can solve. What are, then, the operations to be performed ? Mr. Stone says nothing about it, neither do Messrs. Hutin & Leblanc. Making, therefore all the admissions that one can possibly make, we are still forced to the inevitable conclusion that the disclosures which my opponents have brought forth up to the present time do not enable one skilled in the art to put their alleged inventions into practical operation. Summing up briefly this last part of my testimony, I state : (a) Mr. Stone's theory, so far as he has disclosed it, of the invention in this interference is false. (b) Even if it were true, it is not disclosed in any one of his ex- hibits, nor was it known in the art, so as to enable one to Michael I. Pupin. 219 put his invention into practical operation. (c) Even if it had been disclosed in his exhibits, or if it had been known in the art, it would have been incapable of en- abling those skilled in the art to put the invention in this interference into practical operation. I am ready now to sum up briefly my evidence in re- buttal, referring to Mr. Stone’s exhibits. First. In the exhibits contained in Group 1, we have a certain number of proposed schemes, which a man con- nected with the work of a great telephone company would naturally be expected to be able to devise. They certainly have no direct connection with the invention in this interference. The term resonance, and the phe- nomenon of resonant rise of potential, is never mentioned in them. It is not clear how these schemes could have been employed for the purpose of studying the magnetic properties of iron and the dielectric properties of insulat- ing substances. Mr. Stone has certainly never published anything on the subject, nor has he shown anything in any one of his exhibits which would lead us to the con- clusion that he had employed the schemes for that par- ticular purpose. The mathematical theory which under- lies these schemes is certainly not applicable to them, ac- cording to Mr. Stone's own admissions, and it is extremely doubtful whether any one of those schemes ever received a thorough experimental test. Secondly. Taking up the exhibits contained in Group 2, I can state that none of Mr. Stone’s exhibits show anything which was not contained in the theory published by Hutin & Leblanc and by others several months before Mr. Stone first dis- closed his alleged invention to Mr. Hubbard in his letter dated November 25th, 1891. Mr. Stone's contention that his disclosures show more than is contained in the publications of Hutin & Leblanc and others, is contra- dicted by his own exhibits and his own testimony. Mr. Stone's specification does not enable one skilled in the art to put the invention, which is the subject of this in- terference, into practical operation, for reasons which I 220 Michael I. Pupin. have given above, in the summary of my deposition of to-day. Q. 3 Mr. Kennelly, in the course of his deposition in rebuttal, in answer to the criticism that the formulae shown in Hutin & Leblanc's article of May 9, 1891. were not correct, testified, in answer to Q. 23, as to some experiments which he performed, and in connection with that answer, he introduced Hutin & Leblanc exhibit sketch of Kennelly’s experiment. He also testified with respect to an experiment in x Q. 33 to 37 inclusive, and again in x Q. 43 to 46 and elsewhere. Will you please state your opinion of the experiment as an experimental demonstration of Hutin & Leblanc’s formulae? A. In the exhibit entitled “Hutin & Leblanc Exhibit Sketch of Kennelly’s Experiment,” I see an arrangement of circuits such as I cannot find anywhere in Hutin & Leblanc's article. From the data which Mr. Kennelly supplies, it is evident that he considered an extreme case, evidently, for the purpose of making what I should call, quoting the well known phrase, “the punishment fit the crime.” In his answer to x Q. 46, he estimates that the impedance of his line for one of his frequencies is 20,- 000 ohms, and for the other frequency is 40,000 ohms. That means, that the connection of the two secondary circuits to each other, on the one hand, and to the primary circuit, on the other hand, is an extremely small one. In such an extreme case the secondary circuits behave like simple circuits, and the theory of resonance of a simple circuit is, of course, applicable, to Mr. Kennelly’s system of resonant circuits. The point which Mr. Kennelly had to decide was not, whether the theory given by Hutin & Leblanc, in their article of May 9, 1891, was applicable to simple circuits, but whether that theory was applica- ble to selective systems in general, for only in that case would that theory have been in advance on what was known at that time concerning the theory of alternating currents. I infer, therefore, that Mr. Kennelly’s experi- ment demonstrating that Hutin & Leblancs's formulae Michael I. Pupin. 221 are applicable only when the selective resonance circuits degenerate into simple circuits is of no value, for I am not aware that any one has expressed any doubt on *N point. \ Q. 4 I now call your attention to the French patent N to Hutin & Leblanc, No. 215,901, of which a translation, \ which I have shown you, has been introduced on behalf $, of Iłutin & Leblanc. I also show you a copy of Hutin & Leblanc’s exhibit “Kennelly’s Sketch of Hutin & Le- blanc’s system of Multiplex Telegraphy,” about which he has testified in his Q. 21. Will you briefly compare that sketch by Dr. Kennelly with the patent, and state whether or not the sketch, in your judgment, is a cor- rect exposition of the patent, or of that part of the patent to which it is intended to refer ? A. Kennelly’s sketch is radically different from the system described in Hutin & Leblanc’s French patent. The radical difference between the two consists in that the receiving branches in Kennelly’s sketch can be made selective on account of each one of them containing self- induction and capacity, whereas, in the French patent, the receiving branches do not contain capacity, and can- not therefore be made selective. In a letter dated March 4, 1895, addressed to the Commissioner of Patents by myself, I took the position that the French patent is in- operative, on account of its not having condensers in the receiving branches. The Examiner accepted my argu- ments as valid, and withdrew the French patent as a reference against my applicatlon in this interference. I cannot find any urgent reasons for supplying condensers where the French patentees omitted them. I cannot follow Mr. Kennelly in his eager anxiety to make an in- vention operative which he practically acknowledges to be inoperative when taken in the forma in which it is presented in the diagrams of the French patent. There is one paragraph only in Mr. Kennelly’s deposition re- ferring to this patent which deserves passing considera- tion. It is the paragraph referring to the last paragraph 222 Michael I. Pupin. of the French patent, which says: “It suffices to re- place the cores of the electro-magnets by bundles of iron wire, or by cut pieces of sheet iron insulated from each other, and to join with them a condenser of suitable capacity.” Now, it is a well known practice, established probably before the French patentees were born, to use condensers in connection with the electro-magnet in all sorts of systems of telegraphy. Condensers were used with magnets as early as 1850, during the early history of induction coils. This passage does not say whether , these electro-magnets were to be used in the receiving branches, or in the transmitting branches, whether they were to be simple inertia coils, or electro-magnets of translating devices, or, I don’t know what else. So that the paragraph is perfectly useless, as far as making the French patent operative is concerned. Adjourned to Friday, June 24th, at 10:30 A. M. June 24, 1898. |Met pursuant to adjournment. Present, same parties as before. Direct examination of Prof. Pupin resumed. Q. 5 I hand you herewith a copy of the application of Messrs. Hutin & Leblanc in this interference, and will ask you to discuss the same in relation to the matter in controversy herein. A. I am perfectly familiar with the contents of Llutin & Leblanc's specification, to which you refer. I have made the same, the subject of a careful theoretical and experimental study extending over a period of about three years. I found that the applicants, Hutin & Le- blanc, are entirely ignorant of the theory of electrical resonance, as applied to selective systems of alternating current distribution, and that they are also ignorant of Michael I. Pupin. 223 the more or less well known difficulties which one expe- riences in manipulating resonance circuits. My reasons are as follows. On page 3 of their specification the mathematical formula is given, which, according to Messrs. Ilutin & Leblanc, must be fulfilled in order that a circuit forming a part of a selective system become se- lective for a given frequency }. It is entirely unneces- sary to add here anything more on the subject of the in- applicability of this mathematical formula, (which applies to a simple circuit) to a circuit or a branch line forming a part of a selective system of alternating current distribu- tion. The theory, therefore, on which the applicants base their invention, is certainly incomplete, and would not enable one skilled in the art to put their invention into practical operation. Let us see now whether there is anything outside of this mathematical formula which would in any way en- able one skilled in the art to make their alleged invention operative. They speak of tuned circuits, but they do not mention a single time, either in this specification or in any other specification, how the circuit is to be tuned. In fact, the manner in which they construct their re- action coils seems to exclude all possibility of tuning the circuits. To show this, it is sufficient to refer to those paragraphs of their specification which describe the con- struction of the resonators composing a selector. The diagrams illustrating the construction of the selector is given in Figs. 4 and 5. A study of these paragraphs re- veals the astonishing fact that in spite of what has been published by myself and others on the deleterious effect of iron upon electrical resonance, they use it in as abundant quantities as possible, Ilay, they even go much out of their way and take particular pains to make the magnetic circuits of these resonator coils as closed as possible. This is the worst imaginable construction of a coil to be used as an inertia coil in a resonant circuit. Rowland, Duncan, myself, and, in fact, all investigators 224 Michael I. Pupin. who have devoted any attention whatever to this matter, agree on this particular point perfectly. I refer here to Section 7 of my exhibit entitled “Practical Aspects of Low Frequency Electrical Resonance,” and particularly to the sentence on page 20, which reads as follows: “In one of my experiments I used the primary of a small closed circuit transformer for the inertia coil, and found that as far as I could detect with my apparatus, no resonant rise could be obtained with 100 volts of im- pressed electromotive force, no matter how low the fre- quency was which my machine could produce.” I have since been able to produce some degree of resonance with inertia coils of that kind, but only at very feeble mag- netizations of the iron. My experience, derived from actual experiments, with the reaction coils of the kind described in Fig. 4, teaches me that the current selector, described in Fig. 4, is inoperative, on account of its mag- netic circuits, even if for no other reason. The various coils in Fig. 4 are placed in such a way that when once the iron parts of the selector are put together, the coils become fixed and immovable. There is, therefore, no possibility of varying the self-induction of any one of these coils when the selector has once been made a part of the selective system, and, in fact, the specification calls for no variations of that kind, and more than that, it contains hints which actually forbid such a variation. I shall return to this point later. The condensers which are placed in series with these coils, are simply mentioned in the specification. There is no statement whatever whether these condensers have a fixed or a variable ca- pacity, and since nothing in the specification requires that their capacity should be a variable one, there is no reason to suppose that the more expensive form of con- densers, that is, condensers having a variable capacity, should be employed. As a matter of fact, if we are to follow the formula which is given on page 3 of the speci- cation, and that is what we would have to do if we are obedient to the instructions of this specification—then f _* Michael I. Pupin. 225 the self-induction of each coil and the capacity of each condenser, which are to be used in a selective branch of a selector, are entirely independent of the self-induction and the capacity of the other selective branches. Their values are known before they are put into the selector, and therefore, there is no reason whatever why they should be variable, or, rather, why they should be varied after they are put into the selector. The applicants start from the wrong theory, that the resonator circuit will resonate to the same periodicity when considered as a simple circuit, as it will, when forming a part of a cur- rent selector, described in Fig. 4. The whole construc- tion of that selector is in harmony with this theory. So that if the theory is wrong—and it most decidedly is— the construction of the current selector is wrong. One attempting to put this invention into practical operation, would be completely shut off from correcting the errors of the inventors, because the coils of the selector having a fixed position, their self-induction cannot possibly be varied so as to tune the circuits and perhaps make them operative, in spite of the directions of the applicants. Let us assume, however, that, in spite of the wrong theory given in the specification, in spite of the clumsiest possible construction of the reaction coils, and in spite of the absence of any directions whatever relating to the process of tuning the various circuits so as to make them selective, that some genius has succeeded in overcoming all these deficiencies of Messrs. Hutin & Leblanc's speci- fication, of what good will the system of the selective circuits represented in Fig. 6, be to them In a specifi- cation dealing with an entirely novel and exceedingly complex subject, such as is the subject of selective dis- tribution of alternating currents by tuned circuits, one would expect, naturally, to find the simplest, the most easily operative case described. In place of that, we find in this specification of Messrs. Hutin & Leblanc one of the most complicated cases imaginable. I have sub- mitted its operativeness to a thorough experimental test, 226 Michael I. Pupin. and I have found that, even under the most favorable conditions, the system will not operate when the im. pedence of the line connecting two stations like B and C, is over a hundred ohms. These favorable conditions are, that all the iron from the reaction coils has been very carefully excluded, and, when, in addition to that, other precautions which were the result of my own investiga- tion were taken, as, for instance, very low resistance of the reactions coils of variable self-induction, very carefully prepared condensers of variable capacity, and the re- ceiving apparatus containing iron in as small quantities as is possible, and possessing also very low internal re- sistance. I have the most profound doubt that Messrs. Hutin & Leblanc ever submitted the system described in their specification, to any experimental test whatever. I conclude that the specification of Messrs. Hutin & Le. blanc does not disclose the invention which is in this in- terference. Counsel for Hutin & Leblanc states that he has listened with the most profound surprise to the learned dissertation of the witness, in response to this seemingly innocent and harmless question ; that now, finding that the question was intended to elicit from the witness testimony tending to prove that the application of Hutin & Leblanc fails to describe the operative invention, and that therefore, Hutin & Leblane have no right to * make their claims, and that their invention is not patentable: Counsel for Hutin & Leblanc objects to the last preceding question, as well as to the answer, as incompetent in rebuttal. He bases his - objection upon the following ground: The question of operativeness of the matters set forth in the application of a party to an inter- ference is legitimately open to inquiry; that the rules of practice of the United States Patent Office describe the time and the mode of pro- Michael I. Pupin. 227 cedure for such inquiry. The rules provide for motions of dissolution, if it is found that an al- leged invention set forth in an application is in- operative. The record shows that Pupin, at one time made such motion, and that then, upon care- ful consideration, withdrew the same at the mo- ment when counsel for all parties were assembled before the principal Examiner for the purpose of arguing in support and in opposition to the motion. Since Pupin was silent at the time when he had given solemn notice that he would speak, and when Hutin & Lebane had the right and the chance to reply, he cannot now be heard upon this point, at the tail end of the testimony in this case, when, under the rules of the Patent Office, Hutin & Leblanc have no right and no chance to reply. In view of all this, notice is hereby given that at or before the hearing of this case before the Examiner of Interferences, a motion will be made on behalf of Hutin & Leblanc to have stricken from this record the last preceding question and 3DSWe]". Adjourned until 1:15. Counsel for Pupin states that he has not con- veniently at hand the records in the case prelim- inary to the taking of the testimony herein, but that he is willing to let the foregoing objection pass, with the remark that it must be considered subject to such correction as to the facts alleged by counsel for Hutin & Leblanc, as the record it- self shall show to be necessary. Q. 6 Your last answer closes with the conclusion that the specification of Messrs. Hutin & Leblanc does not disclose the invention which is in this interference. I should like to ask you, since this statement has led to 228 Michael I. Pupin. an elaborate objection by counsel for Hutin & Leblanc, whether this answer was directed solely to establishing that conclusion, or whether there are any other aspects of the specification to which the answer was directed, and if so, please state what? Objected to by counsel for Hutin & Leblanc as incompetent, for the reason stated in the objec- tion to the preceding question, and also for the reason that it is incompetent to discuss an inad- missible answer. º A. When I stated that the specification of Messrs. Hutin & Leblanc does not disclose the invention which is in this interference, I meant that the specification does not contain sufficient directions to enable one skilled in the art to carry the invention disclosed in the specifica- tion of Messrs. Hutin & Leblanc into practical operation. I do not conclude from my investigations of this specifi- cation that the invention disclosed cannot be made operative by one who knows more than is contained in that specification. In fact, I stated distinctly that I did succeed in producing conditions under which the inven- tion was made operative by myself. Q. 7 In the course of his deposition in this interfer- ence Mr. Kennelly has referred to some articles in the Electrical World, and elsewhere, as follows: Electrical World, March 2, 1895, page 259, by Charles Proteus .Steinmetz on Electrical Consonance; Electrical World, June 13, 1896, page 704, 5, 6, by A. W. Chapman, en- titled “Notes on Electrical Consonance.” Elecktrotech- mische Zeitschrift, February 18, 1897, by C. P. Feldman, entitled “Ueber elektrische Roesonand und Konsenanz”; and the Electrical World, June 10, 1897, pages 35 and 36, by Edwin J. Houston and A. E. Kennelly, entitled “On the Theory of Electrical Oscillations of Mutually Inducted Circuits.” I hand you copies of these papers, and will ask you briefly to discuss their bearing upon the matter here in controversy. Michael I. Pupin. 229 Objected to by counsel for Hutin and Leblanc as vague and indefinite. It must be understood that the witness has only the right to testify in rebuttal of any testimony so far given in this case, and the question should, therefore, be so formulated as to direct him to rebut any statements made in behalf of the opposing parties. But it is incom- petent to launch the witness upon an exploring expedition. Question continued. In view of the foregoing objection, I will call your attention to those portions of Mr. Kennelly's deposition which are are to be referred to or discussed, and will ask you to make your reply by way of answer to Mr. Kennelly's discussion of these articles I must add also the article in the Electrical World of Oct. 21, 1893, pages 306–7, by A. E. Kennelly, on the “Impedance of Mutually Inducted Circuits.” A. With reference to Mr. Kennelly’s article of October 21, 1893, and the references which Mr. Kennelly makes to it in his answer to Q. 15, I have the following state- ment to make : The theory of the case discussed by Mr. Kennelly in this article, was given by me in a complete form several months before the appearance of Mr. Ken- nelly’s article. It is contained on the second page of my exhibit No. 36. In fact, the solution given there by me in this exhibit is more complete than Mr. Kennelly's. I fail to find a correct discussion of this problem in Hutin & Leblanc's article of May 9th, 1891, who Mr. Kennelly says anticipated him. But even if it were there, I fail to see the applicability of the theory of this particular case to the theory of a selective system of dis- tribution of alternating currents by means of resonance circuits. In this last system we must have at least one transmitting and two receiving circuits. Now, it hap- pens, as I have shown in connection with my discussion of the theory of the system represented in Fig. 7 of Mr. 230 Michael I. Pupin. Stone's application, that an addition of another circuit, in such a system, changes the theory as much as an addi- tion of an inch to a man’s nose would change his appear- ance. All that I have to do for the purpose of confuting Mr. Kennelly’s arguments in his answer to Q. 15, is to refer to my mathematical discussion of Mr. Stone's Fig. 7. Suffice it to state briefly that Mr. Kennelly’s answer to Q. 15 displays ignorance of a theory of a selective system of distribution of alternating currents by re- SOIla. ITCé. With reference to the other publications cited by Mr. Kennelly in his answer to Q. 15, I state that their ap- plicability to the theory of a selective system such as forms the subject of this interference, is as weak as Mr. Kennelly’s article referred to. The only theory that has been published on selective systems of this kind, is the theory given in paragraph 241 of Prof. Webster's book, referred to above. But even this theory is so general, that it would be of little practical value to anyone at- tempting to carry the invention, the subject of this inter- ference, into practical operation. I have already stated, and I wish to repeat it here, that I have worked out a theory of the particular systems referred to in the various specifications involved in this interference, and that I shall in due time compare it to the theory given by Messrs. Hutin & Leblanc in their article of May 9, 1891. As regards Mr. Kennelly’s article of July 10, 1897, and his references to it, in his answer to Q. 16, I wish to state that the case discussed by him was discussed by Prof. Webster in paragraph 242 of his book referred to above, and also by others, much earlier than the ap- pearance of Mr. Kennelly’s article. I fail to see in it, or in Mr. Stone’s references, referred to in Q 15, an in- telligent discussion of Hutin & Leblanc's theory con- tained in the article of May 9, 1891. With reference to the three remaining papers, which form exhibits in Messrs. Hutin & Leblanc's deposition in this interference, and to which Mr. Kennelly refers in Michael I. Pupin. 231 his answers to Q. 15, 16, 17, 18, etc., I have this state- ment only, that they all deal with electrical consonance, which I first discussed in an article in the Electrical Wor/d of Feb. 9, 1895. A reprint of this article forms Exhibit No. 40 of my deposition. In fact, these three papers are nothing more nor less than simply com- mentaries on that article. On page 4, paragraph 2, of my Exhibit 40, entitled “Electrical Consonance,” I state distinctly that the neutralization of the apparent in- ductance of a circuit has nothing whatever to do with resonance or synchronization. This is one of the prin- cipal points which I wished to bring out in this article. Mr. Kennelly overlooks this point entirely, and attempts to draw conclusions from it regarding the behavior of a selective system of distribution, conclusions to which the article in all respects justifies him; for if this article teaches anything at all, it does certainly teach us one lesson, and that is that the term resonance, as defined by certain phenomena which accompany it in the case of a simple circuit, as, for instance, neutralization of self-in- duction by capacity, neutralization of phase, etc., is not applicable to circuits which are not simple circuits. Adjourned by consent of counsel to July 12, 1898, at 10:30 A. M., at the office of Ewing, Whitman & Ewing, 41 Wall Street. NEw York, July 12, 1898, Met pursuant to adjournment. Present, same parties. Direct examination of Prof. Pupin resumed : Q. 8 You have several times in the course of your de- position, referred to a general mathematical treatment of the different systems presented in the applications in this interference. Preparatory to introducing your discussion as an exhibit, I would like to have you state generally 232 Michael I. Pupin. t%. ! ;ra * what it is, and how it bears on the different systems shown in the various applications in this interference? A. The bearing of the mathematical discussion of multiple resonance, which I shall introduce as an exhibit in this interference, upon the various specifications in- volved, is a direct one and a very important one, because my opponents give certain theoretical formulae which are to serve as directions to those desirous of putting their alleged inventions into practical operation. No other direction is contained in their specifications. If, therefore, the theoretical formulae upon which they proceed are wrong, then their directions are insufficient. At the time when the various specifications involved in this interference were filed, a theory of multiple re- sonance did not exist, so that a purely theoretical direc- tion to those desirous of carrying these inventions into practical operation was an impossibility. A careful analysis of the specifications of my opponents shows that the theory of multiple resonance was just the same thing as the theory of resonance in a simple circuit. Hence their directions that circuits forming a part of a multiple resonance system should be treated in the same way as simple circuits. For the purpose of pointing out their errors, and of giving a brief preliminary statement of my theory, let us consider first what is the meaning of resonance in a simple circuit. Resonance between a simple circuit and a simple harmonic electromotive force means, maximum current which the impressed electromotive force can produce in that circuit. To have maximum current, it is necessary to have minimum impedance, and it so happens that in a simple circuit the impedance for a given frequency is minimum when the reactance is zero. Under most favorable conditions, that is, when there are no magnetic and dielecrtic losses, and when the ohmic resistance is very low, the reactance of a simple circuit is zero when, approximately, the period of the impressed electromotive force and the period of the circuit are equal to each other. Under any other conditions the Michael I. Pupin. 233 equality of two periods has nothing to do with resonance, even in the case of a simple circuit, for it is possible to have resonance between a circuit and an impressed elec- tromotive force when the circuit has no periodicity at all. The definition of resonance, given above, is there- fore broader, and will be followed in this discussion. Now, in the theoretical discussion which I shall introduce here as an exhibit, I show that even in the most complex system of conductors in which each part of the system contains coils and condensers, the current in any part can be expressed by the statement that it is equal to the electro- motive force induced in that part, (owing to its connec- tion to the rest of the system) divided by an impedance. The impedance consists of two parts, in just the same way as the impedance of a simple circuit consists of two parts. One part I call the apparent reactance, and the other the apparent resistance, following Maxwell's terminology. Both the apparent resistance and the ap- parent reactance are functions of the periodicity and of the electromagnetic constants, that is, resistance, capacity, self-induction of each part of the system. In a simple circuit the resistance is not a function of the periodicity, or of anything else, but it is simply obmic resistance, which marks a radical difference between the two cases, just as in the case of a simple circuit by varying the capacity and, the self-induction, or both we can reduce the reactance of such a circuit to zero, so we can, by varying the capacity and self-induction of any part of a complex system of conductors, reduce the apparent re- actance of this part to zero; and just as in the case of a simple circuit, the current passes through a maximum, so in the complex case the current passes through a maximum. But here observe now the radical difference: the maximum which we obtain in the case of a simple circuit is an absolute maximum, that is to say, at no other periodicity will the current be as great as at that period at which the reactance of the circuit is zero. Whereas, in the complex case, the maximum obtained at 234 Michael I. Pupin. the point when the reactance is zero, is by no means the true maximum, that is to say, the current will not be greatest at the periodicity at which the reactance is zero. There are other conditions to be fulfilled. Not only must the reactance be zero, but the impedance must be a minimum. That is, the periodicity must be adjusted in such a way as to make, not only the apparent reactance, but also the apparent resistance, as small as possible. This relation is of course due to the fact that in the complex system the apparent resistance is a function of the frequency, whereas, in the simple circuit this is in- dependent of the same. So far as I know, this theory, and the results which I have just pointed out, have never been published before, but even if it had, and my op- ponents and everybody else had been acquainted with it, the directions which consist simply of the mathematical statement of the conditions which must be fulfilled, in order that a complex system of conductors should be capable of selective distribution of electric currents, will be shown in this discussion to be completely inadequate, for such mathematical statements do not enable one to calculate before hand the values of the self inductions and the capacities of the various kinds of condensers which will make the system selective. So that the bear- ing of this mathematical discussion upon the various ap- plications involved in this interference, may be summed up concisely as follows: It shows that the directions to one desirious of carrying the invention of these applica- tions into practical operation, are completely inadequate as long as these directions give mathematical formulae only. Such are the directions which my opponents give, and, moreover, the mathematical formulae to which they refer are entirely wrong. The answer of the witness to the foregoing question (Q. 8) is objected to by counsel for Hutin & Leblanc as quite incompetent in rebut- tal, for the reasons stated in the objection to the Michael I. Pupin. 235 answer to Q. 5, noted upon the record. At the time the aforesaid objection to Q. 5 was made, counsel for Hutin & Leblanc had not the inter- ference record before him, and only spoke from memory. Since the last adjournment, however, counsel consulted the record, and found that his former recollection of the same was substantially, but not entirely, correct. The true state of facts appears to have been as follows: Before the taking of any testimony, Pupin filed a motion for dissolution, upon the ground that the arrangement shown in the applications of Stone and of Hutin & Leblanc are practically inoperative, for the reason that the same depended for the production of signals upon momentary diminutions of impedance of the main line, pro- duced by momentary diminution of the systems of an inductively associated circuit; and this, so Pupin argued, was insufficient to produce sensible effect in the receiving circuits. At the hearing before the Examiner, counsel for Hutin & Le- blanc was prepared to meet the allegations of 1’upin, and had present at that time an apparatus calculated to furnish demonstrative proof that the allegations of Pupin were wrong. At that time counsel for Pupin withdrew his motion, and afterwards filed a paper, served upon the op- posing parties, in the nature of a motion asking for leave to withdraw that motion without pre- judice. Since no objection was made to that paper, al- though no action was taken upon the same, Pupin may perhaps have had the right to now urge the same grounds of inoperativeness that he had stated in his motion; since it may be presumed that opposing counsel are ready to meet him upon that ground. But he cannot now sail on a 236 Michael I. Pupin. new tack, and assail the operativeness of the in- ventions of his opponents, upon grounds never before intimated, and which he had a right to urge in a motion for dissolution. Ilaving failed to do the latter, he is debarred from taking that step now. Notice is hereby given that at or before the hearing, Hutin & Leblanc will move to have stricken from the record all that testimony of Pupin that is intended as evidence of inoperative- ness of the apparatus shown in application of Hutin & Leblanc. Counsel for Pupin, in reply to the foregoing objection, states that the nature of the apparatus calculated to furnish demonstrative proof that Pupin's allegations were wrong, was not dis- closed at the hearing referred to, and he objects to statements made by the counsel which are in the nature of evidence about the apparatus in question. Attention is also called to the fact that the matter testified to in the last answer of the witness was fairly opened in the cross-examin- ation by counsel for Pupin, of Hutin & Leblanc's expert, Mr. Kennelly, during the cross-examina- tion, in his first deposition. Q. 9 I call your attention to the fact that in the ap- plication of Mr. Stone in this interference, he gives cer- tain numerical values for what he calls effective induct- ance in henrys, effective capacity is microfarads, and critical frequency in complete alternations per second, approximately. Mr. Stones states that the meaning of the terms “effective inductance ’’ and “effective “capa- city” of a circuit for a given frequency, is the induct- ance or capacity of that circuit as measured by the dif- ferent in phase which it is capable of producing in a simple harmonic current of that frequency and the elec- tromotive force producing it. I would like to ask you Michael I. Pupin. 237 whether these values, as they are given by Mr. Stone, amount to definite instruction as to how the circuits can be adjusted to make the systems of his application operative? And, in this connection, I should like to have you discuss the meaning of effective inductance and capacity ? A. These values were calclated from the well-known formula which expresses the relation between the critical period and the capacity and self-induction of a simple circuit namely, that T = 2, VI, C. This formula is not applicable to complete systems, even if the meaning of L and C be extended, as will be shown in the mathematical discussion which I shall in- troduce in this interference Besides, Mr. Stone’s de- scription of what he calls effective capacity and effective inductance, namely, as measured by the difference in phase, etc., is not intelligible, being incomplete, as has been pointed out by me before. I wish it to be under- stood that my discussion of the theory is just as much for the purpose of establishing that my directions, con- tained in my specification, were right, as it is for the purpose of establishing that the directions of my op- ponents were wrong. They have on several occasions in this interference, attacked my specification, and I do not see that at this date I can very well show that my specification was right, without showing that theirs was wrong. Q. 10 Will you state whether or not there is any dis- tinction between capacity and effective capacity A. There is no distinction between the two, as far as my theory goes, and I do not know of any theory which makes that distinction. The only places in which I find this name effective capacity, are the specifications of my opponents. They give, however, no definition of the term. Q. 11 Mr. Stone in his specification, in the part which I have heretofore referred to, speaks of the effective in- ductance and effective capacity as the inductance and 23S Michael I. Pupin. capacity measured by the difference in phase which it is capable of producing between a simple harmonic cur- rent of assumed frequency and the electromotive force producing it. Please state what is known of the phasal relation referred to by Mr Stone? A. In a simple ideal circuit, the zero difference in phase between the electromotive force and the current exists when the point of critical frequency has been reached. This relation does not hold true for a com- plex system; at least, my theory does not show it, and I fail to discover the place in electrical literature from which Mr. Stone derived his information. Q. 12 I call your attention to l’rof. Cross' deposition, in which he discusses the arrangements of circuits shown in Stone's report to Hubbard, where several receiving circuits are connected up to secondary coils which ap- pear to be wound on a common primary, particularly to his answers to x Q. 75, 76, and 77, and will ask you to state whether you agree with Prof. Cross’ reasoning, and, if not, to give your reason for differing from him : A. In his answer to x Q. 75, Prof. Cross says that he does “not see how the one secondary is to act in this way upon the other which is entirely out of tune.” And then he proceeds to quibble about the differences in the way in which the primary reacts upon the secondary, which is in tune with it, and how another secondary will react upon the same secondary which is not in tune with it. All this quibbling is evidently for the purpose of showing that the reaction of two secondaries wound upon the same primary is small, unless the two secondaries are in tune with each other. Now, it is perfectly evident that if a secondary circuit is in resonance with the primary, and in consequence thereof there is a large. current flowing in it, this large current will produce a large magnetic flux, and the large magnetic flux will produce a large electromotive force in all secondary cir- cuits wound upon the same primary, and this induced electromotive force will be large, no matter whether Michael I. Pupin. 239 these other secondary circuits are in tune with the first secondary or not. Now, a large electromotive force will produce a large current, no matter whether the circuit is tuned or not. I have tried on numerous occasions to tune several circuits wound on the same primary to dif- ferent periodicities, and have never succeeded in pro- ducing anything like satisfactory results. I never ex- pected to, for it is self-evident that such arrangements will not work satisfactorily, and I do not see how Prof. Cross, if he really knows anything about the case, can stand up, as he does, and defend arrangements of that kind. Q. 13 Please state briefly why an arrangement in which the secondaries are wound on a common primary, is an unsatisfactory arrangement, compared with an ar- rangement in which the secondaries are wound on indi- vidual primaries, and these primaries are arranged in series in the line? A. Because in the latter case the reaction between the several secondaries is very much smaller, (and can be made as small as we please) than in the first case. Elec- trical tuning is a pretty difficult matter, even under the most favorable conditions, when we are dealing with a complex system of conductors, and when it comes to tuning a system like that referred to by Mr. Stone in his disclosure, where several secondaries are wound on the same primary, then the tuning becomes next to im- possible, and when after many laborious attempts, some result has been accomplished, the slightest change in the speed of the alternators will upset the whole thing. In other words, the system is very unstable. Q. 14 You state in your answer to my question, that in the second case supposed the reactions between the several secondaries will be much smaller than in the first case, and can be made as small as we please. I would like to have you briefly explain why the reactions are smaller, and how they can be made as small as we like 3 240 Michael I. Pupin. A. They are smaller because one secondary can react upon any other secondary only by reacting first upon the main line. Now, if the main line has a very large impedance, then the reaction is very small. This is the way in which Mr. Kennelly showed that under certain experimental conditions, the theory of Messrs. Hutin & Leblanc is applicable. Q. 15 Mr. Kennelly, as I understand it, made an ex- periment which was intended to prove that the formulae for simple circuits would apply where there were several circuits in inductive relation with a main line, and he in- troduced very large impedance into his main line, in order to get conditions under which this would be true. My question is not directed to any such extreme case, but I wish to know how in practice the interaction of the circuits upon one another, where the circuits are in inductive relation with the primary placed in series, can be kept within practical limits. In other words, is it necessary, or is it not necessary, in practice, where the systems are properly manipulated, to use any such great impedance as Mr. Kennelly used in his experiment? A. Not at all. With small impedance in the primary circuit, the several secondaries will have a larger reaction between each other, but nevertheless, they can be tuned to several different periodicities, and act selectively in quite a satisfactory manner, as I have convinced myself by numerous experiments, and equation 6 of my mathe- matical discussion, which I am about to introduce in evi- dence, shows that satisfactorily. A large impedance in the main line is necessary only when we wish to tune the circuits, in accordance with the theory given by Messrs. Hutin & Leblanc. Q. 16 Prof. Cross, in his answer to Q. 7, says, speak- ing of the invention here in controversy, that in his opinion, “everything that was in any way necessary to know regarding the behavior of iron, so far as the operativeness of the invention is concerned, was already known to those skilled in the art.” This statement is Michael I. Pupin. 241 made in the discussion of your exhibit “Practical As- pects of Low Frequency Resonance,” which is Exhibit No. 35. Will you please state whether you think Prof. Cross is correct in that statement or not ? A. I think that Prof. Fessenden has answered Prof. Cross’ statement pretty fully. I shall only add this much. Whatever we may say about the scientific under- standing of electrical resonance, exhibited by Messrs. Hutin & Leblanc in this interference, we must still ad- mit that they have a better right to consider themselves skilled in the art of electrical resonance than Prof. Cross, and yet in their specification of 1894, which is involved in this interference, they recommend large masses of iron in closed magnetic circuits for the reaction coils of the resonance circuits. Q. 17 Does the omission of iron from the inductance coils of resonance circuits necessitate any change in the coils which might raise a question as to whether the omission of iron would be advantageous or not, and if so, what change? A. If the iron offered no other objections except loss of energy due to hysteresis, even then one could not pre- determine from any data known to us, whether the omission of iron from such coils would be an advantage or not, for to get the same inductance, we must, if we omit iron, introduce a much larger number of turns in a coil. Now, a larger number of turns means a higher resistance, and a higher resistance means a smaller amount of resonance. So that as far as one can tell a priori, it might be a positive disadvantage to omit iron. Experi- ment alone could determine that question. As far as I know, I was the first to do the experimental work in- volved in this decision, and the result of this experi- mental work led me to a careful omission of all iron in resonance circuits, as is shown in all diagrams of my specifications involved in this interference. Q. 18. In Mr. Stone's application in this interference, it is suggested that the invention may be applied to the l 242 Michael I. Pupin. transmission of energy, by the arrangement of Fig 6 of his application, as distinguished from its use in signal- ling. Will you please state whether or not, in your opinion, this suggestion is practicable, and give your rea- sons for your opinion ? A. Such a suggestion is absurd on the face of it, for resonance means storing up. Now, if the electrical power transmitted is used for lighting or motor work, it is evident that storing up is out of the question. There- fore, electrical resonance and the consequent selectivity are entirely out of the question in connection with the transmission of power for lighting or motor work. Such a suggestion can only come from one who has had no practical experience with selective systems of the kind involved in this interference. Q 19 Mr. Kennelly, in his answer to Q. 11 of his testimony in rebuttal, in discussing the French patent of 1891 of Messrs. Hutin and Leblanc, which is introduced in evidence, speaks of the conditions of the line in Fig. 4 of that patent as what would be called se ective con- sonance, as that would be considered by you in your article Exhibit No. 40 on electrical consonance. Will you please refer to Mr. Kennelly's answer and to Figs. 4 and 5, which latter is also discussed by him in his an- swer, and state whether you agree with him, and, if not, your reasons ? A. Mr. Kennelly, judging from his answer, does not understand my work on electrical consonance, or, if he does, he does not state it correctly, for consonance does not mean necessarily a maximum current in the primary circuit. In fact, I have shown that the primary current may be much smaller than ordinarily, when the con- denser in the secondary circuit has been adjusted to COI) SO118.In Ce. Q. 20 Mr. Kennelly in his first deposition, in answer to x Q. 64 and 65, discusses the question of the pos- sibility of solving an equation of the fifth or higher order involving differential co-efficients as the unknown Michael I. Pupin. 243 quantity. I would like to have you consider his deposi- tion, and state whether you agree with Mr. Kennelly or not, and also, briefly, what bearing the question has upon the matters here in controversy % A. I shall discuss this matter in connection with the discussion of my article to which I have repeatedly re- ferred, and which I now produce. A copy of the paper referred to in the question is offered in evidence, and is marked “Pupin Ex- hibit, Extract from an article on multiple reson- ance by M. I. Pupin, July 12, 1898.” Q. 21 Will you please explain why this exhibit is called “Extract from an Article,” and explain the fact that it ends with the clause, “To obtain the true maxi- imum theoretically, proceed as follows: ” A. I have called it an extract because it is a part only of a long article dealing with resonance in general, on which I have been working now for several years, and which is now ready for publication and will be published as soon as the proper time arrives. I have taken only that part out of this paper which bears directly upon the questions raised in this interference. Adjourned till Wednesday, July 13, at 10:30 A. M. New York, July 13, 1898. Met pursuant to adjournment. Present, same parties as before. Q. 22 Will you now, in language as free from technical expressions as possible, discuss the various formulae of your article “Pupin's exhibit, Extract from an article on multiple resonance,” offered in evidence, and the con- clusions which you have arrived at therein, and point out the bearing of these conclusions on the matters in controversy in this interference. As you have added 244 Michael I. Pupin. something to the article in question, will you please in- dicate what it is, and where it is, added ? A. One of the principal points which my opponents wish to establish in this interference, is that my original specification does not disclose an invention which is strictly within the issues of this interference. Their principal argument was that I employed what they call ground to ground tuning. All their arguments are based upon assumptions for which they have not shown a theoretical basis. To answer their arguments, it is ab- solutely necessary to have a complete theory of the in- vention which is in this interference. The bearing, therefore, of this exhibit upon the various questions in- volved in this interference, is simply this : It furnishes us a means to discuss intelligently and with mathematical precision the methods proposed in the several specifica- tions for carrying the invention of this interference into practical operation. This discussion, it is hoped, will establish beyond all reasonable doubt which of the three parties in this interference stated the correct method of carrying the invention into practical operation. Now, as to the simple statement of the contents of this article, it discusses the mathematical theory of the current distribu- tion in a complex system of conductors, such as repre- sented by Figs. 1, 2, 3 and 4 when simple harmonic elec- tromotive forces are impressed at given points of the system. The four cases represented in these four figures, are types of arrangements proposed in the various speci- fications which are involved in this interference. That which I wish to establish, and succeeded in establishing, is this : -- First, that in every case the mathematical expression for the current in any part of a complex system posses- sing self-induction, capacity and resistance, is formally the same as in the case of a simple circuit, that is to say, the current is equal to an electromotive force produced in that circuit, owing to the interaction between it and the rest of the system, divided by an impedance. ^ Michael I. P upin. 245 Secondly, the mathematical expression for this im- pedance is formally the same as the mathematical expres- sion for the impedance of a simple circuit. That is, it is a resultant of a reactance and a resistance, in just the same way as the impedance of a simple circuit is a re- Sultant of a reactance and a resistance. With this radical difference, however, that whereas, in a simple circuit the resistance is ohmic resistance, and therefore, a perfectly definite quantity, the resistance of a circuit forming a part of a complex system is a function, not only of the frequency, but also of the constants of every other part of the system. S Third, just as in the case of a simple circuit a maxi- mum of the current can be obtained when the reactance of the circuit is reduced to zero, so in a circuit forming a part of the complex system, a maximum can be ob- tained when the reactance is reduced to zero. But with this radical difference—the maximum obtained in the simple circuit is an absolute maximum ; that obtained in the complex case is not an absolute maximum. Fourth. To obtain the absolute maximum, we have to proceed in just the same way as we do in the case of a simple circuit, that is, we must make the impedance in the various circuits as small as possible for the various frequencies. Now, it happens that in the case of a sim- ple circuit, that is obtained by reducing the reactance to zero, whereas, in the case of complex systems, this result is obtained theoretically by the mathematical operations given in the last part of the article as it stands amended. It will be seen that the mathematical operations involved in this case are entirely different from the mathematical operation involved in finding the condition for which a simple circuit is given a minium impedance for a given frequency. The corresponding experimental operations will also be radically different, as I shall describe pre- sently. Now, the most important bearing which this article has upon the methods proposed by the various parties in 246 Michael I. Pupin. this interference, for carrying their inventions into prac- tical operation, is this: Both Messrs. Hutin & Leblanc and Mr. Stone direct the reader of their specifications that they should calculate before hand the capacity and the self induction of each part of the complex system which will make these parts resonant or selective with respect to different frequencies. The last part of my article, as it stands amended, shows that such a calcula- tion cannot be done, and that the direction which they give is of no practical utility whatever. The next important bearing that this article has upon questions of interference is this: It shows that the theory which my opponents and their experts disclosed in the course of this interference, is not a correct one, and that they are therefore in no position to interpret the meaning of any one of my specifications. This in- terpretation I propose to give now in the light of this article. Equations 14 and the discussion of them shows that a calculation for the capacities, inductances and resistances which will make the various circuits selective, is an im- possibility. What then must be done in order to pro- duce that selectivity ? Why, evidently, we must do the same thing experimentally which we are called upon to do if we attempted to solve equations 14, that is to say, we must provide each circuit with a coil of variable self- induction and a condenser of variable capacity, and then, by the variation of these, adjust the circuits until each circuit is selective. This is a work of experiment entirely. When this is done, the circuits are tuned once for all, and no changes should be introduced into the system which will in any way affect appreciably the adjustments once obtained. This I know from prac- tical experience is a very laborious process, especially when a considerable number of selective receiving cir- cuits is contained in the system. In a complex system consisting of a main line having a reasonable amount of impedance, say, a line between New York and Phila- t Michael I. Pupin. 247 delphia, the connection between the receiving circuits in Philadelphia and the transmitting circuits in New York, should not be a very close one, that is to say. it would be possible to alter considerably the electro magnetic constants of the transmitting branches in New York, without disturbing very seriously any previous adjust- ments of the receiving branches in Philadelphia. Thus, for instance, we could introduce in each transmitting branch auxiliary self-induction and capacity, and by their adjustments, vary the impedance of these transmitting branches in any way we please, without affecting very seriously the receiving branches in Philadelphia Looking now at the diagram which accompanies my first application, it is seen that in each receiving branch there is a coil and a condenser. The specification says nothing about the numerical values of the self-induction and the capacity of these coils and condensers, but it does say distinctly, in the last paragraph, as follows: “If is, of course, to be understood that in the local c reuits a b c will be disposed the means here shown, or any other proper means to affect the tuning of each by vary- ing self-induction, capacity or both.” That describes completely the correct method, and, according to my theoretical article forming Pupin's Exhibit of July 12, 1898, it states the only method by means of which the tuning can be done. Again, my opponents have criticised another passage in this application, and have tried to prove by it that my intention was to have what they call ground to ground tuning. It is the passage which says “The coil Z has a fixed self-induction and the con- denser O has a fixed capacity. This branch is supposed to work the frequency C.” Now, consider this passage in connection with the theory worked out in the above mentioned exhibit, and with the following sentence found in the last part of the aforesaid application : “All that is required is that the various circuits of the system shall be tuned in electrical resonance with the several periodic currents of previously eelected periodicity, 248 Michael I. Pupin. * and that may be done once for all.” As I have already stated, the process of tuning is a difficult one, as may be seen from the theory in my exhibit on multiple reson- ance, and as I know myself from practical experience, and therefore if the receiving branches have once been tuned, it will save much time if this adjustment once accomplished is retained once for all. But under these conditions, the capacity of the condenser and the self-in- duction of the coil will, in any receiving branch, of course retain a fixed value. Again, my opponents have criticised the following sentence in my application: “This branch is supposed to work with the frequency C, hence the operator at 4 will use a fork of frequency C and then adjust auxiliary coil Z until the electrical periodicity of circuit Z 2 1 10 L O A a Gs is C.” They use this sentence as an argu- ment to prove that what I intended in my specification is what they call ground to ground tuning. Recess. Witness resumes. Now, I have already explained the meaning of this sentence over two years ago in answer to Q 37. In all my experiments with the arrangements represented in Fig. 1 of the first application, condensers were used in the transmitting branches, and then the transmitting branches themselves were adjusted by varying the capa- city and the self-induction of each until the current in each was a maximum. This was found by me to be a convenient and a desirable, but not at all absolutely neces- sary operation, for the system operates quite satisfactorily, even without the condensers and transmitting branches, as I have shown over two years ago by the experiments, the exhibit of which is numbered “Pupin's Exhibit 26, Sketch No. 2,” and described in answer to Q. 55 of my testimony in-chief; and in the application the condensers for the transmitting branches were omitted by oversight, Michael I. Pupin. 249 and hence the slight obscurity attached to the sentence which I have just quoted from the specification. I see, however, no reason whatever why, in view of the theories I submit on my exhibit on multiple resonance, such a meaning should be attached to that sentence as my op- ponents tried to attach to it. One who has read my ap- plication carefully and intelligently, and who has also taken the pains to set up the apparatus described in Fig. 1, will introduce in each receiving branch a condenser of variable capacity and a coil of variable self-induction. He will then by the variation of one or the other, or both, tune each circuit to the periodicities impressed. upon the transmitting end. Having done that, he will naturally pass to the transmitting branches and see what with the apparatus at his disposal there, he can do to improve the result so far obtained. Now, in each trans- mitting branch there is a coil of variable self-induction. He will vary the self-induction, therefore, of each until he obtains the best result. Now, these coils are abso- lutely necessary there, because if they were not there, the electromotive force generated in one branch would be short-circuited by the other branches. He might not see exactly the bearing of the sentence which I have just quoted from the specification upon this operation per- formed in the transmitting branches, but I don’t think that he would be disturbed very much by it. There is certainly nothing in the specification which would lead him to the belief that he is expected to perform what my opponents call ground to ground tuning. Summing up the remarks with regard to my first ap- plication, and the bearing of the theory disclosed in my exhibit on multiple resonance upon the same, I can state that the two are in perfect harmony. They each demand that the tuning is a matter of experiment alone, and not of previous calculation, and they both demand that the various selective branches be provided with coils of vari- able self-induction and condensers of variable capacity, by the adjustment of which the selective parts should be 950 Michael I. Pupin. made selective. On the other hand, there is a complete disagreement between the theory disclosed by me and the methods of operation tried in the exhibit and speci- fications of my opponents. With them the tuning is a matter of previous calculation. They speak nowhere of coils of variable self-induction and condensers of variable capacity by the variation of which self-induction and capacity the circuits are to be tuned. In fact, they men- tion expressly in several places that a circuit once tuned when taken by itself, can then be made a part of a com- plex system, and still remain selective with regard to the frequency to which it was tuned when taken by itself. In concluding this answer, I wish to state that the theory disclosed in my exhibit on multiple resonance is the re- sult of very numerous experiments, in which the various arrangements disclosed in my applications and in the ap- plications of my opponents, were subjected to a careful test. Without these experiments, the formulation of the laws of operation for such systems, such as are given in this exhibit, would have been impossible, and vice versa, an intelligent interpretation of these experiments cannot possibly lead to any other formulation of these laws. I infer, therefore, from the theory which my opponents have advanced in the various exhibits, that they have not subjected this matter involved in this interference to a careful experimental study. They certainly have not disclosed in the course of this interference a single ex- periment in the selective distribution of alternating cur- rênts. i I should also add that in my exhibit the matter follow- ing the sentence “to obtain the true maximum theore- tically, we have to proceed as follows” up to the end has been added since yesterday, and that this additional matter is substantially the same thing as my discussion of Stone’s Fig. 7, in answer to question 2 in this present deposition. It should be also added that the comparison between formulae contained in this exhibit multiple resonance and Michael I. Pupin. 251 the Hutin & Leblanc article of May 9, 1891, show that the theory in that article is not the theory of multiple resonance which underlies the inventions involved in this interference, and that, moreover, the Hutin & Le- blanc theory, instead of being a guide, is actually mis- leading. The foregoing answer is objected to by counsel for Hutin & Leblanc as largely incompetent in rebuttal, since instead of rebutting any evidence produced on behalf of Hutin & Leblanc and Stone, the witness attempts to bolster up or rein- force his original testimony. ! Counsel for Stone objects to the answer, or most of it, on the ground that it is volunteered, and not properly given in rebuttal. It is mere argument in support of the position taken by the witness when examined on the same subject mat- ter in his examination-in-chief. Counsel for Pupin states, in answer to the ob- jection that the testimony is volunteered, that in the absence of counsel for Stone, this question was raised by counsel for Hutin & Leblanc while the witness was giving his answer, and it was con- cluded to permit the witness to go on, and to enter objections to the competency of the testimony at the end of the answer. Counsel for Stone withdraws so much of his objection as is based on the mere irresponsiveness of the answer. Q. 22 Will you please discuss briefly Mr. Stone's Analysis of Resonance in reference to Hutin & Leblanc's article of May 9, 1891, and point out what bearing, if any, your article Pupin's exhibit extracts from an article on multiple resonance has upon the analysis by Mr. Stone Ž 2 5 2 Michael I. Pupin. A. In this exhibit Mr. Stone discusses the condition of resonance in one of the circuits of a system consisting of one primary and two secondary circuits connected to each other by mutual induction. His mathematical solu- tion of the case does not in any way resemble the form of the mathematical solution which could be deduced from my article referring to Fig. 4, taking his problem as a particular case of the general problem which I dis- cussed in connection with Fig. 4. It is, however, pos- sible to transform his formulae in such a way as to give them the same form as that which I obtained. Having effected such transformation, it will be seen that Mr. Stone considers a circuit as being resonant to impressed electromotive force, when its apparent reactance is zero with the frequency of that electromotive force. I have already pointed out that under these conditions resonance does not take place. I conclude, therefore, that Mr. Stone's analysis is misleading. Q. 23. In the preliminary statement by Messrs. Hutin & Leblanc it is set up that the inventions in issue in this interference are disclosed in an application filed in the United States Patent Office January 31, 1893, Serial Num- ber 460,318. I hand you a Patent Office copy of United States Letters Patent Hutin & Leblanc, No. 596,017, dated Dec. 21, 1897, which, upon its face, purports to have been issued upon an application of the filing date and serial number stated above. Will you examine the patent, and state whether you find in it the invention or nventions embraced in this interference? Question objected to by counsel for Hutin & Leblanc as utterly and entirely incompetent, not only in rebuttal, but under all circumstances, since not one iota of testimony has been produced in behalf of Hutin & Leblanc in repect to the patent to Hutin & Leblanc, No. 596,017, dated Dec. 2 i, 1897. Notice is hereby given that at or before the Michael I. Pupin. 253 hearing in this case, it will be moved, in behalf of Hutin & Leblanc, to have the above question, and all testimony elicited in response thereto, stricken from the record. A. I do not find any reference whatever in this patent to anything that may have any connection with the issue involved in this interference. Q. 24 I also call your attention to the fact that this patent purports on its face to be for an invention patented in France Sept. 3, 1891, No. 215,901, and in England Dec. 27, 1891 (which date it is believed should be 1892), No, 23,892. I herewith hand you the French patent of the number given, and the English patent to Messrs. Hutin & Leblanc No 22,892 of Dec. 27, 1892, and will ask you whether you find in those foreign patents the invention disclosed in the United States patent referred to 7 Objected to by counsel for Hutin & Leblanc as utterly incompetent under any circumstances, since not one iota of testimony was produced in behalf of Hutin & Leblanc, either with reference to the United States patent, or to the British patent; and notice of motion to be made by Hutin & Leblanc before or at the hearing of this case to have the question and any testimony elicited in response thereto stricken from the record, is hereby given. A. The United States patent refers to a part, only, of the French and of the English patents referred to. It is the part which deals with the method of impressing an electromotive force of high frequency upon a line, the manner in which the inductance of this line can be varied by varying the resistance of the secondary circuit standing in inductive relation to the line, and of special forms of tele- phone and microphone adapted to operate with high frequency currents. No reference, however, is made in & 254 Michael I. Pupin. the United States patent to selective telephony and tele- graphy, which is alleged to be the subject of the inven- tions covered by the French and English patents. Notice is hereby given by counsel for Pupin that this United States patent to Messrs. Hutin & Leblanc, No. 596,017, together with the file wrapper and contents thereof, will be relied upon in this interference as a part of his rebutting testimony and will be printed as a part of the record. Counsel for Hutin & Leblanc is surprised at the persistency of counsel for Pupin in insisting upon a practice that is in violation of all rules of evidence; particularly now since his attention has been called to it by the objections of counsel for Hutin & Leblanc, raised upon the record. Objection is made to any attempt to bring into this record, under the guise of rebuttal evidence, anything that is not calculated to rebut any evi- dence produced on behalf of either Hutin & Le- blanc or Stone. So far as Hutin & Leblanc are concerned, the notice given by counsel for Pupin will be entirely disregarded and considered as non-existent. Notice is hereby given by counsel for Pupin that before the expiration of his time for closing his testimony in rebuttal, he will put in as a part of his testimony in rebuttal a certified copy of the file wrapper and contents of the United States patent referred to, No. 596,017, together with a certified copy of the patent itself; that he will do this without calling another hearing, unless this is desired by counsel for Hutin & Leblanc or coun- sel for Stone. * Michael I. Pupin. 255 Counsel for Hutin & Leblanc reiterates his former objection. Counsel for Stone also gives notice that at the hearing he will refer to the patent to Hutin & Leblanc 596,017, dated Dec. 21, 1897, and to the file wrapper and contents of that patent, and that he will print the same as a part of his record. Counsel for Stone claims the right to make such reference to said patent and the file wrapper and contents, independently of the fact that they have been put in evidence as a portion of the rebutting testimony of Pupin, and independently of the fact that they are public records, to which refer- ence as such may properly be made, because be- fore the issue the said patent, when putting in his own rebuttal testimony, he called upon counsel for Hutin & Leblanc to produce a copy of the ap- plication upon which the said patent has been granted, in order that such copy might be made a part of the rebutting testimony of Stone. Counsel for Hutin & Leblanc replies that it is unquestionably true that opposing counsel have the right to refer to any public record of the United States Patent Office, by way of comment at the final hearing, if notice of that intent has been given; but he denies that independent of that rule of the 1’atent Office, counsel for Stone has any right to refer to the patent in ques- tion, and particularly, that he can derive such right from the fact of his having called for a copy of file wrapper and contents of the application upon which the patent was granted. Counsel for Pupin also gives notice that at the hearing in this interference he will refer, in con- nection of the answer of Pupin to Q. 4 of his present deposition, to a work entitled “Electricity f 2 Michael I. Pupin. *. and the Electric Telegraph,” by George B. Pres- cott, New York, D. Appleton & Co., 1877, and particularly to pages 724 to 728 inclusive, begin- ning with the heading “The American Automatic Telegraph,” and ending with the words “T. A. Edison,” and that he will print the pages of the book referred to as a part of his record. It is stipulated by counsel for the respective parties that Prescott’s book above referred to was published in the year 1877. Counsel for Pupin also gives notice that at the hearings in this interference he will refer to the work entitled “The Theory of Electricity and Magnetism, being lectures on mathematical phy- sics, by Arthur Gordon Webster, London, Mac- millan & Co., Lim., New York, Macmillan & Co.” and particularly sections 241 and 242 of the said work, pages 491 to 502, and that he will print these pages as a part of his record. It is stipulated by counsel for the respective parties that the apparatus introduced in the various depositions on behalf of Pupin, may be retained in the custody of counsel for Pupin, to be produced by him at the hearing herein. Counsel for the parties hereto, finding that in view of the complexity of this case, and the amount of printing that has to be done before preparation for the final hearing can be made; also in view of the difficult nature of the printing, that it cannot conveniently be done before Sept. 1, 1898, it is stipulated that each party shall have the right to give notice of intent to refer at the hearing to public records, up to and including: September 1, 1898; and that under such notice, each party shall have the right to refer at the Michael I. Pupin. 257 hearing to such public record, the same as if the notice had been given within the rule. Direct examination closed. Adjourned till Thursday, July 14, at the same place. NEw York, July 14, 1898. Met pursuant to adjournment. * Present, same parties as before. By Mr. Ewing : Q. 25 I understand that you wish to add a figure to the figure in your drawing on multiple resonance. Will you please produce it as a part of the article? A. I herewith produce a diagram entitled “Fig. 5.” It is a representation of a coil of adjustable self-induc- tion, such as I used in my experiments on which the theory given in my exhibit entitled “Extract from an Article on Multiple Resonance” is based. The coil con- tains no iron ; it is wound on a wooden spool with No. 14 wire, I think, and by means of the crank b c along the brass heads 1, 2, 3, 4 . . . . 9 the self-induc- tion of the coºl could be varied in small steps. I also wish to add that in all the diagrams, wherever a coil is represented, the coil had no iron whatever ; that the condensers were carefully prepared, so as to be as free from singing as possible when under the influence of an alternating electromotive force, and their capacities were adjustable in very small steps, sometimes running down to steps of 1/1,000 of a microfarad. Notice is hereby given by counsel for Pupin that Fig. 5 will be printed in connection with the article in question. Cross-Evamination by Mr. Lyons: x Q. 26 Have you seen the apparatus used by Dr. Kennelly in the experiments which he made with respect 258 Michael I. Pupin. to which he testified in his rebuttal testimony, and which were put in evidence as exhibits in behalf of Hutin & Leblanc & A. No. x Q. 27 But you have read the testimony of Dr. Kennelly in respect to this apparatus, and you will notice from Dr. Kennelly’s answer to Q. 24, that the alternators to be used in the experiments are known in the trade as Kennelly Therapeutic Alternaters. Have you ever seen such alternators? A. I don’t know that I have ever seen this therapeutic alternater to which you refer, or not ? x Q. 2S Are you aware that such alternators are regularly manufactured by the Edison Manufacturing Company of this City, and that they are carried in stock in their store, corner of Broadway and 26th Street, of this City ? A. No, I am not aware of that. x Q. 29 Will you be so kind as to look at these al- ternators during the next recess, so that you may be able to speak about them, knowingly in the course of your cross-examination ? f A. I shall do so if I can possibly arrange it. x Q. 30 Do you know of an alternator on the market, or, indeed, of an alternator found anywhere, that is capable of giving frequencies between 500 and 1,000 per second, that has a smaller reactance than the machines used by Dr. Kennelly, that is to say, reactance of about • 20,000 ohms for the frequency of 500, and 40,000 ohms for the frequency of 1,000? º A. I don’t know, since no publications in this matter exist, and it is a well known fact that it is extremely- difficult, if not impossible, to measure the reactance of the armature of an alternator containing iron, unless it is distinctly specified under what condition this reactance is to be determined. I would be perfectly willing, how- ever, to undertake to construct an alternator giving any frequency within reasonable limits, and having a react- Michael I. Pupin. 259 ance as small as a fraction of an ohm. In fact, when I come to think of it, the Tesla machine, with which I have experimented on several occasions, had a frequency of 10,000 periods per second, and a reactance of a few ohms only. I could tell that from the capacity which I had to employ to neutralize its self-induction at that fre- quency. x Q. 31 When was the Tesla machine builtº A. Mr. Tesla first exhibited this machine some time in 1891 or 1892, I have forgotten which—not later than '92—and I experimented with it in 1893, the machine having been lent to me by Mr. Tesla, and this fact is mentioned in my exhibit 36, page 508. x Q. 32 How many such machines are in existence, to your knowledge? A. I do not know. x Q. 33 You have yourself made experiments in the presence of opposing counsel at Columbia College, in this City; can you give me an idea what the reactances of your alternators were at that time ! A. I do not know, since I never had the necessity of finding out this matter. I am perfectly sure, however, that none of them had anything like the impedance you mentioned. At any rate, a coil of self-induction of about one henry placed in series with any one of those machines, will make the current excessively small, where- as, if the machine is short-circuited, it will burn out. Now, it is a very simple calculation to show that the self-induction of any one of those machines is much less than 1 henry, and therefore, the reactance, even of the one giving the highest frequency, that is, about 700 periods per second, must be much smaller than 2,000 ohms. I do not think that it would be a serious matter at all to take these machines just as they are, change the connection properly, and give them as small a reactance as I may please within reasonable limits. So that on second thought, I venture to suggest that every one of 260 Michael I. Pupin. my machines has a much smaller reactance than the one you mentioned. x Q. 34 Can you give the dimensions of your ma- chines, giving an idea of the amount of iron in the armatures and the amount of wire in the coils thereof so that we may have data for estimating roughly the im- pedance of these machines? A. They are + horse-power machines, wound to give about 100 volts at a speed of 2,400 revolutions per minute. The number of pole pieces are 18, 22, 26 and 30. The intensity of field excitation is about 10,000 C. G. S. lines. x Q. 35 If you should find an alternator that is very much smaller than + horse-power, that is also built and operated to give 100 volts, would you not infer that its impedance is smaller than the impedance of your ma- chine? A. I would infer nothing. x Q. 36 You have stated that Dr. Kennelly, when making his experiments, attempted to make “the punish- ment fit the crime;” and that for this purpose, he selected an “eatreme’ case, meaning thereby that he gave to his primary circuit an abnormally great imped- ance, which he said that he had not measured, but which he roughly estimated, under compulsion, on the cross- examination, at from 20,000 to 40,000 ohms. Since your opinions, upon “second thought,” are at variance from the opinions which you expressed primarily, will you now please state whether a primary circuit con- stituted as Dr. Kennelly has described it, really consti- tutes an extreme case ? A. Yes, indeed, I do think so, and I shall go even- further, and state that Mr. Kennelly went much out of his way to make the case an extreme one, and he had to do so, for how, otherwise, could his experiment be made to agree with the theory of Hutin & Leblanc, which is applicable to an extreme case only. In his answer to x Q. 35, Mr. Kennelly says, “It was sufficient for my pur- Michael I. Pupin. 261 i poses to know that the primary impedance were quite large.” Observe that Mr. Kennelly in his answer acknowledges that he made these experiments for the purpose of testing the Elutin & Leblanc formulae re- lating to secondary circuit resonance, as given in their article of May 9, 1891. x Q. 37. I understand from remarks made by you off the record that you now recollect having seen a machine of the kind used by Dr. Kennelly in his experiments, and I will now ask you to state, without respect to any- thing that Dr. Kennelly has estimated, whether you know of an alternator on the market capable of giving from 500 to 1,000 alternations, that has a smaller im- pedance than the Kennelly therapeutic machine? A. The description of the machine given outside of the record, recalls to my mind Mr. Kennelly’s machine, I have seen the machine, but did not know it under that name. There are no small alternators in the market that I know of, giving that frequency, and I am unable to answer the question. x Q. 38 This being the case, will you now please state what particular thing Dr. Kennelly did that made the conditions of his experiment an extreme case? A. He had too much self-induction, too much resist- ance in the line. In other words, his lines had too much impedance. He could have very easily avoided that by putting his machines A and B in inductive relation with the line, instead of putting them directly into the line; he could also have omitted the coil 7" and the resistance R. In fact, knowing that the impedance was quite large, as he acknowledged himself, and knowing from the criticisms of his opponents that the Hutin & Leblanc theory was a special case only, he should have done just the opposite thing, that is, made the impedance small. Now, I say this for the purpose of pointing out, not only that the impedance was large, but that Mr. Ken- nelly actually arranged his apparatus to make that im- pedance quite large. 262 Michael I. Pupin. x Q. 39 You will notice that with the very small ma- chines that Dr. Kennelly used, he obtained only a very faint current on the line. Does it not therefore seem impracticable to connect his machines inductively with the line, instead of placing them directly on the line? A. No, it does not. x Q. 40 Would the current on the line not have been much weaker if the arrangement you proposed had been made 3 A. Not necessarily, because by manipulating the im- pedance of his line he could have obtained any current he wished. x Q. 41 What do you mean by manipulating the im- pedance of a line ! A. I mean by increasing or diminishing it; by vary- ing the self-induction and the resistance of the line. x Q. 42 You will observe that in the experiments Dr. Kennelly cuts out the artificial resistance at various times, without noting any difference in his results, and you will also notice that the artificial resistance in the line itself was only about 250 ohms, representing, say, about twenty-five miles of ordinary telegraph wire, and that, in order to make the experiment under conditions which approximated that of commercial use, he was bound to have some artificial resistance on the line; so that it would seem that your objection to Dr. Kennelly’s ar- rangement, reduces itself to the placing of the alter- nators directly in the line, and to the use of the artificial reactance of the coil T. Is this correct? A. Not quite, I object to putting alternators of very large self-induction and an auxiliary coil T of large self- induction into the line, when testing the agreement be- tween the Hutin & Leblanc theory and practice, and I also object to putting the two secondary circuits in in- ductive relation with two separate primary circuits which are in series in the line This also is a tendency toward going to the extreme case, for in the Hutin & Leblanc article referred to, the secondary coils are all in inductive Michael I. Pupin. 263 relation to the same primary, which makes the impedance of the primary much smaller than in the case of which Mr. Kennelly has treated. x Q. 43 But since you do not know, as you have stated, in answer tox Q. 37, of any small alternators in the market, that give such frequencies as between 500 and 1,000, which it was desirable to use, except the alternators known as Kennelly Therapeutic Alternators, does it not seem to you reasonable that the machines that were found on the market ready for use, on sale in the store of the prominent manufacturing companies should be adopted ? This question is objected to by counsel for Pupin as purely argumentary. A Yes, indeed, very reasonable, and, in fact, a most admirable practice on the part of Mr. Kennelly to use a machine which he designed himself. x Q. 44 Why should, in your opinion, Dr. Kennelly have taken special pains to reduce the impedance of the primary circuit more than the ordinary commercial ma- chine used in an obvious simple and inexpensive way, would give it? A. I understand that the object of such experiment performed by Mr. Kennelly was to show that the theory given by Messrs. Hutin & Leblanc in their article of May 9, 1891, was a correct and complete theory, and therefore applicable to all cases. An honest, scientific test of a theory, according to my opinion, should satisfy all requirements which could under any conditions be made upon that theory. I conclude, therefore, that Mr. Kennelly should have gone much out of his way to make his experiment as general as it could possibly be made. I have performed this experiment myself on many occa- sions, and I know perfectly well that under general con- ditions, the circuit a in Mr. Kennelly’s Exhibit of Oct. 14, 1897, entitled “Sketch of Kennelly’s Experiment,” is not only not independent of b, as Mr. Kennelly claims, 264 Michael I. Pupin. but that, moreover, a can be actually tuned and made selective by the variations of the electromagnetic con- stants in the circuit b, and vice versa, and this experi- mental fact is in perfect conformity with the theory given in my exhibit entitled “Extract from an article on Multiple Resonance,” but it is entirely at variance with the theory given by Messrs. Hutin & Leblanc. All that part of the foregoing answer that be- gins with the phrase “I have performed this ex- periment myself,” is objected to as irresponsive and purely volunteered. Recess. Cross-ecamination of Pupin , eswºmed: x Q. 45 What makes you believe that the auxiliary coil T that was used in Dr. Kennelly’s experiment, was of large self-induction, as you have stated in answer to x Q. 42? A. Mr. Kennelly's statement about the impedance of the whole line. x Q. 46 Do you not find that Dr. Kennelly said that the coil 7" was nothing but the secondary of a trans- former, having three or four turns about the core ? I refer you to Dr. Kennelly's answer to x Q. 44%, A. If the transformer was small, three or four turns around the core would not give it a large reactance at ordinary frequencies, but if it was not a small trans- former, then its reactance could have been large if the transformer was large. It is not stated in Mr. Ken- nelly’s deposition whether the transformer was large or not. x Q. 47 But it is stated, is it not, in Dr. Kennelly's answer to x Q. 44, that the reactance of that coil was small by comparison with the reactance of the generators, and that its removal from the circuit made no appreciable impression ? ( Michael I. Pupin. 265 A. That is very true, but it does not show that react- ance was actually small. x Q. 48 Does it show that the reactance was large : A. No, I don’t think it shows anything. x Q. 49 Llave you during the last recess inspected one of the Kennelly therapeutic generators at the store of the Edison Electric Manufacturing Company ? A. No, because I thought that you did not consider it necessary for me to do so, after I informed you that the remark made outside the record recalled to my mind that I had seen the machine before, but did not know it under that name. x Q. 50 You know, then, I suppose, that in the Ken- nelly alternator the generating coils are practically the secondaries of the induction coils, the primaries of which are charged with battery currentº A. No, I do not admit that. x Q. 51 Well, then, please give your understanding of the construction ? A. The electromotive force is generated in the gener- ating coils by the variation of the magnetic flux pro- duced by a constant magnetomotive force, and the varia- tion of the flux produced by the variation of the reluctance of the magnetic circuit of the machine. Therefore, the coil which is actuated by the impressed electromotive force can be considered just as much a generating coil as the coil that does not contain the con- stant impressed electromotive force. I see, however, no objection to admitting your view of the matter, and for the sake of saving time, I’lſ admit that. x Q. 52 Referring, now, to the drawings of the IIutin & Leblanc French patents of 1891, do you not find that there also the generating coils of the generator are directly in circuit with the line ! A. No, I do not, for the two cases are not at all similar. In the French patent we have real induction coils, where the electromotive force in the secondary is produced by the variation of the current in the primary. : 66 Michael I. Pupin. In Mr. Kennelly's sketch wé have an induction coil, called so by concession, where the electromotive force in the secondary is produced by the variation of the mag- netic relu 'tance of the magnetic circuit, which is inter- linked with this secondary circuit. Suppose, however, that the two cases are exactly alike, what of it? I’ll make this additional admission for the sake of saving time. x Q. 53 Will you please, for the sake of clearly defin- ing your position in this case, to give a simple definition of electrical resonance in a simple circuit? A. Electrical resonance in a simple circuit means minimum impedance of the circuit to an impressed elec- tromotive force. x Q. 54 So that if the circuit has resistance, as would always be the case, I suppose, in practice, the impedance would be reduced to the ohmic resistance of the circuit. Is this correct : A. No, it is not correct, as I have pointed out in my Exhibit No. 35, page 22, when speaking of simple cir- cuits containing iron and imperfect dielectric. With reference to such circuits, I say, near to the top of page 22, “We have resonance in this case also, as in any other case, but it is evident that the condition of reson- ance are not determined by self-induction and capacity alone The question arises, then, what does resonance mean in this case? Well, it means the largest current and the highest rise of potential, but this maximum potential and current are not necessarily accompanied by zero difference in phase, not by neutralization of self- induction and capacity (observe the foot-note here). The practical bearing of this result needs no further com- ment (notice the foot-note again.)” x Q. 55 For the sake of simplicity and facility of this examination, let us henceforth assume that the circuits we are considering do not suffer from hysteresis and im- perfect dielectrics,; and with this understanding, do you Michael I. Pupin. 267 agree to the proposition stated in the preceding ques- tion ? A. Yes, I do. But I wish to call your attention to the fact that my definition of resonance is broader than the definition which is based on the neutralization of self-induction by capacity. This is one of the reasons why I refer you to my exhibit. x Q. 56 Will you now also please give a simple defi- nition of the conditions of electrical resonance in a cir- cuit that is in inductive relation to another circuit that is not resonant, and npon which an electromotive force is impressed ? A. The definition which I have just given you is sufficiently broad to cover all cases. Omit the word “simple,” answer to x Q. 53, and you will have a definition of electrical resonance which will cover all C3;S6S. x Q. 57 Do I then correctly understand that in your view of the case, a circuit inductively linked with another circuit from which an electromotive force is impressed, will be resonant to that electromotive force if it is react- anceless, so that its impedance is reduced to its ohmic resistance % A. Such a thing is an utter impossibility. The impe- dance of such a circuit can, in my opinion, never be reduced to its ohmic resistance, unless that ohmic re- sistance is infinitely large, in which case it doesn’t make any difference whether the circuit is resonant or not. x Q. 58 Will you please explain what you mean by your last answer, which, to me, is not altogether clear? And it would be of advantage if you attempted to make your explanation without reference to the formidable formulae which you have placed on record in your direct testimony. A. In your x Q. 57, you said, “if it is reactanceless, so that its impedance is reduced to its ohmic resistance.” If you mean that the last part of the sentence is a logical consequence of the first, that is to say, that the impe 268 Michael I. Pupin. dance is reduced to the ohmic resistance because the circuit is reactanceless, then you have stated something which is a theoretical impossibility. x Q 59 Your explanation, is to my understanding, still lacking in clearness. Do you mean by what you have said that owing to the inductive relation of the resonant circuit in question to the primary circuit, there is introduced into the former an apparent resistance, and that therefore the impedance of the resonant circuit will not be simply that of its ohmic resistance 2 Do I thus understand you correctly : A. Not quite. When the secondary circuit is react- anceless, resonance does not take place, because its im- pedance is not a minimum then ; although you are correct in your statement that when the reactance is reduced to zero, the impedance of the circuit is reduced to its apparent resistance, as I have shown for the first time in my exhibit, “Extract from an article on Multiple Resonance.” x Q. 60 In other words, in the condition of resonance in a secondary circuit, there is still some reactance left in it. Do I now correctly understand it ! A. Probably there is. I have, however, not yet settled this point quite satisfactorily to state a law which will cover all cases. I must observe, however, that it is pos- sible in particular cases to bring about a state of affairs in which, when the impedance is minimum, the reactance is zero at the same time. What I mean by reactance, of "course, is apparent reactance, and not the reactance which a secondary circuit would offer when taken by it- self. Minimum impedance is a condition sine qua non. x Q. 61 How about the real reactance of the secondary circuit in the condition of resonance. Is that Zero ! A. Certainly not, unless in particular special cases, as, for instance, when, owing to the enormous resistance, or the enormous reactance, or to put it concisely, owing to the enormous impedance of the primary, the state of affairs in the secondary is not materially affected by what Michael I. Pupin. 269 may happen in the primary. Such a case Mr. Kennelly has shown us in his experiment. x Q. 62 How early in the history of your work on electrical resonance did you come to the conclusion that in the condition of resonance in secondary circuits the eal reactance of the circuit was not real, or, as you have it in your last answer, “certainly not” A. As early as I conceived the invention. It was always a source of constant annoyance to nue, from which I tried my best to escape, in all my experiments, by making the co-efficient of mutual induction between the primary and secondary very small, in comparison to the co-efficients of self induction in the primary and in the secondary. This I did in all my theoretical work published so far, because it took me some time to work out to my own satisfaction the complete theory of mul- tiple resonance. x Q. 63 Please refer to your Pupin Exhibit, No. 36, and particularly to page 509 thereof, and state whether the formula there marked with the numeral 14 is, or is not, intended to express the current in a secondary cir- cuit when the same is in a condition of resonance % A. It is intended to express the conditions of reso- nance under the circumstances which existed when I performed the experiments to which I refer in that exhibit. Now, these circumstances were that the co-effi- cients of self-induction in this primary and in the second- ary were very large in comparison with the co-efficient of mutual induction between the two circuits. . . x Q. 64 Will you point out where it appears in the ex- hibit that the formula in question applies to any such special case as you have described in your last answer. A. You will find it in the description of experiments on page 510 and following of Exhibit 36. The primary circuit had the self-induction of the armature of the alternator, which was very considerable, because the impressed electromotive force of the machine was 600 volts at 2,810 revolutions per minute. In fact, it was 270 Michael I. Pupin. the self-induction of a one-horse power Crocker-Wheeler motor wound for 500 volts. The coil referred to in Fig. 3 had 3,000 turns in the primary, and contained iron. This gave an additional enormous self-induction to the primary circuit. The secondary circuit had an in- ertia coil of 1,000 turns, whereas, the secondary coil con- necting the primary circuit of the secondary had only 120 turns. It is evident from these figures that the co efficient of self-induction in the primary circuit, and also the coefficient of self-induction of the secondary circuit were both very large, in comparison with the co-efficient of mutual induction between the two circuits. That is where it appears in the Exhibit that an approx. imate formula will hold true, although I admit that I did not state it expressly that formula 14 was an approx- imate formula only. x Q. 65 In your Exhibit No. 36, you introduce the formulae defining the conditions of resonance in a second- ary circuit with these words: “Before describing some of my experiments on resonance in mutually inductive circuits with low frequency impressed E. M. F., it seems de- sirable to point out the relations in mutually in- ductive circuits when the primary circuit contains no condenser.” This is found on page 509 of your exhibit, and after that follow some additional remarks and the development of your formulae, and after that the description of some of your experiments. Would not a reader of your exhibit be under the im- pression that the formulae had general application, and that the experiments were only introduced by way of illustration of the verity of the formulae? Counsel for Pupin objects to this question, on the ground that this exhibit was put into the record in Pupin's testimony-in-chief, and that the subject has not been opened in his rebutting depo- sition, and that therefore it is not proper cross- Michael I. Pupin. 271 examination, but is an effort on the part of counsel for Hutin & Leblanc to get into the record what he should have properly gotten in by cross-ex- amination of Pupin in his testimony-in-cheif, or by means of his own rebutting testimony. In reply to the above objection, counsel for Hutin & Leblanc desires to state that the Ex- hibit, No. 36, now inquired into, states the theory of electrical resonance of secondary circuits in absolute conformity with the statement of the same theory by Hutin & Leblanc. That for this reason, counsel for Hutin & Leblanc had no occa- sion to cross-examine Prof. Pupin in respect to this exhibit, since he found that the learned Pro- fessor was in full accord with Hutin & Leblanc. But that now, since Prof. Pupin has shifted his ground, and has emphasized it by a most learned and most complex mathematical dissertation (Pupin Exhibit “Extract from an Article,” etc.) it is time to show the disagreement between his former position and the position which he now as- SUl IOleS. A. The passage which you quote from my exhibit "deserves criticism, because it is misleading, in so far as it states that that which follows in this exhibit refers to resonance in mutually inductive circuits; whereas, in reality, all the experiments described there have really nothing directly to do with resonance in mutually induc- tive circuits. I do not think that the intelligent reader of this exhibit would be under the impression that the experiments were only introduced by way of illustration of the verity of the formulae, for really, the formula which I used in the comparison of my experiments with ‘the theory is formula 16 on page 510, which, as I state ex- pressly in the exhibit, is the same in form as equation 8 ‘on page 426 of Exhibit 34. Now, equation 16, was ob- 272 Michael I. Pupin. tained by successive approximations, as is stated on page 510, and the object of these approximations was, to re- duce the conditions in the secondary circuit in such a way as to make it a simple circuit, in which case, of course, formula 16 cannot help being the same in form as equation 8 on page 425 of Exhibit 34. The question arises now, what was the object of introducing a second- ary circuit here, and then continually introducing ap- proximations and simplifications, until the conditions of resonance in this secondary circuit were the same as in a simple circuit? The answer is very plain and very simple: The aim of the whole paper is to show the effect of iron upon electrical resonance; hence we had to ex- clude from the circuit in which resonance was to be pro- duced, the alternator, whose armature contains iron. It is such an alternator as I had at my disposal, and the only way to exclude it from the resonant circuit was to make the resonant circuit a secondary to a primary in which the alternator was acting, and more than that, in order to exclude the detrimental effect of the iron in the primary circuit upon the resonance in the secondary circuit, it was necessary also to make the mutual induc- tion between the primary and secondary as small as possible, and to such an arrangement only the theory given in this exhibit was applicable. Any impartial reader will see that that theory was written, not for the purpose of discussing the resonance in the secondary cir- cuit in general, but for the purpose of discussing it in a particular case, such as I employed in my experiments on the effect of iron upon electrical resonance. x Q. 66 In your formula, marked with the numeral 14, in Pupin Exhibit No. 36, the current in the secondary resonant circuit is expressed under the assumption that there is no need of reactance in that circuit. Is this so : A. Yes, that is so. x Q. 67 Does this not agree with the Hutin & Le- blanc formula : 3 i , , , i i ; Michael I. Pupin. 273 A. Yes, it does, and that is the very reason why that formula is wrong. Adjourned to Friday, July 15, 10:30 A.M. *ss-s-sºm- NEw York, July 15, 1898. Met pursuant to adjournment. Present, same parties as before. Cross-examination of Prof. Pupin resumed : The witness desires to make a statement as follows: The last word in answer to x Q 67, should read : “ap- proximate ’’, instead of “wrong.” x Q. 68 If you have ever published a corrected or completed formula, will you please point it out 3 A. The formula given in my exhibit entitled “Ex- tract from an article on Multiple Resonance ’’, is the first complete formula ever given. x Q. 69 So that you permitted the world to get along with the incorrect or incomplete or approximate formula up to the present time, notwithstanding the fact that, as you have stated, you knew at an early time in the history of your invention that secondary resonance is not satisfied with real zero reactance of the secondary circuit' A. I knew that from my experiments, but I did not succeed quite as early as that time to which you refer, in formulating my experimental knowledge into mathem- atical language. In fact, even if I had done so, I do not see that the mathematical formula would have helped anybody to put my invention, selective distribution of alternating currents, into practical operation. In fact, the principal point of my mathematical discussion in my exhibit referred to, is that the methematical formula do not help us at all, and that in the tuning of a system which forms the subject of this interference, we have to rely entirely on experiment. In his answer to x-Q. 159, my 274 Michael I. Pupin. witness, Michael J. O’Connor, states the sentiment which I have just expressed, in a very striking way. He says: “Whoever would take the trouble to set up this apparatus after the explanation that I have given, would have to experiment, and find out what relation the capacity and self-induction bear to the periodicity of the machine º’’ That is the best instruction that one can give to a practical experimentalist on the subject of resonance in secondary circuits. So that we lose noth- ing, as far as the practical operation of the invention in volved in this interference is concerned, by withholding any sort of a mathematical theory which we may have worked out in this subject. x Q. 70 Can you refer us to any published definition of secondary resonance, besides Webster's book, to which you have already referred, that agrees with the definition which you have now adopted A. As far as I know, a general definition of resonance has never been given before, either as regards electrical resonance or acoustical resonance, and the definition which I gave is the first general definition ever given : x Q. 71 My last question was perhaps not specific- enough. I understand it to be your conception of the conditions of resonance in a secondary circuit, that the real reactance of the same is, as you have said, “cer- tainly not ” zero. Now, will you please state whether you can refer to any publication, except that of Web- ster, in which this conception of resonance in secondary circuits is stated ? A. My discussion in the exhibit entitled “Extract from an Article on Multiple Resonance,” is the only com- plete mathematical discussion of multiple resonance that I know of. I must therefore refer you in all these matters to this exhibit. x Q. 72 Do I correctly understand your exhibit No. 40, by assuming that you there state that the neutraliza- tion of the inductance of a primary circuit, by capacity in the secondary circuit, establishes a condition in the primary Michael I. Pupin. 275 circuit which you have called consonance, and which is attended either by a maximum or by a minimum cur- rent in the primary circuit 2 A. Yes, such a condition was called by me conson- ance. It is, however, not necessarily attended by a real maximum or a real minimum current, as my attention was called to it by some friends some time ago. x Q. 73 In his answer to Q. 11, Dr. Kennelly, in his rebuttal testimony, also speaks of the neutralization of the inductance of the primary circuit by capacity in a secondary circuit, saying at the time that this would be attended by a considerable current in the primary cir- cuit, and then adding that you would call such a condi- tion selective consonance. Do you find that Dr. Ken- nelly has misrepresented you ? A. Yes, I do, for he puts a word into my mouth which I never used. I never spoke of selective consonance. Nor did I ever maintain that the condition of consonance necessarily implied a large current in the primary cir- cuit. As a matter of fact, I pointed out distinctly my reason in my article referred to by Mr. Kennelly, both by theoretical and by experimental references that the current in the primary circuit may be small, in fact, smaller than under ordinary conditions, that is, smaller than under conditions, when the secondary circuits is not adjusted at all by means of capacity. x Q. 74 You mean to say, then, that if the reactance of the primary circuit is neutralized by capacity in such a way as to give rise to a large current in the primary, that this is not the case of electrical consonance: is this what we are to learn from your exhibit 40? A. Not at all, What I mean to say is simply this: that in my Exhibit 40, the zero value of the phase of the current is a criterion of consonance, and not the value of the current itself. That was the point in my article, and that is the point Mr. Kennelly entirely missed. x Q. 75 Please state now, without reference to Dr. Kennelly, whether a case where the apparent reactance 276 Michael I. Pupin. of a primary circuit is neutralized by capacity in a secon- dary circuit, so as to give rise to a large current in the primary, is, or is not, in accordance with your Exhibit 40, a case of electrical consonance 2 A. Yes, it is a case of electrical consonance, I should think. x Q. 76 Then please state why, in your estimation, Dr. Kennelly, in his answer to Q. 11, displayed ignorance of your work on electrical consonance, as you have stated in your present deposition in answer to Q. 17 ? A. For this reason: In Fig. 4 of the French patent, the capacity of the condenser in the secondary is supposed to be adjusted in such a way as to make the current in the primary greater for the frequency under considera- tion, than for any other. That is not electrical conso- nance, and I never called it so, but Mr. Kennelly main- tains I did. x Q. 77 Please observe that in your Exhibit 40, on page 6, you state as follows: “We see, then, that the neutralization of the inductance does not necessarily increase the pri- mary current. On the contrary, it may diminish it very much and it will do that whenever this neutralization increases the impedance of the pri- mary circuit. In fact, a moment's reflection will convince us that the physical meaning of the ex- istence of the two values for each, the secondary self-induction, the capacity, and the frequency, each of which will neutralize the primary apparent reactance is simply this. One value will make the primary impedance a maximum and the other will make it a minimum.” This being the case, does it not appear from this ex- hibit that the conditions which Dr. Kennelly discussed in his answer to Q. 11, are those of electrical consonance, as defined by you in the exhibit ; and do you look upon it as an imposition if Dr. Kennelly assumes that you would speak of the particular conditions represented in the French patent as a case of selective consonance % t Michael I. Pupin. 277 A. In his answer to Q. 11, Mr. Kennelly quotes the following passage from the French patent: “Indeed, let us suppose that the condenser C is inserted in the local circuit, which includes the microphone m (Fig. 4). If the capacity of this condenser is such that it balances the self-induction of the system formed by the line, the receiver E! and the local circuit, for a current of the period T, then, for the same electromotive force, the in- tensity of this current will be greater than that of a current of another frequency.” You see, then, the French patent demands that the current for that frequency should be greater than for any other. In the case of consonance, the current in the primary circuit is not necessarily greater for the period for which consonance has been established than for any other period. In fact, there is always another period at which the current in the primary is greater, and that is the period with which the primary is in resonance. It is therefore the period of resonance the French patent aims at, and not the period of consonance. I never said that in his answer to x Q. 11, there was anything which Mr. Kennelly said that might be regarded as an impo- sition; what I did say, however, and say still, is that Dr. Rennelly did not understand my article contained in Exhibit 40. x Q. 79 Please state in what part of the year of 1897 Prof. Webster's book, to which you have repeatedly re- ferred, appeared in print? A. In the early Spring. x Q. 80 Who, to your knowledge, besides Webster and Thomson, have published anything on two or more inter-connected oscillating circuits before 1897? A. On this point I refer you to the references given in paragraph 242, page 502, of Prof. Webster's book. x Q. 81 In your answer to Q, 7, after having expressed your opinion of the “ignorance of the theory of a se- lective system, etc.,” on the part of Dr. Kennelly, you criticise his article in the Electrical World for October 278 Michael I. Pupin. 21, 1893; also Mr. Remington’s article in the London Electrical Review for December 27, 1892, and also Dr. Bedell’s book entitled “The Principles of the Trans- former,” by taking them all in one bunch and saying in effect that they are all as weak as Dr. Kennelly’s article. Since it would lead us too far, if we attempted to inquire into the defects of all these writers, I will only ask you to be so kind as to point out, if you can, wherein Dr. Kennelly’s article is incorrect, and weak. I here hand you, a copy of the Electrical World for October 21, 1893, for the purpose of your criticism. A. Messrs. Kennelly, Remington and Bedell’s articles were called weak in their applicability to the theory of a selective system, such as forms the subject of this inter- ference; they were not called weak as such, nor incor- rect as such. Now, that they should be considered weak when considered as a sample of a theory of a selective sys- tem, is, it seems to me, self-evident, for a system consisting of one primary and one secondary is certainly not a system forming the subject of this interference. Mr. Kennelly's article is correct as far as it goes, but, as I have already stated in my answer to Q. 7, it was anticipated by several months in my article of Exhibit No. 36. x Q. 81 Well, as regards your article in Exhibit 36, you have, as I understand it, admitted that it was either not correct, or incomplete; while as regards the article of Dr. Kennelly, you seem now to think that it is cor. rect. It would therefore seem that after all, you did not anticipate Dr. Kennelly by several months? Is it not so? A. Oh, no, for the theoretical part of my article Ex- hibit 36 contains a great deal more than Mr. Kennelly's article. The article in this exhibit contains on the first page and the first half of the second page, all the theory which is contained in Mr. Kennelly’s article, and in ad- dition to that, my article contains an approximate theory of electrical resonance in a secondary circuit under the conditions described in the article. It is this second part of the theory which I admitted to be approximate Michael I. Pupin. 279 only, but not the first part, which deals with the same matter as is contained in Mr. Kennelly's article. I wish also to add that in Mr. Kennelly's article referred to the subject of resonance or selectivity is not mentioned' x Q. 82 Please refer to page 504 of your Exhibit No. 36, and observe that you there say, among other things, as follows : “When the circuits are in resonance to the im- pressed E. M. F. then both L1 and V1 are zero.” Does this not indicate that the first part of your article Exhibit No. 36 is just as much, as you now understand it, in error, or incomplete, as the second part 2 A. I just told you that this article contains on the first page, and the first half of the second page, all the theory which is contained in Mr. Kennelly’s article. I do not see, therefore, what your object is in encroaching upon the second half of the Second page, since you can easily see that the passage quoted by you belongs to the second part, and as such, has nothing to do with Mr. Kennelly’s article. x Q. 83 On October 30, 1896, in your first deposition, in answer to x Q. 115, 116, etc., etc., you manifested a great aversion to the use of the term neutralizing, or neutralization, or words to the same effect, as designat- ing the inter-action of inductance and capacity. It seems that since that time you have overcome that aver- sion. Are we to explain this by the fact that in the meantime you have found out that you yourself, prob- ably by inadvertance, have used that term in print before October 26, 1896? A. I confess with much regret that my scientific ter- minology has suffered a great deal, owing to bad com- pany, which I could not possibly avoid during the prog- ress of this interference. Adjourned to Tuesday, July 26, at 1 P. M. 2 S Michael I. Pupin. NEw York, July 26, 1898. Met pursuant to adjournment and agreement. Present—MR. Jose:PH Lyons, Attorney for Hutin & Leblanc, MR. W. W. Sw AN, Attorney for Stone, MR. THOMAS Ewing, Jr., Attorney for Pupin. Counsel for Pupin states upon the record that there was no session held yesterday, but that the session, by general agreement, begins to-day. Cross-Evamination of Pupin by Attorney for Stone : x Q. 84 In your answer to Q. 2 of your present depo- sition, when considering the conditions for resonance in secondary circuits, such as those illustrated in Stone's report to Mr. Hubbard, you have recourse to Prof. Webster's book, “The Theory of Electricity and Mag- netism,” published in 1897, you say that the case dis- cussed by Prof. Webster, Paragraph 242, page 499 and 502, will suffice for the purposes of your argument, and you go on to say: “Formula 13, page 502, gives the amplitude of the secondary current when a simple harmonic electromotive force is impressed upon the pri- mary. The secondary current will be in resonance with the primary electromotive force when the secondary current is a maximum, and the sec- ondary current cannot be a maximum unless the differential co-efficient with respect to a of the expression on the right hand side of the equality sign of Equation 13 is equal to zero.” I call your attention to the fact that Prof. Webster in the paragraph cited by you, and immediately after stating Equation 13, says: “We get resonance when a) is one of the roots of the quadratic. (ſ. 1,–1) o'-(# %) a)” –H + = 0 K. ' A. { Michael I. Pupin. 281 But I am told that when your direction for obtaining the conditions of resonance, as quoted above, are strictly adherred to, that is, when “the differential co-efficient with respect to a of the expression on the right hand side of the equality sign of Equation 13° of Article 242 of Prof. Webster's book is equated to zero, the re- sulting mathematical expression differs from that given by Prof. Webster, quoted above. I would ask you whether or not I am correctly in- formed. In order to save time, and to save you the trouble of performing the mathematical operations required by the question, I here hand you a paper, in which I under- stand these mathematical operations are correctly per- formed. A. You evidently do not understand the article in Prof. Webster’s book. Otherwise you would not be surprised that Equation 14 is not the same as the equation which one obtains by equating to zero the differential co- efficient of the right hand member of Equation 13 with respect to a). You do not observe that in Equation 14 all the resistances of the system are supposed to be infinitely small. In Equation 13 they are not supposed to be so. If you make that supposition in Equation 13, and then perform the operation which I described, you will, in all probability, get 14 from 13. So that I do not see the point of your question. On page 500, Prof. Webster says that he discusses this system for a particular case, and that is when all the resistances are equal to zero. In fact, I once criticised Prof. Webster for de- ducing 14 from 13, without stating explicitly under what conditions 14 is deducible from 13, and Prof. Webster acknowledged the justice of the criticism. The mathem- atical operation which I gave for obtaining the con- ditions of resonance from Equation 13, is the most gen- eral operation. The operation by means of which Prof. Webster passed from 13 to 14, refers to a very particular C8 S6. 282 Michael I. Pupin. Counsel for Stone puts in evidence the paper handed the witness at the close of his last ques- t on, and the same is marked “Stone’s Exhibit No. 1, Pupin's Cross-Examination.” Counsel for Stone states further that he will produce the ex- bibit at the hearing, and print the same in Stone's record. x Q. 85 Was the criticism, the correctness of which was acknowledged by Prof. Webster, as stated in your last answer, made in print % A. No, it was ruade in a personal conversation. x Q. 86 In your answer to Q. 2, page 39, of your type- written record, (printed record p. 205) you say: “An examination of Figure 2, of Mr. Stone's 1.xhibit entitled, “A Report to Mr. Hubbard, dated November 28, 1891, and also of Figure 3, of Mr. Stone's specification, shows that Mr. Stone’s sonorous transmitting circuits are in inductive relation (as they must necessarily be) with other circuits, and that therefore they will have more than one period.” In support of this and similar statements regarding the effect upon the period of sonorous or oscillatory cir- cuits of an inductive relation to other circuits, you have recourse to the book by Prof. Webster entitled “The Theory of Electricity and Magnetism,” to which you have so often already referred, and you cite a mathem- atical discussion in paragraph 242 of that book. I will ask you whether or not this mathematical treat- ment of the case of two ideal circuits shows that when the first circuit, a £onorous or oscillatory circuit, is brought into inductive relation with the second circuit, which contains no condenser, but simply resistance and inductance, it would still have but a single frequency. To save time, and to save you the trouble of perform- ing the mathematical steps which I undertand in answer to the above question may require, I hand you a paper which I understand contains the necessary operations? Michael I. Pupin. 283 A. Mr. Stone's report to Mr. IIubbard, referred to, the secondary circuit is connected either directly or induc- tively to a number of receiving circuits, each, according to Mr. Stone's own statement, containing self induction and capacity and resistance. In such a case it makes no difference whatever whether the secondary circuit has any capacity or not, the sonorous circuit will still have a multiplicity of periods. Your mathematical demonstra- tion, therefore, deals with a case which does not appear in Mr. Stone's report to Mr. Hubbard, nor can it possibly appear, for what bearing can such a case have upon se- lective distribution of alternating currents : x Q. 87 You will please allow me to judge of the per- tinency of my last question, and answer it? A. If two ideal circuits are brought in inductive rela- tions, and one of them does not contain a condenser, then it is a well-known fact that each one of them still has two periods, one of which is infinitely long, and the other is a period shorter than the period of the circuit containing the condenser when that circuit is taken alone; so that in this case also, the rule given in Prof. Web- ster’s mathematical demonstration at the bottom of page 501, still holds true. It is not at all necessary for you to prove this fact, which was known for many years now. Counsel for Stone puts in evidence the paper handed the witness at the close of x Q. S6, and the same is marked “Stone’s Exhibit No. 2, Pupin's Cross-Examination,” and notice is given as in the case of the other exhibit. x Q. 88 Do you mean that one of the oscillations is of infinite period, and, if so, will you describe the char- acter of such an oscillation in terms that may be readily understood by the Court A. The character of such an oscillation is a periodic, It is the same as the current flow in an electrical circuit containing resistance and self-induction, but no capacity, 284. Michael I. Pupin. when an electrical impulse is communicated to such a circuit. x Q. 89 I hand you another mathematical paper, which I understand deduces from Prof. Webster's for- mulae, on page 501, Article 242, of his book, the fact that if the sonorous or oscillatory cirruits he considers, in paragraph 242, have the same period before they are placed in inductive relation to each other, they will have practically the same period after they are placed in in- ductive relation to each other, if the auxiliary induct- ance of either circuit, or both circuits, is sufficiently great, compared to the mutual induction coefficient ? Is this deduction correct 3 A. I do not exactly understand what you mean by practically the same? I see, however, from the paper handed to me, what the meaning of this word is, and answer in the affirmative. Counsel for Stone puts in evidence the paper handed to the witness at the close of the last question, and the same is marked “Stone’s Exhi- bit No. 3, Pupin's Cross-Examination,” and notice is given as in the case of the other exhibits. x Q. 90 I hand you still another mathematical paper, which I understand demonstrates from Prof. Webster's formulae given on 501, Article 242, of his book, the fact that if the two sonorous or oscillatory circuits he there considers have no auxiliary inductance, and the induction coil which unites them is such as to fulfill practically the condition of no magnetic leakage, the two circuits so united can have but a single period. Is this deduction correct 2 A. Yes. Counsel for Stone puts in evidence the paper handed to the witness at the close of the last question, and the same is marked “Stone's Ex- Michael I. Pupin. 285 hibit No. 4, Pupin's Cross-Examination,” and notice is given as in the case of the other exhibits. x Q. 91 I will now ask you to consider a system of three ideal circuits consisting of two identical oscillatory circuits in inductive relation to a third circuit, which latter has ohmic resistance and inductance, but no ap- preciable capacity, and you may consider the mutual in- duction co-efficients between the two oscillatory circuits and the third, or non-oscillatory circuit, to be the same. Under these circumstances, will, or will not, the two oscillatory circuits have the same period, or periods To assist you in understanding this question, I here hand you a diagram illustrating the three circuits described in my question. A. Yes, I should think they would, since there is no sufficient reason to believe the contrary. Paper handed witness offered in evidence, with same notice as above, and marked “ Stone’s Ex- hibit No. 5, Pupin's Cross-Examination.” x Q. 92 I will now direct your attention to a system of five circuits. Let circuits 1 and 2 be two identical oscillatory circuits, and circuits 3 and 4 be two identical oscillatory circuits, of a different period, however, from circuits 1 and 2, and let circuits 1 and 2 be given each a mutual inductive co-efficient M, to the fifth circuit, which you may consider as only resistance and inductance. Let circuits 3 and 4 be given mutual induction co-effi- cient M, to the fifth circuit. In such a system will, or will not, the circuits 1 and 2 have the same periods of vibration, and will not the circuits 3 and 4 have the same periods of vibration ? In order to assist you in understanding the arrange- ment of circuits described in my question, I here hand you a diagram illustrating this system of circuits. A. Yes, but remember that each circuit will have more than one period. In other words, each circuit will, \ 286 Michael I. Pupin. when disturbed by an electrical impulse, become the seat of a complex harmonic vibration. Paper handed the witness introduced in evi- dence, with same notice as above, and marked “Stone’s Exhibit No. 6, Pupin's Cross-Examina- tion.” Adjourned until 1:30. x Q.93 I call your attention to the system of five cir- cuits, shown in “Stone’s Exhibit No. 6, Prof. Pupin's Cross- Examination,” and described in my x Q.92. In your answer to my question, you pointed out that each cir- cuit will have more than one period. I would now ask you whether, if each of the oscillatory or sonorous cir- cuits contained an auxiliary inductance, would it not be possible, by giving these auxiliary inductances, suitable values, to make the circuits containing them have prac- tically but a single period? A. Judging from what is known to day in electrical literature concerning the theory of complex resonance system, one could not answer your question, because no data bearing on this question exist. If you wish to find out how much I know on those matters, and if you have a right to know that, I will answer your question. x Q. 94 I now call your attention to a system or two circuits, a sonorous or oscillatory circuit inductively asso- ciated with another circuit, containing inductance and resistance, but no appreciable capacity. To make the case concrete in its nature, we will assume that the gonor- ous circuit has twenty ohms resistance, 4 henrys induc- tance, and 1/10 microfarads capacity, that the second circuit has 100 ohms resistance, 1/10 henry inductance, and, further, that the mutual induction co-efficient of the circuits is 4/ hundredths henrys. I would ask you to what extent the period of this sonorous circuit will be influenced by its association with the second circuit. Michael I. Pupin. 287 To save time, and to save you the trouble of perform- ing the necessary computation, I would here hand you a paper, which I understand sets forth the result of the necessary computation. A. The calculation seems to be correct. It must be observed, however, that, as I have remarked on numer- ous occasions before, we can always find cases sufficiently extreme to fit into any figures. For instance, I would like to know how any one could make a coil of 4 henrys self-induction and only 20 ohms resistance, unless he uses a large quantity of iron, and if he does so, the for- mulae quoted from Prof. Webster’s book do not apply. Again, while it may be easy enough to handle a case of two circuits inductively related, so as to force them to have practically one period of oscillation, it will be found that this manipulation is by no means easy, when we are dealing with a multiplicity of circuits, such as form the subject of this interference. It seems to me that the example which you handed to me was entirely unneces- sary, since I have shown in my published papers, and also in the depositions in the course of this interference, that when a secondary circuit has a self induction large in comparison with the co-efficient of its mutual induc- tion with the primary, the secondary circuit behaves ap- proximately like a simple circuit. It is such a case that this calculation considers, for the self-induction of the secondary circuit is a hundred times as large as the mutual induction between the primary and the secondary. I do not see, therefore, the necessity and the object of drag- ging in matters that have been already discussed and settled. The criticism of the question by the witness objected to by counsel for Stone. The paper handed the witness is introduced in evidence, with the same notice as above, and is marked “Stone’s Exhibit No. 7, Pupin's Cross- Examination.” 288 Michael I. Pupin. x Q. 95 In your preceding answer, you state that you have shown in published papers that when a secondary circuit has a self induction large in comparison with the co-efficient of its mutual induction, the secondary circuit behaves approximately like a simple circuit. Will you now, please, point out where in your published papers you have shown this fact? A. In Pupin Exhibit 36, page 510, top of the page, formula 16 gives a resonance condition in a secondary circuit, which is the same kind as the arrangement of circuits in the Exhibit which you have just handed in. In fact, the coefficient of mutual induction was, in com- parison with the co-efficient of self-induction in a second- ary circuit, considerably larger than in the case calcula- ted in the exhibit which you have just handed in. Pupin’s Exhibit 36 contains also an experimental proof of formula 16. x Q 96 In your answer to Q. 2, and elsewhere in your present deposition, when discussing the conditions of resonance in secondary circuits, in a system such as that shown in Fig. 7 of Mr. Stone's application in this interfer- ence, you refer to an elaborate mathematical solution of the problem, which you have prepared, and which is entered as an exhibit in this case, and marked “Pupin's Exhibit Extract from an Article on Multiple Resonance, by M. I. Pupin, July 12, 1898.” I am told that the solution for the current in any one of the seven secondary circuits shown in Fig. 7, of Mr. Stone's application in this inter- , ference, requires no such elaborate determination, and that it could be obtained by one familiar with the ele- mentary theory of the simple transformer by a few steps of reasoning, even if performed mentally. I here hand you a paper containing these simple steps, and will ask you whether or not, in your opinion, one familiar with the elementary theory of the simple transformer, should be able to perform these steps mentally' A. The mathematical discussion which you just handed to me purports to give my solution of the prob- Michael I. Pupin. 289 lem presented in Fig. 7 of Mr. Stone's application in this interference. The formula which is given in this paper for the amplitude I. is far from being the same as the formula which I give in Equation (6) for the same case. So that even if I admit the assumption from which your paper starts, it does by no means follow that Formula 6 of my exhibit can be obtained, and, in fact, I am per- fectly sure that it cannot be obtained by the reasoning employed in your paper. But the assumption from which your paper starts is by no means admissible, for without the mathematical demonstration, we cannot say with any safety that each secondary circuit will produce in the primary circuit the apparent resistance and the apparent reactance from which your paper starts. I ad- mit that after seeing the result of my paper, one can make several short cuts in the demonstration Without seeing those results, however, one could not guess as to the manner in which the several circuits would a t, for if the thing were so easy, why did not Messrs. Hutin & Lablanc, in their paper of May 9, 1891, give an even ap- proximately correct mathematical solution of this prob- lemº The paper handed the witness is introduced in evidence, with the same notice given above. It is marked “Stone's Exhibit No. 8, Pupin's Cross- Examination.” Witness resumes his answer: My mathematical discussion of this case, it should be observed, is just as short as the one given in this paper, although it makes no assumptions whatever, for it really contains just as few mathematical operations, for as far as the matter is covered in your paper, everything will be found on page 2, and the first third of page 3 of Pupin's Exhibit entitled “Extract from an Article, etc., etc.,” and besides, in that space Pupin's exhibit contains a reference also to the phases of the currents, whereas, your paper leaves the phases out of consideration. So that I do not see that even after studying my paper, and 290 Michael I. Pupin. seeing the results, you have succeeded in producing a simplification of my method. In order to avoid a pos- sible misunderstanding as to the scope of Pupin's exhibit entitled “Extract from an Article, etc.,” 2, I wish to point out here that in this extract all possible cases of multiple systems are considered, and therefore the method adopted in the first case was not intended to be the sim- plest one, but the most general one, so that after discuss- ing this first case, one should be prepared to take up in the same manner every other case. x Q. 97. In your preceding answer you have said in substance that the solution for the amplitude of the cur- rent in one of the secondary circuits of the system repre- sented in Fig. 7 of Mr. Stone's application in interference, as given in “Stone's Exhibit No. 8, Pupin's Cross-exami- nation” is far from being the same as the formula which you gave in Equation 6 of your exhibit entitled “Extract from an Article on Multiple Resonance, by M. I. Pupin, July 12, 1898.” I will ask you whether or not there are many possible solutions of this amplitude of secondary current. By the solution, I mean the mathematical ex- pression for the amplitude : I will also ask you whether or not the solution contained in the paper I handed you, (No. 8) is substantially the same as that given in Equa- tion 5 of extract A. Of course it is. How could it be otherwise, since having copied from my extract formulae 2, 3 and 4, par- ticularly 3 and 4, you could not fail getting 5; but formula 5 is not the same as formula 6, and it is the very heart and soul of my exhibit entitled “Pupin's Exhibit Extract, etc.,” to demonstrate that in all cases the ex- pressions for the secondary circuit can be put in form of equation 6. Now this form has the great advantage, as is pointed out in the exhibit just quoted, that in it we have a complete expression of the apparent reactance and the apparent resistance of cach secondary circuit, whereas, Michael I. Pupin. 291 formula 5 does not contain the apparent resistance and the apparent reactance. Adjourned to July 28th, 10:30 A.M. NEw YorF, July 26, 1898. Met pursuant to adjournment. Present—Same parties as before. Cross-examination of Pupºn resumed: x Q. 98 I call your attention to the formulae you gave in answer to Q. 2, page 914 of the record of your present deposition, and will ask you whether or not your formulae require correction? More particularly, should not the series of terms beginning with 1. * M, I L., - ) A25 (a p: C. 1 \? p;" (1. -* Fºo) + R.” and p;" M, R, 1 \? p;" (1. T pº w) + R.” respectively contain terms in M*, instead of terms in M t Also, should not the terms p;" JM; L's and p;" Ms R's p; L'º -- R';* p.” L';* + R';* be written ££4%, and -º, A95 L's + R's A95 L';* -- ſº A. Yes, the M should be squared, as can be seen from formulae 4 and 6 of my exhibit entitled “Extract,” etc. x Q. 99 Referring to these same formulae, I draw your 292 Michael I. Pupin. attention to the fact that you denote by M, to M, the co- efficients of mu ual induction between the primary and the several secondaries. I will ask you whether or not, in view of this fact, the two series of terms beginning with º 1 **(1,-rº) p * (i. p; C, l 2 p;" (1. -zº) + R. and p;" M? R, & 1 \? 2 *(1,-gº) + æ. respectively should, in fact, begin with terms in M, in- stead of in terms M. A. Yes, that is correct. The error arose from the fact that I overlooked having denoted the constants of the primary circuit by symbols which did not contain any suffix. In my exhibit entitled “Extract, etc.,” the sym- bols referring to the primary circuit were always pro- vided with the suffix 1. R.-direct eramination of Pupin: r-d Q 100 In X Q 89 you were asked whether sonorous circuits considered by Prof. Webster, if they have the same period before they are placed in inductive relation to each other, will not have practically the same period after they are placed in the same relation to each other, provided the auxiliary inductance of each circuit, or both circuits, is sufficiently great compared with the mutual induction co-efficient. Please, state the practical mean- ing and importance of the assumption that in a system of multiple signalling or multiple telegraphy, the mutual induction of the resonance circuit with the line shall be small in comparison with the self-induction of the cir- cuits themselves? A. A distinct disadvantage arises from making the mut- Michael I. Pupin. 293 ual induction between the secondary circuits and the main line small because the smaller this mutual induction the less capable will the main line be of communicating en- ergy to the secondary circuits There is no visible gain to be derived from such a procedure, so far as I can see, except to overcome the multiplicity of periods in sonorous circuits. r d Q 101 In x Q 92, you have been asked to consider certain relations of circuits there stated. I assume that this question is intended to have a bearing upon the sys- tem disclosed in Mr. Stone's report to Hubbard of Nov. 28, 1891, and to Fig. 7 of his application. Will you, please, state whether you find in that report or that figure of his specification the conditions which are named in x Q 92, and if not, please, point out wherein there are differ- ences 3 Objected to by counsel for Stone, as the witness has already been fully examined upon this subject in his direct examination, and as not opened by the cross-examination. A I do not find in Mr. Stone's report to Mr. Hubbard, nor in any of his exhibits, a single instance which cor- responds to the cases described by him in x Q 92. So, for instance, in his report to Mr. Hubbard, dated Nov. 28, 1891, the sonorous receiving circuits are wound on the same spool, so that they all have a common primary; whereas, the Sonorous transmitting circuit is in inductive relation with the line only. Again, in Fig. 7 of his speci- fication, to take that with another illustration, the receiv- ing and transmitting circuits have evidently different resistances, and besides Mr Stone says nowhere that his receiving and transmitting circuits are identical in con- struction in their relation to the main line and the other circuits of the system. I will state, however, I attach no importance whatever as to whether or not the exhibits Mr. Stone furnished during this cross-examination are found in his report to Mr. Liubbard and in his specifica- 2.94. Michael I. Pupin. tion. That which is of very much greater importance in this connection is the question whether the system de- scribed by Mr. Stone in his exhibit No. 6, and during this cross-examination, represents, or does not represent, a selective system. In other words, if simple harmonic electromotive forces were impressed upon the main line of periodicities corresponding to the natural periods of the various circuits, would these circuits respond selec- tively with regard to these periodicities? This is a ques- tion which, I think, should be answered, if Mr. Stone’s Exhibit No. 6 is to have any bearing upon the questions arising in this interference. I simply state that they would not act in such a way. Counsel for Stone makes the same objections to the answer that he made to the question, and also objects to the answer, as containing much matter not responsive to the question, as grossly volun- teered and argumentative. r-d Q. 102. In x Q. 96 and 97 it is suggested that some of the results obtained in your exhibit “Extract from an Article,” etc., particularly that part which relates to the solution for the current in the circuits of a system such as Fig. 7 of Mr. Stone's application in this interfer- ence, follow easily from the elementary theory of the simple transformer. I would like to ask you whether your exhibit referred to contains anything indicating the relation of the results you obtained to the familiar ele- Jmentary theory of the simple transformer, and if so, please, point out what it is, and explain it in unmathe- matical language, briefly A. The theory of the transformer is, in its main features, an elaborated statement of Maxwell's solution of the prob- lem of the current flow in two mutually inductive circuits when a simple harmonic electromotive force is impressed in one of them. In the paragraph immediately following Equation 5 of my extract, I state that Equation 5 is an extension, or, rather, a generalization, of Maxwell’s Michael I. Pupin. 295 formula, and I also point out distinctly that this equa- tion is not well adapted to the study of complex systems of conductors, and pass on immediately to deducing Equation 6. Now, this equation is entirely different from Equation 5, and can by no means be deduced by any one who is acquainted with the ordinary theory of the trans- former. As far as my experience goes, I am certain that much additional experimental knowledge is necessary to formulate the mathematical laws relating to complex systems in such a way as to give them the form contained in Equation 6, and I stated distinctly in my Extract that it was owing to this experimental work that I was led to the conclusion that laws like those expressed in Equation 6, must in all probability regulate the current deduced in such systems. Mr. Stone does not show in his exhibit No. 8, that even with the unwarrantable assumptions he made there, could he obtain Equation No. 6 of my Extract, by by means of what he calls “simple elementary reason- ing.” r-d Q. 103 In answer to x Q. 53, as enlarged by your answer to x Q. 56, you define electrical resonance in a circuit as minimum impedence of the circuit to impressed electromotive force. You have further discussed this same matter in your answer to x Q. 57 and several fol- lowing questions. I will ask you, by way of elaboration somewhat, upon these answers, to state how the relations of inductance, capacity and resistance affect resonance in simple and complex circuits? Objected to by counsel for Hutin & Leblanc, as new matter, and as incompetent in re-direct examination. Counsel for Stone makes the same objection. A. Electrical resonance means minimum impedance, and therefore maximum current under the action of a periodic impressed electromotive force. In the case of a simple circuit, or in a circuit which is equivalent to a simple circuit, the impedance is reduced to ohmic re- 296 Michael I. Pupin. sistance. In the case of a complex circuit, no other gen- eral statement can be made as to the apparent reactance, the apparent resistance, and the phase of the current un- der conditions of resonance, except that the apparent re- actance will be such that their resultant impedance be- comes a minimum. ; r-d Q. 104 In your answer to x Q. 44, you refer to certain experiments. Please state why you did not ar- range to show those experiments during this hearingº Objected to by counsel for Hutin & Lablanc, as new matter, and improper and re-direct; also as entirely immaterial and irrelevant. A. Because I could not get the apparatus and the necessary assistance, on account of the College vacation, when all the Laboratories are closed, and all College offi- cers who could render me the necessary assistance are very difficult to get at. There is at this season of the year no electrical current available from the College, ex- cept for lighting the Library building, for which they use a gas engine, just sufficiently powerful for that pur- pose, and for nothing else. Re-direct examination closed. No re-cross. (Sgd) MICHAEL I. PUPIN. Certificate of Officer. 297 Certificate of Officer. STATE of NEW YORK SS. : County of New York, ( * I, GEORGE H. GILMAN, a notary public within and for the County of New York and State of New York, do hereby certify that the foregoing depositions of Reginald A. Fessenden and Michael I. Pupin were taken on behalf of the said Michael I. Pupin, in pursuance of the notice hereto annexed, before me, at 41 Wall Street, in the City of New York, Borough of Manhattan, in said County, on the 14th, 15th, 21st, 22d, 23d and 24th days of June and the 12th, 13th, 14th, 15th, 27th and 28th days of July, 1898; that each of said witnesses was by me duly sworn before the commencement of his testimony; that the testimony of each of said witnesses was written out by Caroline L. Hall in my presence; that the opposing party, John S. Stone, was present, and the opposing party, Hutin and LeBlanc, was represented by counsel during the taking of said testimony; that said testimony was taken at the office of Messrs. Ewing, Whitman & Ewing, and was commenced at eleven o’clock on the 14th day of June, 1898, was continued, pursuant to adjourn- ment, on the 15th, 21st, 22d, 23d and 24th days of June, and the 12th, 13th, 14th, 15th, and the 27th days of July, 1898, and was concluded on the 28th of said month; that I am not connected by blood or marriage with either or any of said parties, nor interested directly or indirectly in the matter in controversy. In testimony whereof, I have hereunto set my hand and affixed my seal of office at New York City, Borough of Manhattan, in said County, this 4th day of August, 1898. GEORGE H. GILMAN, Notary Public, [L.S.] New York Co. (33) 298 Extract from an Article on • “PUPIN ExHIBIT, ExTRACT FROM AN ARTICLE ON MULTIPLE RESONANOE BY M. I. PUPIN. July 12, 1898,” G. H. G. Group I.-n circuits in inductive relation to the same primary circuit as represented in the diagram of Fig. 1. Qſ H |- N A simple harmonic E. M. F. is impressed upon the primary circuit. Multiple Resonance. 299 Let La Ca Ra be the co-efficient of self-induction, the capacity, and the resistance, respectively, of circuit a. Let Mia be the co-efficient of mutual induction be- tween this circuit and the primary. Let 6 stand for # . Applying the law of equality of action and reaction to each separate circuit the following n differential equations are obtained :— (I. ô* + R, 3 + #)---Mºº--....+ 1 + Min ö’a, - i. p E el". Mis 6° an —- (a ô* + R. 64- ),40+...+ • e o e s , s , s e e = • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * M. 6° a + 0 + ....+ | + (1, r + R, a 4 g ). =0. When the steady state has been reached the various currents will be simple harmonics of the same frequency as the impressed E. M. F. E ep". They will differ in phase from it by p, p, . . . . . pa. The currents can therefere, be expressed as follows:— a’ = At Aft(pt-9) s sº sº e º 'º a ºn a * * * * * * * Introducing these values of the currents and employing the abbreviation 1 Åa for La Tzº C. (1) transforms into 300 Extract from an Article on r —? {- —? ( p *, + R) A, e.” + i p Me A, e.” + + . . . . -- ? p Mia An 2-tºn — E' & p Miº A, e “” + ( p \, -i- R.) A, a-º. -- (2) 4 + . . . . —H 0 = 0. s is e s tº e s a tº e. e º 'º " tº dº a tº e º 'º e º e º e e a e º ºs e e s e e s tº e º 'º e s s * p Min A1 • * + 0 + . . . . . -- l + (ipſ. --R) A, cº- = 0 For the sake of brevity the quantities A, a *, A, a *, .... A., a * will be called hereafter phase-amplitude products of cir- cuits 1. . . . . . . . . . . 0. . . . . \ It is evident that the phase-amplitude product of any circuit a can be expressed in terms of that of the primary circuit as follows: — (3) Aa a-'ga p Mia (AEa g- Ž p 2a) A. e-89, 0. where Ia = W pº Aaº' -- Ra” is the impedance of circuit a. Substituting these values of the secondary phase-am- plitude products in (2) the primary phase-amplitude product is obtained. . . / , p" M.” A * Min”. An (9) in ( , -º- ... —” ºr 2 2 2 2 –3 +(ºrºAs E. g ... ºº) {A, *1 – E. 2 Multiple Resonance. 301 Or ( p a + p.) A e * = E. |Hence A = –1 = wpº a.” -- 0.” tan = 2 *. 91 |O1 Following Maxwell’s terminology we shall call on and p, the coefficient of apparent self-induction or apparent inductance and the apparent resistance respectively of the primary circuit. The expressions for o, and pi form an extension of the formula which Maxwell first deduced for the simplest case, namely for a system consisting of one primary and one secondary circuit, the circuits containing no condensers. The amplitudes and phases of the secondary currents are now easily obtained. There are two methods of cal- culation leading to this result. Fºrst Method. ** 7 p Mio (Ra—8pxa) E. 2–ig' Jºº 4/ps of + p.” _ _p Mia F 2-8(g-Hº-Hºpa) Ja W pºdº-E of (5) A. e. “– where tan pa = p#. Equation (5) is a generalization of the expression for the secondary current of a transformer which was first given by Maxwell in his famous essay: “A Dynamical Theory of the Electro-magnetic Field.” Maxwell’s formula has been adopted by all writers on alternating currents. It is, however, by no means the most desirable expression 302 Extract from an Article on that can be obtained, and certainly not well adapted to the study of complex systems of conductors such as form the subject of this paper. The following method of calculation leads to a new expression which is in many respects superior to that contained in (5). Second Method. Substitute in the first equation of group (2) the value of each secondary phase-amplitude product except Aa 2-3%a as given by (3). * * * * ? p Mia A. e. *** -- | ip ( – 24”. 2 2 2 on2 /l/ 2 —d P # *)+(R. + £ ** +...+)}A, 291 Il 2 = E, OI’ sp M. A. “4 (p a 4 p.) A, sº = E Or ? p Mia (pia— ? p a.) Aa e “” + Aerº - 2 10. = *-* Pºiº 11a* F' Multiple Resonance. 303 pa, and pla are evidently the apparent reactance and the apparent resistance of the primary circuit when the secondary circuit a is open. Aa F. W p” oil.” + pla” is the apparent impedance of the primary under the same conditions. In this last equation substitute for —io, A1 e 91 from (3). We obtain r 2 2 } i p (i. –º)+ R. la + p” *: Pla | Aa 2-tºpa la (6)- p M. A 2-3 (3+ele) 1. A (T. Or (? poa + pa) A., e-??a Mia A.' e £(;+elo) tº-º-º- la p oa and pa are evidently the apparent reactance and the apparent resistance of circuit a. 304 Extract from an Article on It is well to consider here the E. M. F. induced in cir- cuit a. If the circuit a were open, the current a would be F' l — COS (p f – ela), Wp” aia” + 01 ..” where G tan ela = £2 01a Pla If ea denote the E. M. F. induced in circuit a, then da, ea = -41. Hiſ = p Mio E'. 7t - ==== *(******) This shows that the right hand member of (6) repre- sents the E. M. F. induced in circuit a by the primary current when circuit a is open. The current in circuit a lags behind the E. M. F. induced in that circuit by the angle ea, where tan ea = * * Oa • According to (6) the circuit a behaves toward this E. M. F. induced in that circuit just like a simple circuit whose reactance is poa and whose resistance is pa. This is a simple statement of what actually takes place in a cir- cuit of this kind, but, as far as the author's knowledge goes, it has never been pointed out even in the simplest case, namely the case of an ordinary transformer. This is in all probability due to the fact that Maxwell’s ex- pression, of which (5) is a generalized form, has been generally followed. Multiple Resonance. 305 A striking feature of (6) is contained in the fact that it suggests a simple method of studying experimentally the behavior of complex systems of conductors like that of Fig. 1. It is this:—Introduce in each secondary cir- cuit an auxiliary coil of adjustable self induction and a condenser of adjustable capacity. By adjusting these two in any one circuit like a we can make the reactance of that circuit, poa, anything we please without chang- ing any term in (6) except Aa. So for instance, we can make 2 2 p” Midº oia == 0 1,2° o a = 2a by giving Aa a proper value. This can be done, for 1 Aa - La Tzº C.’ where La contains the self-induction of the auxiliary coil, and Ca is the capacity of the condenser in circuit a. Since both are adjustable Xa can be given any value. When 2 2 ſ? +a+1a. Oia Ža = −:#–tº– I,” , then aa = 0 and the current in circuit a will reach a maximum. It is through these maxima principally that we can study experimentally the behavior of complex systems of electrical conductors. They form, therefore, one of the principal features of this investigation. It is well, however, to consider several other simple arrangements of circuits, passing gradually to more and more general cases until the most general case is reached. It will be shown that in each case, even the most general one, simple relations like those in (6) hold true and that, therefore, the experimental method of study just pointed out is applicable to all of them. 306 Extract from an Article on GROUP 2:—n circuits 1, 2, .... n. (Fig. 3) of which n-1 are connected through condensers C, CA. . . . . . . CA to the same main circuit 1, in which there is a simple harmonic E. M. F. impressed by the alternator A. (VVVA/V/\/\/\/\/\ſ \ry º & d - * f *A } s f } S The condensers C. C. . . . . . . . . Ca' will be called local condensers. Denoting the potential differences in C, C, ... C., and C.'...C., by P, ...P., and P.' . . . . Pa' we obtain by the ". Multiple Resonance. 307 law of equality of action and reaction applied to each circuit separately J., 6 a., -i- R a., + P + P. -- . . . . -- Pa = E e” for circuit 1. * e º a m = a is ~ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * La. 6 a.a + ſea ala + P'a — Pa = 0 for circuit a. Since dPa =5a d/’a "a dt O. " -dt O'a ša = 21 — 23a El 1 In 00a o ipt Li 6° a + R, 6 a., + * * * – 2 ºf = i. p A e I & 2 (Z * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Introducing the abbreviations * = 1 - 3-4 * * * * * * * * * * * * * * * * * * * * * * * * * and putting • * * * * * e º a s e º 'º e < * * * * * * * we obtain ºw 30S Extract from an Article on 6 p. 4) A, a "4. . § 1 T. –? 2' — ' Aa ?a – (7) { . . . . . . . . tº e º ſº sº. ( p *, + R.) A. e." + fº + *: A, sº = 0 Equations (7) are of the same form as those of (2); *— in (7) takes the place of Mia in (2). Hence p°Ca ſ A, a *. * e-” w"p" a " + p.” where tan p = tan e = * * (7a) { sº £91 1 & Priº, A ſº -??a _ £“ U a –? ($-Heia) Aa e T Z, W pºadº-Hoa" e -º (; +éla U tan éta =? *a, P1a p o' and p, are the apparent reactance and the apparent resistance of the primary circuit. p oa and oa are the apparent reactance and the appar- ent resistance of circuit a. p oia aud pia are the apparent reactance and the appar- ent resistance of the primary circuit when the circuit a is open. • * Multiple Resonance. * 309 Observe now that 1 A ſº * ,-i(;+.) 1, (, gives the amplitude and phase of the difference of po- tential in condenser Oa when the circuit a is open. This difference of potential corresponds to the E. M. F. in- duced in a secondary circuit which is connected to the primary by mutual induction. Observe, further, that (7a) has all the formal characteristic features of (6). By adjusting the local condensers and self induction coils the reactance in any circuit like a can be made zero and the current in that circuit will reach then a maximum. GROUP 3:—n parallel branches (Fig. 3) each possessing self-induction, capacity and resistance; a simple har- monic E. M. F. is impressed in one of the branches, which will be called the main branch. Fig. 3 • * ~ * ~ Consider the circuit consisting of the main branch and any branch like a of the multiple group. For this circuit 310 Extract from an Article on (s) (; p ≤ + F) A, a " + ( p ,--R.) A. cº- -- E' Again it is evident that º *- e tº - G 6 ( p ≤ + Ra) Aa e “* = ( p 26 --Rº) Age” By Kirchhoff’s law A, a “* = A, e.” + A, e^* + + . . . . —HAn 2–??, Each term of the right hand member of this equation º –? º expressed in terms of Aa e “” gives (9) A, sº = | (i p \a + *} (*= p ≤ + 2 +...+º, + º-ipº) a..” – (#1 +%)- - * (# + . . . +%)}( p , + R.A.A. 2-ºpa 2 Il = (7–ip V) (ip , 4- R.) A. e. ** Hence (i pº. 4 R + ####) Ale “” = E Multiple Resonance. 311 Placing V U o, + X, + tº Tºys' * = *, + gºz-y, We have A – T.2T. 2 #H 5 tan 91 = A2 ai 4/p o," + O1 91 o, and 0 are therefore the apparent self-induction and the apparent resistance of the main branch. To find the current in any other branch, say branch a, substitute the value of A, e.” from (9) in (8) we have ( ? p A, -H R1) ( p , + R.)} U — i. p V + +R, Lºp & | A, a ** = E' I? Denoting now by U2 and Via the values of U and V when in them 2, and Ra are replaced by Å, and R, the last expression reduces to ( p * + F) (0. – e V.) ( p , + R, + Uia –H & p º)4. 2-&a - A.' + ja” + p” Via” {}}" (10) ( p \,--R)(U, -īp V.)(`poa-Hp,) Aa e “” = A.' where p oa and oa bear the same relation to branch a as o, and ſo, bear to the primary branch. Hence they must be called the apparent reactance and the apparent resistance of the branch a. 312 Extract from an Article on Again, denoting by Ua and Va the values of U and 7 when the branch a is open we obtain ( ; p X, + R.) (Ula – ? p Via) = = (Ua — ? p Y.)}###4 ºn 4 R. = (Ua — ? p Va) (? pola + pia) where pola and pia are the apparent reactance and the apparent resistance of the main branch when the branch a is open. Substituting in (10) we obtain E (U2–? p |Va) (?p aia-H (1a) ( p oa + pa) A a a-tº a - The right hand member of this equation deserves a closer examination. Let P be difference of potential between the branch points when branch a is open, then E– (; p ≤ + F) A, sº = P now when branch a is open A. e-ºp, - —; E. 1 2 p 0.1a + Pla hence E' (l *Eºgº ####) — P 2 p O'ía + Pla Or” £(Ua + ' p Wa) P 4.9 o'ía + pia Multiple Resonance. 313 Or (11) , g E. = 7-#4-v. (0a – ? p. Va) (? pola + pia) 0.2°,+ p” Va It follows, therefore, that the right hand member of equation (11) is a quantity having the same phase and a proportional amplitude as the difference of potential, be- tween the branch points, when branch a is open. It is the equivalent E. M. F. with regard to branch a. The same remarks regarding local adjustments of self induc- tion and capacity apply to this case as to the two pre- ceding cases. The reduction of apparent reactance to zero is produced here in the same way as in the two other cases. The most general case can now be discussed. GROUP 4:—n circuits, every one of which is inductively zelated to every other of the groups. Fig. 4 is a scheme of this group. A Fig. 4 Using the same notation as before the following n equations are obtained by applying the law of equality of action and reaction to each separate circuit:- 314 Extract from an Article on (p X, − & R.) Al 2–??, + p Mia As a-ºp, + +.... + p M. A. e." = - A p Ms. 41 ,-ºp, + ( p * – ? Rs) A, sº + • * ~ * g g g sº s ºf 4 ºf ºf we w = < * * * * * * * * * * * * * * e º is a tº e º sº is a is at ºf p M. A. " + p M. A. e."--.... + + (p x, — R.) A. e. ** = 0 Consider now the determinant (p 2. — ? R.), p Mis, . . . . p Min p Mei, (p 28–7 Hº), - - - -? Man *-º-º: A. p Mai, p Maº, ... (p. An – ? Iºn) If for any column, say the nth, we substitute a col- umn consisting of the right hand members of above equations, that is the column – ? B, 0, 0, . . . .0, we obtain another determinent 4, let a, be the minor of — ? E' in 4a, then 4. – – i Fa'a. The amplitude-phase product of the current in the nth circuit is then given by n & &=º-mº –4– Consider the last column of the determinant 4; let Multiple Itesonance. 315 0.1n, 0.2n.2 - - - - - - Cºnn be the minors of the terms p Min, p Man. ... (p 2, - ? F.). This determinant expanded will be 4 = p Min Cºin + p Man an–H . . . . -- (1) An — ? RA) Cºnn f - = 0 nn } p M. : +p M. : +...+p.–. R. ºnn Now it is evident that any factor like * can be Cºnn written (Z † ** = p Bºn—? 72n Ønn where 32n and ran are real. Hence 4 = ann [p (ºn + p Min #in + , , +p Ma-ºn 8-in ) — ? (R, + p Min ria + . . . .)] = ann (p an — ? (a) = - ? ann (; p on + pa) Hence (12) (ip o, + p.) A, e “- * E Cºnn It is evident that (12) has the same form as (6). It re- mains to be shown that it has also the same physical meaning. For this purpose it is well to inquire into the physical meaning of ºn E. Cºnn Suppose the nth circuit is open. The simultaneous differential equations between the various currents and the impressed E. M. F. are now of the following form 316 Extract from an Article on (p R. -- ? R.) A, g-ºp, + p Mis As 2–4% -- +...+ p M. A, , e.” = − i B' p Mai Al g-ºp, + ( p X, − 2. It') As 2-’92 -- + . . . . +p Ms. n- 4a– e-ºn- = () • a s a s = e g = * * * * * * * * * * * * * * * * : * * * * * * * * * * * * * * * * * * * * * p Ma-i, 4. a-tºl + p Ma-i, 2 As e-ºp, + + . . . . +(p An-1 - ? F, -) 4n- g-ºn- = 0 Let (p A, - ? (?), p Miº. . . . . . . .p M. a- p M2, 1 ( p 23 – ? R.) . . /9 M, n—-1 = 4 — -1 20 Ma-i, 1 p Ma-i, 2 . . . (p An-1-? Æa-) Then it is evident that 4, is the same as an in (12). The amplitude-phase product of any current like –? & * g tº e A, e “” is now obtained just as in the preceding C8,88. º , / 4a– g-??n- - 4,' Cºnn where 4,' is obtained from 4, by substituting for the last column of this determinant — ? E, 0, ... 0; Let en_1 be the minor of — ? E'in, 41, then - –?o, &n—1 . A, , e, “”— = — ºn- ; E. & - Cºnn Multiple Resonance. 317 Having thus obtained the value of the amplitude phase products of the various currents when the circuit ov is open the amplitude-phase product of the E. M. F. in- duced in circuit n can now be calculated. Denote it by e, then en = * (p Min A, a-tºl + p Man As 2–??, + +...+ p \, , , A., cº- E – #(p Min e, H-p Man sº -i-. . . . H- p Ma-, ea_i) But it is clear that the factor in parenthesis is an: Hence &n = E *n (Ann It follows therefore that the right hand member of (12) is the phase-amplitude product of the E. M. F. in- duced in circuit n. Equation (12) has, therefore, the same physical meaning as (6). The quantities p an and 9a are the apparent reactance and the apparent resist- ance of circuit n. It is well to point out now that the quantities p an and o, the apparent reactance and the apparent resistance possess the same formal characteristics in this general case as in simple cases like those discussed under groups 1, 2, and 3. It is evident that aa contains neither Ån nor Jea. Let \e º —s—a-, * – ? p an = 2n + 2 Bn = W anº + 3, e • Il 4 contains A, and R, but it is clear that these quanti- ties enter the determinant as follows: 318 Extract from an Article on 4 = (p ,-i R. (c. 4 i V.) + S. + i 7. U, V, S, T, do not contain A, or Ir, Since i R, . . . . . R, are the only imaginary factors in the determinant, it follows that the imaginary parts : Vn and . T., will vanish when all the AE’s vanish. & Again T.) ( Un—? V.) ..? +- V.” = (U, -i- i Wº) p (), H- Sº) (R, + 7') 4 = (V, 4 V.) | p.—i R,+*t T'a will vanish when all the ſe’s vanish. Let !, tan s = £, H. A. U. p (An-H Sºn) then we can write (13) A = tan en = — –7(en—sºn) = woº pºisy ECW, ITy, “T” ~, Woº-Hº F' 2–7(en-en-3) * 4. a-'ºn - — VU.' - V. Vpu, --Sºy-H (R, + 7".) Just as in the preceding cases so also here p (An + Sºn) and (R, + 7"n) should be called the apparent reactance and the apparent resistance, respectively of the nth circuit. - The apparent reactance p (2n + Sºn) is the only term in the expression for A, eT *** which contains the self- induction and the capacity of circuit n. By adjusting these properly we may make X, + S^n = 0 Multiple Resonance. 319 and thus reduce the apparent reactance of this circuit to zero without in any way changing either its apparent re- sistance or the E. M. F. induced in this circuit. When this reduction has been accomplished the current in cir- cuit n passes through a maximum. Summing up the results so far obtained we can state briefly: In any complex system of conductors containing coils and condensers the amplitude of the current in any part of the system is equal to the E. M. F. induced in that part divided by its apparent impedance. In the ex- pression for the impedance the self-induction and the capacity of that part enters in one term only and that is in the reactance term. By adjusting these two properly the reactance can be reduced to zero and the current passes then through a maximum. This mathematical analysis discloses, therefore, an in- teresting resemblance between a simple circuit possessing self induction and capacity and a circuit which forms part of a complex system of conductors with coils and condensers. But it should be observed that this resem- blance is apt to lead one into serious errors; for whereas in a simple circuit the current passes through an absolute maximum when its reactance is reduced to zero by ad- justing its coil and condenser, in the complex system the maximum thus obtained is not an absolute maximum as a simple consideration will show. For in a simple cir- cuit the impedance is minimum for a given frequency when the reactance is zero, whereas in a complex system the impedance is equal then to the apparent resistance and this apparent resistance varies with the frequency, so that the impedance may, and in most cases will be smallest at a frequency at which the reactance is not zero than it is at a frequency at which the reactance vanishes. This forms a radical difference between the two cases. Numerous experiments have led me to this conclusion much before I had made any advance at all in theory given above. The theory given above agrees 320 Extract from an Article on Multiple Resonance. with my experiments. To obtain the true maximum theoretically we have to proceed as follows: Let us consider, for the purpose of illustration the system represented in Fig. 1. Let n simple harmonic E. M. F.’s of n different fre- quencies, ps. . . . p. be impressed upon the primary and let it be required that the circuits 2.... n be resonant to frequencies ps...pa . . . . pn respectively. Let us de- note the amplitude of the current in circuit a produced by the E. M. F. whose frequency is pa by Aaa. It is re- quired then that Ass Ass. . . . Aaa.. Ann be maxima fre- quencies ps. . . .pa . . . . pn respectively. This will be the case when - - ° 42– 0 6 Ass 14; 3–5– — ( ); ô ps We have here n — 1 simultaneous equations. The capacities C. . . . . C., and the inductance Za. . . . La must have such value as to satisfy these equations. That is to say, we have 2 (n − 1) unknown quantities to satisfy n — 1 equations. Hence to n — 1 of these we can assign any convenient values and determine the other n — 1. That is to say we can select any convenient values for the capacities C.. . . . C., and then calculate from the above equation the inductances L., . . . . La. These inductances would then produce resonance between the circuits 2, ....n and the frequencies ps. . . pn. It is evident that even in the simplest case, that is when we have one primary and two secondary circuits the calculation becomes an impossibility. Hence it is impossible to calculate the valties of the inductances and capacities for the various parts of a selective system which will make these parts resonant to E. M. F.'s of different frequencies. XXI. An Experiment in Magneto-Electric Induction. By W. R. Grove, F. R. S. &c. * Reprinted from the Philosophical Magazine, Vol. XXXV.—Fourth Series, March, 1868, pp. 184, 185. Shortly after the publication of Mr. Wilde’s experiments on magneto-electric induction, it oc- curred to me that some of the ordinary effects of the Ruhmkorff-coil might be produced by apply- ing to it a magneto-electric machine. I tried an ordinary medical machine with a small coil made by Mr. Apps, of 3% inches length by 2 inches diameter, and having about # of a mile of fine secondary wire. The result was very unexpected. The terminals of the magneto-electric coil being connected with the primary coil of the Ruhmkorff, and the contact- breaker being kept closed so as to make a com- pleted circuit of the primary wire (a condition which would have appeared d priori essential to success), no effect was produced; while if the cir- cuit was interrupted by keeping the contact- breaker open, sparks of 0-3 of an inch passed between the terminals of the secondary coil of the Ruhmkorff, and vacuum-tubes were readily illu- minated. Here there was in effect no primary coil, no metallic connection for the primary current; and yet a notable effect was produced. I did not at the time publish this experiment further than by communicating it to a few friends, hoping to be able to find a satisfactory explanation of it. All I have observed since is that the effect *Communicated by the Author. -------- 2 is dependent upon the condenser; for when that is removed no result is produced. It would appear, then, to depend on an electri- cal wave or impulse shot, so to speak, into the uncompleted primary coil, similar to the wave which will deflect in succession magnetic needles placed at different distances on a telegraphic cable, without the current passing through the whole length of wire, as shown in the experiments of Mr. Latimer Clark and others. But why there should be no effect, or an inappreciable one, when the primary circuit is completed, the current be- ing alternated by the rotation of the coils of the magneto-electric machine, I cannot satisfactorily explain. & XLII.-On Mr. Grove’s “Experiment in Magneto-electric Induction.” In a Letter to W. R. Grove, F. R. S* Reprinted from the Philosophical Magazine, Vol. XXXV.- Fourth Series. May, 1868. pp. 360–363. 8 Palace Gardens Terrace, W. DEAR SIR, March 27, 1868. Since our conversation yesterday on your exper- iment on magneto-electric inductiont, I bave con- sidered it mathematically, and now send you the result. 1 have left out of the question the second- ary coil, as the peculiar effect you observed de- pends essentially on the strength of the currënt in the primary coil, and the secondary sparks merely , indicate a strong alternating primary current. The phenomenon depends on the magneto-electric machine, the electromagnet, and the condenser. The machine produces in the primary wire an *Communicated by Mr. W. R. Grove, F.R.S. #See Phil. Mag. S. 4. March 1868, p. 184, 3 alternating electromagnetic force, which we may compare to a mechanical force alternately pushing and pulling at a body. The resistance of the primary wire we may com- pare to the effect of a viscous fluid in which the body is made to move backwards and forwards. The electromagnetic coil, on account of its self- induction, resists the starting and stopping of the current, just as the mass of a large boat resists the efforts of a man to move it backwards and for- wards. The condenser resists the accumulation of elec- tricity on its surface, just as a railway-buffer re- sists the motion of a carriage towards a fixed obstacle. Now let us suppose a boat floating in a viscous fluid, and kept in its place by buffers fore and aft abutting against fixed obstacles, or by elastic ropes attached to fixed moorings before and be- hind. If the buffers were away, the mass of the boat would not prevent a man from pulling the boat along with a long continued pull; but if the man were to push and pull in alternate seconds of time, he would produce very little motion of the boat. The buffers will effectually prevent the man from moving the boat far from its position by a steady pull; out if he pushes and pulls alternate- ly, the period of alternation being not very differ- ent from that in which the buffers would cause the boat to vibrate about its position of equilibrium, then the force which acts in each vibration is due, partly to the efforts of the man, but chiefly to the resilience of the buffers, and the man will be able to move the boat much further from its mean pos- ition than he would if he had pushed and pulled at the same rate at the same boat perfectly free. Thus, when an alternating force acts on a massive body, the extent of the displacements may be much greater when the body is attracted towards a posi- tion of equilibrium by a force depending on the displacement than when the body is pefectly free. 4 The electricity in the primary coil when it is closed corresponds to a free body resisted only on account of its motion; and in this case the current produced by an alternating force is small. When the primary coil is interrupted by a condenser, the electricity is resisted with a force proportional to the accumulation, and corresponds to a body whose motion is restrained by a spring; and in this case the motion produced by a force which alter- nates with sufficient rapidity may be much greater than in the former case. I enclose the mathemat- ical theory of the experiment, and remain, Yours truly, J. CLERK MAXWELL. Mathematical Theory of the Ecperiment. Let M be the revolving armature of the magneto- electric machine, N, S the poles of the magnets, a. the current led through the coil of the electro- magnet R, and interrupted by the condenser C. Let the plates of the condenser be connected by the additional conductor y. Let M sin e be the value of the potential of the magnets on the coil of the armature; then if the armature revolves with the angular velocity n, the the electromotive force due to the machine is Mm cos nt. Let R be the resistance of the wire which forms 5 the coil of the armature M and that of the fixed electromagnet. Let L be the coefficient of self-induction, or the “electromagnetic mass” of these two coils taken together. Let a, be the value of the current in this wire at any instant, then La, will be its “electromagnetic momentum.” Let C be the capacity of the condenser, and P the excess of the potential of the upper plate at any instant, then the quantity of electricity on the upper plate is CP. Let p be the resistance of the additional con- ductor, and y the current in it. We shall neglect the self-induction of this current. We have then for this conductor, P=0&y. . . . . . . (1) For the charge of the condenser, 67P C + =a:-v. . . . . . . . . . (2 #-a-v. (2) For the current ac M7), cosnt-Rºlff-P-0. . . . . (3) If we assume a;=A cos (m.t-Hº), we find • - A*= M*m' (1+C"p°n.” WICIELCrº) +R.Cº-HåRøFRELn', 1 , R+—/oDC/2n” A=COt- Con, — COt- RCAEx-HL7, The quantity of the alternating current is deter- mined by A; and the value of a only affects the epoch of maximum current. If we make p=0, the effect is that of closing the circuit of ac, and we find A*= M*7,” R*-PL” This expression shows that the condenser has no effect when the current is closed. If we make p=oo, the effect is that of removing 6 the conductor y, and thus breaking the circuit. In this case A*– ; : *w- R*-t-| L –G) ( 72, Cºm, This expression gives a greater value of A than when the circuit is closed, provided 2 CLn” is greater than unity, which may be ensured by in- creasing the capacity of the condenser, the self- induction of the electromagnetic coil, or the veloc- ity of rotation. If CLn’=1, the expression is reduced to Mm A-tº- This is the greatest effect which can be produced with a given velocity, and is the same as if the current in the coil had no “electromagnetic mo- mentum.” If the electromagnet has a secondary coil outside the primary coil so as to form an ordinary induc- tion-coil, the intensity of the secondary current will depend essentially on that of the primary which has just been found. Although the reaction of the secondary current on the primary coil will introduce a greater complication in the mathemat- ical expressions, the remarkable phenomenon des- cribed by Mr. Grove does not require us to enter into this calculation, as the secondary sparks ob- served by him are a mere indication of what takes place in the primary coil. x .* & - 3. :^33 * * 2- ) *...? * r * * t * * .* - *...ſº * 2. 2 & ** # * - y TRANSACTIONS OF THE AMERICAN INSTITUTE O ELECTRICAL ENGINEERS. General Meeting, May 21st, 1890. PRACTICAL ASPECTS OF THE ALTERNATING CURRENT THEORY. BY M. I. PUPIN, PH. D. of Columbia College, (REPRINT FROM ISSUE OF JUNE AND JULY, 1890.) OFFICERS AND MEMBERS OF THE COUNCIL 1891-92. PRESIDENT: ALEXANDER GRAHAM BELL. Term expires 1892. PAST-PRESIDENTS : DR. NORWIN GREEN, 1884-5-6. EDWARD WESTON, 1888-9. FRANKLIN L. POPE, 1886-7. PROF. ELIHU THOMSON, 1889-90. T. COMMERFORD MARTIN, 1887-8. PROF. W. A. ANTLIONY, 1890-91. YICE-PRESIDENTS : FRANCIS B. CROCKER, TIIOMAS D. LOCKWOOD, Term expires 1892. Term expires 1893. FRANK J. SPRAGUE, CARL HERING, *. Term expires 1892. Term expires 1893. JOSEPH WETZLER, WILLIAM J. HAMMER, Term expires 1892. Term expires 1893. MANAGERs: DR. F. BENEDICT HERZOG, HORATIO A. FOSTER, Term expires 1892. Term expires 1893. Dr. W.M. E. GEYER, H. WARD LEONARD, Term expires 1892. Term expires 1893. H. C. TOWNSEND, DR. LOUIS BELL, Term expires, 1892. Term expires 1894. FRANCIS R. UPTON, HERBERT LAWS WEBB, Term expires 1892. Term expires 1894. J. C. CHAMBERLAIN, PROF. ALF1teD G. COMPTON, Term expires 1893. Term expires 1894. P. B. DELANY, JAMES HAMBLET, Term expires 1893. Term expires 1894. TREASUR.E.R. 3 SECRETARY : GEORGE M. PHELPS, RALPH. W. POPE 150 Broadway, New York. 12 West 31st St. New York. Terms expire 1892. BOARD OF EXAMINERS: W. B. WANSIZE, Chairman. GEORGE A. HAMILTON, E. T. BIRDSALL, C. O. MAILLOUX, EDWARD P. THOMPSON. A £after read before the American Institute of Electrica/ Engineers, Boston, May 21, 1890. PRACTICAL ASPECTS OF THE ALTERNATING CURRENT THEORY. By M. I. PUPIN, PH. D. The title of this paper indicates that I propose to consider that part of the alternating current theory only which refers to machinery that has stood the test of practical experience, namely, the alternator and the transformer; the telephone is only a special case of these two machines. That very eminent English physicist, Lord Rayleigh, remarked once that the introduction of alternating current machinery into commercial use would have the salutory effect of elevating the ideas of electrical engineers above the mere conceptions of volts and amperes. His prophecy has been fulfilled—sooner perhaps than he expected. The true electrical engineer of to-day is just as familiar with the exact meaning of impedance, co-efficients of self-induction and mutual induction, difference of phase, static and viscuous hysteresis, etc., as he was with volts and amperes at the time when that severe but well meant remark was made by Lord Rayleigh. There may be, perhaps, several old lessons which he has yet to learn; if so, he must learn them from teachers of considerably wider experience than I can pretend to possess. Not to teach the subject of our discussion, but to analyze it, is the object of this paper. Every one of us knows the very important part which the theory of the continuous, steady current plays in the construction and running of the continuous current machinery. This theory is and always was very popular with the electrical engineer. He never looked around for a better guide in his practical work. It can be safely assumed that this popularity of the theory with practical men was chiefly due to the fact that the theory is very simple. We have here a very simple and well established funda- G 2 PUPIN on ALTERNATING OURRENT THEORY. [May 21, mental law, the Ohm’s law namely, and most of the other relations of which this theory treats are deduced from this law by simple algebraical operations. Simplicity is the soul of truth, compli- cated relations are always suspected. There are many practical engineers to-day who look upon the theory of the alternating current with considerable suspicion. It seems to them to be too complicated and artificial. They also complain of a lack of sufficiently well defined distinctions between fundamental laws and arbitrary assumptions. In fact, this is the face which the alternating current theory, such as given in most of our text books, presents to every one who is not in a position to consider the subject critically, and go just a little bit beyond the badly selected limits of some of our standard text books. There is, therefore, a strong disposition on the part of some engineers to doubt the importance which others attach to the alternating current theory. If the following discussion should succeed in contributing even a small share towards the work which must be done in order to dispel these doubts, I shall be satisfied. The features of the alternating current theory which I propose to point out with particular emphasis are the following: FIRST : This theory, just like the theory of the steady current, rests on a very simple and well established fundamental law of which Ohm’s law is only a particular case. SECONDLY : All the simple relations of which the theory treats are deducible from this fundamental relation by easy mathemati- cal operations. THIRDLY: Problems arising in the practical running of alter- nating current machinery are readily solved by considering the modifications which the exact but ideal relations of the theory must undergo under conditions which we meet in practice. Let us consider a magnetic field made up of permanent mag- nets, electro magnets, closed circuits with steady or variable cur- rents flowing in them ; the magnets and the conductors may be at rest or moving in any continuous manner whatever. Let us next fix two points A and B on one of the conductors. Let now E. denote the electro-motive force in A B due to self- induction. - Let Ein denote the electro-motive force in A.B due to induction between AB, and the rest of the field. - Let E, denote an electro-motive force impressed upon AB in some way or another. 1890.] PUPIN ON ALTERNATING OURRENT THEORY. 3 Let D denote the drop of the potential between A and B; then at any moment we have (E.)+(En)+(D)=(E). This is the fundamental law of the alternating current theory. It is easily seen that Ohm’s law is only a particular case of this fundamental relation. I have enclosed the symbols in paren- thesis to denote that the absolute sign of each quantity is for the present left undetermined. Just as the laws which govern the motions of the celestial bodies are all deducible from the single Newtonian law of gravi- tation, so all the laws governing the generation and the distribu- tion of alternating current energy are deducible from that same fundamental law. The historian tell us that it took Newton twenty years to deduce his law of gravitation. It took more than one Newton to establish our fundamental law, and their labors extended over a period of more than thirty years. These Newtons of electricity were Ampère, Faraday, Lenz, Joseph Henry, F. Neumann, Helmholtz, Thomson and Maxwell. A short critical review of the labors which led to the final formulation of the above fundamental law will not be out of place here. Oersted’s discovery was made in 1820; Ampère's and Arago's investigations of the magnetic properties of a steady electric current were brought to a close in 1823. The result of these investigations were embodied in the great work of Ampère: Theorie des Phemomenes Electro-dynamique. About this work immortal Maxwell speaks as follows: “The whole, theory and experiment, seems as if it had leaped full grown and full armed from the brain of the Newton of electricity. It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deducted and which must always remain the fundamental formula of electro- dynamics.” The fundamental formula to which Maxwell refers is the well known differential law of Ampère. This statement Maxwell made before 1873; in 1874 Professor Helmholtz showed that it must be somewhat modified; for he pointed out for the first time that several other fundamental laws lead to the same integral law as the fundamental formula of Ampère. The in- tegral law is the well known law which expresses the equivalence between a simple magnetic shell and a certain steady electric current. This integral law has been verified by all experimental experience of the last seventy years. It forms the basis of the 4 PUPIN ON ALTERNATING OURRENT THEORY.. [May 21, electro-magnetic units which we use in our electrical measure- ments. The next advance was made by Faraday in 1831, eight years after the publication of Ampère's discoveries, and a gigantic advance indeed it was. If we consider Faraday's discoveries in electro-magnetic induction from the stand-point only that they supplied the electrical science of his day with additional experi- mental facts they would fall very short indeed of the importance which is to-day, and that too very justly, as we all know, attributed to them. It is the experimental method and the scientific reason- ing by means of which Faraday arrived at his brilliant discover- ies, and the view which he formed of the new phenomena that raises his work to that supreme importance to which among all the physical investigations of this century one only can aspire. I refer, of course, to those investigations which led to the final formulation of the Principle of Conservation of Energy. Faraday’s discoveries found immediate appreciation in the scientific world. The view, however, which he had formed about the phenomena discovered by himself, made but a feeble impression upon his contemporaries. It was too novel, and the minds of the physicists of his time were strongly polarized by the irresistible mental force of Ampère, Poisson, Green, Gauss and Weber. At that time Thomson had only just mastered his a b c, and Maxwell was born in the same year in which Faraday published his first investigations on electro-magnetic induction. The first attempt to formulate the laws which underlie all phenomena of electro-magnetic induction is contained in Lenz's discovery of the well-known rule that the direction of the currents induced in a conductor which moves in a magnetic field is always such as to oppose the motion which produces them. This discovery was made in 1834, the same year in which Faraday discovered the phenomena of self-induction. Joseph Henry's in- vestigations on induction in general and self-induction in par- ticular covered the period between 1832 and 1840. It is needless to say that these investigations form a necessary and a beautiful supplement to the investigations of Faraday. The resolution passed a short time ago by the American Metrological Society, to the effect to name the unit of self-induction after Joseph Henry is very appropiate and deserves the heartiest support of all elec- trical engineers. The final mathematical formulation of the law of what is to-day called mutual induction is due to F. Neumann, 1890.] PUPIN ON ALTERNATING OURRENT THEORY. 5 and is contained in his memoirs submitted to the Berlin Academy in 1845 and 1847. It was soon recognized that, since self-induction is only a special case of mutual induction, that the mathematical form of the fundamental law of self-induction must necessarily be a modification only of that of mutual induction. Maxwell. therefore, says this of Neumann: “We may regard F. Neumann, therefore, as having completed for the induction of currents the mathematical treatment which Ampère had employed for their mechanical action.” s This statement of Maxwell contains more than one is apt to get from it at a glance. In Neumann just as in Ampère the mathematician predominates. That both belong to that school of mathematical physicists whose representatives are LaPlace, Poisson, Green and Gauss. Just as these great analysts had deduced most of the laws of electrostatics from the properties of a single function, the potential function, so Neumann succeeds in deducing the fundamental laws of electro-magnetic induction from the properties of a single function, the electro-dynamic potential. But neither were they nor was he at that time aware of that perfectly definite physical meaning which these functions enjoy to-day. This was pointed out for the first time by Helmholtz, and later on also by Sir William Thomson, the discoverers of the Principle of Conservation of Energy (in 1847), the fundamental principle and the infallible test-tone for all the laws of physical sciences. It is to these two men that we owe the introduction into theoretical physics of that most intelligible of all physical quantities, namely, energy and work, in place of mathematical symbols. With them, electrostatic potential of Poissen, Green, and Gauss, and the electro-dynamic potential of Neumann meant work; induced or any other kind of current was simply an evidence that some sort of work is being done upon the conduc. tor. Their investigations extending from 1847 to 1853 showed clearly that the laws of electro-dynamic induction as formulated by Neumann on the basis of Lenz’s discoveries was not only in full harmony with the Principle of Conservation of Energy, but that moreover this principle enables us to deduce these laws directly from the discoveries of Oersted and Ampère. This would seem to indicate that Faraday's discoveries were simply a welcome experimental confirmation of the laws which could have been deduced independently of these discoveries, and that they were therefore not essential to further progress of the 6 PUPIN ON ALTERNATING OURRENT THEORY.. [May 21, electrical science at the time of Ampère. Maxwell, however, pointed out the real importance of Faraday’s work. In 1856, only two years alter he had graduated from the University of Cambridge, with the highest mathematical honors, appears his first research on Faraday's lines of force, and in 1865 already appears his great memoir, entitled: “The Dynamical Theory of the Electro-Magnetic Field.” In these researches, and especially in his great treatise on Electricity and Magnetism, Faraday's dis- coveries, especially those on Electro-Magnetic Induction, appear to the scientific world in an entirely new light. It is on the basis of these discoveries and the view which Faraday had formed of them that Maxwell formulates the most general statement of the laws of induction. It is in the form in which the laws of electro- magnetic induction were first stated by Maxwell that they are generally known to the electrical engineers. This form not only expresses the law but also suggests the view which Faraday had formed about electro-magnetic induction, which view, as we all know, has led to some of the greatest discoveries in electricity during the last 25 years. The fundamental law which underlies the theory of the alter- nator and the transformer, is a convenient statement of these laws of electro-magnetic induction. The terms employed in this state- ment as we all know, bear a definite relation to the co-efficients of self and mutual induction, and these again depend in a perfectly well understood manner on the nature of the substances which form our magnetic field. The laws of electro-magnetic induction have been verifted by every electrical eaſperiment of the last forty years. They are as true as any one of the physical laws known to us, and we see therefore that since the basis of the alternating current theory is an immediate inference from the general laws of electro-magnetic induction, that this basis is as firmly established as the basis of any other department of theoretical sciences. Meat we have to consider some of the most important conse- quences which have been deduced from the above fundamental Telation. Let us take the simplest case; an alternator such as the one used by Joubert in his experiments. No iron in the armature coils, constant strength of the field magnets, constant speed of rotation. If the poles of the machines are not connected we get from our fundamental relation that the electro-motive force due to mutual induction between the magnetic field and the armature 1890.] PUPIN oN ALTERNATING OURRENT THEORY. 7 is equal to the impressed electro-motive force. Simple considera- tions lead us at once to the conclusion that the impressed electro- motive force is a sine function of the time, its maximum value that is its amplitude depending on the strength of the field mag- nets, the speed of rotation and the construction of the armature coils. Let us now connect the poles by a non-self-inductive resistance such as a series of lamps. A simple mathematical operation gives us complete account of the current generated. It is, just like the impressed electro-motive force, a sine function of the time, but its phase differs from that of the impressed E. M. F. by an angle which increases with frequency and self induction, but diminishes with resistance. The relation between the cur- rent and electro-motive force is no more as simple as that given by Ohm’s law. Instead of the resistance we have the impedence. In fact, as the reversals increase more and more the influence of the resistance upon the growth of the current becomes smaller and smaller, and in place of the effect of the resistance the effect of the co-efficient of self-induction forces itself into prominence. The total electrical energy produced in a unit of time is expressi- ble in a great variety of ways. In terms of maximum impressed electro-motive force, impedance and resistance; or in terms of mean current and mean effective electro-motive force; or in terms of mean current, mean impressed electro-motive force and the cosine of the difference in phase, or again in terms of the square roots or the mean squares of the current, and of the im- pressed eleetro-motive force. These relations between the total electrical energy produced and the other electrical quantities enable us to construct certain curves which suggest easy experimental methods of testing the truth of our deductions. These experiments were carried out by Joubert of Paris, Professor Stefen of Vienna, and Esson of England, and it was found that our theoretical inferences were completely verified. For full references consult Sylvanus Thom- son: “Dynamo Electric Machinery,” and the very excellent work of Professor Kittler “Handbuch der Electro-Technik, Vol II., Part 1.” This perfect agreement between theory and experiment will surprise no one who is acquainted with the working of Hughes induction balance, with experimental methods of determining the coefficients of self and mutual induction, and with the beautiful 8 PUPIN ON ALTERNATING OURRENT THEORY.. [May 21, induction experiments of our learned ex-President, Professor Elihu Thomson. All these beautiful experimental designs are also inferences from our fundamental relation, inferences con- siderably more ingenious but also considerably less direct than the inferences which we have considered in the simple case just discussed. - We next consider the energy which is available in the external circuit. This is the part of the energy which is for sale, and it is well to inquire what means we have in determining the cost of production under conditions as simple as the above. If the con- ductors through which we send our current to the consumers have no self-induction, as is generally the case, the task is ex- tremely easy. Simple analytical deductions from our funda- mental law suggest the watt-meter, the electrometer, and a variety of other instruments whose indications depend either on the heating or on the magnetizing effect of the alternating cur- rent. With reference to this point we can consult several very excellent works like Grey’s Electricº Measurements, Ayrton and Perry’s Practical Electricity and Kittler's Book. Our methods of measurement in this simple case are exact de- ductions from an exact fundamental law and can be made in practice as exact as we choose to make them. With reference to watt-meter it is well to observe that under certain conditions, not at all difficult to realize in practice, it can measure the output of a machine even if the current does not follow the simple sine law. With regard to this point I refer you to investigations of Professor Stefen of Vienna, pub- lished in the reports of the Vienna Electrical Exhibition in 1883. Let us now make the next important step in our discussion. We’ll consider now the transformer under the following simple conditions: There are no Foucault currents nor hysteresis in the core of the transformer and the relation between the strength of the primary current and the mass of the iron core is such that the magnetization of the latter never approaches the saturation point. It seems desirable to work out this case analytically and at somewhat greater length. - Let L be the co-efficient of self-induction of the primary coil. {{ AW 46 {{ {{ { % secondary {{ “ M “ & 4 mutual induction. “ R “ resistance of the primary coil. S “ {{ “ secondary coil (both external and internal.) 1890.] PUPIN ON ALTERNATING OURRENT THEORY. 9 Let a, be the current of the primary coil 46 3/ 46 & 4 {{ secondary € $ Our fundamental relation (E.)+(Em)+(D)=(E) | at any moment. will now be L % + M # + R w = E, sin 2net for the primary coil. Nº + M º + Sy=o “ secondary “ E, is the amplitude of the electromotive force impressed by the alternator upon the poles of the primary coil of the trans- former. ~, Our object is to express a, and y in terms of the known quan. tities L., M, W, R, S and t. We proceed in exactly the same way as in the solution of simultaneous equations in Algebra. We simply eliminate one of the unknown quantities, either a or y, and obtain a single equation containing only the other unknown quantity. Seeing that we have not a sufficient number of equa- tions to do that we differentiate again and obtain two more equations, viz.:- 6/? 2 d Zºº i Mºi º –– was E. coºrs. d°y 0%; dy From these four equations we eliminate a and its differential coefficients and obtain, putting 272 = p. 2 - (LN – M*) º +(LS+ WR) %+ RSy = —p E, M cos pt. (1) This relation between the current in the secondary coil and the other quantities must subsist at every moment, and therefore also when t = 0. We have then 67? d *. (Ly–M) [º]. - (Zs-NR) (#). Esq.), The suffix zero along the parenthesis denotes that the value of the quantity enclosed in the parenthesis is to be taken at the time Zel’O. To one dealing with abstract mathematical symbols equation (1) would present considerably serious difficulties of working out the details of his solution. But to you who are dealing with physical things, and to whom every symbol in equation (1) pre- 10 PUPIN ON ALTERNATING OURRENT THEORY.. [May 21, sents something that you have handled for years and years, you can put down the solution of (2) at once. Here it is * 9 = A2 Sin 27t (2t — pº). (3) The only thing that is unknown in this equation yet is the con- stant As. It is evident that it is some function of the constants L., M, M, R, S, E, p and t. We can determine it from equation (2) as we shall presently see. There is one point which I wish to emphasize particularly at this stage of our discussion, and that is the marked difference between abstract mathematical opera- tions and those mathematical operations which are employed in the discussion of physical problems. The abstract mathematician is necessarily more or less indifferent to the physical meaning of his symbols; the mathematical physicist is more fortunate. The physical meaning of his mathematical symbols makes his mathematical operations comparatively easy. Let our example illustrate this feature of mathematical physics. Consider two telephones; one acting as a receiver and the other as a transmitter. We can construct and connect them in such a way, that they will resemble in every particular our example, namely the transformer in series with the alternator. In the case of these telephones the impressed electromotive force is a har- monic function of the time, the same harmonic function which describes the motion of the diaphragm plate of the transmitter. Now since in the receiving telephone we hear the same sound which is acting upon the diaphragm of the transmitter we con- clude that the induced current which causes the vibrations of the diaphragm of the receiver is the same harmonic function as the impressed E. M. F. This induced current corresponds to our current y. Therefore, the secondary current of the transformer is the same function of time as the impressed E. M. F. This con- sideration enables us to put equation (2) down without going through all the mathematical steps which the pure mathematician would have been obliged to make before arriving at that equation. (NotE:—If the E. M. F. which the alternator supplies to the transformer had been of the form 2. An sin 27tent —– 2 Bn cos 27tznt. the induced current would evidently be of the form gy = 2 aa sin 27 (n2t — pa) + 2 C, cos 27t (n2t — pa) where 2 an sin 27tant stands for a sin 27tzt -- a, sin 4t2t + as sin 612t + - - - - - a, sin itnet and a1, as, ---- an ºn are constants to be de determined in the same 1890.] PUPIN ON ALTERNATING OURRENT THEORY. 11 way as we are presently going to determine our constant A2. The same remark applies to the other summation symbols.) The determination of the constants A, and p, is a simple alge- braical operation. From (3) we have (y), - – A2 sin 27tpg [v] = A2 cos 27tp, * = 4. (#) = p A2 cos 27:49, (#) = p A2 sin 27tp, O t = 4. 4 2 - (#) =p” As sin 27tps (#) = -— p" As cos 27tp, O * = 4. 4 and therefore As {[p (LAW — M)—RS] sin 27tp, + p (ZS +AVIP) - cos 27:42,; = p ME, or As a sin 27tp, + b cos 27tps: = p ME, from (2.) - As (a cos 27tps — b sin 27tp:) = 0 “ (2) Q, The second of the last two equations gives tan 2 it p = j = * ( / W. M*)—A' S ; # S–H. He ºw, From the first we get, considering that sin it ps = *= *** * = *== Woº-E 5* 4/a”-- bº A, - £4 4 . 4/ a” + b, a" + b = p (IA Wº-2 M* L W-- M*) -- 2p* R S M* + Rº = p^ Lº (Sº + p” M*)—2 pº M? L W-L pºllſ* -- Fº S? + p" W*) + 2 pº R S M ) ) is ſ pºM*N ) * p"M*S )* 2 2.2 7772 =} [1-4.) +[º]''' (sº | = (S* + p” W*) (R* + p^ Lº) - Hence: As = p M E 2 — *mºmºrs *-*-*m. WS” + p^ W. W.R.L.I. Proceeding in exactly the same way, we get for the current in the primary winding: 12 PUPIN ON ALTERNATING OURRENT THEORY.. [May 21, * = ** Where tan 2 it p, = p + - Fºl This gives us a complete analytical solution of the ideal trans- former. We can assume with perfect safety that the number of electrical engineers is very small indeed who will consider the analytical process through which we have just gone through as very difficult, and yet it is one of the most difficult mathematical processes which we meet in that part of the alternating current theory which I proposed to discuss, and which at the present time is of immediate interest to all practical engineers. You may, perhaps, ask: But what has this mathematical analysis to do with the practical aspects of the alternating current theory ! Simply this: it bears upon the question whether the alternating current theory is or is not entirely within the reach of most of the electrical engineers, and this question is of eminently practical importance. I considered the mathematical problem of the ideal transformer for the purpose of showing that its consideration does not involve any difficult mathematical operations, and not for the purpose of establishing and discussing the well-known relations between the various quantities which we just obtained. Any further consider- ation of the problem seems therefore superfluous. The question of the efficiency and self-regulation in the case of a transformer of this kind is, as we all know, a very simple one, and can be answered at once from the above relations. - The third point which I propose to consider was this: What are the modifications which must be introduced into the relations so far obtained ºn order that our calculations should cover also conditions under which the alternator and the transformer are oworked in practice. In order to get these practical conditions we have to drop one by one, several of the suppositions on which our calculations so far have been based. The first of the suppositions was that the effective magnetic field of our alternator was a simple harmonic one; the second supposition was that the armature coils contained no iron. The immediate consequence of the removal of these two suppositions will be that the impressed electro-motor force. of the alternator will no longer be a simple sine function but a more complicated harmonic function of the time. The same is sin 2 it (et— 9.) 1890.] PUPIN ON ALTERNATING OURRENT THEORY. 13 true of the current, and it is evident from the remark made above in connection with the analytical consideration of the ideal transformer that the current will be expressible by a harmonic function of the same form as that for the impressed electro-motive force. Since the coefficients of induction are now much larger on account of the presence of iron in the armature coils the differences in phase between impressed electro-motive force and the current will be larger than without iron in the armature. Dropping now our third supposition that the magnetic permea- bility of iron is a constant quantity we infer that since for higher magnetizations this coefficient becomes smaller, that the differences in phase will be smaller than calculated for constant permeability. Dropping finally our last hypothesis, namely, that there are no Foucault currents or hysteresis we introduce a further modifica- tion into the values of our coefficient of induction and conse- quently also into the differences of phase. The same remarks ap- ply to the transformer also. In what direction these modifications will effect the efficiency of our machinery is a question familiar to all of us. A complete general mathematical treatment of the alternator and the transformer is in the present condition of our knowledge of the magnetic properties of iron an impossibility; but fortunately for us such a treatment would also be more or less superfluous for practical purposes. Thanks to the profound investigations of Rowland, Hopkinson, Ewing, Warburg, Bidwell, and others, we know just enough of the magnetic properties of iron to enable us to obtain a very approximate solution of the most general form of our problem. On this point we can con- sult the well-known excellent investigations of Blakesley and Fleming and especially of Hopkinson, Kapp and Ferraris. The graphical methods of Blakesley and Kapp are very valuable. This solution of the general problem has been tested experimen- tally by Ferraris, Hopkinson, Ayrton and Perry and others and found to give a satisfactory account of the phenomena which actu- ally take place in the practical working of the transformer. The very valuable experimental investigations of two members of this Institute, Dr. L. Duncan of Johns Hopkins University, and Mr. Ryan of Cornell, we all know and appreciate; they afford us an excellent illustration of a fact which deserves a serious considera- tion on the part of every true electrical engineer, and that fact is that electricians whose methods of investigation show a perfect mastery of the theory can design and carry out experiments of 14 PUPIN ON ALTERNATING OURRENT THEORY. [May 12. eminently practical nature. The secret of it is that there is actually no real difference between the theoretical and the practical side of electricity. As to the question of insulation of wires carrying high tension alternating currents, well, we know Sir W. Thomson's opinion on this point. All these considerations which I could only point out here, but whose complete discussion can be easily gathered from the cur- rent electrical literature, seems to me to justify the following conclusion: The generation and distribution of alternating cur- 7'ent energy is based on as simple a theory as any other form of energy. The agreement between theory and practical eaſperience às so perfect that the two form necessary supplements to each other. Wo difficulty was ever met in practice which the theory did not point out, and no difficulty which the theory can point out is beyond the reach of skilled practical engineers. There is therefore not the slightest ground on which objection could be Taised against the commercial use of this form ºf energy. Standing Committees appointed by direction of Counell: Editing and Library Committee. * GFORGE A. HAM II.TON, JO. STAN FORD BROWN, FRANKLIN L. POPE, Editing. GEORGES D'1N FREV II.L.F., | Library. |FRANCIS B. CROCKER. GEORGE H. S1’ OCKBR] I)GE. Committee on Membership, etc. * - RALPH. W. POPE, Chairman. THOMAS D. LOCKWOOD, Lºcal Secretary, Boston, Mass., Dr. LOUIS DUNCAN, Baltimore, Md., CARL HERING, { % &# Philadelphia, Pa., Prof. EDWARD L. NICHOLS, “ § { Ithaca, N. Y., Prof. W. A. ANTHONY, ${ { % Manchester, Ct. JOSEPH WETZLER, New York, GEO. B. PRESCOTT, Jr., New York. Committee on Finance, Building and Permanent Ouarters. GEORGE M. PHELPS, Chairman. GEORGE A, HAMILTON, DR. SCHUYLER. S. WHEELER, THOMAS A. EDISON, FRANKLIN L. POPE, FRANCIS R. UPTON, T. COMMERFORD MARTIN, DR. F. BENEDICT HERZOG. Committee on Papers and Meetings. T. C. MARTIN, Chairman. GFORGE M. PHELPS, JOHN W. HOWELI, HUBERT HOWSON, DR SCHUYLER S. WHEELER. HERBERT LAWS WEBB, H. WARD LEONARD, Prof. FRANCIS B. CROCKER. Committee on Units and Standards. A. E. KENNELLY, Chairman. GEO: B. PRESCO I'T, Jr., GEO. A. HAMILTON, DR WM. E. GEYER, FRANCIS B. CROCKER. Transactions of the Institute Already Published. [Complete sets of the first four volumes are out of print.] Vol. V, 1887–8. ON FLEctric STREET CARs, witH SPECIAL REFERENCE To METHops of GEARING. Anthony Reckenzaun, of London. No. 1, October, 1887—A Coulomb METER, or INSTRUMENT FOR MEASUR- Ing. The Cossump rion of Eli.ECTRICITY. (Illustrated ) Prof George Forbes, F.R.S.. of London. No. 2. November, 1887—RECENT IMPRove MENTS IN APPARATUS For OCEAN CABLING (Illustrated.) Charles Cuttriss. Supplementary Note on the Siphon Recorder, and Ocean Telephony, by Thos. D. Lockwood. No 3, F. 18_7—PHHNoMENA of RETARD \tion IN THE INDUCTION Coil. (Illustrated.) William Stanley, Jr. No. 4, January, 1888-Revision o’ Tº PATENT L \w. Arthur Steuart, Esq. No. 5, February, 1888.--ELECTRIC ENERGY ProM CARBon WITHouT HE T. Willard E. Case, Auburn, N.Y. No. 6, March, 1883.--ALTERNATING CURREN r Ei.ECTRic Motors. Dr. Louis Ljuncan, Baltimore, Md. No. 7, April, 1888.-MAXIMUM EFFICIENCY OF INCANDEscENT LAMPs. (Illustrated.) John W. Howell. No. 8, May, 1888.--PROT cris N of THE HUM as Body *Rom D NNGEROUS CURRENTs. Patrick B. Delany.—THE Possibili:1Es AND LIMI 1 ATIONS F CHEMicAL GENER AT Rs of ELECT RIct Y. Francis B. Crocker. No. 9, June, 1888—ON CompeN- sATED RESISTANce STANDARDs. I.lustrated:) Edward L. Nichols. A New SYSTEM F Al HR- NATE CURRENT Moroks AND TRANSForMERS. (Illustrated.) Niko a Tesla. UNDERGROUND ELEC- TRICAL ConDUCTo s IN EURoi E AND AM tº ICA. Prof. G. W. Plympton. Til E P TENT C. URT AND UNIForMity IN PATENT OFFIce PRACTICE. - George H. Stockbridge. A Swing NG ARM GALvaNoMETER. (Illustrated.) George S. Moler. No. 10, July, 1888. THE Sol.t Tios of THE MUN1c1PAL RAPID T. ANSIT ProBLEM. (Illustrated ) Frank J Sprague? No. 11, August, 1888. Some objections To THE OVERHEAD CoNPUcroR F9R ELECTPIC RAILWAYS, M. B. Leonard, Note on GEARING For ELECTRIC RAILwAY Motoks, Almon Robinson. No. 12, September, 1888. Vol. VI, 1889. $ [Including October, November and December, 1888.] THE GEveR-BR1stol MeTER For DIRECT AND ALTERNATING CURRENTs. [Illustrated.] Prof. William E. Geyer. THE ABDANk_MAGNETic CALL AND THE ABDANK INTEGRAPH. [Illustrated.] E. Abdank-Abakanowicz. No. 1, January, 1889. Six YEARS PRACTICAL ExPERIENCE witH THE Edison CHEMicAL MET ER. (Illustrated.) Y's. Jenks. No. 2, February, 1889. LIGHTNING AR- Resºra Rs AND THE PHotographic STUDY of SELF-INDUCTION. (Illustrated.) E. G. Acheson. No. 3, March, 1889. A NEw SystEM of Multiplex TELEGRAPHY. (Illustrated.) Lieut. F. Jarvis Patten. Lichth IN's ARREs reks AND THE PHOTOGRAPHIC STUDY OF SELF INDUCTION. Notes by §: Stanford Brown and Chas. T. Child. REPLY TO THE NOTES OF MESS-S. BROwn AND CHILD by . G. Acheson. No. 4, April, 1889. THE EFFICIENCY of METHODS OF ARTIFICIAL ILLUMINATION. Illu trated. Faward L. Nichols. No. 5, May, 1889. SOME RESULTs witH SECONDARY BATTERIES IN TRAIN I.IGHTING. (Illustrated.) Alexander S. Brown. THE INHERENT DEFECTs of LEAD STorAGE BATT ERIEs. (Illustrated.) Dr. Louis Duncan. ELEC RIC MOTOR REGULATION. (Illus- rated.) Francis B. Crocker. Nos. 6 and 7, June and July 1889, (Double Number)., MAGNETISM IN Its Rºlation To INDUCED ELECT R Motive Fosch AND CURREN r. (Illustrated ) Prof. Elihu Thomson of Lynn, Mass. ON THE RELATION BE WEEN THE INITIAL AND The Average EFFI- ciency of INCAN DESCENT LAMPs. (Illustrated.) W. H. Peirce of New York. THE FFFICIENCY of THE ARC LvMP. (Illustrated.) H. Nakano, of Japan, with an introductory note by Prof. E. L. Nichols. THE SPIRAL Coil VoltaMETER. (Illustrated.) Harris J. Ryan, of Ithaca, N. Y. THE PERsonAL ERRoR IN PHoToMETRY. (Illustrated). Prof. Edward L. Nichols, of Ithaca, N. Y. ON ModeRN VIEws witH RESPECT to Electric Currents. (Illustrated.) Prof. Henry A. Rowland, of Baltimore. Md. Ci assified List of MEMBERs. Nos. 8 and 9, August and September, 1889, (Double Number ) No. ro, October, 1889. Som E RECENT ELt. CTRICAI. WoRK on THE F.LEva'i En RAILRoADs. (Illustrated ). Leo Daft, of Plainfield, N. J. "ALTERNATING CURRENT Mor Ors: THE Evolution of A New TYPF. (Illustrated.) Lieut F. Jarvis Patten, of New York. No. 11, No- vember, 1889. ELECTRICAL Notes of A TRANs-ATLANTIC TRIP. Thomas I). Lockwood, of Boston, Mass. Some METHops of REGULATING Accumulators IN ELECTRIC LIGHTING. (Illustrated.) George B. Prescott, Jr., of New York. No 32, December, 1889. ForMAND EFFICIFNcy of INCAN- pascent FILAMENTs. Charles J. Reed of New York. TELEGRAPH Line ADJUSTMENT:--Noth *on a New Gravity CELL, P. B. Delany of New York, --- - * s ... * *. 3. * w ºr * * - r ^- 3/ ~ * * * * w r \ º 3 * : : t { * * * J ... t " Vol. VII, 1890. * * ** - TRANsformers. Ǻ Harris J. Ryan. No. 1, January, 1899. A RRVIEw of THE Modern Theories of Electricity. (Illustrated.) Prof. W. A. Anthony. No. 2. February, 1890. THE PRActical Working of n he Electrical Subways of NEw York CITY. (Illustrated.) William Maver, Jr. No.3, March, 1890. Some TESTs on THE RFIciency of ALTERNATING current Apparatt's. (Illustrated.) Dr. Louis Duncan and W. F. C. Hasson. No.4, April, 1890. Pºgnomena of Auºte: N ATING CURRENT INDuction. (Illustrated.) Prof. Elihu Thomson. E. Ectricity in the Navy. Gilbert Wilkes, No. 5, May, 1890. ELECTRIC LIGHTING IN THE Tropics, Wilfrid H. Fleming, LIFE AND EFFICIENCY of Ang Light CARpoNs. (Illustrated) Louis B. Marks, Practical. Aspects of THE ALTERNATING CURE ENT THEORY. M. I. Pupin, MAGNEric Data of THE SPRAGUE STRFET CAR Motor. (Illustrated.) H. F. Parshall, THE in Jºsrsial Utilization of a He Countrf . ElectroMotive Force of SELF-INDUCTION, Thomas D. Lockwood. Nos. 6 and 7, June and July, (Double Number.) LIFE AND EFFICIFNCY of Arc Light Carbons Discussion. (Illustrated.}_PRACTICAL Astºcts of THE ALTERNATIN CURRENT THrory. Discussion. Notr on A NFw PhotoMETER. (Illustrated.) Dr. Edward L. Nichols of ithaca, N. Y. THE LIMITAtions of St EAM AND FLECTRIC TRANSPORT Tion. (Illus- trated.) Oscar '1'. Crosby, now of New Orleans, AUTOMATIC F : E TRIC WELDING MACHINFS, Hermann Lemp, Jr., of Lynn, Mass... Nos. 8 and 9; August and September, (Double Number.) FFFICIRNcy of TRANSFORMErs. (Illustrated.) Calvin Humphreys and W. H. Powell. NotEs upºn some ExPERIMENTs witH ALTERNATING CURRENt, APPARAtt's. (Illustrated., . Prof. Harris J. Ryan. CATALogue of MEMBERSHIP. Revised to November 1st. 1890. No. ro October. PRRLIMINARY REPort of the S ranD ARD WIriNG Ta BLE Committee. Resolutions on Apoption of AMERICAN NAM's FOR ELECTRICAL UNITs. INvestic Ation of I HE STANLEY ALTERNATE CURRENT Arc DYNAMo. W. B. Tobey and G. H. Walbridge. A NEw MET Hod of ANALYzi NG ARMA rurE REAC 1 Ions, APPLIED to the STANu Ey Arc l, Giat AttrRNATING CURE ENT MACHINE. Tho burn Reid. No. 1 1 November. REvish D REpoRt of THE STAN.) ARD WIRING TABLt. CoMMITT, E. THE THEORY OF CoMPOUND WINDING For Const vint Potenti Al. (Illus- trated ) l Jr. l.ouis Hell, of New York. A N = w \l E riot) or AN \Lyzi G A KMATURE R FACTI Ns of A L ERNA ors. Charles Steinmetz, of Yonkers, N. Y. List of New Associate MEMBERs. Elected Sept. 16th, Oct. 21st. Nov. 18 and Dec. 16th. No. 12 December. Vol. VIII. 1891. INDUCTANCE, AND its Proposed UNIT, THE “ HENRY.”, (Illustrated.) By A. E. Kennelly. THE IMPROVED GRAMoPHoNE. (Illustrated.) By Emile Berliner.' No. 1, January, 1891. INDUCT- ANCE, AND ITS Proposed UNIT, THE “ HENRY''' REPORT of Commit H.E on VALUAT ION of THE H tº NRY. Joint Discussion. No. 2, February, 1891. REPORT of HIGH S FED ELECT Ric RAILw AY Work, (Illustrated.) By O. T. Crosby. THE INventions of THoMA's DAven Port. (Illustrated.) By Frank in L. Pope. No. 3, March, 1891. INDUc I ive Disturbances in TEl E- PHoNE Circuits. (Illustrated ) By J. J. Carty. No. 4, April, 1891. ELECT Rici I y IN THE PRo- Duc 1 Ion of ALUMINIUM. (Illustrated.) By Alexander S. Brown. SoME Possible MoDIF It Al IONS 1N rhE METHODS OF PROTP CT1NG B, ILLINGS FROM LIGHTNING. By N. I.). C. Hodges. No. 5, May 1891. RF Ports’ of Council AND, TRE vst RER, OFFICERS ELFC. ED. THE PEPFECTION of SrAtios ARY ELECTRIC Motors. (Illustrated.) By Francis B. Crocker. . A PhotoGRAPHIc Study of the ELECTRic Arc. (Illustrateu.) Hy Edward L. Nichols. A NEw GRAPH ſcAL METHod of CALCULATING LEADS For WIRING. (Illustrated.) By Carl Hering. A THERMo- El Ecº Ric METHOD of STUDYING STEAM CYLINDER COND ENSATION IN ST+ AM ENGIN es. (Illus- trated.) By Edwin H. Hall. THE PRACTICAL Aspects of ELF ctric WELDING. By Freder c A. C. Perrine. ExPERIM&NTs witH ALTERNATE CURRENTs of Very High FREQUENcy. (Illus- trated ) Hy Nikola ‘I esla, Nos. 6 and 7. June and July, 1891. AN AI.TERNATE CURRENT PotRNt IoM rer. (Illustrated.) By Geo. S. Moler. Consid Frations WHICH SHOULD Govel, N THE SRLECTION OF A RAP, D ‘l R - NSIT SYSTEM. By F. J. Sprague. ELECTRIC METFRs. By Geo. W Walker. A STUDY of AN OPEN CoIL ARC DYNAMo. (Illustrated.) By Milton E. Thompson. THE FUTURE of THE AL MINIUM Pr: , H LEM. From THE CHEMICAL STANDPoin r. By Wm. H. Wahl. SH v1.1 “ALUMINUM" BE * ALT1 M.” By Oberlin Smith. N. Tes on FLECTRicity IN MINING W. R.K. (Illustrated.) By Sydney F. Walker. Nos. 8 and 9 August and September, ON THE RET ATION OF THE A 1R GAP AND THE SHAPE F THE POI.Es to Tue PERFORMANCE OF DYNAMo Flf CTRIC MACHINTERY. (Illustrated ) By Harris. J. Ryan. No lo. October, 1891. MAGN Rtic RFI.UCTAN ‘E, (111ustrated ) By A. E. Kennelly. RE, ort of CoMMITTEE on UNI is AND STANDARDs. R Port of LEUF GA rion to FRANKForT INTERNATION - L ELECTRIC vl Congress. No. 1 r. November, 1891. NoTES ON THE FRANK1 ort E. LECTRICA1, b xHIBITION. By Carl Hering. ON Pol YPHAs vL GENERATORs, (Illustrated.) By M. I. Pupin. CATALOGUE of MEM- BERS AND PUBLICATIONS, December, 1891. w Vol. IX. 1892. ON THE Law of Hysteresis. (Illustrated.) By Charles P. Steinmetz. No. 1, January, 1892. W. * Atº *...*& *** A.Ş. 3 ºr • -* º - ** Yº ########3 * *. * : - The Characteristic F eatures . of THE - • *. Frankfurt Electrical Exhibition - - - By - - . . M. I. Pluſ PIN. - Reprinted from the School. OF MINES QUARTERLY, No. 1, Vol. XIII. - *- : r") ~ /…// THE CHARACTERISTIC FEATURES OF THE FRANK- FURT ELECTRICAL EXHIBITION. PROFESSOR W. P. TROWBRIDGE, Engineering Department, School of Mines, Columtöia College. DEAR SIR.—Please accept the following report which I wrote at your request. I took the liberty of inserting a short essay on “The Theory of Polyphasal Current Systems.” In view of the fact that the subject of polyphasal generators is very new, and that, therefore, there is but very little in the electrical literature to aid us in the study of this exceedingly interesting department of electrical engineering, I thought that the insertion of the above-mentioned essay would prove useful. We are both under great obligations to Mr. Freedman, John Tyndall Fellow of our college, for the pains which he has taken in preparing the diagrams contained in this report. Very respectfully, M. I. PUPIN. THE work of the historian of the Science of Electrotechnics is to a great extent already done in the official reports of the various electrical exhibitions. Each oné of these reports contains a care- fully prepared account of all the advances in electrotechnics accomplished since the preceding exhibition. The future histor- ian of electrotechnics will not fail to observe in his study of these reports that each electrical exhibition had its characteristic features, which were but the reflections of the characteristic fea- tures of the science of electrotechnics at that time. A mere glance at the electrical exhibitions of the last forty years will convince us of the truth of this statement. The London Exhibition of 185 I shows the exhibits relating to telegraphy as the only remarkable practical electrical exhibits. The London Exhibition of 1862 showed but a slight advance in this line. The Paris Exposition of 1867 boasts of the first public exhibition of a dynamo-electric machine. (The dynamo-electric principle was first clearly announced by Dr. W. Siemens, of Ber- lin, on January 17, 1867.) The Vienna Exposition of 1873 was the first at which large dynamos were shown in actual operation of producing light and performing other kinds of useful work. These were the machines of Siemens, of Berlin, and of Gramme, the well known Belgian engineer. The electrical exhibits of the Centennial Exposition in 1876 are to a considerable extent but a \ *- 38 THE QUARTERLY. repetition of those of Vienna. There was, however, one exhibit whose importance was not fully recognized at that time; it was Alexander Bell's telephone. The Paris Exposition of 1878 first demonstrated the superior power of the new science, the science of electrotechnics. There was a complete electric lighting plant; the lamps employed were the so-called Jablochkoff candles. The telephone, exhibited here, was no longer a mere squeaking electrical curiosity, but a perfectly operating physical apparatus, whose prac- tical importance was evident to everybody. The Paris Electrical Exposition of 1881 was a magnificent affair. There were over a thousand exhibitors, and among them some of the greatest inven- tors of the century, as, for instance, Edison, Bell, Siemens, Sir W. Thomson, Gramme, Brush, etc. The practical applications of electricity were shown on a huge scale, especially those relating to electric lighting and electric deposition of metals. Edison's system of incandescent lighting, and Bell's system of telephony were the characteristic features of the exhibition. Other electrical exhibitions followed in rapid succession; suffice it to mention only the Electrical Expositions of London (1881), Munich (1882), Vienna (1883), Turin (1884), London Inventories (1885), Philadel- phia (1888), Berlin (1889), Paris Exposition (1889), Edinburgh (1890). Every one of these had its characteristic features in the form of some important advances, whose practical value was tested there publicly for the first time. Among these important advances suffice it to mention the storage of electrical energy, elec- tric railways, electric propulsion of steamboats, electric transmission of power, transformation, on a large scale, of electrical energy from high tension to low tension, and vice versa, utilization of alternating currents for lighting, etc. The interesting and very important question arises now : What are the characteristic features of the Frankfurt Electrical Exhibi- tion ? In other words, what new information will the future his- torian of electrotechnics gain from the official records of the Frankfurt Electrical Exhibition ? The answer to this question seems plain to every intelligent ob- server who has had the rare good fortune of visiting the exhibition and feasting, intellectually, upon the goodly products exhibited there by the science of electrotechnics. The various exhibits were arranged in such a way that one could obtain almost at a glance a complete survey of all the applications of electricity in any one of the * * rº THE FRANKFURT ELECTRICAL EXHIBITION. 39 various departments of applied sciences and arts, as architecture, civil engineering, mechanical engineering, chemistry and metal- lurgy, sanitary engineering, mining engineering, dentistry, surgery and therapeutics, naval and military Science. Looking upon these exhibits, one could not help seeing in his imagination the vigorous young science of electrotechnics, like an ardent and ambitious youth, strong in arm and quick in limb, with broad shoulders and manly chest, with healthy cheek and luminous eye, with sleeves rolled up and the loins girded for arduous work, a ready, willing, and indispensable assistant of all the older sciences, and more than a mere assistant, a genial companion whose very presence encour- ages them to new efforts and to new spheres of action. One can therefore safely assume that the success of the Framéfurt Exhibition in representing electrotechnics as a very important factor in all tech- nical sciences, will be considered by the future historian of electro- technics as one of the characteristic features of the exhibition. This success was in a great measure due to the men, also, who displayed a particular interest for the exhibition, for they were by no means limited to the electrical profession. Every engineering and scien- tific profession was well represented there ; to prove this, one has only to refer to the list of officers and members of the exhibition, and also to the men whom one had the pleasure of meeting at the Electrical Congress. In discussing at this congress the question of what the training of an electrical engineer should be, W. von Siemens, of Berlin, spoke as if he had been inspired by this char- acteristic feature of the exhibition, for his opinion was that every scientific profession needed a thorough training in electrotechnics, and especially in those parts which have a direct bearing upon each par- ticular profession, whereas additional efforts in higher scientific pur- suits and a life-long practical experience may finally succeed in producing what is usually called an electrical expert. Whose opin- ion on this point is more valuable than that of W. von Siemens, of Berlin P The second characteristic feature of the Frankfurt Exhibition was the size of the electrical generators and their coupling to the steam-engine. Rope and belt transmission looked very much out of place, so numerous were the generators with direct coupling to the steam engine. This is especially true of the larger type of generator, as, for instance, the 600-horse power alternating current generators of Siemens, and the generators of the electric company 4O THE QUARTERLY. “Helios,” of Frankfurt, etc. It seems proper to mention here that F. G. 1 P /\ & Cº. – O E = ?--- TS } Mºs —e. W N- J z- – the writer saw at the great Deptford electric light station, near London, the completed parts of what he was told to be a future # THE FRANKFURT ELECTRICAL EXHIBITION. 41 Io,000-horse power (!) alternating current generator of the Fer- ranti type, which is also to have a direct coupling. Considering that only nine years ago the largest dynamo at the Munich Elec- trical Exposition was an Edison dynamo of about 25-horse power, one cannot help marvelling at the wonderful success of the science of electrotechnics." It seems needless to observe that this direct coupling of the generator to the steam-engine has called into existence new and very superior types of steam-engines. The third and most important characteristic feature of the Frank- furt Electrical Exposition was the Lauffen-Frankfurt Transmission of about 300-horse power of electrical energy over a distance of 175 kilometers (about I I5 miles) through what one may call ordi- nary telegraph wires. This part of the exhibition was a huge ex- periment to demonstrate before the anxious eye of the scientific world that the alternating or wave form of the electrical currents can accomplish easily what engineers sought in vain to accomplish by the direct electrical current. In view of the eminent economic and scientific importance which is attached to this latest advance in the science of electrotechnics it seems proper to give a more detailed account of this feature of the Frankfurt exhibition. THEORY OF THE THREE-PHASE SYSTEM OF ALTERNATING CURRENTs. A brief explanation of the invention to which the above-men- tioned success is due will not be out of place here. Fig. I represents a ring which rotates uniformly in the field of force of the magnet NS, a, b, c, are three equal turns of wire wound around the ring at angular distances of I2O’ apart. For the sake of simplicity assume the magnetic field to be uniform and the ring made of a non-magnetic material, say wood. Call the plane through PP' perpendicular to the field the plane of sym- metry. Consider the loop “a” when it is at the angular distance 6 from the plane of symmetry. Let M = intensity of the field. A = area of the loop. M = number of lines of force passing through the loop. w = angular velocity of rotation. 42 THE QUARTERLY. It is evident that at the angular distance 8 AW = MA cos 69. Electromotive force generated in the loop “a” at the moment t, where 8 = wt * = , = 4 (MA cos 8) = K sin 8 ---. dź dt where K is a constant. The electromotive forces in “b ’’ and “c” at the same moment t will be, respectively, e, H K sin (8 + 120) es = K sin (8 + 240). Since sin 8 + sín (8 + I2O) + sin (6 + 240) = o it follows that ei + e, + es = 0. Now two loops are always on the same side of the plane of sym- metry, hence the electromotive forces generated in them will have the same sign; their sum with opposite sign will be equal to the electromotive force in the 3d loop. In Fig. I el and e, have the same sign at the moment t whereas es has the opposite sign and is numerically equal to el + es: Add now to “a” n more turns all connected in series so as to form an open coil. Let a be the angle between two consecutive turns. Let ei, e, . . . . en be the electromotive forces generated in the turns I, 2, 3, . . . . n. It is evident that e = K sin 8 e, H K sin (6 + [n — II a. The resultant electromotive force in this coil a will be El, where E = e, + ex + . . . . -- en. & It follows, therefore, from a well known formula in trigonometry that THE FRANKFURT ELECTRICAL EXHIBITION. 43 A sin { 6 –– *} sin . = E, sin (8 + 3) sin 2 where E, and 6 are constants. The electromotive force generated in the coil a is, therefore, a simple sine function, or to use a more technical expression, it is a simple harmonic. Add now the same number of equal and similarly placed turns to “b" and “a” and we shall have three equal and similarly placed open coils. Let E, denote the electromotive force in coil 2 and E, that in coil 3. It is easily seen that t E. = E, sin (6 + 3 + 120°) E. = E, sin (6 -H 3 + 240°). Therefore at every moment E. H. E., + E. = o. The three electromotive forces differ from each other in phase by I2O°. Take now three equal lengths of the same wire and close each coil, by one of these wires. Currents C, C, and Cs will now circu- late in each coil. The following well-known relations will hold: A. q=#|sin (6+ 6–2) A, . G= } in (6 + 3 + 120 — ?) Bo . C = 7 sin (8 + 3 + 240 — p). Where I is the impedance and p the angle of lag in each circuit. The relation C + C. -- C = o holds, therefore, for the currents as well as for the impressed elec- tromotive forces El, Es, Es. It is evident that any ordinary continuous-current dynamo which has a uniform effective field can be transformed into a three-phase dynamo by dividing the armature turns into 3 equal parts and treating each part as a separate circuit. 44 7 HE QUARTERLY. We shall show now that the 3 separate circuits can be so con- nected as to save quite a considerable amount of the connecting wire. *. THE FRANKFURT ELECTRICAL EXAIBITION. 45 Consider Fig. 2. The three coils and the three circuits are given. Since C. -- C, -ī- C, = o it is evident that the three wires joined into one from o to B would have no current at all in the junction OB which is common to all the 3 circuits. We can there- fore cut it away without changing anything at all in the distribu- tion of the currents. One coil in this method of connecting serves always as a return wire for the other two coils. Let us go a step farther as indicated by diagram Fig. 3. In this figure let the wooden ring A carry the 3 generating coils whereas ring B is made of laminated soft iron and carries three equal coils distributed over the ring at angular distances of I2O’. It is evident that the introduction of the three coils B into the three-wire system of the generating machine A will change the amplitude and the phase of the three currents, but these two changes will be the same for each current, so that if the values of the three currents be denoted now by C.", C,', C.’ we shall have again C’ + Cº.' -- Cºſ = o. Let the number of turns in each coil of the ring B, Fig. 3, be m, then mC' -- m (...' -- m G.' = o. That is the number of ampère turns of one coil is always equal to sum of the ampère turns of the remaining two coils with the re- versed sign. Therefore the iron ring will at any specified moment be magnetized as if it carried at the extremities of a diameter two equal coils joined in multiple arc through which equal currents circulate. The magnetization is indicated in the diagram by the dotted lines. N and S mark the position of the poles at any mo- Inent. A simple consideration will show us that the poles N and S in the ring B will rotate synchronously with the generating arma- ture A. Let us go back to Fig. 3. Since the ampère turns on one side of the plane of symmetry PP' are always equal to the am- père turns on the other side of this plane, it follows that the mag- netization due to the armature current will remain fixed in space, just as in the case of the ordinary continuous-current dynamo. That is, the magnetic field due to the armature current rotates 46 THE QUARTERLY. relatively to the armature, with the same angular velocity with But, since the distri- which the armature rotates around its axis. F. c. 5 * º S B & } ) P \\ T º 2–ſ S Ø P § & S Ø ãº % | V II) º º : p S D W W Š Ø S T W.© S (N 2. II) § Š Ş T & %| E. É SJ CS S D \\ S S2 G D º 2 º * º c bution of the ampère turns around the rotating armature ring A is the same as around the stationary ring B, it follows that the THE FRANKFURT ELECTRICAL EXHIBITION. 47 magnetic field of B rotates in space synchronously with the gen- erating armature A. If we now add to the ring B three equal coils, S1, S2, Ss, at angular distances of I2O’, and connect them as indi- cated in Fig. 4, then the system S1, S2, Ss, will also be a three- phase system, the difference in the three phases being again 120°. According as the number of turns in S1, S2, Ss, is greater or smaller than the number of turns in the primary coils, the ring B will be an up or a down three-phase system transformer. Suppose that it is an up-transformer, then, by adding another down-transformer C, as indicated in Fig. 5, we can transform the current down, and finally send it at low tension into a coil D, which is the armature of a machine resembling the generator A in every respect, except that instead of the pole-pieces, NS, indicated in the diagram, there is a laminated soft iron ring covered uniformly all over with a great many turns of copper wire. The rotating field induces strong currents in these turns, and these currents will, according to Lenz's law, oppose the motion of the rotating field. Conse- quently, there is a pull between the armature and the ring, and whichever is free to move will move, and perform mechanical work at the expense of the currents induced in the copper wire surrounding the ring. Suppose now, that in Fig. 5 A represents the three-phase gen erator, and B the up-transformer in Lauffen. C is, then, the down transformer, and D the three-phase motor in Frankfurt. There is no attempt made to indicate in these diagrams the actual types of the apparatus used in that famous transmission. They simply appear as the simplest diagrams by means of which the principles involved in the Lauffen-Frankfurt transmission can be explained in an elementary fashion. There is another point in the theory of this transmission whose importance forbids omitting it from this discussion. It is, namely, the strength of the rotating field of B, in Fig. 3, at any moment. A simple consideration will show that the strength of this field fluctuates periodically. Let us fix our attention upon the diagram of Fig. I, and examine the electro-motive forces generated at dif- ferent moments: 1st Position.—Turn “a” is in the plane of symmetry PP'. E1 = O. E2 = E0 Cos. 3O = }Eol/3 = .866 Eo. Es = – Eo cos. 3O = — #E01/3 = — .866 Eo. * : sº *3. ; * 48 THE QUARTERLY. & 2d Position.—Turn “a” is at an angular distance of 30° from the plane of symmetry. In passing from position I to this posi- tion, it is plain that Es increased continuously; hence, E, H- E, in- F 1 g 6 | | | | | | | | | | | | | | | | l l | | | | | | i —1– l 6o 7o /2 o /3 o /$o 2/o 2 creased continuously. In the position 2, Es becomes a maximum, and so does E1 + E. : E = Eocos. 60 = #E0. * E2 = Eo cos. 60 = }Eo. Es = — Eo. 3d Position.—Turn “a” is at angular distance of 60° from the plane PP'. This position is analogous to position I : E = Eo cos. 3O = .866 Eo. E, = O. Es = — Eo cos. 3O = — .866 Eo. That is, in this position we have a minimum again. This is sufficient to show that the maxima and minima appear periodically at intervals of 30°, as indicated in Fig. 6. There will be six maxima and six minima during each revolution. THE FRANKFURT ELECTRICAL ExhibſTION 49 * Let us consider, now, another extreme case; that is, the case in which we have three coils instead of the three turns, each coil one-third of the circumference of the ring. Examining now the electro-motor forces, E1, E2, Ea, in the three coils in the three pre- ceding positions, we find again the same number of maxima and minima, and the ratio of the minima to the maxima is, as before, .866. The same process of consideration can now be repeated for the coils as given in Fig. 2, and it will be found that for these coils, also, the same relation holds true. But the currents follow the same law as the impressed electro-motive forces. Hence, the magneto-motive force in coil B, Fig. 2, and with the magneto- motive force the strength of the rotating magnetic field, fluctuate according to the same law as the impressed electro-motive forces. There are six equal maxima, and six equal minima, in the rotating field, during each complete revolution, the ratio of the minima to the maxima being .866, that is, the maximum variation of the rotating field being nearly 14 per cent. The disadvantages arising from these fluctuations are evident to every electrical engineer, and need no further discussion here. The Allgemeine Electricitaets Gesellschaft, of Berlin, which holds the patents on all the improvements in the three-phase system made by Dolivo v. Dobrowolsky, claim to be in possession of a three-wire system distribution which reduces these variations to a minimum. If so, then they certainly have made a great step in advance of all the other polyphasal systems of current generation. The problem of constructing a three-phase dynamo which will produce a rotary magnetic field of constant intensity has not been investigated yet, as far as my own knowledge goes. I find that there are, theoretically speaking, an infinite number of solutions, but that among them there is only one which is of practical value. Dobrowolsky's generator seems to satisfy many of the conditions required by this solution. It is well, therefore, to consider this problem for a moment as a preparatory step toward the discussion of the details of the Lauffen-Frankfurt generator. Let the equation of the curve in Fig. 7 be y = f(a) Suppose that f(z) fulfills the following conditions: Ist. It is a periodic function of constant period 27t. 5O 7 HE QUARTERLY. * /a)+/ G + i) + / G ++)=0 . \ , 3d. ( / () + r ( 4 i-)+ / G + i)} const. numeri- *-*. cally. In a paper communicated to the New York Mathematical Soci- ety I showed that f(x) can be represented by the following infinite series: f(r)= a, sin a + a, sin 2 a + in which aſ a, an, etc., are arbitrary Constants. + a, sin n a + . . . ad inſin. That is, Fig. 7 F 1 & 8 ºf k . \| \| || B f k \ | . W ſ | ". 2.7" Jr. y jr \ 2Y © Yr # # # ºr A ſo W ſA A" # F \! | º P \ ". \ſ |\ |\ || | \ F-5-FTE-F-5 cº, w H F f(a) represents a peculiar family of complex harmonics. The first peculiarity is, that none of the multiples like n are divisible by 3. The second peculiarity is exhibited in Fig. 8 THE FRANKFURT ELECTRICAL EXHIBITION. 51 During the first and fifth-third of every period all the curves of this class have a constant ordinate. Every other part of the curve is perfectly symmetrical, both with respect to the axis of x, and in addition to that, the upper halves of these parts are symmetrical with respect to the bisector A B of the maxima of the plus ordi- nates, the lower halves are symmetrical to the corresponding lower bisector A' B'. Among this infinitely numerous family of complex harmonics there is one harmonic which has a superior value in electrical en- gineering. It is the curve A B C D F F represented in Fig. 9. It is a broken straight line consisting of five parts. The equation of this curve is *- sin a I . I . I . - y=k{ +--asin 5* +; ºn 74 — H* II+ + . . . . ad infin. } To translate these results from the language of pure mathematics to the language of electrotechnics, consider the magnetic field be- tween the poles N S of a drum armature dynamo. To save tedi- ous repetitions of long sentences, let us introduce a short definition. The component of magnetic intensity at any point of the surface of the drum armature which is perpendicular to the surface at that point we define as the effective intensity. Let the effective intensity vary in the following manner: For an angular inter- val of 60° on each side of the plane of symmetry PP', let it be proportional to the angular distance from PP'; through the next angular interval of 60° on both sides of PP' let it be constant, and finally, through the last intervals of 60° on both sides of PP’ let it be proportional to the angular distance from the lower part of PP'. Let, now, three turns of wire, ab, ed, ef, at angular distances of 120° from each other, be stretched over the drum in the ordinary manner. It is evident, then, that the electromotive forces gener- ated in ab, cq and ef by a uniform rotation of the drum will be represented by the complex harmonic curves A B C . . , A'B'C' . . , A' B' C'' . . . in Fig. 9. It follows, therefore, that this generator could produce a rotary magnetic field of constant strength. In Fig. IO we have the diagram of a stationary ring armature three-phase generator which, with a carefully shaped magnetic circuit, would produce a very nearly constant rotary magnetic field. There are six equal coils; each coil, therefore, occupies 52 7 HE QUARTERLY. * one-sixth of the circumference of the ring. The six coils are di- vided into three pairs by connecting each coil to the diametrically opposed one in series, as indicated in the figure. The ends of the three pairs are connected in the ordinary way of connecting three- phase dynamos. The rotating field-magnet is a solid cylinder minus the excavations on each side and the shavings scraped off from the cylindrical surface of the pole-faces. The cylindrical pole-faces subtend, each an angle of 120° at the centre. Calcula- tion and experiment can certainly succeed in giving to the electro- magnet and the air-gap such a shape as to produce not only con- stant effective magnetic intensity throughout the whole region which at any moment is included between the armature and the cylindrical surface of the rotating field magnet, but also to pre- vent almost entirely any leakage of the lines of force outside of that region,” in which case the electromotive forces developed in the three pairs of coils would be represented very nearly by the three harmonics given in Fig. 9, that is to say, a generator of this kind would produce a rotary field of constant intensity. (The diagram in Fig. IO should be considered simply as a diagram and not as a carefully prepared design). We can pass now to the consideration of the Lauffen generator. The characteristic features in its construction seem to be the fol- lowing: I. Curiously shaped magnetic circuits, something like figure eight (8) drawn on a skew surface. It is possible to trace them in imagi- nation, but almost impossible to draw them on paper. The field magnet is constructed in such a way that one and the same coil supplies the magnetizing force for 32 separate magnetic circuits. The coil is placed on a cast-iron disc (cc, Fig. 12). Two rings, with 16 pole-pieces each (aa, bb, Fig. 12) made of soft annealed steel are then attached to the cast-iron disc, and the pole- pieces of the two rings follow each other alternately along the cir- cumference. The air-space between two consecutive pole-pieces seems to be eaactly equal to half the breadth of a pole-piece. The air-space between the field and armature is exceedingly small for the size of * Mr. Freedman, John Tyndall Fellow of Columbia College, is preparing a paper on a series of experiments which he carried on during last spring while still a student in the electrical department. These experiments prove conclusively the correctness of the preceding statement. THE FRANKFURT ELECTRICAL EXHIBITION. 53 “4. the machine. North and south poles follow each other alternately. The armature is laminated, and the armature windings consist of 96 thick copper bars sunk into the iron of the armature. These 96 bars are divided into three sets. All the bars (those belonging to the same set are similarly marked in the diagram Fig. I3) of FIG. I.2. FIG. I.3. the same set are connected in series, following, of course, the well- known rule which is observed in connecting the armature coils of an alternating-current machine. It is evident that these three sets differ from each other in phase by 120°. - - 54 THE QUARTERLY. 2. The variation of the effective intensity along the circumfer- ence of the armature surface seems to follow very nearly the fol- lowing law: Pass a plane through the axis of the shaft and the median line of a pole-piece. Let this plane rotate gradually until it passes through the line midway between the long edge and the median line of the pole-piece. Throughout this interval the effec- tive intensity is constant. From this point on, the effective inten- sity diminishes proportionally to the angle passed through until the rotary plane reaches the median line of the air space where the effective intensity is zero. From this point on, the effective inten- º =\- gºº. - º º | º ſº º º º || º - º Dobrowolsky Motor. sity increases proportionally to the angle passed through until the line midway between the long edge and the median line of the next pole-piece is reached. From this line on, the effective intensity is constant again, etc. But if this law be true, then the electromotive forces generated in the three sets of rods are represented by the curves A B C . . . ., A'B'C' . . . . A" B" C". . . . . Fig. 9, and therefore the rotary magnetic field, which is produced by this generator, will be constant. The field-magnet rotates 150 times around per minute; hence, there are 40 complete waves or 8o reversals per second. The armature of the motor is stationary and of the same construction as that of the generator; but instead - - - - - - THE FRANKFURT ELECTRICAL EXHIB/7/0N. 55 of the field-magnet there is in the motor a laminated iron cylinder with copper bars parallel to those of the armature passing through the iron near the surface of the cylinder. All these bars Dobrowolsky-Brown Dynamo. are connected in multiple arc by means of copper rings. The ro- tary magnetic field induces very powerful currents in these bars, and thus produces a steady pull upon the laminated cylinder. It *.* ; 56 THE QUARTERLY. is evident, therefore, that this motor will run asynchronously and start with any load within its capacity. The rotary magnetic field being of uniform intensity, all heating and wearing and tearing effects due to magnetic fluctuations are completely avoided, and the motor runs as smoothly and as noiselessly as anybody could wish. A full description of the machinery employed in this transmis- sion would lead me far beyond the limits of this report. On this point it seems sufficient to refer to articles which have appeared during the last six months in the New York Electrical Engineer and the London Electrician. The author has had the pleasure of a personal inspection of the whole plant, and he is very happy, indeed, in confessing that to him every detail appeared to have been designed by the engineers, Dobrowolsky and Brown, and carried out by the Allgemeine Elec- tricitaets Gesellschaft of Berlin, and the Oerlicon Company, with an exceedingly high degree of perfection. The automatic speed- regulation of the turbine-wheel which drives the generator in Lauffen ; the generator itself, which, through each one of its three conductor systems, sends an electrical power of 50 volts and 1400 ampères; the transformers at Lauffen, which take up this power and transform it into electrical power of about 20,000 volts, and only a few ampères; the slender bare wire conductors, which, running along thousands of well-insulated poles, carry this power over a distance of about I I 5 miles to Frankfurt; the transformers in Frankfurt, which take up this high-tension energy and transform it down to only a hundred volts and many hundreds of ampères; the IOO-horse-power motor, and the group of a thousand incan- descent lamps, between which this IOO-volt electrical energy is equally divided; the various devices of controlling, regulating, and distributing the electrical power at every point of the system— all these things remind the careful observer and admirer of the full-armed Minerva springing out of the mighty head of the Olympian Jove. * * That eminent English electrician, Professor Sylvanus Thompson, of London, remarked, in an address before the Electrical Congress in Frankfurt, that the Lauffen-Frankfurt transmission marks an epoch in this passing century which was so productive of great inventions. tº tºº...º. wº; “.” º, "...º.º.º. ... º. º.º.º.º. ;: º: - 4 ºf f** º º: * 3. .** { ~ : • * * & % 3< * * * * º :% * º §§§ {º, % º *:::::: § §§§ #. : # - 3 & # : ‘t.” *º - Y •x; ; || | *. J/o 2? } * -č * tº TRANSACTIONS OF THE g AMERICAN INSTITUTE - * - of - Regular Meeting, December 16th, 1891. ON POLYPHASAL GENERATORS. BY M. I. PUPIN, PH, D. k * (Reprint from issue of December, 1891.) * *. | *-º-º- - | - OFFICERS AND MEMBERS OF THE COUNCIL *sºmºmºmº 1891-92. PRESIDENT: ALEXANDER GRAHAM BELL. Term expires 1892. PAST-PRESIDENTS : DR. NORWIN GREEN, 1884-5-6. EDWARD WESTON, 1888-9. FRANKLIN L. POPE, 1886-7. PROF. ELIHU THOMSON, 1889-90. T. COMMERFORD MARTIN, 1887-8. PROF. W. A. ANTHONY, 1890-91. YICE-PRESIDENTS : FRANCIS B. CROCKER, THOMAS D. LOCKWOOD, Term expires 1892. Term expires 1893. FRANK J. SPRAGUE, CARL HERING, Term expires 1892. * Term expires 1893. JOSEPH WETZLER, -- WILLIAM J. HAMMER, Term expires 1892. Term expires 1893. IMANAGERS - DR. F. BENEDICT HERZOG, HORATIO A. FOSTER, Term expires 1892. Term expires 1893. Dr. W.M. E. GEYER, H. WARD LEONARD, Term expires 1892. Term expires 1893. H. C. TOWNSEND, DR. LOUIS BELL, Term expires, 1892. Term expires 1894. FRANCIS R. UPTON, HERBERT LAWS WEBB, Term expires 1892 Term expires 1894. J. C. CHAMBERLAIN, PROF. ALFRED G. COMPTON, Term expires 1893. Term expires 1894. P. B DELANY, sº JAMES HAMBLET, Term expires 1893. Term expires 1894. TEEASURER, ; SECRETARY : GEORGE M. PHELPS, RALPH. W. POPE 150 Broadway, New York. 12 West 31st St. New York. Terms expire 1892. BOARD OF EXAMINERS : W. B. WANSIZE, Chairman. GEORGE A. HAMILTON, E. T. BIRDSALL, C. O. MAILLOUX, EDWARD P. THOMPSON. A £after read at the sixty-second meeting of the American Institute of Electrical Engineers, New Pork, December 16th, 1891. Past-President Thozozsozz zze the Chazzº. ON POLY PHAS AL GENERATORS. sºmºmºmºmºsºm BY M. I. PUPIN, PH. D., COLUMBIA COLLEGE. Few will deny the importance of the polyphasal current systems; none the fascination of their study. This belief in- duced me to present the following brief essay before the Insti- tute. The experimental researches in this new and promising field of electrotechnics are not yet numerous, but still the results already obtained are of so decisive a character as to leave no doubt what- ever as to the extremely high practical importance which is attached to electrical generators, motors and transformers con- structed according to requirements imposed upon us by this new method of combining a set of variable electromotive forces. For who among us does not thoroughly appreciate the beautiful in- ventions of Nikola Tesla and the completeness of the success which Dobrowolsky and Brown obtained by the practical appli- cations of these inventions Ž The exact quantitative relations involved in the polyphasal system of currents are not, I venture to say, quite as well known as its practical results. To give an impulse to further inquiry in that direction is one of the principal aims of this modest investi- gation. For the present I propose to confine myself to the poly- phasal generators in general, and particularly to polyphasal gem- erators whose system of electromotive forces is capable of pro- ducing a rotary magnetic field of constant strength. The last point seems to me to be one of the vital points in this new method of electrical distribution. It is in this particular point that Mr. Dobrowolsky claims his system to be superior to that of Nikola Tesla. Let us consider the theoretically simplest form of a polyphasal 2 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, generator, as shown in Fig. 1. A non-magnetizable ring with m open equal coils at equal distances from each other rotates uni- formly through a perfectly homogeneous magnetic field Let PP' be the neutral plane of the field. At the instant when coil 1 is at the angular distance 6 from the neutral plane PP' the E. M. F. generated in the various coils will be - e = K sin (6 - a) e e e a * * * * * * * * * * * * * * * g g º e a s = e s - a s = e & © e º º ºr e = e º a tº e e s = & e º 'º s a & e º 'º e º - e º 'º. P N | A \A | B | 1 *- n —S º 2 a- *- | ‘S’ —- - | Sz Ds. a. - - ^- A —Lb--4-3 - zº º n . . C > E A-Z------, t e - r - > N —f e S Jº iſ/. 1. Where K is a constant depending, as is well known, on the field intensity, the speed of rotation, the number of turns in the coil and the area of the plane of a turn ; a is the angular width of one-half of the coil. Since & e 27t, , , º 27: ) . sin(0–H0)+sin (+a++)- * * * * * * —— S]]] | 6–Ho-H(m—1) 70, | = () it follows that é, -i- és –H es + . . . . . . + ea = 0 . . . . . . (1). 1891.] PUPIN ON POL YPHASA L. G ENERATORS. 3 That is to say, the sum of electromotive forces generated in the various coils which are on one side of the neutral plane is nu- Americally equal and of opposite sign to that of the coils on the other side of this plane. This result is well known and self-evi- dent. It is, however, far from self-evident that relation (1), which I shall call the relation of continuity for the electromotive forces, will be satisfied by every magnetic field. Close each coil separately by conductors of equal resistance and self-induction. Let ep G, . . . . . . on denote the currents in the m separate circuits. It is evident that Ci =# in (6 – o – g ) C: E —# sin (0-a-i-º-y) C3 F # sin (6 +a+ 2*-*) Aſ ... 27: l F — S -: {} nº * — — (0 : Cn A SII). l + 0. –– (n. 1) 70, % | Where I is the impedance in each circuit and p the angle of retardation. Hence, we have 6, + c, -i- 63 + . . . . . . + on - 0 . . . . . . (2). That is to say, the relation of continuity is satisfied for the cur- pents also. Let the wires a A, b B. . . . . . . n/V (Fig. 2) represent a part of each of the n conductors of this system. Then, according to re- lation (2), the sum of the currents in these m linear conductors being always zero, if we joined them all into one conductor there would be no current in this wire, but the currents in the n cir- cuits would circulate exactly the same as before. In fact, the com- mon juncture is useless and can and should be cut out. The diagram, Fig. 3, represents this method of connecting for a three-phase system. Consider, now, n equal coils distributed at & , 27- tº & § * angular distances of it over a laminated iron ring B, each coil *- 70, being a part of the m conductors coming from the generator. Di- agram Fig. 4 illustrates this for a three-phase system. Let the n currents be denoted now by ci', cy, . . . . . . ca'. We shall have, now, 4 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, e1 = ſ sin (6 -– a –– 4') J A - A * 27. '', r → . {} † — ar' e = # sin () -- a-- – g ) 6,' =# sin | 94 a +(n-1)* – 2 and therefore o,' -- c, -- . . . . . . + ca" = 0 (3) S 4 * = º B: º – M ºrio ...AB C * The introduction of the iron ring with the n coils into the n phasal system has changed the impedance Z, and the angle of re- tardation p; but this change is evidently the same for all coils. The correctness of this statement might, perhaps, be questioned, if we supposed that the system of the n variable currents was at ºr 1891.] PUPIN ON POI, YPHASA L. G ENERATORS. 5 any moment strong enough to saturate the iron ring, I therefore suppose that the intensity of magnetization in the ring is never over 10,000 C. G. s. lines of force. We shall presently see that in the case of a properly built generator the saturation of the iron ring will not vitiate the correctness of the above statement in the slightest. Let s be the number of turns in each of the n coils. Relation (3) gives 4T sc," + 47 s 65 + . . . . . . +47: s 6,' = 0 (4) That is to say the magneto-motive forces in the n coils of the 'ring b satisfy the relation of continuity. Relation (4) translated into physical language means that the magnetization in the iron ring is due to two equal magneto-motive forces working in multi- ple arc. The magnetic field produced is perfectly symmetrical with respect to the ring as indicated by the dotted lines in Fig. 4. Consider now n iron ring cores of exactly the same dimensions and made of the same material. Let o be the reluctance of each ring. Let each of the ſo coils be interlinked with one of the iron rings, we shall have n homogeneous magnetic circuits; and as long as the magnetization of these rings is considerably below the Saturation point, we shall have 47 s ('' 47 s 6,' 47 s ('n' --- + + . . . . . . . . + { () () () = () That is to say the magnetic induction in the n magnetic cir- cuits obeys the same law as the 10 electric currents; we can there- ..fore employ the method of polyphasal connection for the magnetic circuits also and we obtain what the Germans call a Verkettung der Magnetischen Kreislaufe which may be translated into Eng- lish by a more accurate expression : Polyphasal com/p/?ng of magnetic circuits. A transformer constructed on this principle may be called a coupling transformer, to distinguish it from the Tesla polyphasal transformer. A simple consideration will show that the field rotates around the axis of the ring B synchronously with the rotation in the generator which produces the impressed E. M. forces. Consider the armature of the generator. Since the ampere turns on one side of (1) This will be strictly true when the number of coils over the ring B is even, because then the distribution of the ampere turns over the ring is per- fectly symmetrical. It is therefore always strictly true because the number of these coils may be made even in odd number of phases as well as in even num- ber of phases. 6 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, the neutral plane is always equal and opposite in sign to the ampere turns on the other side of this plane it is evident that the magnetic field due to the ampere turns in the armature is fixed in space and perfectly symmetrical with respect to the plane of symmetry PP'. We can therefore say that this field, though fived in space, rotates with respect to the armature with the same angular velocity with which the armature rotates in space. The distribution of the ampere turns over the stationary ring B be-, ing at any moment the same as that over the armature ring, it follows that the magnetic field of B also rotates with respect to B synchronously with the rotation in the armature. An inspec- tion of the diagram in Fig. 4 will show that when the rotation in the generator is reversed the rotation of the field B will also be neversed. - The strength of the rotating magnetic field will vary because the strength of the two equal magneto-motive forces which are working in multiple are will vary. The following simple con- sideration will show us the law of this variation. Two cases must be considered separately. First, when m is an odd number; secondly, when n is an even number. - CASE 1. A simple definition will save me tedious repetitions of long sentences. I define the sum of all the electromotive forces generated in all the turns which are at any moment on the same side of the neutral plane of the generator as the resultant &m- pressed E. M. F. at that moment. The magneto-motive force of the rotating field will evidently vary according to the same law as the resultant impressed E. M. F. To find the law of variation of the resultant impressed E. M. F., consider the armature of the generator when the angle 6 of coil 1 is zero. To make the rea- soning shorter, I make now the angular width of each coil equal to 27: 70, , so that the m coils completely cover the ring, which 7t tº g º ſº § wº . makes a = *-. If this angular width is smaller, then a simple 70, consideration will show that the law of variation which I am about to deduce will be exactly the same. In the position just & e n — .,, . mentioned, the coils 1, 2, 3, . . . . . 9 will all be on the same .." * 1891.] PUPIN ON POLYPHASA L. GENERATORS. 7 m –– 1 side of the neutral plane, whereas coil will be just half on One side and half on the other side of this plane. There is no elec- tromotive force generated in this coil. As the above mentioned t º & g 1 ſº angle 6 begins to increase from zero, coil n + 1 begins to con- 2 tribute to the resultant impressed E.M.F., but this contribution is just counterbalanced by the loss due to the entrance of coil n into the opposite region of the neutral plane. The variation in the result- ant impressed E. M. F. is therefore due solely to the change of position of the turns in the coils 1, 2, 3, . . . . . º , on one side and the corresponding turns on the other side of the neutral 77 –– plane. This will be the case until coil 2 * has completely te ~! passed to one side of the neutral plane and coil n is just bisected by it. During this interval 6 has increased from zero to 27t 7t # T- = −. The value of the resultant impressed E. M. F. at 72, 70, any moment during this interval is easily found. Denote it by E, then - AC | sin (0-- i)+sin (0-- + * ) + * e is e 70, +in Hi + (ºr 9–1)* - A sin ( 4. -) + sin (5 + ; +*) + * * * * * * +sin a + i + [*** *} 2F)] n J T —3 - | Kisin(0+ ... -- “Tº = K, sin [; + 0– ) • 7ſ U SIIl 70, = K, cos (0– #) 8 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, It is evident that the resultant impressed E. M. F. E. varies dur- ing the interval from 6 = 0 to 6 = ºf just like cos (0– # ); -- 7?) 370, that is to say, it varies just like a simple harmonic. When 6 = 7t g o º * • . 27, ” F' reaches a maximum which is equal to Kº, it has a mini- 70, - - : mum both when 6 = o and when 6 = ºf , each of these mini- ma equals K, cos sº The ratio of the minimum to the maxi- 70, . - mum value equals cos 㺠For a three-phase system this ratio 72, - . is .866, and it diminishes very rapidly as n increases. It is evi- dent that after 6 has reached the value ºf the armature is, as 70, . far as concerns the resultant impressed E. M. F. in exactly the same position as at the start when 6 = o. We conclude there- fore that E has 2n equal maxima and 2n equal minima during each revolution of the armature. In diagram Fig. 5 these fluc- tuations of E for a three-phase system are represented graphi- cally. CASE 2. - Similar relations hold good when n is even. The maxima - 27t 47t tº ſº take place when 6 = 0, #, " , . . . . . . The minima when 8 70, 70, 7t 37t 57t tº e º - - , -— ; , . . . . . and the ratio of any minimum to any 7?, ??, 70, - & wº T & - e - e maximum is cos -º- . Since the magneto-motive force varies 70, according to the same law as the resultant impressed E. M. F., it follows that the strength of the rotary magnetic field fluctuates periodically, having 2n equal maxima and 2n equal minima dur- ing each revolution and the ratio of any minimum to any maxi- - 7t g & g mum equals cos ºn That is, when n is odd, but when n is A70, even then there are only n maxima and n minima and the ratio T of any minimum equals cos ºn 1891. PUPIN ow Poſ, YPHASAL GENERATORS. 9 A polyphasal generator of this kind would produce a rotary magnetic field of constant strength only when n= oc. For a three phase system the maximum variation would be nearly 14 per cent. of the maximum value. This agrees perfectly with Mr. Dobrowolsky’s caleulations, but I fail to see how these calculations could justify any one to assume that they hold good for all types of polyphasal generators ’. The gene- rator which we have considered could be actually constructed but its output would be so small in proportion to its size that we may dismiss it at once as an impracticable machine. We can make it practicable by substituting for the non-magnetizable ring which carries the armature coils a laminated iron ring, and for the uni- form magnetic field, the magnetic field of a well made field mag- net with its pole pieces placed with respect to the armature coils ºzººlºº s ====} º Pé -— =A==+ Pé---> 8 . ----- | | | | ! | | | | i | i } | | | | | | | O | | | | | | | | | | | | | | | { | | | | | | | | | | | | | | f | 8 0. | | | | | | ſ | | | | | | | | | 5 3. § O 3. O , 30 60 90 1 20 150 t JFig. 5. O 270 S 00 in any one of the various ways sanctioned by practical experience. But in a generator of this kind the resultant impressed E. M. F. will no longer vary according to the law which I have pointed out a little while ago. To be sure, we shall still have the same num- ber of maxima and minima, as may be inferred readily from our knowledge of the shape of the E.M. F.curve of a continuous current dynamo. We all know that this curve is not in general a straight line, but a wave line having as many maxima and as many minima as there are sections on the commutator. But the ratio of the max- ima to the minima is no longer an a priori calculable quantity. If we knew the mathematical relation between the intensity of the field (2) M. v. Dolivo-Dobrowolsky : Der Drehstrom und seine Entwickelung; Officielle Austellungs Zeitung, Electricitaet, Heft 12. 10 PUPIN ON POLYPHASAL GENERATORS.. [Dec. 16, at any point of the armature surface and the co-ordinates of this point with respect to the neutral plane then we could calculate that ratio, but the amount of experimental and practical work in- volved in this problem would be very great. A much easier and practically much more important problem is to determine the conditions which must be fulfilled in the construction of a poly- phasal generator, in order that it may be capable of producing a Totary magnetic field of practically constant intensity in the simplest possible way, that is without the application of brushes and commutators, and also without employing too many phases. Mr. v. Dolivo-Dobrowolsky seems to think that a three phasal generator is incapable of doing that, for he distinctly says that such a generator necessarily produces a rotary magnetic field whose strength varies 14 per cent. He also states that (evidently to obviate these fluctuations) the Allgemeine Electricitaets Gesell- schaft employ a method of transmitting currents of smaller dif- ſ \ º 'ſ A i w W \ ( \ |\ |\ 27ſ 27 | | W7 || || 27. c B C B c B' \ W | { I | B O 7ſ o 4 ºr Kłºſt As ºf * 3 \ \} \|| || * ! g \ A B \ t \ſ - {\ g \ f \ ºr ºf . ºf $ - #-5-É-5-É-5 I'iſ/. 6, I'iſ/. 7. Fig. 8. ferences of phase than one-third of the period through three wires. In this point they claim to be ahead of Tesla, Bradley, Haselwander and Wenström. In fact if one is not exceedingly careful in the perusal of Dobrowolsky’s discussions of this subject he will be led to believe that the rotary field in some of Tesla's motors varied as much as 40 per cent. and certainly not less than 14 per cent. I do not think that Mr. Dobrowolsky wishes to be understood as holding that opinion ; for neither he nor anybody else excepting Tesla himself can know what these variations were. The number of phases employed tells us nothing definite about the range of these variations. . A polyphasal dynamo which is capable of producing a rotary magnetic field of constant intensity must be constructed in such a way that its resultant magneto-motive-force must remain constant as long as speed and the magnetic field of the field magnets re- 1891.] PUPIN ON POLYPHASAL GENERATORS. 1 i main constant. As long as the variable electromotive force de- veloped in each coil follows the law of a simple harmonic that re- sult can never be accomplished by a finite number of phases, but it may, perhaps, be accomplished by producing in each coil a variable electromotive force which varies according to some de- finite complex harmonic law. In a well made commercial ma- chine the electromotive forces developed in the various turns of the armature always vary according to some such a law. The form of this complex harmonic law depends on the form of the magnetic field of the field magnets and also on the distribution of the coils over the armature. The problem that remains to be investigated consists therefore of three parts: 1st.What must be the particular form of the complex harmonic E. M. F. developed in each coil of a polyphasal generator, in order that both the con- dition of continuity be fulfilled and also that the resultant im- pressed E.M. F. be continually constant. 2nd. What form of the magnetic field of the field magnets will be capable of producing such an E. M. F. 3d. Can a continually constant resultant E. M. F. produce a rotary field of constant strength. 1st. The first part of this problem is purely mathematical. In a paper read before the New York Mathematical Society I indicated a method of discussing this part in a general way, and worked out completely two particular cases, namely the cases of a three and four phasal system. The paper is given in the appendix. 2d. For a three phasal system the form of the complex harmonic E. M. F. given in Fig. 7. will satisfy all the conditions. The form A, B, C, E, F, given in Fig. 8, is only a particular case and ought to be aimed at in the construction of the machine. When there are only three turns within a space through which the armature moves with respect to the field during the time that corresponds to a complete period as in the case of the Lauffen 12 PUPIN ON POLYPEIASA L. G E NE RATORS, [Dec. 16, generator (see Figs. 11 and 12), then the field of the field-magnets must be constant in intensity during an angle which corresponds to one-sixth of the period. I have indicated that, in the diagram Fig. 9. In the case of bipolar three phasal generators as indicated in the diagram Fig. 10, where we have six coils, the diametrically opposite pairs being connected in series; the pole faces must Fig. 11. I’ig. 12. have an angular width of 120 degrees and the field must be con- stant in intensity within the region bounded at any moment by the armature and the pole faces. This is a practical problem offering no serious difficulties judging from the experimental results obtained by S. Thompson, Isenbeck, Mordey and others, 1891.] PUPIN ON POLYPHASAL GENERATORS. 13 and also from the experimental results obtained lately by a gradu- ate of our school, Mr. Freedman, John Tyndall Fellow of Colum- bia College. * The curve of impressed E. M. F, which must be produced in the case of a four phasal generator is given in Fig. 13, and needs no further commentary. Larger number of phases offer no special advantages whereas the disadvantages arising from employing a large number of phases are self-evident. 3d. When a coil, in which a simple harmonic E.M.F.is developed is closed by a resistance, whether self-inductive or non-self. inductive, the current which is set up in the closed circuit will be a simple harmonic, having therefore all the characteristics of the impressed E. M. F. This, however, is not necessarily the case when the impressed E. M. F. is a complex harmonic. A complex harmonic E. M. F. is composed of a large number of simple har- monic E. M. forces of different frequencies, all the higher fre- I'iſ/. 13. quencies being multiples of the fundamental frequency. When, therefore, a coil in which a complex E. M. F. is generated, is closed by a conductor, and the current is started,the current will be also a complex harmonic, each simple harmonic component of the complex harmonic E. M. F. producing its own simple harmonic current which is a component of the resultant complex harmonic current. But since the component simple harmonic E. M. forces have each a different frequency, it follows that they will have a different impedance and the shifting of phase will be also differ- ent for each component current, currents of higher frequency having a larger shifting in phase and also the ratio of the ampli- tude of any one of the component currents to the amplitude of any other component of lower frequency, being smaller than the ratio of the amplitudes of the corresponding component E. M. forces. In this respect the propagation of the complex harmonic 14 PUPIN on PoEYPHASAL GENERATORS. [Dec. 16. current-wave resembles very much the propagation of a complex harmonic sound-wave or a complex harmonic light-wave through an absorptive medium like air. The component simple harmonic waves of light and sound will in general suffer the less through the transmission the longer their wave-length. Just as the sound and light-waves, after such a transmission, lose a great many characteristics of the original vibration which produced them, so an electric wave in its transmission through a conductor possess- ing ohmic resistance and electro-magnetic, not to speak of the electro-static, inductance will lose a great many characteristics of the impressed E. M. F. - To put this into simple symbolic language of mathematics, Let L be the coefficient of self-induction of the circuit, “ R be the total resistance, OO “ AZ >, am sin m p t be the complex harmonic impressed 1 E. M. F. where p = 27 X fundamental frequency, “ a be the value of the current at any moment t. We shall have, then, - OO % I ºf + R a = A >, am sin m p t. - U. 1 The solution of this differential equation gives CC) Q? ~ K >, Cºm - sin (m p t — pm) t l 4/ Fº + m” pº Lº 9m * where tan ºn = *% L The current as is a complex harmonic, its component simple harmonic eurrents being * * = 0} + æs –H . . . . . . + æm + . . . . . . ad infin. The current ac. – A. a. = sin (a p t – p.) Cº- Aſ ſº -i- dºp’ſ.” * Cº. a p 1, tan p. = A2 Let E be the impressed E. M. F., then A.' - €1. –– 62 –H 63 + & e º 'º e is + &m –H tº ºs e º ſº tº ad &njin. 1891.] PUPIN ON POLYPHASA I, GEWERATORS. 15 The component simple harmonic E. M. F. e., is given by é. = @.. Sin 2 pt These relations give an exact quantitative expression to the preceding physical description. These considerations made me hesitate at first in taking as granted that a polyphasal generator producing complex E. M. forces, such as I deduced mathematically in the course of my pa- per, would be capable of producing a rotary magnetic field of constant intensity. But I was glad to find out that my hesitation was groundless, at any rate in certain particular but important .C8,S62S. Consider the three-phasal generator whose diagram is given in Fig. 10. Take, now, another well-laminated armature wound in a similar way as the armature of the generator. Connect the three pairs of coils of the generator to the three sets of coils in armature 2. We shall have three separate circuits, the ohmic re- sistance and the self and mutual inductance in each circuit being the same. Denote by E. E. E., the three complex harmonic E. M. forces in the three circuits. Let a, y, 2 be the currents at any moment. Then we shall have - da, dy d2 -Y L dy Mſ da, M d2 3,--- M -º- + M-n + R y = E. d2 da: dy L dt + M-7, H M + –– R 2 ~ A. But since E + Ey + F = o for all values of t it follows that d d . º, (a + y + 2) + 2 M i, (a + y + 2) + R (a + y + 2) = 0 for all values of t. This can be true only if a + y + 2 = 0 for all values of t. That is to say, the currents fulfill the condi- tion of continuity. We can therefore employ the method of polyphasal connection. Substitute now in the first of the three differential equations J. 2 = — (a + y) 16 PUPIN ON POLY PHASAL GENERATORS. [Dec. 16. and we obtain da, - * (L–M) iſ + ſea = E = R >, an sin m p t 1 The solution of this equation gives OO (l, a = AC II) l]] - º t — ſºm ſº > ºH=# in ºpt-º Similarly (l, Ill v= k >, ºr Lºy in m (p +*)—e.)} - A: Cºm - == sin | m (pt-H 4. )- pm l 2 E Fm V /*-i- mºp"(L–M)” 3 | In the case under consideration both L and M are pretty small when the metallic parts of the magnetic circuits are near the saturation point, so that L – M is small, and m” p" (L– M)* may be small in comparison to R* even for large values of m, unless the frequency is very high. Also, since º, L– 1 tan Ørn = m p ( A2 M) pm is exceedingly small unless p is very large, we shall have for moderate frequency generatcrs Tſ) a = − S &m sin m p t #5 ºn 1 and similarly for y and 2. The same method of reasoning may be easily applied to any number of phases. The mathematical operations will be considerably larger, but still the same results will be deduced without much difficulty. - That is to say, the curves for the currents are the same com- plex harmonics as those of the impressed E. M. F. The currents therefore, produce a rotary magnetic field of constant in- tensity; this is evidently true even if these currents produce a saturation in the iron part of the magnetic circuits - The resemblance between a polyphasal generator and a con- tinuous current dynamo, which these relations bring into view, is exceedingly striking and instructive. 1891.] PUPIN ON POLYPHASAL GENERATORS. 17 The advantages gained from a polyphasal generator capable of producing a rotary magnetic field of constant intensity would be very much diminished indeed if it should turn out that it is im- possible to devise a simple and efficient method of transformation * by means of which the polyphasal system of currents producing a rotary field of constant intensity (a constant rotary field system) can be transformed any number of times without losing its dis- tinguishing characteristic. I intended to discuss this problem also, this evening but having been disappointed by the mechanician who is constructing several pieces of apparatus illustrating this problem I decided to postpone this discussion to some other time. To sum up : 1st. The consideration of simple harmonic impressed E. M. Fs does not tell the whole story of the polyphasal generators. 2nd. The law of variation of the strength of rotary magnetic field which a polyphasal generator can produce is not as simple as Mr. v. D. Dobrowolsky thinks. - 3rd. Polyphasal coupling transformers must be worked at low magnetizations and low frequencies, otherwise they will not satis- fy the condition of continuity. It follows, therefore, that they will probably be very large for the output which they can give. 4th. It is very probable that nearly constant rotary magnetie fields can be produced in practice by a small number of phases; perhaps not more than three. (3) Not only transformation of the power supplied by the generator into elec- trical power of higher or lower potential, but also transformation of this power into mechanical power. This, of course, leads into the discussion of rotary magnetic fields produced under practical conditions. [PUPIN ON POLYPHASAL GENERATORS.–APPENDIX.] ON A PECULIAR FAMILY OF COMPLEX HARMONICS. Read before the New York Mathematical Society, December 5, 1891. The following investigation was suggested by the practical problem : Can a polyphasal generator be constructed which will be capable of producing a rotary magnetic field of constant inten- sity ? It seems, therefore, sufficient for the present to discuss only those features of the mathematical side of this question which have a direct bearing upon its practical side. The mathematical theory of polyphasal generators involves a discussion of harmonic functions, or harmonics, to use a shorter expression. - A simple harmonic is defined by the following expression:- a + b sin (a + a). This harmonic differs in phase only from the harmonic a + b sin, a. The angle a is called their difference of phase. A complex harmonic is defined by the following expression : 70, 770, > a. sin a a -- > C. cos a a O O - If n and m are infinite the complex harmonic is sometimes called infinitely complex. The multiples o are integral numbers. Consider a periodic function f(a) whose period is 27—p. If this function with its differential coefficients is finite, continu- ous and singly valued for all values of a, with the exception of certain values which are at finite distances from each other, and if in addition * f(– a = – f'(a) and f(0) = 0, then by Fourier’s theorem f(a) = a, sin a + a sin 2n +a, sin 3a –H . . . . . . - + am sin m a + ad infºn. 2 . " - where a m = ºf ſ f(a) sin m a. daº O 1891.] APPENDIX. 19 It is required now that f (a) fulfill the following two condi- tions: - - 1st, f(x)+f(x + i)+f(x + 2 +)+...... + f [a, + (n − 1) +] = o for all values of a 2d, f(x)+f(x + i)+f(x + 2 +, + ........ — 1 +,f(a + 70, 2 #) = const. for all values of a betw.o and *— when n is odd, and 27, 2 % n–2 p f(x) + f(x + i)+...... +f (a +-g- i) = const. for all values of a betw. o and + when n is even. The coefficients a, as . . . . . . am . . . . . can of course be always so determined as to fulfil not only these two, but also any other number of possible conditions. The first condition, which I call the condition of continuity, can be written a sin a + as sin 2 a + . . . . . . + am sin ºn a + . . . . . . - e * º Ø –– a sin (a +, ) + a sin 2 (a + , ) + . . . . . ... + am sin m (a. ++) + • * * * * * + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + a sin }* +(n-1)}} + . . . . . . +a, in m \, 4-(n-1)} | + s tº e º e tº E O do º ( ++++). 7m p SIn m (a + -j- - ) Sin Tai- or 3 a. * * † – = o ...... (1) m p Sln — — 2 m, 20 PUPIN ow PotypHASAL GENERATORS. (Dec. 16, This function I call the resultant of n identical component harmonics f(a), differing from each other in phase, only, by one nth of the period. It is evident that every term in the resultant vanishes, excepting those terms whose multiple of a is divisible by n. The resultant can therefore be written o, (n) — 1) OO >, (–1) C. sin o. n w = F(a) 1 . Since # 4 C = — F (a) sin a n a da; 7 ſ. - it follows that if F(a) = o for all values of a betw. a = o and I a = −3– then every coefficient C. is zero. That is to say, f(a) willfulfil the condition of continuity if it contains no terms of the form am sin m a where m is divisible by n. w - Those acquainted with the theory of dynamo-electric machin- ery will easily translate this into the following physical lan- guage: The algebraical sum of all the electromotive forces generated at any moment in the various coils of a polyphasal dynamo will not necessarily fulfil the condition of continuity; that is, will not necessarily vanish. The form of the magnetic field must be such that the harmonic electromotive force generated in each coil does not contain in its mathematical ea:- pression a multiple of the variable angle which is divisible by the number of the phases. . The first part of the second condition can be written a sin a + as sin 2 a + . . . . . . + am sin m a -- . . . . . . + a sin ( ---. ) + ...... +a, sin m (a + i)+...... + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g n – 1 p . - 1 p + a sin (a + 2 †)+ tº gº tº ſº e ..+ am sin m (+ æ T2- ...) 1891.] APPENDIX. 21 CO * 70 – 1 % . m (n + 1) © or ~, an sin m (4 + I- ; ) sin -i- ; l - - - F. C. . m. @ SII) — — 2 70, for all values of a between a = o and a = } –– The second part of this condition may be written OO i, 2 ºr *-*** * ~ * >, 0m sin m (a + -i- i) sin ºn 1 e p - C , , ... (2) 1 sin * * 2 7). C for all values of a betw. a = o and a = % 70, From these two relations, I infer the following physical theo- rem: If the terminals of the armature coils of a polyphasal dynamo capable of producing a constant resultant rotary im- pressed E. M. F. be connected to a commutator and the machine be run as a direct current dynamo, it will give an absolutely constant electromotive force, speed and field intensity being 'maintained constant. It must be observed, however, that in the case when the num- ber of phases is an odd number, then the armature should have twice as many coils as there are phases, and when the machine Žs run as a polyphasal dynamo, then the diametrically opposed pairs are connected in series. Relations (1) and (2) enable us to determine in each case the simplest forms of the component harmonics which will satisfy these two relations. As the simplest forms I define those forms which can be produced in polyphasal generators by the simplest devices of construction. PARTICULAR CASEs. Any further general discussion would have only an indirect bearing upon the practical side of the problem which I propose to discuss at present. I therefore pass to particular cases. Let n = 2. The above relation gives 22 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, OO 2, a. SID 7%, Q3 - C 1 for all values of a between a = 0 and a = 7t. except when ſo = 0 and a = 7t. This solution has no practical value. I therefore dismiss it. . Let n = 3. The relation given above reduces to OO 7t 27t >, am sin m (a + †) sin m = 1 m, ſt SIn – 3 On e 7t 77,7t $ > , 2 sin m (a + -) cos º- = c Oł l) l Cºm 3 3 1 & 7t for all values of a betw. a = 0 and a = T: . Since f(a) has only two conditions to fulfil, all the coefficients am, where m is an even number, may be suppressed and still leave more than a sufficient number of coefficients, their number being infinity. In that case the last relation reduces to OO >, am sin m (~-- -:) - C. 1. OO or > a.m. sin m & = & 1 w 7: - 27: for all values of 5 betw. § = 3. and 3 = 3.T. That is to say, the function,f(a) itself must be such as to have 7t 27t a constant value between a = -- and a = 3- and, therefore, º 4 {) also between a = a ſt and a = 3 7t. 2, Since f(a) + f(x + +) = const. for all values of a be- tween a = 0 and a = + , I infer that the curve f(a) may have 1891.] APPENDIX. 23 any one of those forms, one of which is given in Fig. 7 (of the preceding paper). That is, the curve is symmetrical both with respect to the axis of a, and also to the bisector A B and A' B' of the upper and lower maxima. The curve given in Fig. 8 (of the preceding paper) would perhaps be aimed at in the construction of polyphasal dynamos. Its equation is f(a) = K (sin a – 1. 1 sin 5 a -- † sin 7 a-II, sin 11 a- Tjº 1 12 Let n = 4 Equation (2) gives - C > 2 a.m. sin m (4 + i) COS 777, 7t and therefore - 2 a.m. 7t 7t for all values of a between a = 0 and a = 2 The last equation can also be written &m Cºm * 7t ſº - > * cos 7%, Q2 — > * SłIl 7?? – SII). 777. , tº 7??, 772, 2 --- * * G. (a, T. 3 * – g (2-3) This relation enables us to determine the form of the com- ponent complex harmonic function,f(a) which will fulfil all the conditions. It is easily seen that there is in this case just as in the case of three phases an infinitely numerous family of com- plex harmonics which will fulfil these conditions. The simplest harmonic is obtained by putting 7t Qºm * – – “ ( – i. > . COS 772, Q} à (º 3:) 24 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, 7: 7: Q,..., 7. C 2 G 7t 2 . Cºm 4 ſ ſ ... — , -- = — - a cos ºn a da; as-wº- cos m. a. d. a. 7m 4 2 + 4 O O G 2 mº and therefore 2 C. Qm = — IOO T I conclude therefore that the harmonic f(a) = º * — º 8 * - º & º; Q? + . . . . . ad infin. fulfils all the conditions. Its form is given in Fig. 14. (It is only a special case of the curve given in Fig. 13 of the preceding paper.) Fig. 14. The component harmonics fulfilling these conditions may be deduced similarly for any other value of n. But as the problem which I originally proposed to myself does not extend beyond these limits which I have just reached I prefer to postpone further considerations of the subject. The character of these curves points out clearly the physical fact that it is an easy matter to construct three and four phase generators which will be capable of producing a constant resul- tant impressed E. M. F. Whether such generators will also be capable of producing a rotary magnetic field of practically constant intensity is a problem which I propose to discuss in a series of papers which will be presented shortly before the American Institute of Electrical Engineers. 1891. DISCUSSION. - 25 DISCUSSION. THE CHAIRMAN [Prof. Thomson]:-You have heard the inter- esting and instructive paper by Dr. Pupin. I would say that it is perhaps the first exposition of some of the principles underly- ing this system of polyphasal transmission that I have seen, and I hope that the discussion may be indulged in by the members so that we may have some points cleared up by those conversant with the subject. It is now open for discussion. MR. CHAs. P. STEINMETz:—Having had the pleasure of hear- ing Prof. Pupin's paper at the New York Mathematical Society some days ago, I might be allowed to make the same remark I made there—that it would be perhaps more advisable to use a shape of the electromotive force similar to Fig. 7, than the shape in Fig. 8, because, as you see, in shape Fig. 8 the curve has a sharp corner, and even if we could produce waves of electromo- tive force that have sharp corners, it can hardly be expected that FIG. 15. we can derive from such a sharp-cornered E. M. F. a current which, after being sent through step-down transformers, over lines of considerable electrostatic capacity, and again through step-down transformers into a motor of high self-induction, would still have retained this sharp-cornered shape. But the theory requires that the electric current in the motor has the shape given in Figs. 6 to 8. Even if the E. M. F. had the shape of Fig. 8, the current in such a highly inductive circuit would differ considerably, having lost the sharp corners, etc. Hence Fig. 8 would be less com. mendable. But the shape of Fig. 7 might easily be chosen, so that there would be no sharp corners, but a steady and continuous variation, as shown in Fig. 15. Then, with regard to the equations of the currents a, y, z, on page 576, I wish to make a remark. As stated by Dr. Pupin, the complex harmonic of the electromotive force produces a current 26 DISCUSSION. [Dec. 16,. which is a complex harmonic too, and it is identically the same complex harmonic as long as the circuit has no self-induction and no capacity or, what amounts to the same, as long as self-induction and capacity have a certain ratio with each other. But as soon as the circuit has self-induction, the complex harmonic of current differs from the complex harmonic of electromotive force, and differs the more, the heavier the self-induction of the circuit is, by the decrease of the higher terms of this infinite series of simple harmonics which constitute the complex harmonic of electromo- tive force, these having a high self-induction; and therefore if we produce such a type of electromotive force and let it send a cur- rent through an inductive circuit, it will probably break to pieces entirely and show a current resembling a simple sine-wave as closely as one egg to another. In the equations for a, y, 2, on page 576, as the condition that the shape of the current does not differ from the shape of the electromotive force, was found that the second term, m” pº (L – M)”, can be neglected against the first term, Hº. This means, in plain language, that the shape of the current-wave is the same as that of the E. M. F., if the self. induction of the circuit is negligible. For the first term, R, is the resistance ; the second term, m p (Z. — M), is the inductance of the circuit. Hence neglecting the second term means neglecting the induc- tance—that is, it means that the motor circuit has no self-induc- tion. Now, anybody who ever tried to design an alternating mo- tor, has found out to his disgust, generally, that the self-induction of such a motor, even under the most favorable conditions, is any- thing but negligible. Unfortunately, I could not get any data on these rotary motors, but on some other alternate current motors I can give data. In the Ganz and Company synchronous motor, the plant efficiency is claimed—by the manufacturers—to be 90 per cent. This unusually high plant efficiency, this unusual/y low retardation, might be explained by the fact that the motor is syn- chronous and the field fed by rectified alternate currents, that only the self-induction of the armature is in circuit, and the field adds no self-induction whatever. Furthermore, that the frequency used in those motors, 42 periods per second, is somewhat less than the one-third of the frequency of our American alternators. If this current were a complex harmonic we would have in the main wave 26 degrees retardation and 90 per cent. plant efficiency —that is, the intensity of the current would be 90 per cent. of that value it would have with no self-induction present. The second harmonic has only the plant efficiency of 72 per cent.; the third harmonic of 7, the fourth of 47, the tenth only 20 per cent.—that is, is decreased to 20 per cent., while the first wave is decreased only to 90 per cent. Hence, even in a motor circuit of such unusually low self-induction, if a wave of shape Fig 8 is applied, it will come out entirely broken up, so I do not think that really the self-induction can be neglected. The more, as just 1891 ) DISCUSS/OW. 27 the first term, R, is small, because we do not want to have the re- sistance of the circuit large, for the resistance determines the loss of power, and we do not want to have so much loss of power. We want to run motors with these currents. Indeed, if we run a motor from this alternating current, we get a counter-electro- motive force in the motor, and to make these same equations hold we might represent this counter-electromotive force by apparent resistance. But in such a motor, the counter-electromotive force is not of equal phase with the current, but lags behind the cur- rent the more, the lighter the load, and will come nearer in phase to the phase of the current when we increase the load. Hence, the apparent inductance is not even a constant, but a variable of the circuit, and exceedingly variable, too. The inductance is small, almost nil, if the motor is at rest under full head of pres- sure. As soon as the motor starts, its self-induction increases, up to a value which corresponds to the load the motor is carry- ing, so that if the motor is heavily loaded the inductance is com- paratively small, though very far from negligible, while, when the motor is running fight, its self-induction increases to such a value as to almost entirely shut off the current. Now I come to the consideration of this quantity (L — M). This quantity is really nothing but, or rather proportional to, that amount of magnetism, or that magnetism which constitutes the rotating magnet poles. So if the motor is at rest, heavy eddies in the short circuit armature-circulating coils, the useful magnetism is almost nil; almost no magnetism passes through the armature. Hence L is almost identical with M. The circuit has almost no self-induction. If the motor starts, runs with heavy load, then a certain amount of magnetism passes through the armature. Lis different from M. L has increased, and we get a difference of phase of the current and a different shape of the current wave. Mow, suppose the motor runs with almost no load, then the self- induction of the motor is very large and we can neglect R, the first term, entirely. - In this case the original shape of the electromotive force curve is entirely broken up and has changed into a somewhat harmonic shape. So I cannot think there is any hope to transfer any other shape of the curve but a simple harmonic through a circuit of heavy and very variable self-induction. That would be rather disappointing and very disagreeable for the builders of motors if the working of such rotary motors depended upon a certain shape of alternating current waves. Indeed, we all have heard and read half a dozen times—some of us even oftener—how bad and worthless the Tesla motoris, because there the fluctuations of the magnetism amount to, I believe, 41 per cent., and how grand and beautiful the improvements of Mr. Dolivo von Dobrowolsky are, because in his motor the fluctuations amount to only 14 percent., and if having heard and read something very often proves its truth, then it must certainly be true. At least this statement 28 PUPIN ON POL YPHASA L. GENERATORS. [Dec, 16, about the fluctuations of the intensity of the rotary magnetism seems generally to have been accepted as true. For I neverheard any doubt expressed on the correctness of this fluctuation theory. And, nevertheless, in the very first publication of Ferraris on ro- tating magnet poles, in the very publication which introduced this rotary magnetism to the public years ago, it has been shown that if you sent two alternating currents, one lagging behind the other by one-quarter of a period, through two coils at right an- gles with each other, those two currents produced in the centre of those coils a magnetic field which revolves with constant strength and constant speed. Let A in Fig. 16 represent the one, B the other one, of the two perpendicular coils, which are excited by two alternating currents \-Z JB FIG. i 6. * of 90 degrees difference of phase. Then the magnetism pro- duced by coil A at any time can be represented by the line, O m, = M sin % The magnetism produced by coil B at the time t is O my = M cos p where 27. % = 7 f T being the time of one complete period. These two magnetisms, 0 m, and 0 m, combine by the law 1891.] DISCUSSION. 29 of parallelogram, which as a consequence of the law of conserva- tion of energy holds, to the resulting magnetism: O m = M of constant strength, at the phase : m, O m = p = * of constant velocity. That means, the magnet poles revolve with constant strength and constant velocity, produced by true harmonic or sine- (waves." Coming, now, to the conclusion, we see 1. It is possible to produce rotary magnetism of constant strength and constant velocity of rotation by means of true sine- W8,VeS. - 2. It is hopeless to try to produce rotary magnetism of con- stant strength and velocity by means of a particular shape of the wave of E. M. F., because in a circuit of considerable and variable self-induction the shape of the current wave will differ in a con- siderable and a variable degree from the shape of the E. M. F. wave for any shape of the E. M. F. but the true harmonic or sine- Wa,Ve. - 3. Hence it is more advisable not to build the generators so that they produce that shape of E. M. F. which in a particular type of rotary motors will give magnetism of constant strength and velo- city; but to build motors which will give magnetism of constant strength and velocity from true harmonic or sine-waves, as the only waves which can be transformed, transmitted through in- ductive and other circuits without changing their shape; to build the rotary motors for sine-waves, as the possibility has been shown by Ferraris, and as already in the oldest Tesla motors it evidently has been the aim of the designer. [Applause.] DR. PUPIN :—Mr. Steinmetz went a little beyond the limits of this paper by talking about the motors. I said at the start that I was going to confine myself to the polyphasal generators and particularly to polyphasal generators which could under certain well defined conditions produce a rotary field of constant strength. I am going to consider in future the question of transformation and the question of rotating field used for driving a motor. Now, in the case that I considered, I simply had an iron ring sur- rounded by a set of coils and nothing else. I had no motor ar- mature here. In this case, L – M could very easily be made small in comparison to R, the resistance, and therefore may be neglected. But you need not neglect it. If (L – M) is not negligible, then the magneto-motive force will vary, but its varia- tion will be less than 14 per cent. How much less remains to be 1. Kapp : Alternate Current Machinery, page 82 30 PUPIN ON POf YPHASAL GENERATORS. [Dec. 16, seen. I don’t think that I can show it very well without entering fully into the discussion of the polyphasal motor and transformer. But this subject requires a carefully prepared paper to form a basis on which it can be advantageously discussed. If Mr. Stein- metz will have a little patience, I will promise to give him a chance to discuss these things also. As far as the Ferraris contrivance is concerned, I never saw that paper to which Mr. Steinmetz refers. There must be a hitch in it, I think. Perhaps Mr. Steinmetz will exactly explain the contrivance, so that we can see the magnetic circuit and see whether his ideas are correct or nºt. I know a great many mis- takes have been made on this very point of the magnetic circuit. Not enough attention was paid as to whether the magneto-motive forces worked in series or multiple arc, nor to the shape and dis- tribution of the magnetic circuits. But still, I would like to know the exact form of the Ferraris motor and the magnetic cir- cuits before I decide to comment upon it. MR. STEINMETz:—Ferraris built only a little toy, and his mag- netic circuits, so far as I know, were completed in air, not in iron, though that hardly makes any difference. The only possi- ble error there could be is the use of the law of parallelogram in combining M. M. F.’s acting in different directions upon a point, and this law of parallelogram, or polygon, is a consequence of the law of conservation of energy, and therefore its correctness can hardly be questioned. But as soon as you accept that, then the reasoning I have given here must be correct." So there is no pos- sibility of any error if the whole phenomenon takes place in air. Suppose, now, the phenomenon does not take place in air, but in any other medium of constant magnetic conductivity, then you have exactly the same conditions. The air space between arma- ture iron and field iron might introduce some discrepancy, though I hardly think so. But, then, the next problem would simply be how to shape the motor iron, how to distribute the wire coils, to get in the iron circuit separated by the air cap the same magnetic distribution as would take place without any iron in the air Dr. PUPIN :–As you have heterogeneous media, you cannot have complete homogeneous magnetic circuits, and that is where the difficulty comes in. Your parallelogram of magnetizing forces will not apply here, and you are forced to be satisfied with the ap- plication of Ohm's law to magnetic circuits, which will not give you the result you claimed a little while ago. MR. STEINMETz:—Consider that wire coils of iron are closely embedded in iron, then there is no question that the same phe- nomenon takes place in the iron as in Ferraris's experiment in air. So the only problem would be how to shape the iron practically, { 1. Exactly the same conclusion I find now given in Kapp, Alternate Cur rent Machinery, page 82. 1891.] I) ISO USSION. 31 to get rotary magnetism of constant strength and velocity from SIO €-W8,VéS. This three-phase current system has been brought up the last time as something entirely new. I cannot agree with that in the least. For already in the old Tesla motor the three phases of current, only that in the three wires that go out from the cen- tral station the three currents have not a difference of phase of exactly 120 degrees, but two have a difference of 9 degrees, and either one of these two currents has with the third a difference of hase of 135 degrees. But if now the “Allgemeine Electricitaets Gesellschaft” transmits currents of less than 120 degrees differ- ence of phase—well, then the Dobrowolsky system comes back exactly to the old three-wire system of Tesla, only that the motor is certainly built somewhat differently. But that does not matter. Mechanically, the motor is undoubtedly improved, for there are several years' time between the old Tesla three wire motor and the new German three phaser. Whether the latter shows any improvements in its principles, is a question which is anything but beyond doubt. - But in the new Dolivo von Dobrowolsky system of electric dis- tribution, I really cannot see anything new but the mechanical construction of motors and generators That it became so famous is, I think, entirely due to the success of the grand transmission of power over such an enormous distance as 116 miles, which cast a halo around everything that was used with this transmission, and so made the rotary motor famous; but, in reality, I think ordina- ry synchronous motors might just as well have been used, and would have worked just as successfully, so that the choice of the particular motor had nothing to do with the success of the power transmission. PROF THOMSON:—I should like to make some remarks upon the general subject of the paper. It is a matter to which I have given considerable thought. The subject is somewhat allied to the old Thomson-Houston arc machine. In fact, I remember long ago putting in a patent specification a machine connected so that it had not the three segment commutator but three rings, and it was rejected at the Patent Office on the ground that it was not an invention to put three rings on a three coil armature, any more than it was for any alternating current. But times have changed since then. . [Laughter.] It seems to me some light would be thrown on the matter of this discussion by a few simple considerations. We will take the three coil in its simple form— symbols for it, Fig. 17. Now let us lead a wire, J, here, which would be a neutral wire. If we wrap that wire around a mag- netic core, the effect should of course be the same or it should act the same as though these three wires, a, b, c, were wrapped around the magnetic core. So that if any fluctuations of magnet- ism were set up in this core by wrapping this neutral wire around the magnetic core, the same effect would be produced by 32 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, - wrapping these three wires around the magnetic core. That would show that no fluctuation might be expected in such a sys- tem. But there is another question that comes in just here. If we look into the manner of generating ; if we take our armature and put on three coils, and have a magnetic field which magne- tizes this armature core with a constant number of lines, a number of lines which does not change during the rotation—it is evident, then, that whatever actions occur in these coils will be accom- panied by no fluctuations of magnetism You cannot generate. in a system of coils any difference of condition which is not ex- pressed by the magnetic field in which it is generated. If the magnetic field is constant, then we have constancy of magnetism in the core. That is, we have no fluctuations. S. it would * (º, I, C FIG., 17. seem to me, looking at it from this standpoint, that putting an- other armature in connection with these corresponding terminals and having a magnetic field for it of constant strength, we would have a rotating field produced in this second armature which would result in the rotation of the armature itself—that is, the tendency to rotate the field would turn the coils backward and this would seem to indicate that under certain conditions we can, with the ordinary arrangements, produce exactly what we want, steady rotative effect without magnetic fluctuations, which would go to bear out the Ferraris idea. . Now, how far the production of a rotating magnetic field in the presence of a short circuited armature may modify these conditions, I have not investigated. It does seem to me, however, that in such case the remarks of 1891.] DISCUSSION. 33 Mr. Steinmetz are quite true, that we will have a large self- induction on a light load in such a motor and therefore a waste current, a leakage current corresponding to the leakage current in the transformer. Just how much it will be will of course de- pend on the general design and the proportions, and of course on the frequency of the alternations. I think the system demands that the frequencies shall be much less than we are accustomed to use in transformers for lighting. That the system will have a considerable application, I have not the slightest doubt. It will have a large application. Whether the best form of it is not to place two corresponding armatures in fields, or use synchroniz- ng machines, is a question. I should say, reasoning at the start, that this is probably the chief merit of the system. We have the possibility of getting rid of commutation on high potential trans- mission of power by making corresponding machines and run- ning corresponding armatures in the fields that are excited. Of course there is a great desire to get a motor which shall enable us to get rid of this constant excitation and which will give us the power of starting under load. The generator reversed and used as a motor, demands that in starting the generator shall also start, that the two machines shall come up together. I have, indeed, taken one Thomson-Houston arc machine and put on three rings and simply delivered the current by three rings to the armature of another machine, and it would start and run up to speed, having no load on it, at least no large load. It would get into synchronous rotation when the power delivered is, after exciting the field fully, considerable. I have constructed some small machines which are almost exactly like Fig. 10. There are six coils on the armature and a field excited separately. The field, by the way, rotates and the angle covered by the field poles is about what is covered there, Fig. 10. , I have no indication at all of anything wrong with these machines. They work, we think, perfectly, and so far as the heat generated in the armature goes, it is re- markably small. It is no greater, from actual experiment, than one would expect from an ordinary machine with a commutator. In fact, it is probably less. Probably more fluctuation is intro- duced into the magnetism by the commutation than there would be in this case by the simple use of three coils without commuta- tion. I would say further that I have never had much confidence in some of the reasoning of Mr. Dobrowolsky in relation to this matter. I have always thought that he was a little out in his ar- gument. He has attempted to show how, by using three phased currents, he could get polyphasal currents from them, by wind- ing the armature in a different way. It strikes me as nothing more than spreading that coil over a certain angle of the arma. ture surface. This, of course, would prevent sudden sharp jumps in the field and might be useful and undoubtedly is useful in the perfection of a motor working upon a closed circuit arma- ture. These matters of discussion would undoubtedly be best 34 PUPIN ON POI, YPHASA I, GENERATORS. [Dec. 16, settled by a simple experimentation on the basis of what I indi- cated a little while ago. It may be that the very fact of the dif- ferences of composition of the wave may make a very great difference in the effect. We may not be called upon to reason upon fluctuations of magnetism due to sine curves when those sine curve currents are put in different angular positions. They may act, as in that Ferraris affair, to balance each other and often- times these considerations escape us. I would say that there is another matter which probably ought to be taken into consideration. That is that a mass of iron does not always change its magnetism when you think it ought to. That is, it may hold up by its own inherent property of º ing reversal—by hysteresis. This would tend, in fact, to hold the magnetism up rather than to allow it to suffer fluctuation. We know that in a closed circuit transformer it is necessary to put energy into the iron to cause it to drop its magnetism. It would tend to remain magnetized if we cut off the current at any portion of a wave, at least up to a certain point, and this would tend to help us out in this very matter of getting rid of fluctua- tions of magnetism, which of course would be a serious loss of energy in the case of large bodies of iron, the magnetism of which should be allowed to go up and down through large ranges. There is another matter, too, that comes in here. It is whether we get in the motor or in the machine a motion that is equal ve- locity—that is, whether it is an even pull all the way around, the sum of the magnetic lines being the same, or whether it is a jerky motion, a motion of difference of velocity. Of course, it will naturally be seen at once that unless we get a perfectly uni- form flow, our efficiency could not be as high in the case of a fluctuating movement of the lines, and the lines which hesitate and then move forward and then hesitate again and then move forward, that would be only efficient in case the armature was negligible which, of course, could not be the case. R. C. S. BRADLEY :—Did I understand Prof. Thomson to say that he thought the increase of the phasing by Dobrowolsky’s plan was applicable especially to the closed armature ? PROF. THOMSON:—No, I made no distinction between the kind of armatures. I simply say that Dobrowolsky’s plan of multiplying the coils and connecting them up, did not differ very much, so far as I could see, from simply spreading those coils on the armature. MR. BRADLEY:—I understood you to say at the last that it applied especially to the closed circuit armature. PROF. THOMSON:—You mean by closed circuit armature, closed field and with connections taken out and around 3 MR. BRADLEY : —Yes. PROF. THOMSON :—No ; I did not make such a distinction. I should say that the closed circuit here would be just as effective for getting the polyphasal circuit, provided the coils do not cover too large an angle. 1891.] DISCUSSION. 35 MR. BRADLEY:—It is a pretty difficult thing to make a test as to the efficiency of the different armatures. But I have always had an idea that the closed coil armature was exactly adapted to the carrying out of the three phase, because the currents can pass in more directions. There are more subdivisions than there are in the open circuit. With three open coils the position of each would determine its phase. But if it were completely closed and taken out at three points, there is a chance for two wires to operate and leave the third one nil, and the current has a chance to pass clear around the armature. That is, it will pass 120 degrees on one side and 240 degrees on the other side, making a multiple arc circuit. In other words, the closed coil armature carries out the plan that Dobrowolsky is trying to carry out, and does exactly what Dobrowolsky is trying to do by placing on the extra coils, without the extra coil. * PROF. THOMSON:—I think that matter is made clear by consid. ering the movement of the armature with respect to the lines. It does not seem to me to make very much difference what the coil is, providing the two armatures—suppose we take that as the typical system—the two machines are connected similarly. The movement. of lines in one will be reproduced in the other, pro- vided of course that the order of the connections and the symme- try of the apparatus are preserved. MR. BRADLEY :—I tested machines running that way. They were direct current machines altered to the three rings. I took them first and ran them as direct current machines. Then I had them changed and put three rings on each one and connected them up, and ran them together with the same power, and took off the same power, and I found the machines ran so nearly alike that I could not detect the difference. By the way, in your speaking of two machines, you have not at any time said motor and dynamo. PROF. THOMSON:—I, of course, meant motor and dynamo. It might interest the members for me to say that at one time, I think it was about 1882, I happened to have a three coil are ma- chine that had three rings on the shaft, and I discussed with my assistant. Mr. Rice, who is now superintendent of the Thomson- Houston works, this matter of connecting on three rings on two machines, and we found that the machines would work well as a means of transmitting power. But we had not facilities for building such apparatus in any quantity. However, it is an in- teresting reminiscence, as coming up at this time. MR. STEINMETz:—With regard to the spreading out of the coils on the armature, I think this makes very little if any differ- ence in the shape of the wave, because if we had a coil of one single turn we would get a simple harmonic or sine wave where the maximum electromotive force = 1.414, the effective E. M. F. Now, only a few days ago I had occasion to draw the curve of electromotive force under exactly the opposite conditions, the 36 PUPIN ON POLYPHASAL GENERATORS. [Dec. 16, most extreme case of spreading out the coils. A smooth contin- uous current armature changed into a bipolar alternator by con- necting two opposite commutator bars with sliding rings, and I found as ratio between maximum E. M. F. and effective E. M. F.: 1.415 ; that is, exactly the same value as the sine wave gives. I found a wave somewhat similar to the sine wave, slightly differ- .."; with a tendency to the shape that Dr. Pupin showed us here in Fig. 8. * . Fºr THOMSON –In making the remark as to the covering of the coils, I meant a motor with a closed circuit armature—not in relation to the generation of the current. MR. KENNELLY :—This is a paper which, I think, has to be studied from two points of view. Like all mathematical papers, it presents two different aspects. We are face to face with a condition in the art of electrical distribution which is not only somewhat novel, but is also very intricate, and consequently any assistance, even of the most elementary description, which will enable us to fathom the mysteries of this difficult system of distri- bution, is one which should be only too gladly welcomed, I think, at the hands of this Institute. We have presented to us in this paper, a mathematical disquisition on the very simplest and most elementary type of the three phase generator, in which it is assumed that there is no armature reaction, no hysteresis and no eddy currents. Under those conditions, just as in the correspond- ing ideal transformer with constant coefficients, which has been called by some one the “phantom' transformer, that we all aspire so much after but so very seldom see—the fundamental opera- tions of this particular machine are readily capable of being ana- lyzed by the skill that has been presented in this paper. I think that we should be content to take one subject at a time, to con- sider that we have arrived at a position where modifications which will certainly present themselves by disturbing influences, will ultimately resolve themselves into this fundamental type, as they are lessened and removed. This is the starting point, so to speak, from which the various roads branch from the theoretical machine to the practical machine. I think, therefore, that while the paper gives us what may be called almost a little discovery, in its way, in practical mathematics, that it should be treated for its own value on the side of a mathematical essay, and not brought into the question of practical and everyday machines. We have the very remarkable fact that although the electromotive force which is capable of being produced by a complex condition of magnetic fields can be a uniform one, and while the currents which are set up by the electromotive force cannot possibly be the prototype of the electromotive force, graphically, when there is any self-induction in the circuit, yet that under the influence of mutual induction, that prototype may be restored. That is a beautiful conception, even although it may not have a very direct bearing on the practical side of the question. It seems to me that 1891.] DISCUSSION. 37 the practical issue of the question is not whether we can produce artificially and with considerable care a constant rotary magnetic field or a constant rotary electromotive force, for by theory we can produce any continuous curve; and any periodic wave can be established as the resultant of a number of simple harmonic waves, it only is a question of how many compounds we want. Sometimes we should want an infinite number. But however interesting that may be from the theoretical point of view, the next step in this difficult pathway which has been outlined here to-night, is not how to produce perfection, but how far differ- ences from perfection will affect the practical result; not how necessary it may be to have a perfectly continuous field, but how far the fluctuations which will almost inevitably present them- selves, will affect the efficiency and efficacy of these particular machines. At the same time, while we have to remember that the paper is a theoretical disquisition, it is also the first step towards practice, because theory follows ever slowly in the steps of practice, and it is in the direction of such a theory that we have to hope for the ultimate apprehension of all the difficulties before us. DR PUPIN :—The method which I have employed, as Mr. Ken- nelly remarked, is to go step by step from the ideal to the more and more practical, and see what the real difficulties are. Now, as long as we deal with simple harmonic waves, the question is exceedingly simple and is readily solved. The authorities on theoretical electrical engineering invariably consider the simple sine waves whenever they discuss the subject of periodically vary- ing electric currents. Nobody has ever tackled the problem of complex harmonic waves. We really do not know what a com- plex harmonic wave will do. We can only guess at it. There are no quantitative relations. Now, I think that I have shown in this paper what a complex harmonic current wave will do in a particular case. I also propose to show before long what it will do in other practically important, but more complicated cases. Mr. Steinmetz points out that a combination of two simple sine waves can produce the same thing which I claim for the complex wave. But the correctness of his statement requires the employ- ment of a homogeneous magnetic medium in which his two coils are to act. I would be very much obliged to him for the proof of the contrary. The remark of Prof. Thomson with reference to the machine which he put on the blackboard, three coils rotating in a uniform field, has been answered in the very beginning of my paper. They will produce a constant rotary field, although the producing field, the exciting field, is constant. The relation of the coils with respect to the exciting fields, is continually varying, and the electromotive force produced in each one of those is a simple sine wave, and as long as we have simple sine waves and three phases, there will be a maximum variation of fourteen per cent., 38 PUPIN ON POLYPHASAD GENERATORS. [Dec. 16, no matter what you do. Now wind the three wires on a piece of iron. The neutral wires will produce no magnetization. The three wires, if they are wound around the same coils in the same way will also produce no magnetization. So I do not think that the experiments suggested by Prof. Thomson could give us any record of any fluctuations in the rotary field. With respect to the production of that particular wave, Mr. Steinmetz remarked that it is impossible to produce anything like it. Of course, in nature there are no discontinuities. Nature hates discontinuity, and there are no absolutely discontinuous functions. Here, you see (Fig. 8), the tangent is continually constant at all points until the corner is reached, when the tangent suddenly becomes zero. This discontinuity is, of course, physically impossible, but in practice we can come as near to it as we choose to do, if we care to take the trouble. Of course, we would employ a practically discontinuous field. That is, you are in a place where there are lines of force, and suddenly you step into a place where there are practically no lines of force. Now, absolutely, that is impossi- ble. But we can come as near as we choose to, by simply shaping the magnetic circuit in such a way that it will be nicely rounded and allow the lines of force of the magnetizing coils to follow it without getting too much out of their way. If you do that, then there will be practical discontinuities. Now, I have an electro- magnet which will do that very nearly, where the lines of force of the magnetizing coils never deviate too suddenly from the magnetic circuit, and therefore there is very little leakage. I hope at some future time to show before the Institute, this electro-magnet. It is a very simple device. I do not say that I can produce that electro-magnet without sacrificing several practical advantages. But if it is only for experimental purposes, I do not care if I do sacrifice them. I dare say I will not rest until I get that electromotive force given in Fig. 8, plotted on paper from experimental results. But it is very difficult to do anything in New York in a hurry, because mechanicians will not attend to their orders when you wish them to, and you have to wait for them. As Mr. Kennelly remarked, I do not think it is time yet to consider what will take place when we apply this rotary field to drive a motor, because I wish to limit the discussion to the limits of the paper. - MR. STEINMETz:—With regard to this Ferraris scheme, I only wanted to show that under certain conditions a rotary field can be produced by sine waves of electric current Suppose you have two equal coils at right angles with each other, entirely embedded in iron. The armature of the Pacinotti, or a similar type, with a very small clearance between armature iron and field iron, so small a clearance that the air reluctance can entirely be neglected against the reluctance of the iron—then you have exactly the conditions where you get from two sine waves of 90 degrees difference of phase, a system of magnet poles which revolve with constant intensity and constant velocity. Standing Committees appointed by direction of Council : Editing and Library Committee. GEORGE_A. HAMILTON, JO. STANFORD BROWN, FRANKLIN L. POPE, Editing. GEORGES D'INFREVILLE Library. FRANCIS B. CROCKER. ČEöRöE. H. STOCKBRfISGE. Committee on Membership, etc. RALPH. W. POPE, Chairman. THOMAS D. LOCKWOOD, Local Secretary, Boston, Mass., Dr. LOUIS DUNCAN, { % $ 4 Baltimore, Md., CARL HERING, 4 º' { * Philadelphia, Pa., Prof. EDWARD L. NICHOLS, º . Ithaca, N. Y., -, Prof. W. A. ANTHONY, JOSEPH WETZLER, New York. GEO. B. PRESCOff, jr., New York. Committee on Finance, Building and Permanent Ouarters. GEORGE M. PHELPS, Chairman. GEORGE A. HAMILTON, Dr. SCHUYLER S. WHEELER, THOMAS A. EDISON, FRANKLIN L, POPE, FRANCIS R. UPTON, T. COMMERFORD MARTIN, DR. F. BENEDICT HERZOG. Committee on Papers and Meetings. T. C. MARTIN, Chairman, GEORGE M. PHELPS, New York, JOHN W. HOWELL, Har- rison, Nj., HüBERT Howson, New York, is S&Hüyüß’S, WHEELER, New Yºrk. Committee on Units and Standards. A. E. KENNELLY, Chairman. GEO. B. PRESCOTT, Jr., GEO. A. HAMILTON, DR, WM. E. GEYER, FRANCIS B. CROCKER. & Manchester, Ct. Transactions of the Institute Already Published. [Complete sets of the first four volumes are out of print.] Vol. V, 1887–8. ON ELECTRIC STREET CARs, witH SPECIAL REFERENCE to METHops of GEARING. Anthony Reckenzaun, of London. No. 1, October, 1887—A Coulom B METER, or INSTRUMENT For MEASUR- ING THE Consumption of Electricity. (Illustrated.) Prof. George Forbes, F.R.S., of London. No. 2, November, 1887—Recent IMProveMENTS IN APPARATUS For OºAN CABLING. (Illustrated.) Charles Cuttriss. Supplementary Note on the Siphon Recorder, and Ocean Telephony, by Thos. D. Lockwood. No 3 December, 18.7—PHENOMENA of RETARDATION IN THE INDUCTION Coil. (Illustrated.) William Stanley, Jr. No. 4, January, 1888.-REVISION of THE PATENT.L.Aw. Arthur Steuart, Esq. No. 5, February, 1888.--ELECTRIC ENERGY PROM CARBON WITHOUT HEAT. Willard E. Case, Auburn, N.Y. No. 6, March, 1888.--ALTERNATING CURRENT ELECTRic Motors. Dr. Louis Duncan, Baltimore, Md. o. 7, April, 1888.-MAXIMUM EFFICIENCY OF INCANDESCENT LAMPs. (Illustrated.) John W. Hºeſ o. 8, May, 1888.--PROTECTION of THE HUMAN Body FROM DANGEROUS CURRENTs. Patrick B. Delany.—THE Possibilities AND LIMITATIONS OF CHEMical GENERAtors of ELECTRICity. Francis B. Crocker. No. 9, June, 1888–ON ComPEN- sATED Resistance STANDARDs. (Illustrated:) Edward L. Nichols. A NEW SYSTEM of ALTER- NATECURRENT Motors AND TRANSFORMERS. (Illustrated.) Nikola Tesla. UNDERGROUND ELEC- TRICAL ConDUCTors IN EURoi E AND AM &RICA. Prof. G. W. Plympton. THE P TENT Court AND UNIForMITY IN PATENT OFFICE PRACTICE. - George H. Stockbridge. A Sw1NGING ARM GalvanoMETER.T (Illustrated.) .# S. Moler. No. ro, July, 1888. THE Solu Tio N of THE MUN1cipal RAPID TF ANSIT ProBLEM. (Illustrated ) Frank J. Sprague. No. 11, August, 1888. Some onjections to the OYERHEAD CoNPuctor For Electric Railways, M. B. Leonard, Note on G#ARING For ELECTRIC RAILway MotoRs, Almon Robinson. No. 12, September, 1888. Vol. VI, 1889. [Including October, November and December, 1888.] THE GEveR-Bristol METER For DIRECT AND ALTERNATING CURRENTs. [Illustrated.] Prof. William E. Geyer. THE ABDANK_MAGNET1c CALL AND THE ABDANK INTEGRAPH. [Illustrated.] E. Abdank-Abakanowicz. No. 1, January, 1889. Six YEARS PRACTICAL ExperiFNCE witH THE Edison Chemical METER. (Illustrated.) W. J. Jenks. No. 2, February, 1889. LIGHTNING AR- resters and THE PHOTOGRAPHIC STUDY of SELF-INDUCTION. (Illustrated.). E. G. Acheson. No. 3, March, 1889. A New SystEM of Multiplex TELEGRAPHY. (Illustrated.) Lieut. F. Jarvis Patten, LightNING ARREstERS AND THE PHOTOGRAPHIC STUDY OF SELF INDUCTION. Notes by o, Stanford Brown and Chas. T. Child. REPLY TO THE Notes of MESSRS. Brown AND CHILD by }. G. Acheson, No. 4, April, 1889. THE EFFICIENCY of METHODs of ARTIFICIAL ILLUMINATION. Illustrated. Edward £. ichols. No. 5, May, 1889. Som E RESULTS witH SECONDARY BATTERIES IN TRAIN LIGHTING. (I)lustrated.) Alexander S. Brown. THE INHERENT DEFECTS OF LEAD Storage BATTERIEs. (Illustrated.) I) R. Louis Duncan. ELECTRIC MOTOR REGULATION. (Illus- rated.) Francis B. Crocker. Nos. 6 and 7, June and July 1889, (Double Number). MAGNETISM IN Its Relation To INouced ELECTR, 'Motive Force AND CURRENT. (Illustrated ) Prof. Elihu Thomson of Lynn, Mass. ON THE RELATION BETWEEN THE INITIAL AND THE Average EFF- ciency of INCAN descENT LAMPs. (Illustrated.) W. H. Peirce of New York. THE EFFICIENCY of THE ARc LAMP. (Illustrated.) H. Nakano, of Japan, with an introductory_note by Prof. E. L. Nichols. The SPIRAL Coil VoltaMETER. (Illustrated.) Harris J. Ryan, of Ithaca, N. Y. THE PERsonal ERRoR IN PHoToMETRY. (Illustrated). Prof. Edward L. Nichols, of Ithaca, N. Y. ON Modern Views witH RESPECT To Electric CURRENTs. (Illustrated.) Prof. Henry A. Rowland, of Baltimore. Md. CLASSIFIED List of MEMBERs. Nos. 8 and 9, August and September, 1889, (Double Number.) No. ro, October, 1889. Some RECENT ELECTRICAL WoRK on THE ELEVATED RAILROADs. (Illustrated.) Leo faſt, of Plainfield, N. J. ALTERNATING CURRENT MOTORs: THE. Evolution of A New Type. (Illustrated.) Lieut. F. Jarvis Patten, of New York. No. 11, No- vember, 1889. Electrical Notes of A TRANs-ATLANTic TRIP., Thomas D. Lockwood, of Boston, Mass. Somºg METHops of REGULATING Accumulators IN ELECTRIC LIGHTING. (Illustrated.) George B. Prescott, Jr., of New York. No 12, December, 1889. ForMAND EFFICIENCY OF INCAN- DRscent FILAMENTs. Charles J. Reed of New York. TELEGRAPH LiNE ADJUSTMENT:--Nots on A New GRAVITY CELL. P. B. Delany of New York. * Vol. VII. 1890. TRANSFormers. (Illustrated.) Harris J. Ryan, No. 1, January, 1890. A RRVIEw, of The MoDERN. Theories of ELECTRIcity. (Illustrated.) Prof. W. A. Anthony. No. 2. February, 1890. Tºg PRActical Working of a HE Electrical Subways of New York CITY. . (Illustrated.) William Maver, Jr. No.3, March, 1890. Some TESTs on THE EFFICIENCY QF ALTERNATING CURRENT Apparatus. (Illustrated.) Dr. Louis Duncan and W. F. C. Hasson. No.4, April, 1890, biºgnomeNA of Alternating Current INDUCTION. (Illustrated.) Prof. Elihu Thomson. E. Ectricity IN THE NAvy. Gilbert Wilkes, No. 5, May, 1890. ELECTRIC LIGHTING IN THE Tropics, wilfrid H. Fleming, LIFE AND FFFICIENCY of Arc Light QARBONs. ſº Louis B. Marks, Practical Aspects of THE ALTERNATING.CURRENT THEORY: , I. Pupin. MAGNetic DATA of the SPRAGUE STREET CAR Motor. (Illustrated.) H. F. Parshall. HE inpusrº Al Utilization of THE Countrir ElectroMotive Force of SELF-lnDUCTION, Thomas D. Lockwood. Nos. 6 and 7, June and July, (Double Number.) LIFE AND EFFICIENCY of ARC LIGHT CARBons Discussion. (Illustrated.) PRACTICAL ASPECTs of THE ALTERNATING Currºr THFory. Discussion. Note on A New PHOTOMETER. (Illustrated.) Dr. Edward L. Nichols of Ithaca, N. Y. THE LIMITAtions of S. EAM AND ELECTRIC TRANSPORTATIQN. (Illus- trated.) Oscar T. Crosby, now of New Orleans, AUTOMATIC ELECTRIC WELDING MACHINFS, Hermann Lemp, Jr., of Lynn, Mass. Nos. 8 and 9. August and September, (Double. Number.) #FFICIENcy of TRANSFormers. (Illustrated.) Calvin Humphreys and W. H. Powell, NoTES gººn some Experiments witH ALTERNATING CURRENT. APPARATUS. (Illustrated., --Prof. Harris j. Ryan. CATalogue of MEMBERSHIP. Revised to November 1st. 1890, No. ro October. PRELIMINARY REPORT of the STANDARD WIRING TABLE Committee. REsolutions on Adoption of AMERICAN NAMEs for Electrical UNITs. INvestigation of THE STANLEY ALTERNATE CURRENT Arc DYNAMo, W. B. Tobey and G. H. Walbridge. A NEw METHod of ANALYzin G ARMATURE REACTIONS, APPLIED TO THE STANLEY ARC LIGHT ALTERNATING CURRENT MACHINE. Thorburn Reid. No. 11 November. Revised REpoRT of THE STANDARD WIRING TABLE Committee. THE THEORY OF COMPOUND WINDING For Constant Potenti AL. (Illus- trated.) Dr. Louis Bell, of New York. A NEw MEthod of ANALyzing ARMATURE REACTION's of ALTERNATors. Charles Steinmetz, of Yonkers, N. Y. List of New Associate MEMBERs. Elected Sept. 16th, Oct. 21st. Nov. 18 and Dec. 16th. No. 12 December. - Vol. viii. 1891. INDUCTANCE, AND its' Proposed UNIT, THE “HENry.” (Illustrated.) By A. E. Kennelly. THE IMPROVED GRAMoPHoNE. (Illustrated.) By Emile Berliner. No. 1; January, 1891. INDUCT- ANCE, AND its Proposed UNIT, THE “HENRY”’ REPokt of Committee on VALUATION of THE HENRY, Joint Discussion. No. 2, February, 1891. REPORT of HIGH SPEED ELECTR1c RAILw AY Work. (Illustrated.) By O. T. Crosby. THE INVENTions of Thomas DAVENPort. (Illustrated.) By Franklin L. Pope. No. 3, March, 1891. INDUCTive DISTURBANces IN TEl E- PHoNE CIRCUIts. (Illustrated.) By J. J. Carty. No. 4, April, 1891. ELECTRICITY IN THE PRO- Duction of ALUMINIUM, (Illustrated.) By Alexander S. Brown. Some Possible MoDIFICATIONs IN THE METHods of Protecting Buildings FROM LIGHTNING. By N. D. C. Hodges. No. 5, May 1891. REPORTs of Council AND TREASURER. OFFICERS ELECTED. THE PERFECTION of Station ARY ELECTRIC Motors. (Illustrated.) By Francis B. Crocker. A Photographic STUDY of the ELECTRIC Arc. (Illustrateu.) Ry Edward L. Nichols. A New GRAPH icAL METHop of CALCULATING LEADS For WIRING. (Illustrated.) By Carl Hering. A THERMo- ELEctric Method of Srudying STEAM CYLINDER Cox DENSAtion IN STFAM ENGINEs. (Illus- trated.) By Edwin H. Hall. THE PRACTICAL Aspects of ELF ctric WELDING. By Freder c A. C. Perrine. ExPERIMENTs witH ALTERNATE CURRENTs of VERY HIGH FREQUENCY. (Illus- trated.) By Nikola Tesla. Nos. 6 and 7, June and July, 1891. AN ALTERNATR CURRENT Potentiometer. (Illustrated.) By Geo. S. Moler. Considerations WHICH SHOULD Gover N THK SELEction of A RAPID TRANSIt SYSTEM. By F. J. Sprague. ELECTRIC METERs. By Geo. W. Walker. A Study of AN OPEN CoIL ARC DyNAMo, (Illustrated.) By Milton E. Thompson. THE FUTURE of the ALUMINIUM Problem from TF, E CHEMICAL STANDPoint. By Wm. H Wahl. SHALL “ALUMINUM '' BE “ALIUM.” By Oberlin Smith. No.TEs on ELECTR1city IN MINING Work. (Illustrated.) By Sydney F. Walker. Nos. 8 and 9 August and September, ON THE RET ATION of the AIR GAP AND THE SHAPE ºf THR Poi.Es to THE PERForMANCE of DYNAMo ELECTRIC MACHINERY. (Illustrated.) By Harris. J. Ryan. No Io, October, 1891. MAGNRT1c Reluctance. (Illustrated.) By A. E. Kennelly. Report of CoMMITTEE on UNI is AND STANDARDs, RFPoRT of DELEGATION to FRANKFort INTERNATION AL Electrical Congress. No. 1 r. November, 1891. NotES on THE FRANKFort ELECTRICAL Exhibition. By Carl Hering. ON PolyPHAsal GENERATORs. (Illustrated.) By M. I. Pupin. Catalogue of MEM- BERS AND PUBLICATIONS, December, 1891. - §§§º: {33tº rºº º § R; §§ §§ Wºº... - - •º , ºr - - T- Nº 3-v ſ : - ~ 2:- :*: *iz, * ºt: * > & + ºr - - - - *** * * : ,5: Sº & º; ..." º ; : XXº ; : *:3-2:... . . … w r - º & sº • • *-*...* - × - & - - 2 - * * * • * *** .. Y. ce. * Yºº º 4, X: , * * * * , ***, * ,\ . w 4." * * * * * ***** . . *.*.*.* ... "…” *- - s" - ºf- .*, * , ºzº'º * ~ ºf ‘’ : . * > * * * * FV. . . . . . . .'; . . . ." :* --. * -, - * * *: - f ...' º 7~ r - - "… c - .." - APRIL, 1892. Established by BENAMIN sILLIMAN in 1818. T H E AMERIC AN JOURNAL OF SCIENCE EDITORS JAMES D. AND EDWARD S. DANA. Associate EDITORs PROFEssoRs JOSIAH. P. COOKE, GEORGE L. GOODALE AND JOHN TROWBRIDGE, of CAMBRIDGE. Professors H. A. NEWTON AND A. E. VERRILL, of - NEw HAven, PROFEssoR GEORGE F. BARKER, of PHILADELPHIA. T H 1 R D S E R I Es. VOL. XLIII.-[WHOLE NUMBER, CXLIII.] No. 256.—APRIL, 1892. WITH P LATE XII. --- - - - - - ------- - - - - - - - ---4--- NEW HAVEN, CONN.: J. D. & E. S. DANA. 1 S 9 2. | TUTTLE, MOREEIOUSE & TAYLOR, PRINTERS, 371 STATE STREET. *-- - - -ā- Published monthly. , Six dollars per year (postage prepaid). $6.40 to foreign sub- seribers of countries in the Postal Union. Remittances should be made either by money orders, registered letters, or bank checks. - A. E. FOOTE, 4116 Elm Avenue, Philadelphia, Pennsylvania, U. S. A. CALIFORNIA RUBELLITES. We have just received from a new locality in California, some remark- able specimens of Rubellite. The well defined, columnar crystals, many of them from one to two inches long and showing distinct ter- minations, occur principally in radiated aggregates imbedded in a Lepidolite rock. These specimens are exquisitely beautiful, all of them. presenting the same uniform shade of rose-pink in a pale lilac setting of Lepidolite, forming a combination of colors rarely equalled. NEW MEXICO MINERALS, From our collector in the Organ Mountains we have just received eight boxes of minerals, the result of several weeks work at the Wulfenite locality. Among the finer specimens of this shipment are several large, beau- tiful Aragonites and a new type of Wulfenite, brownish yellow in color, occurring in crystals of from one to three inches in diameter with perfect terminating edges. Also some beautiful, transparent yellow Wulfenites with perfect terminations. * Among other recent arrivals are Colemanites; translucent doubly terminated Vanadinites; Guanajuato minerals, including Calcites, Poly- basites, Argentites and other silver minerals. A fine lot of precious Opals in the matrix. From Arkansas, crystallized Eudialyte, Perofskite in the rock ; Manganopectolite and fine crystals of Pseudoleucite. A large and fine assortment of Diaspores and Margarites, Polished sections of Jasperized Wood from Arizona. Rare and inter- esting crystallized Gold on Galenite from Colorado. Cobaltite, Linnae- ite, Stannite, Euchroite, Libethenite and many others. We shall be glad to send any of the above on approval to those wishing to see them. The new Catalogue of Minerals and Mineralogical Books, 128 pages, containing many illustrated scientific articles, will be sent free to all intending purchasers who request it, on headed paper and to all cus- tomers; to others it will be sent post paid on receipt of 5 cents, or on heavy paper 10 cents, bound in cloth 35 cents. Many pages are devoted to a mention of the Minerals collected by Prof. Foote in various parts of the world. * The Leisure Hour containing full details and price list is sent free, or on heavy paper for 5 cents. The full Mineralogical Book list of over 50 pages is sent free, or on heavy paper 5 cents. Book lists on all the departments of Science are sent free, or on heavy paper 5 cents, except the Medical list which being extra large costs 10 cents on heavy paper. The following are a few of the many thousands of extra rare and valuable books in stock. Kent. Manual of Infusoria. 3 vols. 53 plates. ht. mor. 1882-- $18.00 Morgan. American Beaver. 1868 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5.00 Popular Science Monthly. Complete set to 1892 - - - - - - - - - - - - - - - - 35.00 Nature. Complete set to 1892 - - - - - - - - - - -------------- - - - - - - - - - - 50.00 Works of Hugh Miller, 13 vols., hf. cf. ------------------------ 6.00, Lesley. Dictionary of Fossils. 3 vols. 3,000 illustrations. 1890 3.00 Harvey. North American Marine Algae. 50 colored plates. 4to. 15.00 Greville. Tables of Diatomes. 81 plates-------- - - - - - - - - - - - - - - - - 5.00 LeConte and Horn. Coleoptera of North America.-- - - - - - - - - - - - - - 2.00 Fig. 3 Fig. 5 T H E AMERICAN JOURNAL OF SCIENCE [THIRD SERIES.] <-O-º- ART. XXXII — on the Action of Vacuum Discharge Streamers upon each other; by M. I. PUPIN, Ph.D., of Columbia College. With Plate XII. - VARIOUS phenomena which I observed in the course of an investigation on the coronal effects produced by electrical dis- charges through rarefied gases, led me to the belief that under certain conditions two electric current filaments in a rarefied gas may act upon each other oppositely to the direction of their mutual electrodynamic action, and that this additional action may sometimes be far predominant over the electro- dynamic action; that is to say, we have a strong repulsion where electrodynamic action would produce an attraction. A brief account of these investigations was given on Feb. 8th, before the Astronomical Section of the New York Academy of Sciences. The following paper is limited to the description of the experiments by means of which the existence of the above mentioned action was definitely proved. Fig. 1 represents the apparatus first employed. Four glass bulbs, A, B, C, D, each having a capacity of about a liter, are connected by four glass tubes of small bore to a glass reservoir E. A stopcock F serves to connect the apparatus to a mer- cury pump. The reservoir has a diameter of 10° and a length of 22". The mouths e, f, g, h, of the four narrow-bore tubes form a square whose side is 10° long. The bulbs are covered with tinfoil and the tinfoil is then well coated with paraffin. AM. Jour. ScI.--THIRD SERIES, Wol. XLIII, No. 256.-APRIL, 1892. 17 264 Pupin—Action of Vacuum Discharge Streamers. Each tinfoil covering has a well insulated copper wire attached to it. Fig.1. After producing a 2* vacuum in the apparatus the bulbs A and B were connected to the secondary poles of a small Ritchie induction coil, whose primary was fed by an alternating current of 125 periods per second. The electromotive force in the secondary coil was varied by varying the current in the pri- mary; this was done by means of a resistance box in the pri- mary circuit. The electric flow between the bulbs is, of course, due to the condenser effect between the tinfoils and the V8,Oll Ul II] . - At the pressure of 2* the discharge was easy, steady and very diffuse along its path through the reservoir. Discon- necting AB and connecting CD to the induction coil the dis- charge was the same in character as before. Connecting both pairs of bulbs in parallel to the induction coil, that is, the bulbs A and C to one pole and B and D to the other pole, the two discharges, going on simultaneously, were the same in character as before, except that they were somewhat convex towards each other. - - g The pressure was then increased by turning the stopcock once around and allowing some air to get in. The discharges were less diffuse but more luminous, and less convex toward each other. - With the increase of pressure the discharges became less and less diffuse and their convexity towards each other diminished until, when a certain gas pressure was reached, it disappeared. At this point the discharges were very little diffuse and when allowed to pass through the reservoir simultaneously they re- mained rectilinear, but somewhat unsteady, oscillating quite appreciably about their rectilinear paths through the reservoir, Pupin–Action of Vacuum Discharge Streamers. 265 but the oscillations were always in the plane common to their rectilinear paths. - The pressure was still increased by turning the stopcock once around and allowing some more air to get in. The dis- charges became still less diffuse along their path through the reservoir and when allowed to pass one at a time they were quite steady and rectilinear. Both being allowed to pass through the reservoir simultaneously they were appreciably concave toward each other, but the concave arcs were in the plane passing through their shortest path in the reservoir. There was evidently a repulsive force acting between the dis- charges. This repulsive force increased continually with the increase of pressure in the vacuum, but with the increase of the force the steadiness of the discharges along their paths through the reservoir when they were both passing simultaneously gradually diminished. Fig. 3 (Plate XII) is a photograph of the discharges when taking place simultaneously in a vacuum in which the repulsive force just described was moderate. Fig. 2 is a photograph of the same discharges, but when taking place one at a time. Fig. 2 indicates that there is a repulsion between the discharge and the nearest wall of the reservoir, but this repulsion is very small in comparison to the repulsion acting between the streamers, when they take place simulta- neously, as fig. 3 indicates. The photographs were taken by very short (1 to 1% second) exposure, so strong is the luminosity of these discharges. They were taken when the repulsion was moderate, because when the repulsion is very strong the dis- charges oscillate very rapidly, so that they could not be well photographed with the apparatus employed. When the repul- sion was so strong as to cause the streamers to curve way out and from time to time strike the nearest wall of the reservoir, the vibrations became very violent every time the streamers struck against the walls. They rebounded against the walls just as if they were luminous vibrating strings. At this pressure in the vacuum it was very difficult to start the discharge and I had to strain the alternating machine and the induction coil to their utmost to make the start.” But when once started the discharge continues without any inter- ruption even if the potential at the tinfoils is lowered 15 to 20 per cent. The rate at which the temperature of these discharges in- creased with the increase of pressure in the vacuum seems to be much more rapid than the increase of the pressure; (the impressed e. m. f., of course has to be increased with the pres- sure) and with the increase of the temperature the luminosity .* A gentle touch of the apparatus with a conductor will sometimes start the discharge at once when all other means of making this start fail. 266 Pupin—Action of Vacuum Discharge Streamers. of the discharge increased also. With the increase of lumin- osity the color of the discharge changed from the pink color, which is the characteristic color of the ordinary Geissler tube discharges through rarefied air, to a color which inclined more and more toward the white. With the increase of the pressure the diffuseness of the discharge disappeared, but instead of the diffuse pink color there appeared a beautiful green phospho- rescent light which filled the whole reservoir. This phospho- rescent light is so strong, that even an almost instantaneous exposure is sufficient to give it time to act upon the sensitive plate, as appears from the photographs in figs. 2 and 3. At some future date I shall describe experiments which seem to be a strong proof that phosphorescence produced by electrical discharges depends on the temperature and only in so far on quantity of the discharge and on the vacuum, as the tempera- ture of the discharge depends on them. The investigations of Crookes, Goldstein, and others lead to the conclusion that a high vacuum with its cathode rays is most favorable if not indispensable to the development of strong phosphorescence. In my experiments a good vacuum (of about 2") gave no phosphorescence whatever, whereas a poor vacuum (even with as high a pressure as 100*) gave very strong phosphorescence, and that too not only in places where the discharge struck the walls of the vessel but also in places which were far away from the discharge. Presently I shall describe an experiment which shows that the gas as well as the glass becomes strongly phos- phorescent. My observations cannot, therefore, be well recon- ciled to those of Crookes, Goldstein, etc., unless the cathode rays be supposed to be very thin and very hot discharge filaments. I have several experimental facts which speak in favor of this hypothesis, but a discussion of them would lead me beyond the limits of this paper. I find that some astrophysicists assume the existence of a repulsive force acting between the streamers of the solar corona; it was the peculiar behavior of the corona-like vacuum discharges which, in addition to other phenomena that came under my observation, forced me to assume that repulsive forces must be active between the filaments of these discharges, although at that time I was perfectly ignorant of the details of the various electrical theories of the solar corona. The streamers of these discharges are very unsteady and very much split up when the vacuum is poor. A photograph of a dis- charge of this kind is given fig. 4. As the vacuum improves the corona-like discharges become a great deal steadier, less torn up and quite diffuse, but never uniformly distributed over the whole spherical electrode. Fig. 5, represents the photograph of a discharge in the vacuum of about 20" pres- Pupin–Action of Wacuum Discharge Streamers. 267 sure. These photographs belong to my collection of photo- graphs of corona-like vacuum discharges, an account of which I expect to give at some future time. The question arose then, naturally, what is the cause of this repulsion ? Electrostatic action suggested itself first, of course. But various observations which I made during my investiga- tions on vacuum discharges made me favor another view, the view namely, that the repulsive force between vacuum dis- charge streamers is due to a strain in the vacuum produced by the peculiar distribution of the gas pressure resulting from the peculiar distribution of temperature. If this view is correct then there should be no action between two vacuum streamers passing in two separated vacua. This suggested the following experiment: - Investigate the action of two discharge streamers upon each other when two separate discharge reservoirs are employed. Fig. 6, represents the apparatus (with its dimensions in cm. marked), containing one of the reservoirs, two of which were placed side by side in the experiment. The bore of the capil- lary tubes e, c, d, f, was about 1:5*. The bulbs AB were coated with tinfoil and the whole arrangement was the same as in the experiments with the apparatus given in fig. 1. The two apparatus communicated with each other by means of a stopcock, so that the pressure was the same in each. The dis- charge in one apparatus did not influence the discharge in the other, no matter what the pressure was, up to the limit at which I could still obtain a discharge, which was about 60". From this I conclude that the repulsion which I observed in the previous experiments was probably not due to electrostatic 268 Pupin–Action of Vacuum Discharge Streamers. action. The probability of the correctness of the other view is therefore considerably strengthened. The apparatus for this experiment was constructed with two other objects in view, which ought to be mentioned here. 1st. To locate the phosphorescence. In this I was quite suc- cessful. It surrounded the hottest parts of the discharge, and therefore it was most intense in the narrow parts of the appa- ratus. Within the reservoir it extended from 6 to d in form of something like an ellipsoid of revolution, with the extremi- ties of its longest axis at 6 and d, and at times this ellipsoid did not fill out the reservoir at all, which proves that the phosphorescent light in this part of the apparatus is due to the phosphorescence of the rarefied air and not to the phospho- rescence of the glass, although in the narrower parts of the apparatus where the hot discharge was very near the glass the glass was also phosphorescent. 2d. To study what I call the ramification of the discharge. As soon as the pressure reached a certain limit the luminosity in the bulbs (which at low pressures was more or less uniformly diffused throughout the bulbs) became streaked, and at still higher pressures the whole discharge in its path through the bulbs divided itself into a number of distinct streamers, the number of streamers diminishing with the increase of pres- sure; given pressures produced invariably the same number of streamers. In this experiment I did not succeed in reduc. ing the number of these streamers to less than two. The streamers rotated more or less uniformly in one direction or the other. The angular velocity of rotation seemed to increase considerably with the current of the discharge. An exhausted glass bulb without electrodes when brought into the vicinity of these discharges emits a faint yellowish light which looks very much like the light of some forms of the aurora borealis. The bulb seems to remain perfectly cool. Lack of time and facilities have prevented me from deter- mining the spectrum of this cold glow. My thanks are due to Professors W. P. Trowbridge and J. K. Rees for the interest which they took in my work; also to Mr. Mann, of the Astronomical Observatory, for the very valuable service which he rendered to me in photographing these discharges. I hope to continue this work with improved facilities as soon as time will permit. - . Department of Electrical Engineering, Columbia College, February 28th, 1892. [FROM THE AMERICAN Journal OF SCIENCE, Vol. XLIII, JUNE, 1892.] ON ELECTRICAL DISCHARGES THFOUGH POOR. WACUA, AND ON CORO– NOIDAL DISCHARGES, By M. I. PUPIN, Ph.D. * [FROM THE AMERICAN, Journal of SCIENCE, Vol. XLIII, JUNE, 1892.] ART. LIX.—On Electrical Discharges through poor Vacua, and on Coronoidal Discharges;* by M. L. PUPIN, PH.D., Columbia College. With Plate XIV. INTRODUCTION. THE behavior of electrical discharges through poor vacua does not seem to have received the attention of experimental investigators which it deserves. This may seem strange in view of the uncertainty of our knowledge of the process by which the transfer of electricity through gases takes place. Considering, however, that it was generally customary to employ in experimental investigations of this kind a vacuum jar with metal electrodes in connection with an electric gene- rator of small capacity, it is easily explained why the discharges through poor vacua should have received so much less atten- tion than the discharges through high vacua and the spark discharges through gases at ordinary pressures. Neither the vacuum jar, nor the working of the electric generators ordi- narily employed, admitted of rapid, easily adjustable, but essen- tial variations in the conditions of the experiment; as for instance, variations of the size and shape of the electrode, of the frequency of the discharges, of the strength of the electro- motive force, etc. But, as I shall point out in the course of this paper, it is through these very variations that certain fun- damental features in the character of an electrical discharge through poor vacua are brought out prominently. The fact that electrical discharges in poor vacua resemble in many characteristic details the appearance and behavior of the solar corona attaches additional interest and importance to that class of experimental investigations which are pointed out, only, in this paper. Neither time nor facilities permitted me to aim at anything approaching completeness. The principal aim in my presenting this paper was to recommend my subject and my method of investigating it to those who command over a larger experience and skill in experimental investigations, and who also have more leisure and greater experimental facili- ties than I could even pretend to possess. DESCRIPTION OF THE EXPERIMENTAL METHOD. A brief description of the method by which I obtained my yacuum discharges seems in place now. It consists in produc- ing an electrical current in a vacuum by means of the con- * Read before the National Academy of Sciences, Washington, April 22nd, 1892. 464 M. Z. Pupin—Electrical discharges through poor denser effect of tinfoil coatings or other conductors placed on the outside of a vacuum jar. The following experiment which I performed over a year ago will explain my meaning more fully. The poles ºf g (fig. 7,) of a small Ritchie induction coil were connected to two glass I. beakers a b containing water. The primary was fed by a 4 h. p. alternator A, giving an alternating current of about 80 periods. A resistance box R, regulates the strength of the primary cur- rent. The speed of the motor which drives the alternator regulated the periodicity of the current. A vacuum jar 6 d, consisting of two glass bulbs (each about 8* in diameter) connected by a tube of narrow bore, was im, mersed into the beakers, one bulb in one beaker the other into the other. The jar contained rarefied air at about 5” pressure. As soon as the bulb reached a certain depth a discharge took place producing a perfectly steady and continuously diffused crimson luminosity. The intensity of the luminosity increased with the increase of the surface of contact between the water and the bulbs. The same effect was produced by substituting Vacua, and on Coronoidal discharges. 465 a Holtz machine for the induction coil and the alternator. In this case the effect was due, of course, to the oscillations pro- duced by the spark discharge between the poles of the machine. The two vacuum bulbs with the water surrounding them act like two condensers connected in series by the narrow tube. It seems superfluous to describe the obvious experiments which I had to perform to prove the following relation: The intensity of the luminosity increases with the condenser surface of the bulbs, with the frequency of alternations, and with the effective electromotive force of the charging appara- tus. Other things being equal the total amount of light pro- duced will increase with the increase of the conductivity of the vacuum. This relation may have been understood before, but to my knowledge it was never clearly stated. The luminous effects which I succeeded in producing in the manner described were so powerful, that I thought it worth while to construct an electrical lamp on this principle. I mention this for the purpose of pointing out that this method of producing very powerful vacuum discharges was worked out by me several months before the publication of Nikola Tesla's and Professor J. J. Thomson’s magnificent experiments. A considerable number of results which I obtained in my ex- periments are simply repetitions, on a small scale, of the results . obtained by these scientists. There is, however, one line along which there seems to be but very few points of contact between their work and mine. This line runs in the direction of inves- tigating the relation between the character of the discharge, the pressure in the vacuum, and the effective e. m. f. which produces the discharge. The following experiments will show Some of the characteristic features of this relation. I. ON THE CRITICAL POINTS OF THE DISCHARGE. A vacuum jar of the form and dimensions as given in fig. 8, was substituted for the small double bulb e d, in fig. 7. The bulbs A and B were totally immersed in large glass beakers containing clear, distilled, acidulated water. The air pressure in the bulbs was a little less than 2". Instead of the small alternator a large alternating current machine fed the primary. On closing the primary circuit the discharge between the bulbs started long before the resistance box R, indicated that the e. m. f. in the secondary coil had reached its maximum. The Crimson luminosity was very soft, steady, and distributed in accordance with the distribution of the potential which one would expect in an electrical system of the above description. Touching the narrow tube at any point increased the lumin- osity below the point touched; evidently due to the increase 466 M. Z. Pupin—Electrical discharges through poor of the static capacity at that point. , Diminishing gradually the e. m. f., the luminosity of the discharge diminished with it and then stopped suddenly as if a critical point had been suddenly reached. Reducing the e. m. f. gradually to zero and then gradually increasing it again, it was found that the discharge would cease at a point much lower than the point at which it would start again, the difference between the two points diminishing considerably with the rapidity with which these variations were made. The discharge will start at a much lower e. m. f. if solicited, that is to say if the long tube is touched at one or more points. A wire bent in the shape of a Leyden jar discharger does very good service as a discharge “solicitor.” The discharge was similarly affected by varying the capacity. Performing the last experiment, but with the small vacuum jar 6 d given in fig. 7, it was found that with a given potential (just above the critical point) the discharge did not start until the bulbs c d had reached a certain depth and then it started suddenly. Raising the bulbs gradually, and therefore dimin- ishing the capacity, the discharge became fainter and fainter, but it did not cease until the bulbs were entirely lifted out of the water. On immersing again, the discharge did not start until a certain depth was reached. The depth at which the dis- Wacua, and on Coronoidal discharges. 467 charge would start this time was smaller than in the first case and the smaller the shorter the interval between the time of taking the bulbs out and immersing them again. This differ- ence is, of course, due to the improved conductivity of the gas and this again may in a certain measure be due to the rise in temperature of the gas on account of the heating effect of the discharge; but only in a small measure, for the bulbs were under water, so that the rise in temperature must have been very small. Besides, heating the bulbs with a Bunsen burner before immersion did not diminish the depth at which the dis- charge would start nearly as much as a previous discharge would, no matter of how short a duration. As stated above, the discharge may be started far below the critical point by touching the connecting tube. But if the touch lasts only a very short time (a fraction of a second) the discharge ceases as soon as the touching conductor leaves the tube. In this man- ner the vacuum tube may be made to blaze up in quick suc- cessions. This behavior of the discharge at all pressures, but very much more striking at pressures higher than the pressure under consideration, seems to support the dissociation theory of Prof. J. J. Thomson (Phil. Mag. 1891, vol. xxxii, pp. 329, 454, 455). II. PHENOMENA INDICATING A DISSOCIATION OF THE MOLECULEs. The following phenomenon appears to be an additional sup- port of this theory : - A close inspection of the discharge going on in the bulbs A and B, fig. 8, seemed to reveal the strange fact that the elec- trical flow was confined to a thin layer of the rarified gas which is in immediate contact with the inside surface of the bulbs, especially when the e. m. f. was not too far above the critical point and therefore the supply of the current not too plentiful. To all appearances there was a gliding film of luminous gas in each bulb extending from the mouths of the connecting tube, spreading over the inside surfaces and ending at the bottom of the bulbs in violently agitated luminous clouds which gave the discharge a hazy appearance. When the vacuum was véry good both the film and the clouds were absent. There was no suggestion of a motion on the part of the gas, and the discharge had a clear luminosity. To study this phenomenon more closely the following experiment was performed : A glass bulb a, fig. 9, blown out at one end of a thick glass tube of narrow bore was filled with acidulated water and 468 M. I. Pupin—Electrical discharges through poor placed at the center of a N Fig.9 large glass bottle, as in- dicated in the figure. - A wide strip (c b) of / tinfoil was placed on the "e- outside of the bottle, covering about one-third of the surface. The air was exhausted through the tube d, until the pressure was about 3*. The liquid in the bulb a and the tinfoil were connected to the secon- dary poles of the induc- tion coil. When the e m. f. was not too far above the critical point the discharge was in form of numerous, quiv- ering streamers, which looked like the genera- tors of a conical surface with the center of bulb a as vertex and the edge of the tinfoil as directing curve. There was no visible dis- charge between the bulb and the central parts of the tinfoil. But the discharge spread out and gradually approached these parts and at the same time the streamers became less numer- ous and steadier, giving the discharge a more diffused appear- ance as the potential gradually increased. When the e. m. f. was gradually brought back to its original value the discharge diminished in intensity but did not return to its original form of distribution. It did that when the e. m. f. was consider- ably lowered below its initial value, which showed that the original distribution was not altogether due to the fact that at any moment the density of the electrostatic charge of the tin- foils was considerably larger near the edges. In this experi- ment as well as in the preceding one the number of streamers, their definition, their quivering motion, and their preference for the paths along which the discharge started, increased with the increase of pressure in the vacuum. A discharge (espe- cially in vacua of poor conductivity) will always start between parts of highest electrical density and each successive dis- charge prefers the passage along the path of the first discharge on account of the increased conductivity along this path. |Wacua, and on Coronoidal discharges. 469 But if this increase in the conductivity is due to a rise in the temperature of the gas along the path of the first dis- charge and to nothing else, how can the fact be explained that a long, thin, discharge streamer when forced through a poor vacuum can be maintained steady, and permanent in form, even if the discharge continues for several minutes ? It should broaden out continually and become more and more diffused as the adjacent particles of the air get heated. In my experiments on solitary discharge streamers in poor vacua (see this Journal, April, 1892), I did not observe any appreciable widening out, but I did observe a phosphorescent halo around the streamer which, as Prof. J. J. Thomson assumes, (l, c.) was very probably due to dissociated oxygen molecules that were ejected from the path of the discharge. (See further below the effect of a blast on a discharge streamer). Still another experiment which shows that something of the nature of a dissociation of the gas molecules is going on along the path of the discharge. A thick German silver wire, 60° long, was bent zig-zag fashion into 12 zig-zag parts and placed in horizontal position at the bottom of a bottle like the one in fig. 9. A wire passing through a rubber stopper in the neck of the bottle connected this zig-zag electrode to one of the poles of the induction coil. The other electrode, a small brass sphere, was vertically above the zig-zag electrode, imme- diately under the rubber stopper. The shortest distance be- tween the two was about 30°. The vacuum was about 3". The discharge started between the nearest points of the elec- trodes, that is between the lowest point of the sphere and one extremity of the zig-zag electrode. It had the form of a band about 3" wide, intensely luminous at each end, but only very faintly luminous along the intervening three-fourths of its length. The length of the less luminous interval increased with the decrease of the e. m. f., but diminished with the increase of the gas pressure; it also seemed to have a different color, but I did not care to examine this point more closely. The phenomenon that interested me more was the gradual creeping of the discharge along the zig-zag electrode from one of its extremities towards the other. It did not increase in breadth but left its trail along the zig-zag electrode in form of a faintly luminous halo . surrounded this electrode just like a narrow luminous tube. Both the color and the gradual lateral motion of the discharge reminded me very much of the aurora borealis of Feb. 13th, 1892. (In this connection it is well to remark that when the e. m. f. is below the critical point this auroral discharge can be started by powerful disrup- tive discharges of a Leyden jar in its vicinity. This in con- nection with observations on coronoidal discharges given in the 470 M. I. Pupin—Electrical discharges through poor latter part of this paper may perhaps furnish a clue in tracing the connection between sunspots and auroral discharges). III. PHENOMENA INDICATING A TRANSLATIONAL MOTION OF THE GAS. An interesting phenomenon was observed in the experiments with bulbs A, B, fig. 8, when the vacuum was diminished by turning a stop-cock C several times around. The vacuum pres- sure was about 20". The induction coil had to be strained considerably to force a discharge through the long glass tube. The discharge looked like a luminous jet shooting from the tube into the bulbs, and in its path around the corners it seemed to strike against the necks of the bulbs at a and b from which points it was reflected and glided along the surface towards the points e and f. Inside of the bulbs the jet oscillated rapidly; it was also split up in several parts, each part consist- ing of numerous more or less intense streamers. A slight modification in the curvature of the necks modified the general outline of the luminous jet without changing its general charac- ter. With the increase of the gas pressure the phosphorescence appeared and seemed to be strongest at a and b. It was very strong in the tube C, leading to the stop-cock, although this tube was entirely free from the discharge proper. The height to which the phosphorescence rose in this tube increased with the current. Every slight variation in the current strength caused a simultaneous variation in the height of the phosphor- escent column in C. (When the discharge ceased there was a strong phosphorescent after-glow all along the long tube). A similar behavior on the part of the phosphorescent gas, which I observed in the experiment described in this Journal, April, 1892, leads to the conclusion that the phosphorescent gas must have a translational motion due to its being ejected from the path of the discharge proper. This strengthened my belief in a translational motion of the gas along the path of the discharge proper, which belief was due to the phenomena in the experi- ment just described. It was also strengthened by the phe- momenon observed in the experiment described by me in the paper cited above, the phenomenon namely that a discharge streamer made to curve out (by the repulsive action of another parallel streamer) so as to strike against the walls of the vacuum jar will rebound from this wall just as a curved jet of water would if it struck against a rigid surface. In another experi- ment with an apparatus similar to that described in the above paper a thin rectangular sheet of mica was suspended between and parallel to two discharge streamers and it was found that it prevented their action which I described in that paper, but |Vacua, and on Coronoidal discharges. 471 it was made to swing back and forth as if acted upon by a wind coming from the path of the discharges. This action was hardly perceptible in high vacua but increased quite consider- ably with the increase of the gas pressure. It may, however, be due to a great variety of causes, like peculiar distribution of pressures due to a peculiar distribution temperature; so- called apparent (in my case continually varying) electrostatic charge over the surface of the mica, etc. IV. ON CORONOIDAL DISCHARGEs. Wishing to perform additional experiments which could throw some more light on this particular feature of the dis- charge, I constructed the apparatus given in fig. 10. A large Fig. MO * cºrºl /|\ glass bulb was coated with tin foil along those parts of its ex- ternal surface which would approximately correspond to its temperate zones, its neck being one of the poles. This tinfoil coating had a wire g attached to it by means of which it could be connected to the pole of the induction coil, and serve as an electrode of the bulb. The other electrode was a brass sphere a attached to a brass rod b. This brass rod was surrounded by a glass tube c d and the space between the two was filled with Sealing wax. In this arrangement the pressure could be varied between very wide limits (up to about 100”) without running the risk of refusal on the part of the induction coil to force a AM. Jour. SCI.--THIRD SERIES, VoI. XLIII, No. 258.-JUNE, 1892. 31 472 . M. J. Pupin—Electrical discharges through poor discharge through. A camera was placed in front of the bulb as indicated in fig, 10, and the discharges photographed. Figs. 1, 2, 3, 4, 5, 6, (in the plate facing p. 462) are photographs of the discharges obtained in this manner but in various degrees of rarification. I shall discuss the discharge given in fig. 6 first. In this case the vacuum was very poor (about 60* pressure). The dis- charge started in the form of four large streamers together with a very large number of short luminous jets, which were more or less uniformly distributed over the sphere. In consequence of these jets the appearance of the sphere reminded one very much of the granular structure of the sun’s disc as revealed by Rutherfurd’s, Janssen's, and Vogel's photographs of the sun. Very luminous spots appeared from time to time at sev- eral points of the surface, which reminded one very much of the sun's faculae. Both the jets and the large streamers rotated rapidly. This rotation is indicated very plainly in the photograph ; for the number of streamers in each wing repre- sents the number of maxima in the alternating discharge dur. ing the time of the exposure, which was a small fraction of a second. The thickest streamers indicate the place where the discharge started. It is evident that the streamers were dis- tributed nearly symmetrically over the sphere at the start of the discharge and that then one-half of them were gradually and almost uniformly displaced in the direction of motion of the hands of a watch, the other held in the opposite direction. The peculiar curvature of some of these streamers indicates the presence of two kinds of motion, one a translational along the prolongation of the radii of the small sphere and the other a rotational. It was this rotational motion which led me to assume that there must be some sort of repulsive action between the streamers of a vacuum discharge. The existence of this action was demonstrated conclusively by the experi- ment described in the paper cited above. Additional re- searches in this direction lead me to the conclusion that two discharge streamers tend to blow each other out owing to the motion of the cooler gas between them, this motion being pro- duced by the enormous heating effect of the discharge. The result is that the particles of the gas which at any moment form the path of a discharge are continually displaced (partic- ularly in a discharge through a poor vacuum), and since every successive discharge prefers the particles through which the preceding discharge passed (for reasons given above) it fol- lows that a sort of rotary motion is set up in the various parts of the discharge. An additional evidence in favor of a translational motion along the paths of the streamers is furnished by the fact that Yaoua, and on Coronoidal discharges. 473 all along the inside surface of the large glass bulb, which is below the tinfoil coating, there is a hazy luminosity which in- creases with the increase of the discharge, and which to all appearances is due to an accumulation of incandescent gas molecules which had impinged against and were reflected by the surface of the bulb. If the inside end of the exhaust tube e, fig. 10, is lowered, so that it reaches the region of the discharge it is observed that from time to time the incandescent gas shoots through this tube toward the stop-cock way out of the bulb. EFFECT OF A BLAST ON A. DISCHARGE STREAMERS. Granting that there is a translational motion along the path of the streamer it follows that a rectilinear streamer may be transformed into a curved one by imparting to the gas in each part of its path a component velocity perpendicular to its original velocity. This inference was confirmed by the fol. lowing experiment: Fig. J/ To reservo ºr Two bulbs A B (fig. 11) coated with tinfoil on the outside (the electrodes of the system) communicated with a reservoir (which I call the principal reservoir) by means of glass tubes 474 M. J. Pupin—Electrical discharges, etc. b c of narrow bore. An L-shaped tube a with a small orifice was fitted by means of a rubber stopper into the neck of the reservoir. By means of this tube and the tube d of the prin- cipal reservoir communicated with two other reservoirs, which I call the external reservoirs, The external reservoir connected with d communicated with a mercury pump. When the exhaustion had reached the point at which a steady rectilinear discharge could be forced from b to 6, a stopcock connecting d to its external res- ervoir was shut off and the exhaustion continued until a good vacuum was obtained in the external reservoir d. The dis- charge was then started. It was a perfectly steady, narrow, rectilinear column of crimson luminosity, surrounded by a phosphorescent ellipsoidal column. But as soon as the above mentioned stopcock was turned on, the blast coming from the orifice a played up the column and the rectilinear path became curved at the point where the blast was acting. The dis- charge acted as if it bent around to get out of the way of the blast. The observation that the effect of the blast upon the phosphorescent column was incomparably stronger than upon the crimson column needs no comment. The weaker the dis- charge the stronger is the effect of the blast, and vice versa. The effect of a blast upon the oscillatory spark discharge of a powerful Leyden jar battery is not perceptible. In discharges through very poor vacua the heating effect is very unequally distributed throughout the vacuum jar. The temperature at certain points is enormously higher than at others. The result is that a very violent motion of the gas is set up, which motion may sometimes, on account of the effects pointed out in the last experiment, produce streamers of double curvature. During an experiment with the apparatus given in fig. 10, which I performed on February 8th, 1892, before the astro- nomical section of the New York Academy of Sciences, a leak occurred so that the vacuum was exceedingly poor by the time I was ready to start the discharge. Finding that the discharge gave no sign of starting, I risked turning the whole power of the 10 h.p. alternator on the induction coil. Long sparks shot immediately from almost every point of the edge of the tin- foil. The discharge between the brass sphere and the tinfoil looked like a black-faced Medusa with fiery serpents dancing all around her head. On repeating this experiment I found that in very poor vacua the discharge streamers very often assume the form of spirals of very long pitch. All these phenomena suggested to my mind a very strong similarity between the streamers of an electrical discharge M. I. Pupin—Electrical discharges, etc. 475 through poor vacua and those of the solar corona, and for the purpose of pointing out this similarity to others otherwise than by verbal description, only, I resolved to photograph these discharges under conditions similar to those under which the solar corona is observed. Photographs 1, 2, 3, 4, 5, 6 are the result. The discharges were obtained with the apparatus given in fig. 10. The only additions were that a circular tinfoil disc was pasted on the outside of the large bulb, in the line of sight between the camera and the brass sphere a. The diameter of this disc was about equal to that of the brass sphere. Also, the inside surface of the large bulb which formed the back- ground of the brass sphere was blackened by means of cam- phor smoke to avoid reflections. The discharge in fig. 1 is that of a good vacuum (about 2"), the succeeding ones repre- sent discharges in poorer vacua, the pressures varying between 2mm and 60mm. * The bearing which these experimental results may have upon the theory of the solar corona I prefer to leave to others to decide. That they may prove a suggestive guide in the study of Solar phenomena seems not unreasonable to expect. *- I am greatly indebted to Professor John K. Rees for the interest which he took in my work, and to Mr. Mann of the Columbia College Observatory, for the very valuable service which he rendered me in photographing the coronoidal dis- charges. - Department of Electrical Engineering, Columbia College, March 31st, 1892. Fig. 1 Fig. 2 Fig. 5 Fig. 5 CORONOIDAL ELECTRICAL DISCHARGES (PUPIN) ~ , s , . ) 23 — - %&@*…, M. M. Pupin—Electrical Oscillations, etc. 325 ART. XXXVIII.-On Electrical Oscillations of Low Fre- quency and their Resonance; by M. I. PUPIN, Ph.D., Columbia College. Part I. On the Production of Simple Harmonic Currents of Constant Frequency by Electrical Resonance. THE sensitiveness of the telephone for exceedingly small alternating currents is well known. It is probably as great as that of the most delicate Thomson galvanometer for direct currents. Just as this instrument, so the telephone is especially suited to zero-methods. But the telephone does not enjoy that popularity in the precision room which its direct current rival, the Thomson galvanometer, enjoys, although the field of phys- ical research in which alternating currents must necessarily be employed is very extensive indeed. The fault lies with our alternating currents and not with the telephone. The alterna- ting currents which the ordinary induction coil as employed in physical laboratories produces is far from being a simple har- monic current. The consequence is that in very many cases the zero method, for which the telephone is especially suited, has to be abandoned, and the minimum method substituted for it, which, of course, is a poor substitution. Being engaged in a research in which I had to employ alter- nating currents I tried, for reasons just given, to devise some method of producing simple harmonic currents of constant frequency, the frequency to be easily and very accurately deter- minable. The following is my solution of this interesting problem: A. On the Production of Alternating Currents of Constant Easily and Accurately Determinable Frequency. My earliest solution of this problem consisted in producing an alternating current in the secondary of a very small trans- former by making and breaking very rapidly and at a constant rate the primary. The interruptor of the primary current con- sisted of the following arrangement: A stiff brass wire was stretched between the pole-pieces of a permanent horse-shoe magnet. . The wire was supported, just as in a monochord, on two hard rubber bridges, aud by varying the distance between the bridges and the tension of the wire it could be made to vibrate any note between about 60 and 1,000 complete vibrations per second. The middle part of the wire was between the pole pieces of the permanent magnet and carried just a short distance outside of the pole-pieces, a short, thin amalgamated copper wire which dipped into a mercury cup once during each vibration. At every dip it 326 M. I. Pupin–A lectrical Oscillations of closed the circuit of a gravity cell and the action of repulsion between the current now flowing through the stretched brass wire and the poles of the permanent magnet kept up the vibra- tion of the wire when once started. In fact, when well ad- justed the wire would start to vibrate of itself, making the primary current at every downward stroke and breaking it at every upward excursion. The current in the secondary was an alternating current, of course, of exactly the same frequency as the vibration of the wire. The frequency of the vibrating wire could be varied by varying the tension gradually until the vibration of the wire was in exact unison with a standard tuning fork. Varying the tension (in a manner which will be described below) of the brass wire did not interfere with its vibration, so that the tuning could be made very accurately by watching the beats. In this form, this what I call electrody- ^amic interruptor, was shown to Professors Abbe, Barker, Mendenhall, Michelson, and Rowland, during the autumn meet- ing of the National Academy of Sciences in New York, in 1891, and was very favorably commented upon by these scientists. In the meantime experience suggested the form given in fig. 1, as best suited to the purpose for which the interruptor - Fig. 1. I | was first designed. The diagram of fig. 2 explains the con- struction of the apparatus more clearly. A stout aluminium, or phosphor-bronze wire, the vibrator, is stretched between the polepieces d, and e, of two permanent Weston magnets, such Fig. 3 as this distinguished electrician uses in his iº --—- voltmeters. Fig. 3 gives the front view of one of the magnets. The cross section of the vibrator is seen there between the polepieces N S as a black dot. The short line, a, b, extending from the vibrator to the mercury cup below is the dipper, a short, thin amalgamated cop- per wire, which is soldered to the vibrator. The vibrator rests on two hard rubber bridges, Low Frequency and their Resonance. 327 f, g. One of its ends is rigidly attached to the wooden frame of the apparatus, the other end is attached to a lever h which, worked by a micrometer screw, varies the tension of the vibra- tor. There are three mercury cups, a, b, c, and three dippers (which unfortunately do not appear in fig. 1). The middle cup, c, is fixed in position, and the middle dipper, being at the modal point of the vibrator, makes a permanent contact there. The other two dippers make contact with mercury cups which can be raised or lowered by means of a nut and screw as rep- resented in fig. 1, and indicated in diagram 2. The construc- tion of the adjustable mercury cups and the stretching lever were copied from Dr. Max Wien's magnetic interruptor (Wiedem. Ann. 1891 and 1892). The middle cup (see fig. 4), is connected to one pole F, of the gravity or storage cell, the other two cups are connected one to one end, and the other to the other end of the primary of the small coil A, B. From the middle point, C, of the primary a wire leads to the other pole of the cell. Auxiliary small coils, E and D, and conden- sers, H and G, are inserted in the circuits as indicated. Their functions will be explained further below. The vibrator vibrates with a node at the middle dipper as soon as the tension has reached a certain, by no means high, limit. A permanent contact is therefore maintained at this point, and the contact is made at one of the other cups just at about the same moment as it is broken at the other cup. Leaving the condensers out of consideration for the present, it is evident that this form of the current make-and-brake pro- duces the same effect upon the iron core of the coil as an alternating current would. The advantage of this needs no comment; for although the iron core consists of the finest iron wire that can be obtained in the market, yet it must be remembered that the vibrator is expected to work sometimes at the rate of 512, or more, complete periods per second. Another immediate advantage which this interruptor offers is a considerable diminution of sparking. The addition of con- densers, besides performing other fineº, which will be discussed presently, reduces the break sparks almost to invisi- bility, even when currents as large as half of an ampere are used. Each half of the primary coil consists of 532 turns of No. 22 silk-covered wire wound over an iron core of 30° in length, 4" in cross section, and consisting of very fine, soft iron wire. & The vibrator when at work gives a pure, but not objection- ably loud, musical note in which the overtones are scarcely perceptible. The frequency ordinarily employed in my work is 256 complete periods per second, and it is obtained by bringing the vibrator in unison with a König standard tuning 328 M. I. Pupin—Electrical Oscillations of fork. The tuning is done in a few seconds, without any diffi- culty, by simply stretching the vibrator gradually by means of the lever and micrometer screw and watching for the beats. The stretching does not interfere in the slightest with the vibrations of the vibrator. The secondary current is, of course, an alternating current having the same frequency as the vibrator. But it is by no means a simple harmonic current. On the contrary, it is a very complex harmonic, its complexity depending on the fun- damental frequency, on the ohmic resistances, and especially on the self-induction and electrostatic capacity of the primary and secondary circuits. A telephone placed in shunt with a part of the secondary circuit shows that without the condensers sparking is rather strong, producing that peculiar rattling noise which is full of those exceedingly high notes for which the telephone is especially sensitive. These high notes are due, as is well known, to rapid electrical oscillations which accompany the sparks. If the condensers are put in as indicated in fig. 4, Fig. 4. …” *~ ^ = -s: H. A *— + º' thiſ | | y – ar L then the telephone shows that it is simply a question of ca- pacity whether this or that overtone is particularly prominent. These overtones mean, of course, that in addition to the alter- nating current of the fundamental frequency there are also in the secondary circuit higher harmonic currents. In fact, the Low Frequency and their Resonance. 329 telephone shows plainly that sometimes these upper harmonics are apparently much stronger than the fundamental current. The method of reducing the complex harmonic current ob- tained by the means just described forms the next part of this paper. B. On the method of weeding out harmonics by electrical resonance. If a coil, A, (fig. 5) is connected with a condenser B Fig. 5 and an impulse starts an electrical disturbance in this sys- tem, then electrical oscillations will result from this disturb- ance. Electrical equilibrium is restored again after the elec- trokinetic energy produced by the impulse is partly radiated off and partly transformed into heat by the ohmic resistance of the circuit. Not to mention losses due to magnetic and dielec- tric hysteresis and to convection currents consisting of dust particles charged by contact with the systems. In Hertzian oscillations and in Tesla frequencies the period depends on the self-induction and the capacity of the system only, as is well known. But even in systems of large self-induction and large capacity, where d priori we can expect a long period of oscil- lation, this period can be easily shown to be independent of the ohmic resistance of the system in the majority of cases. An analytical discussion of this matter, as well as of other matters relating to resonance of slow oscillations is reserved for a future paper. Suffice it for the present to refer to these things, only in so far as they bear upon the subject of this paper. The period of the system represented in fig. 5 is given (pro- vided certain well-known conditions are fulfilled) by T=}.1/10 10 where T is the period in seconds, L the coefficient of self- induction in Henrys, and C the capacity in microfarads. I shall refer to this period as the “natural period” of the sys- tem. By varying the capacity or the self-induction of the circuit we vary its natural period. I call this variation the tuning of the electrical circuit. 330 M. I. Pupin— Electrical Oscillations of Let a complex harmonic, alternating electromotive force E act upon this cirucit. By Fourier's theorem E can be represented by E= a, sin pt-- a, sin 2pt + . . -- a, sin mpt + . . . where p = # T being the fundamental period. It is well to observe here that in complex harmonic e. m. forces as produced by ordinary methods the amplitude a, of the fundamental harmonic is largest and the amplitudes of higher harmonics diminish with the period of these harmonics. The current produced in the circuit by the action of this complex e. m. f. will, of course, be a complex harmonic con- sisting of the same number of single harmonics as the e. m. f. and of the same periodicity; but the ratio of the amplitudes will be different now. The various simple harmonic compon- ents have also different phases. In general every one of these harmonics is a forced oscillation of the circuit, but by tuning the circuit we can bring it (within certain practical limits) in zesonance with any one of the harmonics. - In my work I generally bring the circuits in resonance with the fundamental harmonic. A resonant circuit behaves toward a complex harmonic e. m. f. just the same as an acoustical resonator toward a source of complex sound. It brings out prominently that harmonic with which it is in resonance. To express this numerically, say that the ratio of the amplitude of the fundamental harmonic e. m. force to that of the next higher harmonic (supposing it even to be no higher than an octave) is 2 to 1. Then the circuit can be easily brought into resonance with the fundamental harmonic, in such a way as to increase the ratio of the amplitudes of the corresponding simple harmonic currents to 60:1. Theoretically (and to a great extent practically also) that ratio can be made anything we please by increasing continually the coefficient of self-induction and diminishing the capacity, without destroying the resonance. In other words, we can by proper single tuning weed out the upper har- monics as much as we please. But, as will be indicated later on, it is not always advisable to avail ourselves too much of the means of weeding out the upper harmonics by using very large self-induction. The best method of tuning depends on the nature of the problem before us. I propose to discuss two cases, after stating briefly the experimental method which I consider as the simplest in detecting resonance. Con- sider the circuit represented in fig. 5. Put a telephone in shunt with some part of the circuit between the coil and the condenser; insert a small auxiliary coil with movable iron core in series with the large coil. Say the fundamental frequency Low Frequency and their Resonance. 331 is 256 per second, make the condenser capacity larger and larger until the deepest note in the telephone (in our case 256), comes out strongest. It is easily recognized, for the difference between the sound of the telephone with the upper harmonics strongly represented and the sound without them, is just about the same as between the sound of a clarinet and that of a drum when playing the same note. Having done that, I then move the iron core of the auxiliary condenser until the tele- phone sounds loudest. The circuit is then in resonance with the fundamental harmonic. An interesting phenomenon is observed during the first part of the tuning process. While plugging the condenser, so as to bring the capacity nearer and nearer to the point of reson- ance, a certain point is reached, when taking out a condenser plug is followed by a bright, Snapping, spark. The spark is a sign that the point of resonance is very near, for resonance pro- duces a difference of potential between the condenser plates which is many times higher than the amplitude of the impressed electromotive force. # proceed to consider this phenomenon a little more fully. Case I.-Method of Tuning for the purpose of producing a high rise of potential at the Condenser plates. When resonance is established the ratio of the amplitude E. of the impressed e. m. f. to the amplitude E, of the difference of potential at the condenser plates is given by E, 10" E.T27. ſº #CR Where C is the capacity of the condenser in micro-farads, R the resistance in ohms and T the period in seconds. On the other hand, 27ſ T= ~~ 10° A/LC Hence E. 27, L sº Inductance f E.TTR - Resistance If the priod T=a ºr and E2 = 5 volts, then 271 × 400X L E=*****x5 Hence to get the rise in potential as large as possible it is necessary to make the resistance as small, and the coefficient of self-induction as large as mechanical (and financial) considera- 332 M. I. Pupin—Electrical Oscillations of tions will permit. It is not difficult at all to construct a coil whose L=5 and R=5, in which case E,-over 12000 volts. In a circuit of this kind the amplitude of the fundamental : harmonic would be at least 2000 times as large as that of any of the upper harmonics. In other words, we should have a simple harmonic current in the circuit. In such a circuit the condenser has very small capacity and can be replaced by vacuum bulbs partially coated with tinfoil on the outside and electrical discharges could be produced in them by this enor- mous rise in potential. Hence the interest attached to this method of tuning. I expect to take up this interesting sub- ject in another communication as soon as time will permit. Case II.-Method of Tuning for the purpose of supplying a TWheatstone Bridge with a simple Harmonic Current of con- Stant frequency. In this case the method of tuning is governed somewhat by the well known conditions under which the flow in a Wheat- stone bridge system will have the highest sensitiveness. These conditions exclude the possibility of using self-inductions which are very much larger than those in the principal branches of the bridge. Two kinds of apparatus can be em- ployed. The first and in a great many respects the most con- venient kind of apparatus is the interrupter described above. In this case the most difficult, but at the same time the most interesting part of the tuning consists in establishing resonance between the circuits ADGC, BCHE (fig. 4) and the vibrator. It is done in the following way: The vibrator is first tuned up to any frequency we wish, say, 256, in the manner described above, all the iron having been previously removed from the coils and a high resistance inserted between F and C so as to reduce sparking at the dip- pers. The iron cores are then gradually pushed in and the capacity of the condensers G and H varied until the sparking is reduced to a minimum. This process is continued until the iron core of the principal coil AB is entirely in the coil. The final touches to this part of the tuning are given by means of shifting the iron cores of the small auxiliary coils D and E. By watching the sparks in the cups a and 6 the point of maxi- mum resonance can be determined with great accuracy. For at this point the sparks are scarcely visible. If there is any defect in this adjustment it shows up immediately when the current is increased, by gradually diminishing and finally re- moving the resistance which, as a matter of precaution, was inserted in the circuit between F and C. The voltage of the generator F does not (within reasonable limit) seem to cause a Low Frequency and their ſeesonance. 333 variation in the size of the sparks if the adjustment is properly done. I have used as much as four storage cells in series as my exciter and have no doubt that with a properly constructed vibrator as much as 100 volts could be used without any an- noyance arising from the sparks. But the interruptor must be kept in a place entirely free from jars or vibrations. . For even with the storage battery just mentioned, when the voltage is only 8 volts, vibrations of the floor or table or singing a note which is nearly in unison with the vibrator will disturb its vibrations sufficiently to cause a dissonance between the vibrator and the circuits. This dissonance manifests itself at once by lively sparking which subsides as soon as the dis- turbance ceases. It is this very state of extreme sensitiveness of the electrically tuned up system which makes the work with the vibrator exceedingly instructive and interesting. The secondary coil affy (fig. 4) supplies the alternating cur- rent for the bridge. The number of its turns is small in com- parison to the number of turns in the primary and the current in it is also small in comparison with the current in the pri- mary, on account of comparatively high resistance in the bridge, so that the variation of the secondary current does not inter- fere with the established resonance in the primary. We can therefore tune this circuit without disturbing the adjustment of the primary. The tuning is performed by means of the auxiliary coil I, the condenser M, and a telephone placed in shunt with a part of the circuit whose resistance is high enough to give sufficiently intense sound in the telephone. Finally, the bridge itself containing the telephone T is tuned by means of the auxiliary coil K and condenser L. This part of the tuning does not interfere with any of the previous ad- justments on account of the extremely small value of the cur- rent which has to pass through the telephone to make the sound in it sufficiently intense. It is needless to observe that the upper harmonics which the wibrator tends to produce are completely wiped out in the tele- phone circuit and that, therefore, with this arrangement we can employ the 2ero method of measurement, using as our de- tector the ordinary Bell telephone. . The second kind of apparatus that can be employed is a coil in series with a condenser as in fig. 5. A spark space is inserted in the circuit between the coil and the condenser and the ex- tremities of this spark space are connected to the poles of an influence machine, or a high Voltage electromagnetic gener- ator, and an air blast is applied to the spark space when the sparks begin to pass. An alternating current of any frequency may thus be generated in this coil-condenser circuit by a proper adjustment of capacity and self-induction and by gradual trans- 334 F. A. Gooch and P. E. Browning—Determination formation and tuning deprived of all its upper harmonics. This method is to be preferred when we wish to obtain a sim- ple harmonic current of definite frequency to drive a synchro- nous alternating current motor, that is to say, a simple harmonic current, carrying with it a large quantity of power. I hope that I shall be pardoned for observing here that this last method was worked out by me some time ago. But in conversation with Mr. Nikola Tesla this distinguished experimentalist informed me that he obtained a patent about a year ago on the method of generating alternating currents of any frequency by means of disruptive discharges. The discovery that I was anticipated in a pretty invention caused me some disappointment at first, but I consoled myself very soon with the idea that a method patented by so excellent an experimentalist as Mr. Tesla, would enable me to obtain the object for which I invented it, the object being to construct a synchronous alternating cur- went motor which would spin around with great but perfectly constant angular velocity, the angular velocity to be just as adjustable and just as accurately determinable as the time of wibration of my vibrator, the motor to perform the function of a microphonograph. I expect to be able to offer a favora- ble report on this matter very soon. A communication of the results of some of my experiments with the simple harmonic currents obtained by the method de- Scribed in this paper will be given as soon as time will permit. Electrical Engineering Laboratory, School of Mines, Columbia College, March 8th, 1893. ART. XXXIX.-On the Determination of Iodine in Haloid Salts by the Action of Arsenic Acid; by F. A. GOOCH and P. E. BROWNING. [Contributions, from the Kent Chemical Laboratory of Yale College—XXI.] THREE years ago we demonstrated” the possibility of deter- mining iodine in mixtures of alkaline chlorides, bromides, and iodides, with rapidity and exactness, by taking advantage of the behavior of arsenic acid toward the haloid salts in presence of sulphuric acid of definite strength. We showed in brief, that when amounts of potassium iodide ranging from 0:005 grm. to 0.5 grnm. were dissolved in 100 cm” of water contain- ing 2 grim. dihydrogen potassium arseniate and 20 cm” of a mixture of sulphuric acid with water in equal volumes, the en- tire amount of iodine was expelled on boiling down the solu- * This Journal, vol. xxxix, p. 188. of Iodine in Haloid Salts by Arsenie Acid. 335 tion from 100 cm” to 35 cm”; and further, that arsenic, re- duced to the arsenious condition to an amount the exact equivalent of the iodine liberated, remained in solution and was determinable, after neutralization of the acid, in presence of an alkaline bicarbonate, by titration against standard iodine according to Mohr's classical method. We studied carefully the behavior of alkaline bromides and chlorides under identical conditions and determined that 0.5 grm. of potassium bromide acted upon the mixture of arseniate and acid to the extent of reducing arsenic equivalent to 0-0008 grm. of iodine, and that 0.5 grm. of sodium chloride did not reduce arsenic but did cause, under the conditions, a volatilization proportional to the amount of arsenious oxide present, the loss amount- ing at the most — when 0-56 grm. of the iodide was present to exert its reducing action upon the arsenic — to 0.0011 grum. We showed, furthermore, that these maximum errors, due to the action of bromides and chlorides, though not large and tending to neutralize one another when both bromides and chlorides are present, may be eliminated by the application of a numerical correction to the results whenever the amounts of bromide and chloride present become known. Recently Messrs. Friedheim and Meyer” have recognized the value of our reaction and applied it to the elimination of iodine from mixtures of haloid salts. They have, however, taken issue with us (unadvisedly, as we think) as to matters of detail. They have, in the first place, put themselves upon record as being unable to titrate arsenious oxide by iodine in alkaline solution under the conditions of our process. They account for their failure by the wholly unsupported hypothesis that the iodine reaction is unavailable in presence of the amounts of salts present, and modify the treatment by distill- ing, collecting the iodine in the distillate, and determining it by the thiosulphate method, thus introducing complexity of apparatus and manipulation, and sacrificing the simplicity and rapidity which are chief advantages of our process. Had they read our paper with intelligent care it must have been evident that we had given special attention to the question of the in- fluence of the salts present upon the iodine reaction ; for we expressly stated that “ due correction was made for the amount of iodine necessary to develop the test-color in a solution pre- pared and treated similarly in all respects to the experimental solutions excepting the introduction of the iodide—the correc- tion amounting to a single drop more of the decinormal iodine than was required to produce the end reaction in the same vol- ume of pure water containing only the starch indicator.” It * Zeitschr. f. Anorg. Chem., i, p. 407. 336 F. A. Gooch and P. E. Browning—Determination is obvious that such errors as 0.003 to 0:006 grim., which Messrs. Friedheim and Meyer found even in the absence of bromides and chlorides, are not explicable by the action of the salts which we used. Our errors ranged under like conditions from 0.0009 grn. — to 0-0003 grm. --, with a mean error in nine determinations of 0.0002 grm. —. Everybody knows that the starch iodide test is most delicate in acid solutions and in presence of combined iodine, but Mohr’s method of titrating arsenious oxide and iodine against one another in alkaline solution is sufficiently delicate for very exact work provided only that the alkali in excess is in the form of the bicarbonate, that the starch emulsion is used in abundance, and that the volumes of solutions titrated are reg- ulated to low and uniform measure. In many determina- tions of iodine made by our method at different times and with different materials it has never been our ill-fortune to chance upon results so extraordinary as those of Messrs. Friedheim and Meyer, though we have met in the course of our work with potassium arseniate so contaminated with nitrates as to be unfit for use and with alkaline hydroxides too impure to em- ploy. Most analytical processes depend for their exactness upon the use of proper materials: ours is no exception to the rule in this regard. As to the correctness of the main reaction there appears to be no difference of opinion between Messrs. Friedheim and ourselves. We have, therefore, taken the pains, perhaps un- necessarily, to make experiments in which the estimation of the iodine of the same identical portions is effected both in the distillate and in the residue, in order that the two modes of estimation may be brought into direct comparison. It is scarcely needful to add that we took care to work with pure reagents. The potassium iodide, like that which we employed in our former investigation, was prepared by acting with re- sublimed iodine upon an excess of iron wire, pouring off the solution from the iron when the color of iodine had vanished, adding iodine equal to one-third the amount of that originally used, pouring the filtered liquid into a boiling solution of the calculated equivalent of potassium carbonate (from the bicar- bonate), and filtering off the precipitated magnetic oxide of iron. The slightly alkaline solution thus made, containing ap- proximately 2 grm. of potassium iodide in 100 cm’, and free from chlorine and bromine, was standardized by precipitating the iodine from weighed portions in the form of silver iodide and weighing upon asbestos. The other reagents—the sul- phuric acid, the sodium hydroxide, the acid potassium carbon- ate, the dihydrogen potassium arseniate—when present in the proportions used in our process, and mixed with 5 cm’ of clear ¥33. Že foss. M. I. Pupin’s Discussion of A. E. Ken- nelly’s Paper on Impedance, April 18th, 1893. Reprinted from Transactions of the American Institute of Elec- trical Engineers, Vol. 10, 1893, pp. 221–225, and referred to in Mr. Pupin's deposition, Questions and Answers 60 and 61. 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. Ken- nelly has done very good service to practical elec- trical engineers in making tables to which the electrical engineer can always refer, just as he re- fers 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 eu- logistic 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 alternating current theory. I pointed out in a paper read three years ago at the Boston meeting of this Institute," that the alter- nating current theory is just as simple as the con- tinuous current theory; it is based on one single law, namely, Ohm’s law. But, of course, we have 1 “Practical Aspects of the Alternating Current Theory:” TRANSACTIONs, vol, vii. p. 204, 1890. 2 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 sym- bolical 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 com- posed with the resistance, just the same way as two forces, namely, by the parallelogram of forces—two forces which are at right angles to each other. We have therefore the simple rule that the resistance can be composed with the in- ductance 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 com- ponent representing inductance speed. 3 I call this graphic method of representing im- pedance 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 con- siderable practical importance. The primary law is Ohm’s law in its generalized form, and its ap. plicability 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. The next point which I wish to discuss very briefly is the so called Ferranti effect. I am, how- ever, 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 Fer- ranti 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 twenty-five 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 if is very in- teresting to observe this circumstance. Maxwell was spending an evening with Sir William Grove 1 April, 1893. 4 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 induc- tion 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. Max- well, 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 prob- lem, 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 con- denser, 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 elas- ticity. Without capacity the circuit has no elas- ticity. 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 position 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 alter- nating current circuit which has no appreciable capacity. The electromotive force working on 5 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 the period of the swing will depend on the moment of inertia of the weight, and on the elas- ticity 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 elas- ticity large, one of the two, or both. Now the co-efficient of self-induction in the circuit cor- responds to the moment of inertia of the swing- ing weight, and the capacity in the circuit cor- responds 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 mag- net away from the coil, you will start an elec- trical disturbance there, and the electricity will swing back and forth, just as a pendulum swings back and forth, the period of that swing depend- ing on the coefficient of self-induction and the capacity of the circuit. The electricity in the cir- cuit 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 im- pulse, but a periodically varying in pulse 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 oscil. lation 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 in- 6 crease, 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 in- definitely. But what happens to the wire? Re- Sonant swinging means simply this:—The kinetic energy of the swinging weight is periodically re- duced 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 differences in the condenser, so that by acting upon the circuit by means of an electromotive force whose period is exactly the same as the natural period of the cir- cuit, we produce an electrical flow which continu- ally increases until it has obtained a maximum value, and at that time, of course, the potential difference in the condenser may be many times higher than the voltage of the impressed electro- motive force. I have produced, by very simple means, a rise of potential from 60 volts to 900 volts just that way, and from 80 volts to nearly 1,200 volts by putting a condenser in series with a coil, and a proper adjustment of the two. I took the secondary of a transformer and placed with it a large coil, large Self-induction, in series, and then, in series with this, a condenser; and then I adjusted my capacity to the self-induction in such a way that I brought the period of the circuit in resonance with the frequency of my alternator, and the con- sequence was, that the difference of potential (in- dicated by a Thomson electrostatic voltmeter) went from 80 volts to 1,200 volts. - If you create too much rise of potential your condenser goes. I am working at that problem yet, and I expect to be able very soon, in fact I 7 have already promised, to read a paper before the Institute on this very thing. I have no doubt that it is quite possible to transform 50 or 60 volts into 10,000 or 15,000 or any number of volts in that way. On page 178 of the paper it is mentioned that the reason for the non-equality of the voltage on the series of the two impedances with the arithme- tical sum of the voltages measured on each im- pedance in turn, is due to the fact that the cur- rents in the two coils are usually out of step. I should like to point out that this is misleading. The current must have at any moment the same phase at every point of an alternating current circuit, otherwise there would be an accumulation or absorption of electricity at the points where a change of phase existed. There is evidently a laps7ls linguae in the paragraph referred to, and I have no doubt that Mr. Kennelly will easily change the paragraph. Compliments of the Author. [FROM THE AMERICAN Journal of SCIENCE, Vol. XLV. MAY, 1893.] ELECTRICAL OSCILLATIONS OF LOW FRE- QUENCY AND THEIR RESONANCE. PART II. By M. I. PUPIN. [FROM THE AMERICAN Journal of SCIENCE, Vol. XLV, MAY, 1893.] ELECTRICAL OSCILLATIONS OF LOW FRE- QUENCY AND THEIR RESONANCE. PART II. By M. I. PUPIN. 420 M. I. Pupin—Electrical Oscillations of ART. L.I.—On Electrical Oscillations of Low Frequency and their Resonance; by M. I. PUPIN, Ph.D., Columbia College. [Continued from page 334.] PART II. THEORETICAL DISCUSSION witH SPECIAL REFERENCE To THE THEORY OF RISE OF POTENTIAL BY RESONANCE. I. Introduction. A very faithful mechanical picture of the periodically vary- ing flow in an electrical circuit possessing localized” capacity and self-induction is obtained by considering the motion of a torsional pendulum, that is a heavy bar, say of cylindrical form, suspended on a stiff elastic wire. The moment of inertia of the bar and the elasticity of the suspension wire correspond to the coefficient of self-induction and the capacity of the circuit. The frictional resistance of the air corresponds to ohmic re- sistance, internal friction in the bar and the elastic suspension correspond to magnetic and dielectric hysteresis; angular dis- placement of the torsional pendulum corresponds to the elec- trical charge of the condenser, and therefore torsional reaction of the suspension to difference of potential between the con- denser plates. Angular velocity in the one case stands for the current in the other, kinetic energy for electrokinetic energy, potential energy of the torsional forces stands for the electro- static energy of the condenser charge. In slow mechanical vibrations the decrement of the kinetic energy is chiefly due to external and internal frictional resist- ances. But as the frequency of the vibration increases other losses causing this decrement become more prominent ; so the losses due to radiation in form of sound waves. Similarly in electrical oscillations of very high frequency; the decrement of the electrokinetic energy due to radiation in form of electro- magnetic waves becomes considerably larger than that due to dissipation in consequence of ohmic resistance, magnetic and dielectric hysteresis. The analogy, therefore, supplied by mechanical vibrations is by no means a poor guide in the study of even very rapid electrical oscillations. For slow vibrations the analogy is very striking and instructive. To return to the torsional pendulum :— Let I = moment of inertia of the bar, 6 = angle of displacement at any moment. * The term localized is employed to distinguish the circuits considered in this paper from those electrical circuits in which self-induction and capacity are more or less uniformly distributed over the whole circuit, as, for instance, in the case of a Herzian Resonator. Low Frequency and their Resonance. 421 Let the torsional force be as ordinarily assumed proportional to angle of displacement and the frictional resistance to angu- lar velocity. An impulse having set the pendulum in motion it is required to describe the motion. The differential equa- tion of motion is obtained by writing down the symbolical statement of the principle of moments, viz: Rate at which the moment of momen- | Moment of all the tum about the line of suspension | , - forces about the Varies--------------------------- same line. That is dſ / d6 06 - — — º ſº — ? . . . . . . #(1%) a #4-6 (1) g”6 d6 OI’ I; +a;+60=0 tº e º 'º º & (2) Certain well known conditions being fulfilled the following integral is readily obtained: C. — = t 6 = Ae T * sin: (3) * T 27 where T = natural period of the pendulum = Väſ.a.” 4' T-II, The arbitrary constant A depends on the energy of the im- pulse and can be easily determined by well known rules. 2 OT . * tº When II is small in comparison to f then that is, the natural period of the pendulum is independent of the frictional resistance. I venture to discuss briefly this rather familiar mechanical problem ; for, the discussion seems to throw a strong light upon some of the electrical problems which form the subject of this paper. Let T. = natural period calculated by (3) T. = 66 6 & & 4 CG (4) By a simple transformation it is easily shown that I 2 T = T,(1+g r" – . . . . + . .) . . (5) 422 M. I. Pupin—Electrical Oscillations of where r = −3 a. = ratio (approx.) of frictional loss during any half period to the amplitude of the kinetic energy during the same half period. I shall call it the dissipation ratio. It follows therefore that whenever the dissipation ratio is smaller than + then T, differs from T, by less than fºr of one per cent. But since on the other hand R; 2ł * *mme — 7" — 2L - € T2 ~ € It follows that when the dissipation ratio r = + then the pendulum will be practically reduced to rest after 16 com- plete oscillations. This simple calculation shows, therefore, that even ºn very damped oscillations the period can and in most cases will be practically independent of the frictional *esistance. The following observations are too well understood to need a mathematical commentary:--a. If a periodically varying force is applied to a torsional pendulum the oscillations will be free oscillations if the period of the force is the same as the natural period of the pendulum, that is if the force and the pendulum are in resonance to each other. When this resonance does not exist the oscillations are forced. b. Of two periodically varying forces of the same mean intensity the one which is in resonance with the pendulum will produce the largest maximum elongation. The maximum elongation is reached when the work done by the resonant force during a complete period is equal to the frictional losses during that time. c. The torsional force of the suspension varies periodically, its period being the same as that of the impressed resonant force, but differing from it in phase by a quarter of a period. The amplitude of the torsional force can be much larger than the amplitude of the impressed force, especially when the frictional resistances are small, the moment of inertia large and the oscillations rapid, that is the torsional coefficient large. For in this case that part of the work of the impressed force which is stored up in the kinetic energy of the pendu- lum will become large before the maximum elongation has been reached. But since this large kinetic energy has to be stored up in the potential energy of the torsional forces once during each half oscillation it is evident that a large torsional force will be called into action. The amplitude of the tor- Low Frequency and their Resonance. 423 -8ional force is evidently an accumulative effect of the im- pressed force, and can easily be made so large as to break the suspension. This is a complete analogy to the breaking down of condensers due to a great rise in potential produced by 'resonance described further below. The analogy can be carried further by considering the mo- tion of a torsional pendulum A which is acted upon by a periodically varying force F, not directly, but through another torsional pendulum B to which A is suitably connected. The study of the motion of this system under different conditions as regards resonance between A, B and F gives a complete mechanical picture of the electrical flow in an electrical system consisting of a primary and a secondary circuit, each circuit having localized self-induction and capacity, when a periodi- cally varying e. m. f. acts upon the primary circuit. An ana- lytical discussion of the motion of this mechanical system would lead far beyond the limits of this paper. It seems suffi- cient to point out, that the analysis is almost identical with the following mathematical discussion of the electrical flow in resonant circuits and that it is possible to imitate in a mechan- ical model most of the electrical effects discussed below, by properly constructed torsional pendulums connected to each other in a suitable manner. II. On the Watural Period of an Electrical Circuit Possessing Localized Capacity and Self-induction. The circuit consists of a coil, whose coefficient of self-induc- tion is L henrys, connected in series to a condenser of capacity C farads. Let the ohmic resistance be R ohms. An elec- trical impulse having started the electrical flow it is required to describe the flow. Let Q be the positive charge of the con- denser in coulombs, at any moment, then the differential equa- tion of the flow is obtained by writing down a symbolical ex- pression of the generalized form of Ohm’s law (disregarding losses due to magnetic and dielectric hysteresis) d /r d0\_r, dG} , 1 3. & d’Q , r, d0 , 1 o à • Of L º +Rº: +aq=0 tº . tº (2 ) ‘Comparing these equations to (1) and (2) we see that certain well known conditions being fulfilled the familiar integral first discussed by Sir W. Thomson, can be written down as follows: 424 M. I. Pupin—Electrical Oscillations of R; T2L" .. 27. Q= Ae 2L sin Ft. where T = natural period of the circuit 27: **-*- l R” LC; T 4L” 2 R” . e ſº l When II* * small in comparison to LC then T=27 A/LC that is the natural period of the circuit is independent of the ohmic resistance. * To show that it is only under very exceptional circumstances that this condition is not fulfilled, I shall consider a circuit consisting of a large Bell telephone connected in series with a condenser of 1 microfarad capacity. The resistance of the telephone is 100 ohms, very large indeed, considering that its coefficient of self-induction is only about 0.5 henrys. Making this circuit a part of the secondary circuit of the small trans- former excited by the electro-dynamic interrupter described in part I of this paper* it is found that the sound of the telephone is loudest when the frequency of the vibrator is about 225. The pitch of the sound is not sensibly altered by changing the resistance within very large limits; a result re- quired by theory. For the period calculated from formula T=271 VLC gives 224,4 vibrations per second. Adding the correction given by formula (5) we get for the corrected period T-224,9 a difference of only about # of one per cent. Since the dissipation ratio ra we get for the 2,25 1 27, damping factor e " ", that is to say the electrical oscilla- tions would disappear almost completely after only 10 complete oscillations, which shows that the ohmic resistance produces a very strong damping and yet the period is practically inde- pendent of it. - In circuits consisting of well made coils with finely divided but split iron cores the dissipation ratio r is very small even for frequencies as low as 100 periods per second. The period, therefore, will be independent of the dissipation losses even if * This Journal, April, 1893. { Low Frequency and their Resonance. 425 hysteresis and Foucault current-losses approach the order of magnitude of the losses due to ohmic resistance. The natural period of such circuits, especially when tuned up to a fre- quency of over 200 periods per second will be given very accurately by the formula T=27r A/LC To such circuits only the following discussion refers. III. On the Electrical Flow in a Resonant Circuit. Let a simple harmonic e. m. f. of period T act upon a cir- cuit having localized self-induction and capacity, coil and con- denser being connected in series. By the generalized form of Ohm’s law we have in the usual notation Lº FR-4 P=E sin pt (6) The integral obtained by well-known rules is p CE º Q0 - sin (pt—q) (7 W(1–p’CL)*-Ep" C” R2 ( ) ) _1 —p"CL where tan ºp TzRCT which can also be written •==== sin (pt + q2) w/pºlº-ER’ Ø, tan p=# The integral written in this last form shows, as Oliver Heaviside first pointed out, that a condenser of capacity C in series with a coil changes the impedance of the circuit in such a way as if the condenser had a negative coefficient of self- induction equal to * It produces also a shifting of phase. l p'C' The impedance is reduced to ohmic resistance when L-0 or p'LC–1, that is when the period of the impressed e. m. f. is equal to the natural period of the circuit, or in other words, . the two are ºn resonance. - The current and therefore the amplitude of the charge of the condenser reach then their maximum value. * It is well to observe here that later on in the analysis of more complicated circuits possessing localized self-induction and capacity, I simplify my calculations º I very much by substituting Li = --L-- pºC for the coeffic. of self-induction and treating the circuit then as if it had no capacity. 426 M. I. Pupin—Electrical oscillations of The resonant flow consists in a conversion of electrokinetic into electrostatic energy, and vice versa, during each semi- oscillation, accompanied by a loss due to obmic resistance which is the only work which the e. m. f. does. The ampli- tudes of the electrokinetic and electrostatic energies must therefore be equal to each other, hence where P2 = amplitude of the potential difference in the con- denser. The last relation gives, remembering that owing to resonance p'LC = 1, E pI, p Inductance g or pGR - R. E – Resistance * (8) If L and p are large and R small the rise in potential can be ſmade as large as we please, or rather as large as the condenser will stand. The analogy between this rise of potential due to resonance and the torsional reaction of the suspension in the resonant swinging of the torsion pendulum mentioned above is striking. In both cases the reaction is produced by an accumulative effect of the impressed force. * A rough experiment only, bearing on this point and which can be easily repeated in a few minutes in every electrical laboratory, will be briefly described here. Two large choking coils and a Marshall condenser were con- nected in series with the secondary of a transformer. The core of the smaller of the two choking coils consisted of a removable bundle of soft iron wire. The condenser terminals were con- nected to a Thomson Electrostatic Voltmeter. The frequency of the impressed e. m. f. was about 100 periods per second. The capacity of the condenser was adjusted until the removal of the plug was accompanied by bright snapping sparks, which was a signal that resonance was near. Then the removable iron core of the smaller choking coil was moved up and down grad- ually until the Voltmeter gave the largest deflection. A rise from 60 volts (generated in the secondary and indicated by a Cardew Yºlº to about 900 volts in the condenser was easily obtained. hen the impressed e. m. f. was raised to 80 the condenser indicated about 1200 volts, which showed that the rise in the condenser was proportional to the impressed e. m. f, as the theory requires.” The rise of potential is practically * I feel that it is only just to mention here that Mr. Marshall's ordinary con- densers stood these voltages very well indeed, considering that they are guaran- teed to stand a 1000 volts as their upper limit. Low Frequency and their Resonance. 427 confined to the condenser, for the voltage on the line, indica- ted by the Cardew Voltmeter, does not change sensibly when resonance is established. There is a large and rapid change in the current with the approach of resonance which can be studied in a rough way by the pull which the choking coil exerts upon the removable iron core when the core is moved up and down during the process of tuning. The variation of this pull indicates very plainly that the curve expressing the relation between the current and the self-induction (resistance, capacity and frequency being constant), has a very steep crest which is in perfect accordance with the carefully plotted curve of equation (7) in Bedell and Crehore's volume on alternating currents.” There are, however, several large maa'ima in this curve, each corresponding to a different capacity and self-induction; the simple experiment just described shows their presence very forcibly. The maximum corresponding to the largest capacity with about the same self-induction being however consider- ably the highest. With the condensers that I had at my dis- posal at that time I did not dare to tune the circuit for the highest maximum. The existence of several maxima will be seen presently to be a necessary consequence of the theory. IV. Electrical Resonance in a Circuit with a Complete Harmonic Electromotive Force. By Fourier's theorem a complex harmonic alternating e. m. f, can always be represented by the following series: E = a, sin pt + a, sin 2pt + . . . . a, sin mpt . . . . OC - = 2a aa sin apt l In this expression I shall call a, sin pt, a, sin 2 pt, . . . . the component harmonics, a, sin på is the fundamental harmonic, its frequency, the fundamental frequency. The other harmon- ics will be referred to as the upper harmonics. The order of magnitude of their amplitudes is a, X a,X a, > . . . . » a, x . . . The symbolical expression of Ohm’s law is this: d QC L; + Raj + P= Pºa aa sin a pt. I º this to (6) it is seen from the integral in (7) that this differential equation has the following expression for its integral: *See Bedell and Crehore's treatise: Alternating Currents, p. 138, published by W. J. Johnston Co., New York. AM. Jour. SOI.--THIRD SERIES, Vol. XLV, No. 269.-MAY, 1893. 30 428 M. I. Pupin—Electrical Oscillations of & apCaa Ç a = 2a —sin ( 0.70%- *V=ºgs" (*-*) 1 — a "p"CL Where tan ºpa = apCR If we make 1–p"CT1=0, then the circuit is brought in zesonance with the fundamental harmonic and the current is given by CC O'Cºa. Xa 2 Aſp"(1–a7)*L*-Ha"R" If the coefficient of self-induction is large then it is perfectly evident that the amplitude of the fundamental harmonic cur- rent is by far the largest especially when the frequency of the fundamental harmonic of the impressed e. m. f. is high. For instance, let L = 2, R = 5, p = 27 × 100. I select these values so as to be near the conditions under which the above experiment was performed. Under these conditions we should have for the amplitude of the next harmonic, Sup- posing it to be an octave 0, ...; a: = B; sin pt + R sin (apt— ºpa). 0, * 671 × 10° (very nearly). The amplitude of the fundamental is therefore at least 360 times as large. In all probability this ratio is considerably larger, considering that a, is generally several times larger than a. & - The higher harmonics have even much smaller amplitudes. The rise of potential in the condenser is therefore just the same as if a simple harmonic e. m...f. of amplitude a, and pulsation p, acted upon the circuit. The tuning of the circuit produces therefore two distinct effects: 1st, It produces a rise of potential in the condenser, and 2nd, It weeds out the upper harmonics. It may happen, however, that the circuit is tuned to one of the upper harmonics, as for instance when ap"CL = 1. In this case the current is given by Oſ, º - "g sin a pt + 2 2 2 \ 22.2T 2 2 2 R A/(a”–6°)"p"L*-i-/*R £ to take integral values from 1 to o, except the value a. Cla. 90 - sin(6p– pg) It is evident that now the fundamental harmonic with all the upper harmonics eacepting the harmonic a is practically weeded out on account of the strengthening of the harmonic Low Frequency and their Resonance. 429 *. sin apt by resonance. The rise of potential according to formula (8) is given by apD. Pa = TRT Oſ, a. * To show how this rise of potential compares to the rise ob- tained by resonance to the fundamental harmonic, let a = 5 and let the coefficient of self-induction be the same as before.* — pl P, - R. C/ _ 5pſ. P. = # a. P. Oſ, Hence P. T. 5a, . It is a well known fact that well made alternators are con- structed in such a way that a, is generally larger than 5 a. ; hence, P, will be generally considerably larger than P. This was confirmed by the above experiment. (It is well to observe that this suggests a rather interesting method of analysing a complex harmonic e. m. f. into its com- ponent harmonics and of determining the relative value of the amplitude of each component.) The bearing of this on the method of producing a simple harmonic current by electrical resonance, described in the first part of this paper (l.c.) needs, I venture to say, no further dis- CUISSIOIl. The study of resonance in electrical systems consisting of a primary and a secondary circuit with localized self-induction and capacity presents several features which deserve careful attention; a brief discussion of these together with a descrip- tion of several experiments bearing upon the theory of low frequency resonance will be given in my next paper. Electrical Engineering Laboratory, School of Mines, Columbia College, April 15th, 1893. [To be continued.] * In the experiment described above the capacity was the principal variable; for, the first approximation to resonance was obtained by plugging the condenser until the vicinity of resonance was reached. The maximum point was finally ob- tained by a, comparatively speaking, slight variation of the coefficient of self- induction. Practical Aspects of LOW Frequency Electrical ReSODance. *ss BY M. I. PUPIN, PH. D., COLUMBIA COLLEGE. A Lecture delivered at the Tenth General Meeting of the American Institute of Electrical Engineers, Columbia College, New York, May 17th, 1893, Reprinted from Vol. X. of the Transactions, OFFICERS AND MEMBERS OF THE COUNCIL 1so:3-94. PIRESIDENT: PROF. EDWIN J. HOUSTON, Term expires 1894. PAST-FERESIDENTS : DR. NORWIN GREEN, 1884-5-6. PROF. ELIHU THOMSON, 1889-90. FRANKLIN L. POPE, 1886-7. PROF. W. A. ANTHONY, 1890-91. T. COMMERFORD MARTIN, 1887-8. ALEX. GRAHAM BELL, 1891-2. EDWARD WESTON, 1888-9. FRANK J. SPRAGUE, 1892-93, YICE-PRESIDENTS : Terms expire 1894. Terms expire 1895. A. E. KENNELLY, PATRICK B. DELANY, NIKOLA TESLA, H. WARD LEONARD, OSCAR. T. CROSBY, WILLIAM WALLACE. MANAGER,S : Terms expire 1894. DR. LOUIS BELL, PROF. ALFRED G. COMPTON, HERBERT LAWS WEBB, JAMES HAMIBILET. Terms expire 1895, CHARLES WIRT, DR. MICHAEL I. PUPIN, ANGUS S. HIBBARD, CHARLES P. STEINMETZ. Terms expire 1896. PROF. HARRIS J. RYAN, J. J. CARTY, t CHARLES HEWITT, WILLIAM J. HAMMER. Terms expire 1894. - TREASUR.ER, . SECRETARY : GEORGE M. PHELPS, RALPH. W. POPE 203 Broadway, New York. 12 West 31st St. New York. Board Of Examiners : W. B. VANSIZE, Chairman, GEORGE A. HAMILTON, E. T. BIRDSALL, - C. O. MAl LLOUX, EDWARD P. THOMPSON. Standing Committees appointed by direetion of Couneil : Editing and Library Committee. GEORGE A. HAMILTON, l J. STANFORD BROWN, * FRANKLIN L. POPE, Editing. GEORGES D'IN FREVILLE, Library. FRANCIS B. CROCKER. | GEORGE. H. STOCKBRIDGE. Committee on Finance, Building and Permanent Ouarters. GEORGE M. PHELPS, Chairman. - GEORGE A. HAMILTON, Dr. SCHUYLER S. WHEELER, THOMAS A. EDISON, FRANKLIN L. POPE, FRANCIS R. UPTON, T. COMMERFORD MARTIN, Dr. F. BENEDICT HERZOG. Committee on Papers and Meetings. T. C. MARTIN, Chairman. GEORGE M. PHELPS, JOHN W. HOWELL, HUBERT HOWSON, Dr. SCHUYLER S. WHEELER, HERBERT LAWS WEBB, H. WARD LEONARD, PROF. FRANCIS B. CROCKER. Committee on Units and Standards. A. E. KENNELLY, Chairman. GEO. A. HAMILTON, DR. W.M. E. G.E.Y.ER FRANCIS B. CR ().C.K.E.R. Official Headquarters, I2 WEST THIRTY-FIRST STREET, NEW YORK CITY. World’s Fair Headquarters, ELECTRICITY BUILDING, SEction S. A Zecture delizered at the Tenth General Meet- ing of the American Institute of Electrica! Aºngineers, Columbia College, Wew York, May 17, 1893. President Houston in the Chair. PRACTICAL ASPECTS OF LOW FREQUENCY ELEC- TRICAL RESONANCE. BY M. I. PUPIN, PH. D., COLUMBIA COLLEGE. Mr. President and Gentlemen of the Institute:-A large part of the subject of the following discourse was discussed by me, but in a different way, in three papers. Two of these appeared in the April and May numbers of the American Journal of Science. The third will appear in the June number of the same journal. The method which I have adopted in the following discussion seemed preferable to the mathematical method which I followed in those papers. It is probably just as exact, and cer- tainly a much clearer way of viewing the variable flow of elec- tricity, especially those features of it, which have a more or less direct practical bearing. 1. ON THE NATURAL PERIOD OF AN ELECTRICAL CIRCUIT. An electrical circuit possessing self-induction and capacity be- haves in a great many respects as a body does in consequence of its inertia and elasticity. The fundamental reason for this analogy is simply this:—The electromagnetic energy of a coil through which a current flows, has all the characteristic proper- ties of the kinetic energy of a moving body, whereas the energy of the static charge of a condenser has all the characteristic prop- erties of the potential energy of a strained elastic body. If the neutral state of such an electrical circuit is disturbed, it will re- turn to it again after performing a certain number of oscillations about the position of its neutral state. But a return to the neutral state is impossible until the energy which is spent upon the circuit to disturb its neutral state has left the circuit, or to Sue a more technical expression, until the energy has been dissi- 2 PUPIN ON ELECTRICAL RESONANOE. [May 17, pated or given off to some other circuit. The two principal causes which produce dissipation and compel the circuit to return to its neutral state again, are frictional resistances and radiation. Just as in the case of vibrating bodies, so also in the case of electri- cal oscillations, losses due to radiation, especially when no other electrical circuits are near, are exceedingly small when the oscilla- tions are slow. In Herzian oscillations they are quite consider- able. In oscillations of the Tesla frequency they are probably not negligible. My remarks refer to electrical oscillations of long period, therefore losses due to frictional resistances are the only losses which I shall consider. Consider now an electrical circuit consisting of a coil A and a condenser B (Fig. 1) in series with it. It is a circuit with localized self-induction and capacity. I trust that my discussion will lose as little in its generality as it will in its practical bearing if I confine it to such circuits only. B FIG. 1. Let a sudden electrical impulse disturb the neutral state of this circuit; electrical oscillations will result. These oscillations fol- low laws practically identical with the laws of the motion of a slowly vibrating body. Their period is constant, as we all know, and it is in general completely determined by the electromagnetic moment of inertia and the dielectric elasticity of the circuit—that is, by its coefficient of self-induction and its capacity. When, however frictional losses due to ohmic resistance, magnetic and dielectric hysteresis are large, then the period of this circuit is no longer defined by the self-induction and capacity alone, but it is also in- fluenced by these frictional losses. When ohmic resistance and hysteresis losses are small enough, then the natural period of the circuit is given by the well-known formula { ar, 27 Z = 1. 4/ L. O. 1893.] PUPIN ON ELECTRICAL RESONA WC.E. 3 Where T is the natural period of the circuit in seconds, L its coefficient of self-induction in henrys, and C its capacity in mi- crofarads. For instance, a large Bell telephone whose coefficient of self-induction is 0.5 henrys when connected in series to a con- denser of 1 microfarad capacity will have a natural period of very nearly sºr seconds, that is to say, an electrical disturbance would set up oscillations in it, 225 of which would take place in one second. If a permanent magnet were brought into the vicinity of the tele- phone coil and then suddenly removed, the telephone would sing a note whose pitch would be a little below the well-known note C. But it would not sing it very long. For since the ohmic resistance is 100 ohms these oscillations would disappear almost entirely after NA *. * Nº. * * º * Q SJ T - - - - Tº- - - g * ‘l - I 2 | |\ |\ sſ \ 6/TV iº-5-s=9-seaſ. Time in #sths | W \| \ſ U-v-e- of a second FIG. 2. 10 complete oscillations, somewhat in the manner represented in diagram Fig. 2, that is to say the telephone would sing only during about s's part of a second. By diminishing the resistance We could prolong its song. But diminish the resistance as much as you please, the pitch of the note of the telephone will remain the same, because, as I said, the natural period of the telephone circuit just described is within wide limits independent of the Ohmic resistance. - 2. ON THE TUNING OF AN ELECTRICAL CIRourt. To change the note, say to make it higher, it would be neces. sary to diminish the capacity of the condenser. When a piano tuner wishes to raise the pitch of a piano string he gives it more 4 PUPIN ON ELECTRICAL RESONANOE. [May 17, tension; so in tuning an electrical circuit, in order to change its pitch, it is necessary to change its electrical elasticity that is, its capacity. But there are other ways of tuning an electrical cir- cuit, just as there are different ways of tuning musical instru- ments. Consider a reed pipe, say a clarionet. The musician places a little bit of wax on the reed. When the instrument is too low in pitch he takes off some of the wax, so as to diminish the moment of inertia of the reed, and when the pitch of the in- strument is too high, he sticks on more wax so as to increase the moment of inertia. At any rate this used to be the method of old-fashioned country musicians. And so it is in tuning an elec- trical circuit. Instead of varying its electrºcal elasticity, that is, its capacity, we can vary its electro-magnetic moment of inertia, that is to say, its coefficient of self-induction. To show how this may be done in the telephone circuit just mentioned, insert into this circuit a small coil, a, [Fig. 3] an auxiliary coil, with a remov- able iron core e made up of very fine iron wire. In doing this FIG. 3. we do exactly what the country musician does when he puts wax on the reed of his clarionet. If the electrical pitch of the cir- cuit does not suit, say it is too high, then simply put on more electro-magnetic wax, that is to say, insert the iron core and move it back and forth until the correct position is found which will give the correct electrical moment of inertia, that is to say, the correct coefficient of self-induction. This is, briefly stated, what I mean by the expression tumºng an electrical circuit. From the simple expression given above for the natural period of an electrical cir- cuit, it is evident that the tuning of an electrical circuit, if not simpler, is certainly quite as simple a process as the tuning of a musical instrument. 3. ON THE DETERMINATION OF THE PITCH OF AN ELECTRICAL CIRCUIT. If we wish to know the pitch of a musical instrument, say of a tuning fork, to choose a simple illustration, we simply give it 1898.] PUPIN ON ELECTRICAL RESONANCE, 5 an impulse, say a tap with the finger, and then listen to the vibrations, which in general will last for several minutes, and give us sufficient time to make up our minds as to what the vibrations sound like. In examining the pitch of an electrical cir- cuit it is more convenient to adopt a different method. Thereason is that as a rule electrical oscillations are, as pointed out in the ex- ample above, much more damped, so that the oscillations resulting from a single impulse would not last long enough to give us suffi- cient time to see what they look like, or to listen and hear what they sound like. The method suggested by the stroke of a violin bow over the string is preferable. The stroke of the bow produces a series of impulses which quickly succeed each other and main- tain the string in uniform vibration. It is interesting now to observe that the same thing can be done with an electrical circuit. Consider the circuit A B C Fig. 4. The condenser B represents the tension on the violin string, coil A represents its inertia. The air-gap C stands for the point where the bow by its stroke excites == º —e Gl, FIG. 4. the string. If you now wish a musician who plays with a one- sided stroke, use a high potential direct current generator D, and for an alternating stroke substitute an alternator. The discharges at the air-gap C succeeding each other quickly enough, and at proper intervals will maintain in the circuit A B C practically uniform electrical oscillations. This is one of Tesla’s favorite circuits, and I have no doubt but that he will accomplish great things with it yet.' Bring a few turns of wire of a telephone circuit into inductive influence of this circuit, and you will have in the telephone a musical note of exactly the same pitch as the pitch of the electrical oscillations in the circuit A B C. The note is not perfectly pure. It is marred by the noise of the spark discharge of the air-gap c. Neither is the note of the violin string pure; there is always more or less of the scraping noise of the bow. Just as it is necessary to keep the bow well rosined . 1. It must be observed, however, that Hertz, in 1887, produced his oscilla- tions by a circuit of this identical form. 6 PUPIN ON ELECTRICAL RESOWAWCE. [May 17, \ so as to give it a good grip upon the string, so it is necessary to apply a strong current of air or the action of some other of Tesla's devices upon the air-gap c, otherwise an arc is formed and the generator D loses its grip upon the circuit A B C.” If we had a number of different coils with condensers like A and B alongside of each other, and arranged in such a way as to be able to place them at will, now the one and now the other, and now again a number of them in multiple under the action of the elec- trical bow which the generator D keeps moving over the air-gap C and at the same time vary the capacities, we should be able to change the electrical vibrations of our system with that ease, precision and grace which the violin player displays when with the one hand he guides his obedient bow, while the busy fingers of the other hand glide over the trembling strings, eliciting from them delightful notes which blend into pleasing harmonies. So with our system of properly tuned electrical circuits, we could pro- duce harmonies, but they would be harmonies of silence, harmo- nious oscillations in the ether that affect neither eye, nor ear, nor taste, nor smell. But bring a part of a telephone circuit into inductive action of our harmonic system, and let a skilled experimentalist manipulate a properly constructed keyboard which controls the coils and condensers of the various circuits, and harmonies which before were as silent as the grave, will now agitate the responsive diaphragm of the telephone and produce music that could be made to re-echo in every telephone in the United States. But after all, such an arrangement when used for such a pur- pose, would be a mere toy in comparison to the purpose for which our distinguished colleague, Mr. Tesla, employs it. To convert high-potential but small current electrical energy into low-potential big current energy, or vice versa, accompanied by all possible variations in the frequency of oscillations was the purpose for which Mr. Tesla constructed the device. To a physicist who delights, not less than the engineer, in neat, simple devices for the accomplishment of big and brilliant effects this device of Tesla naturally appeals more than all his other ingenious inventions. Many a delightful hour have I spent in watching experiments on a circuit like the one in Figure 4. The 2. The importance of blowing out the arc for the production of powerful oscillations seems to have been first recognized by H. Classen, Wiedemann Annal. d. Physik und chemie, Band xixxx, p. 647, 1890. 1893.] PUPIN ON ELECTRICAL RESONA WC.E. 7 coil A consisted of a short, stout copper wire; the condenser B consisted of a battery of Leyden jars, which my distinguished teacher, Professor Rood, of Columbia College, kindly lent me. The wires ad were thin copper wires connecting the air-gap C to the poles of an induction coil which is now in the hospital. It is a delightful sight to see the stout wire aglow under the power- ful agitation of the rapid oscillations, whereas the thin wires aa adjoining them remained perfectly cool. Twist now the thick wire A into a few convolutions, say ten or twelve, and surround them by a few hundred turns of fine wire and you will have the now well-known oscillatory transformer with which Mr. Tesla and Professor Elihu Thomson produced some brilliant effects, a trans- former that will give you any number of volts especially if, and now I am going to touch a point which forms the central point of my discourse, especially if the thin wire coil contains capacity in series with it, so that the natural period of this cir- cuit is the same as the period of the thick wire coil, that is Åf the two circuits are in resonance. 4. ON RESONANCE. Here again I have borrowed a term employed in music. But a few simple considerations will show you that it is very natural that I should, for the phenomena of sound and those of oscilla- tory flow of electricity are governed by nearly the same laws. Very high frequency electrical oscillations would in all probability be identical with light, as first announced by immortal Max- well. It is, therefore, not surprising to find that low frequency electrical oscillations should resemble so much the other group of oscillatory phenomena which next to light pleases our senses best, namely, the phenomena of sound, especially agreeable Sound, that is music. To gain a clear conception of what is meant by electrical resonance consider the following simple mechanical analogon—I call it the torsonial pendulum :—I used it often with my students in discussing alternating current phenomena and they liked it very much. A heavy bar A (Fig. 5) is suspended on a stiff elastic wire B, which is attached to a plate c whose weight may be neglected. This plate C slides in a groove aa which in consequence of friction acts like a brake. Suppose now that the friction be- tween C and aa is such that when the angular velocity of c is a the rate at which heat is generated by the friction between c and 8 PUPIN ON ELECTRICAL RESONANCE. [May 17' aa is equal to o R where R is independent of the angular veloc- ity. This torsional pendulum resembles then very much an electrical circuit having localized self-induction, capacity and ohmic resistance. The moment of inertia of A, the elasticity of B, and the friction in C act exactly the same as the coefficient of self-induction of the coil, the capacity of the condenser, and the ohmic resistance of the circuit. Let h stand for the elastic ca- pacity of the wire, that is if the wire be twisted through an angle 6, then the moment of the elastic force which opposes this twisting is 0. . Let I stand for the moment of inertia of the A weight A, then as long as the frictional resistance is within cer- FIG. 5. tain limits we shall have for the natural period of the pendulum T = 2 it 4/ / × B. You see that this expression is exactly the same as the one which expresses the natural period of the circuit in terms of its coefficient of self-induction and capacity. - If this pendulum is set in motion by a single impulse it will oscil- late with a constant period. The first elongation will be largest, and the successive elongations will be smaller and smaller, just as represented in Fig. 2, until the pendulum is reduced to rest again. This will happen when the energy of the impulse has been entirely dissipated into heat, which is the work done against frictional re- sistances in the break at C. The smaller this frictional resistance, the longer will the pendulum swing in consequence of the im- 1893.] PUP1 N ON ELECTRICAL RESONANCE. 9 pulse, before it is reduced to rest. On the other hand we can in- crease the resistance in C to such an extent as to make the Swing a-periodic or dead beat, as is for instance the case in the Weston voltmeters and ammeters. - Repeat the impulse at regular intervals, alternating them, the pendulum will keep on swinging ; but you can easily see that if the intervals of the impulses are measured off in such a way that every time the pendulum passes through its position of equilib- rium, the impulse strikes it, and strikes it in the direction in which the pendulum is moving, then the amplitude of the swing will be much larger than if the intervals of the impulse are not meas- ured off in such a way. In other words when the period of the impulses is the same as the natural period of the pendulum then the Swing is largest. The impulses are said then to be in reson- ance with the pendulum. The same effect will be produced if for the impulses we substi- tute a periodically but gradually alternating force, say a simple harmonic force, having the same period as the natural period of the pendulum. Such a force when acting upon the torsional pendulum just described will continually increase the amplitude of the swing, until the swing is so large that the work done during a swing against the frictional resistances, is just equal to the work of the moving force during that time. From that point on, the pen- dulum will swing with constant amplitude. It is evident, there- fore, that the larger the amplitude of the moving force and the smaller the frictional resistances, the larger will be the amplitude of the Swing. But a large amplitude implies two things:–1st, A large torsional reaction in the suspension wire, and secondly, a large velocity whenever the pendulum passes through its posi- tion of equilibrium. The bearing of this mechanical analogon upon the electric cur- cuit having self-induction and capacity is very direct, as I shall presently point out. Let a simple harmonic E. M. F. E. sin pt. act upon such a circuit. I shall presently consider a complex har- monic E. M. F., and also circuits possessing Foucault current losses, and losses due to magnetic and dielectric hysteresis. They will form the last, and in my opinion the most important part of my discourse. A simple harmonic E. M. F. acting upon an elastic electrical circuit in which the only frictional losses are those due to ohmic resistance, will when its period is the same as the natural 10 PUPIN ON ELECTRICAL RESONANOE. [May 17, period of the circuit, that is when it is in resonance with the circuit, continually increase the amplitude of the electric displacement, that is the amplitude of the condenser charge and therefore also of the current, until the work done against the ohmic resistance is exactly equal to the work of the impressed E. M. F. From this point on the amplitude of the current will remain constant and equal to the amplitude of the impressed E. M. F. divided by the ohmic resistance. Or, to state it in terms which are more gen- erally employed: Capacity and self-induction neutralize each other when the circuit is in resonance with the impressed E. M. F. It is evident also that in a resonant flow, there can be no differ- ence in phase between the current and the impressed E. M. F. Since in this case the current at any moment depends on the E. M. F. and the resistance, and on nothing else. It is clear, however, that if losses due to Foucault currents, magnetic and dielectric hysteresis are present, then the current cannot be made equal to the ratio between the E. M. F. and the ohmic resistance by any combination of capacity and self-induc. tion, although as a simple reflection will show, the difference in phase between the current and the E. M. F. may be reduced to 2ero Žn this case also, in which case we should have no false current, as it is generally called. I shall presently discuss this point a little more fully. 5. RESONANCE IN CIRCUITs witH AN IMPRESSED CoMPLEx HARMONIC ELECTROMOTIVE FoRCE. If the impressed E. M. F. is a complex harmonic, then the cir- cuit may be brought into resonance with any of the component harmonics. I have an apparatus here which is capable of pro- ducing E. M. F.'s of almost any complexity. I call it an electro- dynamic current interruptor, for want of a better name. It con- sists of a phosphor-bronze wire, the vibrator, a, b, e, (Fig. 6), stretched between the poles of a Weston horseshoe magnet d. A short, thin, amalgamated copper wire b, the dipper, is soldered on the vibrator. The vibrator is stretched like the wire of a monochord, over two hard rubber bridges a e, and its tension can be varied by a screw and lever f. The dipper c whenever it 1. Professor Duncan, of Johns Hopkins University informed me yesterday that he deduced the same result in the course of an investigation, a short account of which he read before this Institute at its General Meeting in Chicago in 1892, “ Note on some Experiments with Alternating Currents.” TRANSAC- TIONs, vol. ix, p. 179. 1893.] PUPIN ON ELECTRICAL RESONANCE. 11 dips into the mercury cup closes an electrical circuit F.fe b a g A, and the vibrator is then repelled upward by the force of repulsion between the magnet and the current flowing through the vibrator. One gravity cellfis sufficient to work this apparatus. It is evident that the fundamental period of the interrupted cur- rent will be equal to the period of the vibrator. To change this period, say to make it equal to the period of this tuning fork, which is 256 complete vibrations per second, I siniply strike the tuning fork, hold it then near my ear and by turning the screw f of the stretching lever I vary the tension of the vibrator until the rate of the vibrator and that of the tuning fork are in per- fect unison, which can be easily recognized by watching the beats. This whole process of tuning takes up, as you see, only a few seconds. In series with the cell F and the vibrator, we have a small coil A, containing a well packed bundle of very thin iron wire, and in shunt with A is a condenser D. This con- denser performs the function of bringing this primary circuit into partial resonance with the vibrator which is recognized by the circumstance that at the moment of resonance the spark at the dipper is a minimum. A simple reflection will show you that the current generated by this interrupter is a complex harmonic. To analyze it into its component harmonics I shall adopt the method employed in acoustics. - A complex sound is analyzed by the well-known resonators of Helmholtz. These resonators are constructed in such a way that 12 PUPIN ON ELECTRICAL RESONAWGE. [May 17, they will respond to one vibration only, and also in a measure to its upper harmonics. To any other vibration they are practically mute. By a number of such resonators we can find out, in the manner first pointed out by Helmholtz, all the vibrations which are contained in a complex sound. The secondary circuit B C T E, given in the diagram of Fig. 6. performs the function of such a resonator, it is in fact an adjust- able electrical resonator; C is a small auxiliary coil which you see here; E is a Marshall condenser, and T is a telephone whose note tells me to which of the component harmonics the electrical resonator responds. The telephone is silent now, at any rate as far as you can tell, because the condenser plugs are all out. Now, with this plug, I insert a small capacity. The note which you hear is evidently much higher than even the octave of the vibrator. The electrical flow in the resonating circuit is approx- imately the same as if we had in it a simple harmonic E. M. F. of the same frequency as this note. I insert another plug, so as to increase the capacity. The note which you now hear is deeper. The difference between the two notes is rendered very striking by making and breaking the contact of the second plug in rapid successions, as I do now. The sound of the two notes, succeed- ing each other at regular intervals, resembles very much the sound of bagpipes. I insert another plug, so as to increase the capacity still more. The note which you now hear is still deeper. It is the note of the fundamental electrical vibration, which is the same as the vibration of the vibrator. I know that, because, as I continue inserting more and more plugs, you do not perceive any further change in the sound. The capacities which I intro- duced by the three plugs are to each other very nearly in the ratio of 1 : 9:25, hence the frequencies of the three harmonics contained in the impressed E. M. F. and which I have detected by the resonating secondary circuit are to each other in the ratio of 1 : 3 : 5. The impressed E. M. F. can therefore be written E = E, sin pt + B, sin 3 pt + E, sin 5 pt. Still higher harmonics are present, but they are too weak to be heard all over this room. I shall presently discuss a method by means of which we not only detect the presence of these harmonics, as I have just done by means of this telephone, but also determine the relative 1893.] PUPIN ON ELECTRICAL RESONANCE. 13 strength of each. The method imitates in a certain measure Prof. Langley's bolometric method of determining the distribu- tion of energy in the spectrum of a given complex luminous vibration. Before making the next step in my discourse I wish to call your attention to an application of resonant circuits (in connec- tion with the electro-dynamic interrupter) to a method of producing simple harmonic currents of constant and easily deter- minable frequency.' I simply tune the vibrator by means of a standard tuning fork, and then weed out the upper harmonics by successive transformations. In this connection I Ought to men- tion that Professor Duncan of Johns Hopkins University informed me several weeks ago that he was also weeding out har- monics. I now remember that I got the expression “weeding out ’’ from him, but I have used it in my papers on “Low Fre- quency Resonance ’’ without giving him credit for this beauti- fully selected expression. 6. ON THE RESONANT RISE OF POTENTIAL. The question arises now, how are we to tell experimentally whether a circuit is in resonance to an impressed E. M. F. or not ? Several methods suggested themselves to my mind in the course of my work. I selected the one which appeared to me to be the most sensitive and most interesting. It also suggests a new way of transforming electrical energy which some day may perhaps be of some practical importance I wish to discuss this method now, but only very briefly. As I observed before in the discussion of the motion of the torsional pendulum, represented in Fig. 5, when the moving force and the pendulum are in resonance then both the amplitude of oscillation and the amplitude of the velocity reach their maxi- mum value. And so it is also with a circuit possessing self-in- duction and capacity. By varying gradually the one or the other, the current (which corresponds to the velocity of the pendulum) will continually increase. But the difference of potential in the condenser (which corresponds to the elastic reaction of the sus- pension wire) will also increase continually. When the point of resonance has been reached then evidently both the current and the difference of potential in the condenser have reached 1. Pupin, “Electrical Oscillations of Low Frequency and their Resonance,” American Journal of Science, April, 1898. 14 PUPIN ON ELECTRICAL RESONANOE. [May 17, their maximum values. This maximum difference of potential in the condenser can be many times greater than the impressed E. M. F., because just as in the case of the torsional pendulum the elastic reaction of the suspension wire is an accumulative effect of the moving force, so in the electrical circuit, the potential dif- ference in the condenser is an accumulative effect of the im- pressed E. M. F. Now since a resonant electrical flow, which we have just considered, consists simply of a transformation of elec- trokinetic into electrostatic energy, and vice versa, during each half period accompanied by a frictional loss due to ohmic resistance, it is evidentthat the amplitudes of these two kinds of energies must be equal to each other, that is, we shall have in the usual notation 2 4 P* C = # Z #. But since owing to resonance we have p" Z 0 = 1, the preced- ing relation reduces to 2 P* = p * Z” #. Ol' P = p 1%." It is evident, therefore, that with a little more than ordinary frequency, say 350 periods per second, and an inertia coil of con- siderable self-induction and small resistance high potentials can be obtained in the condenser by bringing the circuit in resonance with the impressed E. M. F. Connecting, therefore, the con- denser to a voltmeter we can tell very accurately when in the course of our tuning of the circuit we have reached the point of Tesonance, because, as I shall presently show you, the voltage goes up very rapidly when the condenser capacity or the Self-induction are near the point of resonance. It is this electrometric method which I have employed in my investigations on “Low Frequency Resondºnce.” The same method can be, and has been employed by several in- vestigators in the study of Herzian oscillations. ~~ To show you how strong this resonant rise of potential can be I have within the last few days wound these two inertia coils (see coil a’ b' in Fig. 8) and borrowed this most excellent mica conden- ser from our well-known electrician, Mr. Wm. Marshall, for which kindness I feel very grateful to him. The impressed E. M. F. is ob- 1. This relation was first obtained, I believe, by Prof. Oliver Lodge. (See a letter by Prof. O. Lodge, London Hlectrician, April 24th, 1891.) 2, American Journal of Science, April, May and June, 1893, 1893.] PUPIN ON ELECTRICAL RESONANOE. 15 tained in the following way: A small 16-pole alternator running at about 2800 revolutions per minute and generating an E. M. F. of about 600 volts feeds the primary of this small transformer (c d, Fig. 8.) Diagram Fig. 7 gives the form of armature A and field B of yº Oy & © R5 Tº Tº {T> C /TS C O O C E *TO F \L& O () () º XXJS2999.82×2 C \ / D & 2 o' o 0 , , o o 0 , , , \ſ)00000 FIG. 7. the machine. Coils a b c de show how the machine is wound. The transformer consists of a hard rubber spool wound with about 3,000 turns (Fig. 8) of No. 20 A. w. G. wire for the primary. The secondary h k consists of about 500 turns of No. 16 wire. A well packed bundle e of very fine iron wire is the iron core. FIG. 8. This transformer is indicated by c in Fig. 7. In series with the secondary we have inertia coils D and the above mentioned mica condenser E of 0.2 M. F. capacity. The inertia coils consist of hard rubber spools like a b' Fig. 8 wound with No. 14 wire. The 16 PUPIN ON ELECTRICAL RESONANOE. [May 17, total self-induction of the secondary circuit is about 1 henry, with- out iron in the inertia coils. The poles of the condenser E are con- nected to a Sir William Thomson electrostatic voltmeter F and also to a vacuum tube G with condenser electrodes, that is to say tinfoil coatings on the outside of the tube. (Indicated by the shaded part in the diagram.) I now start the machine and by weakening the field of the driving motor, I gradually increase the speed of the machine. As you see the voltmeter needle is steadily advancing with the speed. To get the greatest deflection of the needle I ought to have about 350 periods per second. Now I shall advance to very near this speed. The voltmeter indicates now 2,000 volts. The impressed E. M. F. in this secondary reso- nating circuit is only about 100 volts. Instead of increasing the speed so as to reach the point of perfect resonance I prefer to leave the speed constant, and by gradually inserting these five iron wires to increase the co-efficient of self-induction until that value is reached which with the given speed and capacity brings the circuit in resonance with the impressed E. M. F. I am doing this now and watching the voltmeter needle at the same time. Now the voltmeter indicates 3,000 volts, which is 30 times the value of the original E. M. F. This is the point of resonance, be- cause if I push the iron wire lower, the needle goes back. The point of resonance is very sharply defined, because the slightest motion of the iron wire one way or the other makes quite consid- erable difference in the reading of the voltmeter. The point of resonance can be shown to a large audience like this much more easily by connecting the poles of the condenser to the tinfoil electrodes of the vacuum tube G. A discharge starts in this tube at about 2,000 volts. Now as I insert these iron wires into the inertia coil you see the intensity of the discharge increases. [The room was darkened.] The point of maximum resonance is clearly marked by the intensity of the discharge, as you see. Now I insert the iron wire too far; as you see the discharge is stopped. I can - start it again by raising the iron and stop it again by taking the iron wire entirely out, as you see. - - By working with high frequencies and small ohmic resistance any voltage within practical limits can be obtained. Ohmic re- sistance, however, is not the only thing which limits the resonant rise of potential. Dielectric hysteresis and the peculiar behavior of iron when under the inductive action of a rapidly alternating current, modify this rise very much. The other day I employed 1893.] PUPIN ON ELECTRICAL RESONANOE. 17 this home-made condenser in parallel with that Marshall mica condenser. I obtained only 2,000 volts rise, whereas preliminary calculation led me to expect at least 4,000 volts. But the smell of melting waa, reminded me forcibly of the cause of this discre- pancy. The home-made condenser got so hot ºn about two mºn- vtes that all the waa (which when boiling hot was compressed between its mica plates to drive out the air and moisture) between its plates was melted. The energy which was thus used up in overcoming the dielectric hysteresis of the wax had prevented the resonant rise from reaching that value which it ought to have reach- ed according to calculation. Taking this condenser out and using the mica condenser alone the rise went right up to a point consider- ably above 3,000 v. Paraffin and glass behave in a similar way So that owing to dielectric hysteresis alone the resonant current (which takes place when capacity and self-induction neutralize each other) is never equal to the electromotive force divided by the ohmic resistance, and it can be very much less. The presence of iron is incomparably more powerful in destroy- Žng the resonant rise of current and potential, as will be seen presently. This is very unfortunate in view of the brilliant eapectations which not a few electricians hoped to realize from the employment of condensers in the running of alternating current machinery. - It is well to observe here that if we substitute a Weston volt- meter for the Thomson Electrostatic Voltmeter F Fig. 7, then we shall have practically the condenser in parallel with the inertia coils. It is easy to see from purely theoretical considerations that the resonant rise will be less in this case. Experiments show that the rise can be then very much less if the resistance of the voltmeter circuit is reduced. The bearing of this observation on the so-called Ferrant effect with and without a load in the nains needs, I venture to suggest, no further discussion. 7. EFFECT OF IRON ON THE RESONANT RISE OF POTENTIAL. I have already remarked that iron behaves in a peculiar manner when under the inductive action of a resonant flow of electricity. Allow me to call your attention to the diagram of Fig. 9. This curve was obtained with the machine and the circuits which are given in Fig. 7. Except that the inertia coil D had smaller self. induction. Keeping the speed of the machine and the self- induction of the circuits constant, the difference of potential in 18 PUPIN ON HALECTRICAL RESONANOE. [May 17, the condenser was varied by varying gradually the capacity of the condenser. Taking then the capacities for abscissae and the corresponding voltmeter readings for ordinates, the curve in Fig. 9 was obtained. As you see the curve has two maxima. The corresponding capacities are to each other as 1:9. Hence the # 1O-' Farads. FIG. 9. impressed E. M. F. can be represented by E = E, sin pt + E, sin 3 pt. A comparison of the smaller maximum to the larger shows that E, the amplitude of the upper harmonic, is very small in com- parison to É, the amplitude of the fundamental. This is sur- 1893.] PUPIN ON ELECTRIOAL RESONANOE. 19 prising, because from the construction of the alternator one would expect a much stronger deviation of the impressed F. M. F. curve from the simple harmonic. A similar harmonic analysis of the impressed E. M. F. obtained by means of the electrodynamic interruptor gave curves I, II and III Fig. 10. Curve I was obtained by inserting a certain capacity in shunt with the primary coil, and then varying the capacity in the secondary and recording the corresponding volt- meter reading. Capacity was measured off as abscissa and the corresponding voltmeter reading as ordinate. Curves II and III were obtained in the same way but with different capacities in the primary circuit. The impressed E. M. F. in each case can be represented by the following complex harmonic: E = E. pt + E, ºn 3 pt + E. sins pt. But the amplitudes, E, E, and E, are different in each case. ; FIG. 10. You see, therefore, that this method of harmonic analysis by the resonant rise of potential is very sensitive in detecting upper harmonics. Hence the natural conclusion that curve Fig. 9 in- dicates no strongly developed harmonics, simply because they were not present. Yet it is very difficult to suppose that my alternator generates practically a simple harmonic E. M. F. when one considers the shape of its armature core." This point evidently deserved additional investigation. - I inserted a few iron wires into the inertia coil D, Fig. 7, and found that the upper harmonic, weak as it was, disappeared entirely. The iron wires became hot in a very short time. I suspected that iron when subjected to strong magnetization wipes out the upper harmonics in a resonant circuit. With the electro- dynamic interruptor the magnetization of the iron cores is very weak, hence the persistence of upper harmonics. This suspicion was verified in subsequent experiments. 1. The armature core was a Crocker-Wheeler tooth armature, 20 PUPIN ON ELECTRICAL RESONANOE. [May 17, When the inertia coil D was packed with iron wire then the resonant rise was very much diminished as is evident from the curve in diagram Fig. 11. & Various considerations led me to the conclusion that Foucault current and hysteresis losses were not the only causes of this re- markable diminution of the resonant rise due to the presence of iron. I will mention one only. In one of my experiments I used the primary coil of a small closed magnet circuit trans- former for the inertia coil and found that as far as I could detect with my apparatus no resonant rºse could be obtained with 100 volts of impressed E. M. F., no matter how low the frequency was which my machine could produce. About 75 periods per second was the lowest frequency which I employed. If, however, the # 1O-' Farads. FIG. 11. secondary coil of this transformer was short-circuited then the resonant rise appeared, but not nearly as strong as it ought to have been, even Foucault currents and hysteresis losses taken into account. The self-induction of the primary (with secondary short-circuited) calculated from the capacity which produced res- onance was far too high. There were unmistakable evidences in thºs, and in all my other eaſperiments in which iron was present in the inertia coils, that the lower the frequency the Stronger were the zesonance effects. When an alternator giving 125 periods per second was substituted for the alternator in Figure 7, (which gave about 350 to 375 periods per second,) then the resonant rise with iron wire core in the inertia coil D was one-half of that when no core was 1893.] PUPIN ON ELECTRICAL RESONANCE. 21 used, the impressed E. M. F. being 45 volts. If, however, the im- pressed E. M. F. was raised, then this difference in the two cases continually diminished. When the impressed E. M. F. was 200 volts, then the resonant rise with iron was more than without it. There seems to be in the iron a certain reluctance against get- ting into full swing when under the inductive action of a resonant current. The higher the impressed E. M. F. and the lower the frequency the easier it is to overcome this reluctance. When the iron has once been set into full swing, then it is possible by careful manipulation to lower the impressed E. M. F. and increase the frequency without getting the iron out of this swing. In a closed magnetic circuit this reluctance seems to be exceedingly great. With a frequency of 50 periods per second the resonant rise # 1O-S Farads, FIG. 12. with iron was invariably more than without it. Two features in the peculiar behavior of iron were brought out by the reso- nance experiments with this low frequency machine. These two features, I venture to suggest, deserve more than ordinary attention. The first peculiar feature is exhibited in the two curves Figure 12. Curve II was obtained when the whole iron wire core (about 500 wires each 40 cm. long and 1 mm. in diameter) was inserted into the inertia coil. The other curve was obtained when only one-half of the core was employed. The frequency was main- tained constant. From the critical capacity in the two cases it is evident that there was much less difference in the coefficient of self-induction in the two cases than one might expect from the 22 PUPIN ON ELECTRICAL RESONANOE. [May 17, difference in the quantities of iron, that is, if we suppose that in this case also the natural period of the circuit is independent of the frictional resistances due to magnetic hysteresis. But even if we drop this hypothesis, still the small difference in the ca- pacity in the two cases appears as puzzling as ever. We have resonance in this case also as in any other case, but it is evident that the conditions of resonance are not determined by self-in- duction and capacity alone. The question arises then, what does resonance mean in this case ? Well, it means the largest current and the highest rise of potential, but this maximum potential and current are not necessarily accompanied by zero difference in phase nor by neutralization of self-induction with capacity." The practical bearing of this result needs no further comment.” There is another point to which I wish to call your attention in connection with curves I and II of Fig. 12. It is this: Al- though curve II was obtained with twice the quantity of iron and therefore, with at least twice the losses due to Foucault currents and hysteresis, [since the magnetizing current which circulated in the inertia coil with resonance corresponding to curve II was con- siderably larger than that corresponding to resonance of curve I, yet the rise of potential in curve II was larger than that in curve I. I do not wish to take up too much of your time in showing you all of the difficulties which one encounters in endeav- oring to explain these matters satisfactorily. Suffice it to point out merely that these difficulties do exist and that they deserve our most careful attention. * Before making the next step in my discourse I wish to remark that a circuit consisting of the armature of an alternator, a large Žnertia coil without iron and a condenser, all in series, does not eahābit any of the peculiarities just mentioned, at any rate not to any considerable eatent. Such a circuit can be tuned and a high zesonant rise of potential can be thus produced, provided, of course, that this rise of potential is not accompanied by so heavy a current as to produce a serious armature reaction. Foucault current and hysters is losses in the armature iron cannot, of course, influence this resonance, since they are taken care of by the motor which rotates the armature. 1. Professor Duncan informed me yesterday that he arrived at this conclusion in a somewhat different way. ' See paper already referred to. 2. Especially when Dr. Duncan's more definite conclusions on this point are taken into account. º 1893.] PUPIN ON ELECTRICAL RESONANCE. 23 The second peculiar feature in the behavior of iron when it is under the inductive action of the resonant current of an inertia coil will be exhibited to you in the following experiment: The arrangement is just the same as that given in the diagram of Figure 7, with the following exceptions: This alternating cur- rent ammeter is in the resonant circuit. The motion of its index, which I hope can be seen all over the room, will indicate to you the progress of tuning. I watch it on this side by means of a multi- cellular voltmeter which is denoted by F in the diagram of Fig- ure 7. This four-pole 1 H. P. alternator which Dr. Laudy, of Columbia College, kindly lent me, takes the place of the 16-pole alternator. Inertia coil, alternator and condenser are all in series. The driving motor can easily take care of 2 H. P., so that the speed will remain constant during all variations of the load since as you will presently see the load will never be over 150 watts. The condenser has now 16 M. F. capacity plugged in. The fre- quency is about 50 periods per second. The impressed E. M. F. is 45 volts. To bring the circuit in resonance with the impressed E. M. F. it is necessary to insert iron wires into the inertia coil. I insert now about 400 wires. It is, as I can see from the volt- meter reading, considerably too much and, therefore, there is no resonance as you can see from the ammeter. I take the iron wire bundle and raise it slowly, and now I can feel by the pull on the bundle and also by the voltmeter reading that I have reached the point of resonance. You can see it by the ammeter deflection. The ammeter indicates 1 ampere; in reality it is about 2 amperes. [This instrument is a lecture room model and its reading must be multiplied by a large correction factor.] Now I lower slowly the iron wire bundle again; the resonance persists. I have reached now the same position from which I started and when there was hardly any resonance effect. But as you see this time the resonance effect is very strong. But it is a resonance which *ésembles very much a supersaturated 2ine sulphate solution. A very small crystal thrown into such a solution will cause a sud- den precipitation of innumerable small crystals. So it is with this resonance. If I now bring a single iron wire near the bundle, its mere approach upsets the resonance almost completely, as you see from the sudden drop of the ammeter needle. But if I add this wire whose mere approach upsets the resonance almost completely and even five other wires to the bundle and them by gently raising it start the resonant flow I can then lower it again 24. PUPIN ON FLECTRICAL RESONANOE. [May 17, without disturbing resonance, as you see it from the deflection of the needle. I shall vary now the capacity by taking out carefully one plug after the other. But I must take out these plugs without causing a spark. Here is one plug out, and here another and four more. I have reduced the capacity by 1 M. F. or nearly 7 per cent. of the total capacity. There is hardly any change in the resonance effect, as you see from the ammeter needle. Now I shall care- fully put back the plugs and even more than I have taken out, but carefully avoid sparking. As you see, resonance still persists without any apparent change. Wow I take out one plug and wary the capacity by only 0.1 M. F., but I take it out in such a way as to produce a strong spark by the removal of the plug. The eaſperiment does not succeed. But here it succeeds at the removal of a 0.3. M. F. plug. The collapse of the resonance effect Žs as you see almost complete. Generally I succeed with even less than a 0.1 M. F. plug. The same pecularities appear also at higher frequencies, but they are not nearly as clearly defined at frequencies over 100 as they are at those of less than 50 periods per second. They are certainly not due to any change in the speed of the machine, produced by the variation of the load due to the rise of the reso- nant current. Nor is it probable that they are due to armature reactions. This last point, however, deserves a closer examination than I have been able to give it as yet. One more point I feel that I ought to mention before I end my discourse. It is a point which I think may have some prac- tical importance sooner or later. When a large inertia coil with- out iron is joined in series with the armature of an alternator and also with a condenser and then the circuit is tuned, so as to analyze harmonically the shape of the impressed E. M. F. curve, Ifind in all the machines that I have tried so far that this curve is almost perfectly free from upper harmonics, even with fre- quencies of 50 periods per second. If, however, the armature is closed by the primary of a transformer then upper harmonics will appear, as for instance, in the arrangement ºn Figure 7. I do not think that these upper harmonics are entirely due to the variation of the permeability of the transformer core during each complete cycle, as has been suggested by very competent authority." 1. See Professor Duncan's paper already cited; also H. A. Rowland:—“Notes on the Theory of the Transformer;” Phil. Mag., July, 1892. 1893.] PUPIN ON ELECTRICAL RESONANCE. 25 A different interpretation of the phenomenon is possible. My ex- perience in this matter favors the view that the upper harmonics are due to the interference between the electromotive forces generated in the alternator and the transformer. I prefer, however, to devote more time to the examination of this exceedingly important subject before venturing to discuss the validity of this possible new interpretation. Allow me now to sum up briefly the main points of this dis- COUll"Se. The practical bearing of “Low Frequency Electrical Reson- ance” in so far as I have worked out the subject seems to rest on the following characteristic features: It brings out very prominently the purely mechanieal charac- ter of the phenomena of electricity, and it does that not by referring to carefully prepared delicate experiments of a skilled physicist, but by referring to phenomena which every electrical engineer can observe every day in the testing room, telegraph and tele- phone stations, and in central stations for power and lighting. A full appreciation of this purely mechanical character of the phenomena of electricity is of the greatest practical importance, for we must remember that the founder of this mechanical view, the immortal Maxwell, in opening this new view of electrical phenomena contributed to the advance of this science as much as, if not more than, any other investigator of this century. It offers a new, simple, and exceedingly convenient method of transforming electrical energy from low to high potential. It enables us to observe very accurately the behavior of dielec- trics and of iron when under the inductive action of resonant currents, and thus to determine the exact limits within which condensers can be employed in the solution of electrical engi- neering problems. It offers a new and exceedingly simple method (the method of harmonic analysis mentioned above) of studying the working of alternating current machinery under various conditions of load. It points out a new and apparently very promising direction in which the difficult but exceedingly important study of the magnetic properties of iron can be pushed ahead. In closing my remarks I wish to thank my pupil, Mr. Milton C. Canfield, for the very efficient assistance he has given me in the preparation of this lecture. 26 PUPIN ON ELECTRICAL RESONANOH}. [May 17, DISCUSSION. THE PRESIDENT:-Gentlemen, you have heard Dr. Pupin's admirable paper. Does the INSTITUTE wish to make any remarks on it! MR. TESLA :—Gentlemen, I do not know whether I can con- tribute in any way to the clear and skillful exposition which Prof. Pupin has made of the phenomena of resonance. They have been familiar to me for a long time. In fact, two or three years back I began to work on lines in which an observation of some of the rules advanced by Dr. Pupin is an absolute necessity, and one of the reasons why I have only reluctantly consented to deliver a lecture on some high frequency phenomena, which I have shown on two or three occasions was, that I felt inadequate to the task, because in every experiment one has to depend on certain delicate balances and one cannot always feel sure of suc- ceeding in the experiment, especially in a public lecture. Dr. Pupin has admirably succeeded in performing before an audience a number of difficult experiments. I saw this marvellous experi- ment with the iron core, performed by him last week, I believe, and I have been much impressed with the importance of the molecular condition of the iron. Any observation relating to the iron must be of interest, as it may lead to valuable results, and since I am called upon, I may mention a few of my own exper- iences, though they might not be in direct connection with the subject treated by our lecturer. About two years ago I observed a curious effect which I abstained from mentioning so far, because I could not explain it to my satisfaction. It was this:—I had an a ternator of high frequency operating an induction coil. The secondary of this induction coil was connected to a Cardew voltmeter, and I had made the windings so as to bring the deflection into the best range of voltmeter. A condenser was connected to the alternator. I varied the amount of iron in the core of the coil and observed the rise in the electromotive force. As iron wires were added the electromo- tive force would continuously rise up to say 100 volts, Then there was a point at which when I added a few iron wires. the electromotive force fell off, about two volts. A further ad- dition did not make any change whatever. I observed that effect repeatedly and repeatedly, but could not satisfactorily explain it. Now in the light of the experiment of Dr. Pupin and with the knowledge we presently possess, I cannot think else than that there was something of the same nature in the phenomenon. The delicate balance which, as Dr. Pupin has shown can be easily upset by the introduction of a single iron wire in the coil, re- minds me of an experience with a machine which was regulated by means of an “auxiliary or third brush,” a very interesting device, but owing to the extreme sensitiveness not quite com- mercially available. The idea is to take a dynamo, having the field magnet in series with the circuit and connect a point of the 1893.] DISCUSSION. 27 field coil or of the external circuit by means of an auxiliary brush with a point of the commutator. The sensitiveness obtain- able by this means can be anything one chooses, and so great can it be made that the slightest disturbance on the machine may up- set the whole circuit, and if there be arc lamps in the circuit, for instance, one may barely tap a lamp thus causing an imperceptible movement of the carbon rod and all the lamps will go out, if the auxiliary brush is in such a position and the field coil so connected that the shifting of the neutral line is an accumulative effect. In order to improve the action of the lamp mechanism I had the machine constructed in such a way as to give periodic impulses of a certain intensity, which produced a noticeable vibration in the field magnet, and so well did I know the machine, operating it day and night (for at that time practically all my life was passed in the laboratory), that I could tell from these vibrations, by hold- ing an iron bar in a certain position to the field magnet whether the machine was working properly. I noted then that sometimes all of a sudden the lights would go out. After this had occurred about a dozen times, I recognized that when I came with the iron bar near to, or touched the field magnet I disturbed the field enough to displace the neutral line and the lights would go out because the machine would discharge itself. Another observation which I may mention about the iron, came to my attention in 1886. I then made some experiments on a so- called “thermo-magnetic generator. This nihil bonum prin- ciple has no doubt occupied the time of many inventors. I had attacked the problem in quite a different way, sufficiently promising to justify an engineer to enter into an investigation and see what could be done. The method I followed was to enclose in a stove an iron core which closed the circuit of a mag- net, this iron core consisting of a box of iron with small sheets of iron running through offering an enormous cooling surface. I used steam passed through the interstices to cool down the iron. My expectation was that the iron would just cool down a little so as to become magnetized when steam was admitted by means of a valve. The circuit of the magnet would then be closed and the valve , was automatically shut, thereupon the iron was again heated and demagnetized. To a certain measure the valve worked well, but the vibration was too slow. It generally so happened that when the steam was admitted it would be decomposed and a greenish flame would shoot out of the stove. This indica- ted that the temperature of the iron was too high. I would bring the temperature of the iron down by admitting two or three times the steam in pressing upon the valve. Every time I did this, the flame would shoot out of the stove. Then there would be a miss for about two or three times in succession, no flame appear- ing, the iron being cooled sufficiently, but upon doing it the fourth or fifth time which took about a second or two, the flame would shoot out once more. I could not explain this phe- 28 PUPIN ON ELECTRICAL RESONANOE. [May 17, nomenon. A little later, I obtained the classical work of Dr. Hopkinson on the recalesence and other properties of iron at high temperatures and plainly saw that it was recalescence. The temperature must have just been varied around the critical point. Still another fact which I recollect to have observed in experi- ments with high frequency currents is, that an iron rod or wire, when an arc is formed through it, burns and sputters with vio- lence, considerably more so with high than with low frequency or direct currents. It is possible that the effect is solely due to the magnetic properties of the iron, but it might be more or less pro- duced by the increased resistance and consequently more intense heaf evolution. With great magnetizing forces an iron wire in- serted in a high frequency coil is instantly brought to a high temperature. This I have before pointed out, but Dr. Pupin has observed a similar thing with low frequency currents when a con- denser is in circuit and resonating action takes place. I wish to say in regard to converting to high potential, starting from a low potential dynamo, by simply combining capacity and self-induction with the circuit, that is by resonating action, I have in my paper, which has just gone to print, dwelt specifically upon converting in this manner, and in fact I am delighted to see that Dr. Pupin has taken the views he has here expressed. My usual method was to attach to the alternator a coil consisting of a great number of sections, and to associate adjustable capacity with the coil, and then to vary the number of sections and the capacity until the best resonance was obtained. This obviated the employment of a secondary coil; but I found that in adjusting, it was preferable to convert first the low tension currents to such a high potential that the necessary capacity would become extremely small, so as to be reduced merely to that of two small plates, because of the great difficulty of producing a condenser of large capacity adjus- table by extremely small steps, which it is necessary to employ when the potentials are small. If we convert to a potential of say 50,000 volts then the capacity becomes very small, and we can just use a few plates immersed in oil, which permit varying the capacity by extremely small degrees, and without sudden, dis- turbing breaks. This is one of the reasons why I have always preferred to convert in a secondary circuit. The adjustment by varying self-induction by means of an iron core is, as Dr. Pupin's experiment now plainly shows, not always practicable. I think that the experiments we have seen here demonstrate that we are as yet far from having studied the properties of iron thoroughly, and that much remains to be done in this direction. I agree with Dr. Pupin that the condenser, which I had thought was going to be of great help in alternating work, does not really appear to have a great future in connection with apparatus with large iron cores, as motors or transformers, because of the action of the iron, and for one more reason besides, namely, that we can, es- pecially if we have a high potential or high frequency, always 1898.] COMMUNIOATION. 29 wind a coil so as to take up just enough capacity to be in reso- nance with the circuit, in so far as the iron core will permit. I only have to add, that I sincerely thank Dr. Pupin, (which probably is the wish of all), and that I have profited very much by his lecture, which is a clear and precise exposition of the principle, as well as a most interesting experimental demonstra- tion of electrical resonance with a dynamo machine. [Adjourned.] [CoMMUNICATED AFTER ADJournMENT BY Dr. PUPIN.] Mr. Tesla is very kind and generous with his compliments. I do not think, however, that his statement of facts is free from ambiguity. He states that the phenomena of resonance which I have discussed were familiar to him for a long time. My dis- cussion referred to low frequency resonance, whereas Mr. Tesla has, I think, always worked with high frequency apparatus, so that his familiarity with low frequency resonance, the subject which I discuss, is probably not based upon his own experimental investigations. At the time when the Ferranti effect called forth so much valuable discussion in England, Mr. Tesla" contributed some remarks to this discussion, which remarks culminated in the following:—“The writer looked for a case of resonance,” but he was unable to augment the effect by varying the capacity very carefully and gradually, or by changing the speed of the machine. A case of pure resonance he was unable to obtain. When a con- denser was connected to the terminals of the machine * * * the capacity which gave the highest E. M. F. corresponded most nearly to that which just counteracted the self induction with the eacisting frequency.” Mr. Tesla states also in this article that the highest value of the augmentation of the potential which he was able to obtain by connecting a condenser in series to the armature of his high frequency (10° periods per second) machine was only four or five times the impressed E. M. F. What then could Mr. Tesla infer from this result in regard to resonance effects with low frequency! Certainly nothing that was encouraging. At no other time did Mr. Tesla, so far as I am aware, approach the subject of resonance any closer than in the article just referred to. Perhaps Mr. Tesla means that he was acquainted with the phenomena of low frequency resonance which I discussed from the investigations of other men, like Fleming, Kapp, Glazebrook, Swinburne, Lodge, Blakesley, etc.8 I appreciate fully the value of the labors of these men, but still I fail to see a very close re- 1. Electrical World, N. Y., Feb. 21st, 1891. - 2. The meaning of this term Mr. Tesla did not explain. 3. See London Electrician for 1889, 1890 and 1891, also “Fleming's Alter- nate Current Transformer,” vol. ii., p. 401, 30 PUPIN ON ELECTRICAL RESONANCE. [May 17, lation between their work and mine, excepting in one point, and that is, that they as well as I, have shown theoretically that it is possible to produce a high rise of potential by a combination of self-induction and capacity. I have shown it ea perimentally also. But I think that I have pointed out very clearly in thecourse of my lecture that I did not regard the resonant rise of potential as an end but simply as a means to an end, the end being har- monic analysis of E. M. Fs, behavior of iron and dielectrics under the inductive action of resonant currents of low frequency, weeding out of harmonics by means of resonance, etc. With these phenomena Mr. Tesla does not appear to be familiar, either from his own experimental investigations or from investigations of others, excepting those phenomena which Dr. Duncan had in- vestigated some time before me and which I mentioned in the course of my lecture. Cornmittee on Membership etc., ~~ RALPH. W. POPE, Chairman THOMAS D. LOCKWOOD, Local Secretary, Boston, Mass., Dr. LOUIS DUNCAN, $4 {{ Baltimore, Md., CARL HERING, $$. 4 * Philadelphia, Pa., Prof. EDWARD L. NICHOLS, “ * { Ithaca, N. Y., Prof. W. A. ANTHONY, k . { % Manchester, Ct. JOSEPH WETZLER, New York, Members of Joint Committee on Entertainment European Engineers. General Comtm it?ee. Special Committee. FRANKLIN L. POPE. FRANCIS R. UPTON. ELIHU THOMSON. JOSEPH WETZLER General Committee on International Electrical Congress. T. COMMERFORD MARTIN, Chairman, RALPH. W. POPE, Secretary 203 Broadway, New York City. 12 West 31st St., New York City PROF. W. A. ANTHONY, THOMAS D. LOCKWOOD, PROF. ALEX. GRAHAM BELL, C. O. MAILLOUX, Prof. FRANCIS B, CROCKER, PRoF. HENRY MORTON, -** Prof. CHARLES R. CROSS, DR. EDWARD L. NICHOLS, Dr. WILLIAM E. GEYER, GEORGE M. PHELPS, LUDWIG GUTMANN, FRANKLIN L. POPE, * GEORGE A. HAMILTON, NIKOLA TESLA, CoL. CHAS. H. HASKINS, Prof. ELIHU THOMSON, CARL HERING, HERBERT LAWS WEBB, Prof. EDWIN J. HOUSTON, EDWARD WESTON, A. E. KENNELLY, DR. SCHUYLER S. WHEELER. Sub-Committee on Provisional Programme. CARL HERING, Chairman. Prof. W. A. ANTHONY, A. E. KENNELLY. Contents of Vol. X. 1893, already Published. REPORT of CoMMITTEE ON PROVISIONAL PROGRAMME For CoNGRESS OF 1893. ELECTRICAL REcoRDING METERs. (Illustrated.) By Caryl D. Haskins. No. 1, January 1893. ELECTRICAL REcoRDING METERs. (Discussion). SUPPLEMENT To REPORT of SUB-COMMITTE E on Provision AL Program M.E. NotE on DISRUPTIVE DiscHARGE THROUGH DIELECTRics. (Illustrated.) C. P. Steinmetz, THE Most EconoMICAL AGE OF INC ANDEscENT LAMPs. (Illustrated.) Carl Hering. No. 2, February, 1893. THE Cost of STEAM Power PRODUCED witH ENGINES of DIFFERENT Types UNDER PRACTICAL ConDITIONs; witH SUPPLEMENT RELATING To WATFR Power. By Chas. E. Emery, Ph.D., of New York City. THE Most Econowical AGE of INCANDEscENT LAMPs. (Communications and Discussion.) NoTE on DISRUPTIVE DISCHARGE THROUGH DIE- LECTRICS. (Communications and D1scussion.) No. 3, March, 1893. THE CoST of STEAM Power, ETC. (Discussion ) IMPEDANCE. distºdj By A. E. Kennelly. No. 4, April, 1893. IMPEDANCE. By A. E. Kennelly. (Discussion and Correspondence ) ON THE BEHAv.or of FUSE METALS IN DIRECT AND ALTERNATE CURRENT CURcuits (Illustrated.) By Chas P. Matthews. A MoDIFIED DEPREz D’AssonvaL GALVANOMETER. (Illustrated.) By Chas. D. Parkhurst. AN AUTomatic Ps INTING SPEED-Counter For DYNAMö SHAFTING. (Illustrated.) By Geo. S. Moler. THE WARIATION IN EcoMony of THE STEAM ENGINE, Due to VARIATION IN LOAD. (Illustrated.) By Prof. R. C. Carpenter. APPENDIx IV. Report of Sub-Committee on Provisional Programme World's Electrical Congress. No. 5, May 1893. ANNUAL MEETING, May 16, 1893. REPORTS OF COUNCIL AND TREASURER. REPORT of TELLERs. ON THE BEHAvior of FUSE METALS. (Discussion.) A MoDIFIED DE PREz-D’Arsonval. GALVANOMETER. (Discussion.) THE WARIATION IN ECONOMY OF THE STEAM ENGINE. (Discussion.) HEATING of ARMATUREs. (Illustrated.) By A. H. and C E. Timmerman. PRActIcAL Aspects of ELECTRICAL REsonANCE. (Illustrated.) By Dr. M. I. Pupin. CoMPILATION of Discussions, SUGGESTIONS AND CRITICISMs, APPEARING IN THE TECHNICAL AND SciENTIFIC PREss UPoN THE REPORT AND PROVISIONAL Pro- GRAMME of THE SUB-CoMMITTEE Appointf D BY THE AMERICAN INSTITUTE of Electrical ENGINEERS. PROGRAMME OF World's ELECTRICAL Congress. (Discussion.) ON THE NotArion PROPOSED BY M. HospitaL'ER, By Prof. Alex. Macfarlane. Comments ON THE REPORT of • THE CoMMITTEE ON THE PRovisionAL PRogRAMME For THE Congress. By Dr. John Sahulka. Nos. 6 and 7, June and July, 1893. Compliments of the Author. [FROM THE AMERICAN Journal of SCIENCE, Vol. XLV., JUNE, 1893.] ELECTRICAL OSCILLATIONS OF LOW FRE- QUENCY AND THEIR RESONANCE, PART II. (Concluded). By M. I. PUPIN. [FROM THE AMERICAN Journal of SCIENCE, Vol. XLV, JUNE, 1893.] ART. LXI.-On Electrical Oscillations of Low Frequency and their Resonance; by M. I. PUPIN, Ph.D., Columbia College. PART II. [Continued from page 429.] W. Electrical Resonance in mutually inductive circuits. a. The impressed Electromotive force is a simple harmonic. —The primary circuit consists of a coil which is in series with a condenser and an alternating current machine which gene- rates the impressed e. m. f. E sin pt. The secondary circuit consists of a coil joined in series to a condenser. The second- ary coil consists of several parts, some or all of which are under the inductive action of the primary circuit. The 504 M. I. Pupin—Electrical Oscillations of electrostatic capacity of the coils is small in comparison to the capacity of the terminal condensers. Foucault currents and hysteresis losses are supposed to be negligibly small. The symbolical expressions of the generalized form of Ohm’s law will be, in the well-known notation of Maxwell:— * Lº: + M% + Ra -- P, F- E sin pt N* + M* + sm + P. = 0 o dt dt $/ 2 – “. . . Remembering that a circuit consisting of coils whose coeffi- cient of self-induction is L and a condenser of capacity C in series with these coils may be treated analytically like a closed circuit with no capacity but having a coefficient of self-induc- tion equal to +z-L,” where p is the pulsation of the im- l p” C pressed e. m. f., it is clear that the integrals of (9) are obtained from the well-known integrals of the ideal transformer + by the following substitutions:— _ ! . ' — p°M*N, L = go - I L = L -;Niš. _ ! ' — p"M’s When the circuits are in resonance to the impressed e. m. f. then both L, and N, are zero. Hence Q3 = SE_ sin pt Y T p"M*4-RS & & & © _ plyLE , tº $/ cº- p"M*-ERS COS f) tº º ſº º J The corresponding amplitudes of the condenser potential differences are given by SE P. F. pI, pºMFIRS * † º º | (11) rº-ºs.º. 2 p"M*--RS ' ' ' ' Let W. = work done in the primary circuit. W. = heat developed in primary circuit. * See this Journal, May 1893, p. 425, footnote. + Fleming: Alternate Current Transformer, vol. 1, p. 154. Pupin: Practical Aspects of the Alternating Current Theory, Transactions of the American Institute of Electrical Engineers, Vol. vii, May 1890. Low Frequency and their ſeesonance. 505 Hence W. - W. = work transferred from the primary to the secondary circuit. W, - W, = 8 = ratio of transference w, * Wºw º & A simple calculation gives - p"M" T p"M*--RS' The higher the frequency the higher will be the ratio of transference other things being equal. The curves expressing * the relation between the resistance in the secondary circuit as abscissae and the amplitudes of primary and secondary currents and potential differences in primary and secondary condenser 506 M. I. Pupin—Electrical Oscillations of as ordinates are given in Fig. 1. The current curves are given in Fig. 2. (I am very sorry that these diagrams have come out very indistinct in the reproduction.) With small resistance in the secondary the efficiency is high but the output is very low, and vice versa, when the resistance in the secondary is large then the primary current is large but the efficiency is low. With ordinary transformers we have just the opposite re- lations, namely, the lower the resistance in the secondary the larger is the current in the primary. Here, however, owing to the fact that the counter electromotive force in the primary produced by the variation of the secondary current differs by half a period in phase from the primary impressed e. m. f., it is evident that the larger the secondary current the smaller is the effective e. m. f. in the primary circuit and hence the smaller is the current. - Let E = counter electromotive force in the primary due to variation of the secondary current. r Then E. = M % - – gºs sin pt. Hence effective e. m. f. in the primary = E sin pt — E. RSE te = pºMERS Sin pt. When S = 0 then the primary current would be equal to zero but the secondary would have its highest value _ E Tom These few remarks seem sufficient to clear up the rather sur- prising relations which the curves in fig. 1 illustrate. When the frequency is very high, say 10° periods per second, then as long as S. does not increase beyond the value at which RS is comparable to p"M” so long will = # sin p N - * p"M” & * e º E v = i, ºr . . . . . f SE (10%) P, == pI, ŽM. tº gº tº º º f E P. tºº PN ºn tº & & & J Denoting the limiting values of these quantities (for S = 00) by brackets we shall have Low Frequency and their Resonance. 507 (a) = # sin pt (y) = 0 & } (11%) (P,) = # E | (P.) = 0 J as it should be. The curves given in fig. 1, fig. 2 hold true in this case also but with this characteristic difference that for all variations of S between 0 and a considerably large limit (especially if R is very small, as in the case of Tesla's high frequency circuits) the secondary current and secondary potential are practically constant. The higher the frequency the larger is this limit. More than ordinary interest is attached to the relations given in (10%), because they give an approximately correct account of the electrical flow in the secondary circuit of an induction coil when the primary is excited by a Tesla high frequency alternator, the primary coil of the induction transformer, a condenser of suitable capacity and the alternator being con- nected in series. It must be observed, however, that since in general the induction coil which Mr. Tesla employs in his experiments does not differ essentially from the ordinary induc- tion coil except that practically no iron is used—it is evident that the secondary coil has distributed capacity which if not necessarily as large as the capacity which would bring this cir- cuit in resonance to the impressed e. m. f. at Mr. Tesla's high frequencies is certainly far from being negligibly small in com- parison to it. For this reason equations (10%) do not give the exact mathematical relations of Mr. Tesla's circuits. It is evi- dent, however, that the values which these equations assign to the secondary current and secondary potential are the largest values which Mr. Tesla's circuits can possibly yield. I do not find a single discrepancy between the theory just given and Mr. Tesla's experimental results. A full discussion of these results from the standpoint of this theory would lead me far beyond the limits of this paper. A few brief observa- tions relative to the agreement between theory and Mr. Tesla's experiments” seem desirable : a. On account of the considerable internal capacity of Mr. Tesla's induction coils there is a critical speed of the generator at which a large secondary coil by its own internal capacity will be in resonance to the impressed e. m. f. If it is desira- * See Mr. Nikola Tesla's lecture in the N. Y. Electrical World, vol. xviii, July ll, 1891, p. 20. AM. Jour. SCI.-THIRD SERIES, WOL. XLV, No. 270.-JUNE, 1893. 35 508 M. I. Pupin—Electrical Oscillations of ble to add capacity to the terminals of the secondary coil then the speed of the alternator must be below this critical point. b. By diminishing the speed it is possible to increase the terminal capacity without diminishing perceptibly the second- ary voltage. Hence the secondary current will be thereby increased and therefore the physiological effect of a lower fre- quency Tesla current may be considerably more powerful than that of the higher frequency. c. At very high frequencies, say 10° periods per second the Tesla current will in general be exceedingly small, considering that the impressed e. m. f. of his generator is about 140 volts only. Hence the physiological effect of these currents will also be small. (But I do not wish to be understood as deny- ing that the rapidity of reversals in itself diminishes the physiological effect.) 4 d. Since the rise of potential will be the higher the smaller the dissipation of the work which the impressed e. m. f. does it is evident that dielectric hysteresis, in consequence of which the dielectrics are heated, will pull down considerably the sec- ondary voltage. It is therefore desirable to employ liquid or solid dielectrics of small specific inductive capacity, since in these the heating due to dielectric hysteresis is smaller than in dielectrics of high inductive capacity. e. It is evident that by a suitable diminution of the coefficient of mutual induction M within the limits within which p" M* is considerably larger than RS for the highest value of S at which the high frequency system is expected to run both the secondary current and the secondary e. m. f. can be increased very considerably. This could be done by dividing the sec- ondary coil into two parts and allowing one part only (and that too probably the smaller part) to surround the primary coil, in which case the remaining part would be employed as additional inertia coil in the secondary circuit, this inertia coil performing the function of assisting the impressed e. m. f. to produce a high rise of potential in the secondary circuit. In one of his papers” Mr. Tesla mentions that, by removing partly the primary coil from the secondary, higher potentials can sometimes be produced, and the output of the secondary cir- cuit very much increased. “ St. Elmo's Hot Fire’ is the name which Mr. Tesla gives to the powerful flame discharge obtained, by this arrangement of the two coils, from one of the secondary poles, when the other pole (the terminal of the secondary turns which are nearest to the primary coil) is con- nected either to the primary or to a body having considerable capacity. Mr. Tesla states that his object in arranging the * See Mr. Tesla's article cited above, p. 23. Low Frequency and their Resonance. 509 coils in the manner just described was for the purpose of avoid- ing the brush discharges between the primary and the sec- ondary coils. He does not seem to have been aware at that time of the fact that by this method of arranging the two coils it is possible to obtain another and probably quite as important advantage, namely: to diminish the number of turns in the secondary coil very much and thus diminish its resistance, capacity and self-induction and all the evils connected therewith and therefore to increase the secondary terminal capacity and po. tential. In such an arrangement the relations of (10%) are very nearly true and the nearer they are to the truth the higher will be the output and the efficiency of the high frequency system. These few observations will suffice to point out that on the one hand the high frequency currents as developed by Mr. Tesla are resonant electrical oscillations, whose period is very long in comparison to the period of Herzian oscillations, and that on the other hand their mathematical theory is simply the theory of the ordinary low frequency resonance given in this and the preceding paper. * It is my pleasant duty to thank Mr. Tesla on this occasion for the favor which he conferred upon me by lending me his remarkable apparatus for a few days. My short experience with it has taught me many an instructive lesson for which I feel very grateful to Mr. Tesla. Before describing some of my experiments on resonance in mutually inductive circuits with low frequency impressed e. m. f. it seems desirable to point out the relations in mutually inductive circuits when the primary circuit contains no con- denser. When an alternator containing iron in the armature is em- ployed to generate the impressed e. m. f. then this method of arranging the circuits must be adopted in experiments on res- onance, especially when the frequency is over 100 periods per Second. The reason for this will be apparent further below. For this arrangement of the circuits we shall have when reso- nance is established in the secondary circuit ES * = −7-######HR; sin (Pº-p (13 v/p"L’S*H (pºM*-ERS)" ) ) - pME º */ = ------ *==== -- - Sin ( 0t — l; 14 * = visiºn. Hisy " (*~ *) (*) * = — plS tan q = cot b = p"M*--RS' Hence q) = # + b. 510 M. I. Pupin–Electrical Oscillations of Let P, - amplitude of the potential difference in the secondary condenser, then = PN →º-###. 15 - A9 w/p"L’S 1 (p"M*-ERS)" ( ) When R* is small in comparison to p"L" and p"M" is small in comparison to p"L*S* then M E = p N = 2= P. = pn L S (16) which is the same in form as relation (8) in the preceding aper * p These relations differ very little from those in (10) and (11); hence curves fig. 1 and fig. 2 will apply to this case also. The theory of low frequency resonance in mutually inductive circuits when the impressed e. m. f. is a complea harmonic is of no importance in connection with eaſperiments in which the &mpressed electromotive force is generated by an ordinary alter- nating current machine, because the upper harmonics, as will be seen presently, are almost entirely absent then. When the alternating current is produced by transforming an interrupted current, then, since in this case the currents employed are small and therefore the iron cores but slightly magnetized, the harmonics are incomparably more persistent. I prefer to discuss first those experiments in which circuits with "iron cores subject to considerable magnetizations are employed, and where a marked difference exists between theory and experiment because the behavior of iron is so peculiar then and so strongly brought out by resonant circuits that these experiments appeared to me of much greater im- portance than the experiments with circuits without iron which circuits, having no hysteresis losses, bear more directly upon the theory of what may be called Ideal Low Frequency Resonance. • JDescription of Experiments. The alternator was a 1 H-P machine consisting of a Gramme ring armature with 16 poles, such as is used in the Crocker- Wheeler motors. Its field magnet consisted of a cast iron ring with sixteen pole-projections. The field was separately excited. The armature rotated at the rate of about 2810 revolutions per minute, the e. m. f. had therefore about 375 periods per second. The amplitude of the impressed e. m. f. was about 600 Volts. The primary poles cd (fig. 3) of an induction coil were con- nected to the poles of the alternator. The primary of this coil consisted of 3000 turns of No. 20 B. & S. W. G. wire having a * See this Journal, May, 1893, p. 426. Low Frequency and their Resonance. 511 resistance of nearly 40 ohms. The secondary consisted of 120 turns No. 14 B. & S. W. G. wire. The iron core e was a cylinder of well packed fine iron wire. The diameter of this cylinder was 5* and its length 40*. High voltage was measured by a Thomson electrostatic voltmeter, small volt- age by a Thomson multicellular voltmeter or a Weston alter- nating current voltmeter. It is, however, not advisable to use this last instrument in resonance work when the voltage ex- ceeds 50 volts. An inertia coil a’ b% fig. 3 was connected in series with the secondary of the induction coil and also with an adjustable Marshall condenser of 1.9 microfarads, the smallest subdivision being 0.05 M.F. The inertia coil consisted of about 1000 turns of coarse copper wire, about No. 16, so that its resistance was only a few ohms. A removable iron wire bundle could be inserted into this coil, so as to study the effect of iron upon resonance. * The first series of experiments was done without iron in the inertia coil. The speed of the alternator was maintained at 2810 revolutions per minute or nearly 375 complete periods per second. The capacity was gradually varied from 0 to 1-6 microfarads when the maximum point of the voltage of the condenser was reached. The values are tabulated in table 1, curve fig. 4 (unfortunately very indistinct in the reproduction), was plotted from this table, by taking the capacities in 10" Farads for abscissae and the corresponding difference of potential in volts in the condenser for ordinates. TABLE I. Condenser Corresponding value of the capacity in difference of potential of the 10-4 Farads. condenser in volts. •0 40°5 O'5 43 * 1-0 46" 1 °5 5 l' 2-0 56*5 2-5 53° 3-0. 5 l "5 3'5 52- 4-0 53° 5'0 57-5 6'0 . 63-5 7:0 7 0-5 8:0 77. 9:0 89. 10-0 103 • II () | | 8- | 2-0 140° 15 °0 750. | 6-0 1090- 512 M. I. Pupin—Electrical Oscillations of A simple consideration will show that the curve in fig. 4 is exactly the curve which theory demands; but, as I stated Low Frequency and their Resonance. 513 before, I prefer for the present to discuss those cases in which there is an apparently striking disagreement between theory and ea:periment. When the maximum point is reached then the slightest variation of the capacity one way or the other causes a very large variation in the potentials. The curve of potentials looks and behaves just like a sensitive flame. The maximum po- tential is at about 1.66 microfarads. There is however another maximum at about 0.18 microfarads which would correspond to the first upper harmonic. This second maximum has been determined with exceedingly great care, so that there is not the slightest doubt about its existence. From the shape of the curve one is led to infer that the form of the impressed e. m. f. is given by E = a, sin pt + a, sin 3 pt. where the amplitude a, is exceedingly small. This was rather surprising, since, owing to the peculiar shape of the armature one would have expected a much stronger development of the upper harmonics. Before I obtained the alternator just described my experi- ments on the rise of potential by resonance were all performed by means of alternating currents obtained from the interrupter described in my first paper.” In these experiments, an ac- count of which will be given at some future time, the upper harmonics appear very strongly in curves corresponding to the curve in fig. 4. In fact, the crest corresponding to an upper harmonic can be made considerably higher than that corres- ponding to the fundamental. In the experiment with our large alternator giving about 100 periods per second, which experiment I described in my last paper + the upper har- monics seemed to be present in strong force although the armature of this alternator has no iron projections nor is the machine in any other respect as apt to generate a complex e. m. f. as the small machine described above. The considera- tion of the circumstance that since the small machine generated an e. m. f. of nearly four times the frequency of that generated by the large machine and that therefore in the case of the small machine the self-induction is much more effective in destroying upper harmonics did not seem to explain matters quite satisfactorily. There was evidently, something going on in my circuits during those experimentst that I did not under- stand clearly. * This Journal, April, 1893. # This Journal, May, 1893, pp. 426,427 and 429. 514 M. I. Pupin–Electrical Oscillations of IV. On the Effect of Iron upon Resonance and the Relation between this Effect and the Frequency. Experiment 1.-A few iron wires were then introduced into the inertia coil and the secondary circuit was tuned To my great surprise, I found that now the upper harmonic maximum had disappeared and the maximum rise had dimin- ished quite perceptibly, although the self-induction of the inertia coil and therefore of the whole resonant circuit had been considerably increased. But I must mention here that the iron got so hot in a few seconds as to cause the fibre spool of the inertia coil to smoke where the wire touched it. There was a serious discrepancy between experiment and formula (15). To bring out this discrepancy very strongly I placed all the iron wire into the inertia coil (about 500 wires, each 40” long and 1” in diameter). On tuning the circuit it was found that the maximum potential was reached at considerably smaller capacity and that the rise of potential was incomparably smaller than in the previous case. Table II gives the experimental data, the curve in fig. 5 was plotted from this table. The frequency was maintained nearly the same as in the previous experiment, namely 375 complete periods per second. TABLE II. Capacity in Difference of potential in 10-7 Farads. the condenser in Wolts. 'O 35'5 O'5 39'5 l'O 43' I ‘5 48° 2-0 54." 2.5 60° 3-0 62° 3°5 61 - * 4'0 58. 5-0 52" 6'0 45° In the experiment (described in my last paper) with our large alternator giving 100 periods per second I obtained with similar inertia coil and the same iron wire a rise from 60 to 900 volts. In this experiment with four times the frequency I expected to get nearly four times the rise and instead of that there was hardly any rise at all. I inferred, therefore, that the presence of iron in all probability diminishes at higher frequency the rise of potential due to resonance. To investigate the relation between this damping of the iron and the frequency I substituted for the small alternator our Low Frequency and their Resonance. 515 large alternator. The impressed e. m. f. was maintained constant and equal to about 1000 volts. The frequency was also maintained constant and equal to nearly 125 periods per second, hence just about # of the frequency obtained by the small machine. The secondary was now tuned first when there was no iron wire core in the inertia coil. The condenser potential rose steadily until the maximum point was reached. There was no sign of an upper harmonic. This distressed me very much in view of the statement which I made in my last article concerning the presence of upper harmonics in the e. m. f. generated by this alternator. I had evidently blun- dered somewhere in my previous experiment with the large alternator. In my endeavors to locate the blunder / discovered a very peculiar behavior of the iron when it is under the *nductive action of a resonant circuit, which behavior ex- plained to me perfectly why in the experiment, which I described in my last paper,” there was a much higher rise of potential when the capacity was considerably increased without apparently increasing perceptibly the coefficient of self- induction. - Faperiment 2.—I next placed the iron wire bundle into the inertia coil and found that the maximum rise was one half of the rise which was obtained without the iron, which showed that with the diminution of the frequency the damping effect of the iron upon resonance was much less. If a high impressed e. m. f. is employed in the resonant circuit just described then the rise of potential can be made even higher with iron than without it at this frequency. Increasing the capacity considerably and then raising the wire bundle until the maxi- mum deflection in the Thomson voltmeter was obtained I found that only a slight displacement of the bundle was neces- sary to reach the point of resonance. The maximum voltage, or the resonant rise, was considerably higher. (It will be seen presently that under certain conditions the bundle can be lowered again without destroying resonance or diminishing the resonant rise and it was owing to this circumstance that in the experiment described in my last paper I believed that I was tuning the circuit to respond to an upper harmonic of the impressed e. m. f.) Increasing the capacity again and then raising the iron wire bundle a little more the maximum potential was again increased until a point was reached at which the maximum rise of potential began to diminish when the capacity was increased and the iron wire bundle raised in order to establish resonance again. From this point on, which I shall call the * This Journal, May, 1893, pp. 426, 427, 429. 516 M. I. Pupin—Electrical Oscillations of critical point, the rise of potential due to resonance fell off gradually until the iron wire bundle was entirely removed. It is very instructive to observe that the position of the critical powt changes perceptibly with the amplitude of the impressed €. 772, 7 O7°66. * It ; evident, of course, that on account of hysteresis losses the rise of potential produced by resonance will be less than the theoretical value given by (15). And the first explanation which one will naturally offer for the above discrepancy between the theoretical and the actual value will be that as the quantity of iron wire in the interia coil is increased the increase of the coefficient of self-induction tends to increase the reso- nant rise but that on the other hand the increase of hysteresis losses due to the increased mass of iron tends to pull this rise down and that it is then simply a question of adjustment which one of the two tendencies will predominate. This explanation does not, however, cover the ground completely as will be found by the following experiments: Eºperiment 3.—In order to experiment with lower frequen- cies, as they seemed to bring out this peculiar behavior of the iron more clearly, I substituted a one H. P. four-pole alter. nator for the large alternator. The speed was such as to give the impressed e. m. f. a frequency of 50 periods per second. - TABLE III. |Part A. Part B. Part C. . *. Capacity Voltage Capacity Voltage Capacity Voltage in of the in of the in of the 10–6 Farads. Condenser. 10–6 Farads. Condenser. 10–0 Farads. Condenser. 0-0 32 ° 0-0 32- {}*() 32" 0.5 32°5 0°5 33°5 1 ‘9 32°5 1'0 34' 1 - 0 34°5 4-9 35° 1 9 36. 1 *9 37. 6 ‘I 36." 4' 1 , 39. 4 * 1 42* 7-9 37. 4-9 47. 4 '9 52. 1 1-0 38° 6-1 51 6 - 1 62-5 12-9 39°5 7:0 62.5 7:0 77 15-9 42 7.9 77-5 7-9 97 18.9 44 8-2 79. 8-2 100 21 - 1 46 9 : 1 97. 1 1-0 130° I 1 °0 120° | 1-5 122°5 12'4 1 || 1 | I 1-9 I 12' 12.9 103. 13.9 94' 15°9 65 • 14" | 77. 18-9 45° 1 5 9 57. 18.9 4 l Low Frequency and their Resonance. 517 One-half of the bundle of the iron wire was placed into the inertia coil and the circuit tuned. Table III, Part A, gives the data from which curve I, fig. 6, was plotted. Next all the wire was placed into the inertia coil and the circuit tuned. Table III, Part B, gives the data from which curve II, fig. 6, was plotted. Finally the circuit was tuned without any iron and from the data of Part C, Table III, curve III, fig. 6 was plotted. From the curves I and II it is evident that the doubling of the mass of iron produced very little change in the values of the capacity and self-induction which established resonance between the circuit and the impressed e. m. f., and yet although the losses due to magnetic hysteresis were more than doubled (since the magnetizing current was a little larger with double the mass of iron in the inertia coil), yet the rise of potential due to resonance was increased. This experiment seemed to me to indicate that hysteresis and Foucault current losses do not explain quite fully the discrepancy between the theoretical and the experimental values of the rise of potential 518 M. I. Pupin—Electrical Oscillations of due to resonance. Thinking that perhaps the development of Foucault currents in the rather coarse iron wire or that the mechanical vibrations of the wire may in some way or another modify the period of the circuit and the self-induction of the coil, I endeavored to devise some simple experiments which would test the hypothesis just mentioned. Experiment 4.—About 19 microfarads were plugged in the condenser and then the iron wire was gradually introduced into the inertia coil and the rise of potential was observed closely. The potential went up continually until a maximum of about 100 volts was reached. From this point on the electrometer needle remained stationary although I kept on adding more and more iron wire, one wire at a time. Suddenly the addition of another wire caused the electrometer needle to drop down con- siderably below the midway point between zero and the maxi- mum point. I tried then to bring it back by removing the iron wires slowly one at a time from the inertia coil and found that I had to remove a considerable number of wires (about one fourth of the total number which was about 300 wires) before the electrometer index began to move up rapidly toward the maximum point previously obtained. The wires were now gradually replaced into the coil and the same phenomenon ob- served as before. The experiment was repeated over and over with invariably the same result. Ecperiment 5.—After the collapse of resonance (as described in the last experiment) by the addition of the last fatal wire, as it were the last straw that broke the camel's back, resonance, indicated by the large rise of potential and the singing of the iron wire, was established again by gradually lifting the whole bundle until the electrometer indicated the highest point. Then the bundle was lowered again very gently until it was entirely in the coil again. The electrometer needle would then remain stationary, apparently for an indefinite time. But the mere approach of an iron wire toward the bundle would upset the resonance suddenly and cause the electrometer needle to drop way down. That this approach of the single iron wire did not disturb resonance by the increase of the coefficient of self-induction was proved by the circumstance that if this iron wire was introduced into the coil and then the whole bundle raised until resonance was established and then slowly lowered again the maximum potential previously obtained was reached again and maintained apparently indefinitely although the iron wire bundle contained now that wire also by whose mere approach resonance was upset before. In fact it is possible to increase in this way, the number of iron wires in the bundle by four or five wires without changing perceptibly anything in the resonant effect, whereas the mere approach of a single Low Frequency and their Resonance. 519 wire from outside was sufficient to upset it entirely. In the course of these experiments it was observed that a gentle handling of the iron wire produced much more sensitive instability in the resonance. I suspected therefore, that mechanical vibrations of the wire might have something to do with the phenomena observed, and although I have been unable as yet to determine exactly to what extent these vibrations do influence the effect of iron on the resonance yet I feel that this effect is to a considerable extent due to molecular action of the iron. The following two experiments will, I venture to suggest, throw some light upon this point. *periment 6.—A sensitive resonance was obtained by plac- ing a sufficiently large number of iron wires into the inertia coil until the addition of another wire caused a collapse. After the collapse the wire bundle was gently raised and then lowered again, 19 microfarads being plugged in the con- denser. Now the capacity was .. by removing carefully one plug after another from the condenser. The capacity could thus be diminished fully 6 per cent without anything like a corresponding change in the resonant rise of potential. But a critical point in the variation of the capacity is then reached, after which the slightest change in the capacity will cause the resonant rise of potential to collapse suddenly, after which collapse the plugging in of the condenser plugs did not restore resonance. To bring resonance back again it was nec. essary to raise and lower again the wire bundle in the manner described above. If however the capacity was varied by even less than 1 per cent, but in such a way as to allow a bright, snapping spark to take place when the condenser plug was "emoved, then the spark had almost invariably the effect of causing a collapse of resonance. Jºeperiment 7–All the preceding experiments were now repeated with the iron wire tied very tightly together and when the whole bundle was introduced into the inertia coil it was pressed tightly against the table so as to prevent mechan. ical vibrations as much as possible, but the phenomena de- scribed above appeared again. I observed however that the sensitiveness of the instability of the resonant flow was not quite as great as when the iron wires in the inertia were stand- ing loosely. All these phenomena are observable at high frequencies also but they are not marked as strongly as at low frequencies. While working with weak alternating currents obtained by my electrodynamic interruptor, this peculiar behavior of iron was never observed by me, probably because in these circuits the magnetizations are so weak that iron is capable to follow every impulse of the magnetomotive force. Hence the persist. 520 M. I. Pupin—Electrical Oscillations, etc. ance of the upper harmonics in resonant circuits through which weak currents flow, and their entire absence from pesonant circuits traversed by strong currents. I expect to follow up this subject more closely and I do not know of any method by which it could be studied with greater ease and accuracy than by the method of resonant rise of poten- tial. The circumstance that low frequency resonance offers so delicate a method for the study of electromagnetic phenomena such as I just described seems to me to make the subject of slow frequency resonance even more important than the fact that by it rise of potential and weeding out of harmonics can be produced. Before closing this paper I must thank my pupil Mr. M. C. Canfield, postgraduate student in Electrical Engineering, for the very efficient way in which he has aided me in these exper- iments. Electrical Engineering Laboratory, School of Mines, Columbia College, New York, May 8th, 1893. werr MEETING oct. 17th. PAPERs phſwrep ſw This issue. | Entered as matter of the second class at the New York, N. Y. Post Office, November 26th, 1890. VolumE XI. } _ = [copyRIGHT, 1894.] Annual Subscription $5.00 NUMBER 10. oc70BER, 1894. * * * OF THE AMERICAN INSTITUTE ELECTRICAL ENGINEERS. CONTENTS. Test of a Closed Coil Arc Dynam O. By Prof. R. B. Owens and C. A., Skinner, May 1 6th . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative Advantages of Toothed and Smooth Core Arma- tures. By A . A danns, May 1 6th , , * * * * * * * * - * * * Standardizing Electrical Measuring Instruments. By E. C. Willyoung, May 1 7th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Qptical Phase Indicator and . Synchronizer. By Prof, Geo. S. Moler, and Dr. Frederick Bedell, May 17th . . . . . A New Method of Recording any Kind of Variable Current. By Prof. A. C. Crehore, May 1 7th. . . . . . . . • * s - a e s p & © - e < * * Resonance Analysis of Alternating and Polyphase Currents. By Prof. M. I. Pupin, May 18th . . . . . . . . . . . . . . . . . . . . . . . . . Associate Members Elected, Se ot. 19th . . . . . . . . . . . . . . . . . . . . . . . . Theory of Two and Three Phase Motors. By Lieut. Sam'ſ Reber, Oct. 1 7th . . . . . . . . • * * * * * * * * * * * * * . * * * * * * * * * * * * • * * * * * * * * * * * * * * : * * * * * * * * * * * * * * * * * * * * s a e < * * * * * * * * * * * * * * * * * l’UBLISHED MONTHLY BY THE INSTITUTE, UNDER SUPERVISION OF THE COMMITTEE ON PAPERS, - MEETINGS AND EDITING. . . . . . RALPH. W. Pope, Secretary, 12 wrst thirty-pinst Street New York City. ... telephone, 15 12. 38th. 50 | TF ANSACTIONS P AG E. 525 54-9 5 6.O 586 59 1 6O7 637 652 669 683 THE ~~~~~~~~ -,-,-, ... • - - - - - - - - ------------ * ------------ ~~~--------- ~~~ ---------~~... ----- - - - - - - - - - - - - - - - - - - , , -- - - -- ~~~- ~~~~3---~~~~. +. --- * -----------> *. OFFICERS AND MEMBERS OF THE COUNCIL, 18921-95. PRESIDENT: PROF. EDWIN J. HOUSTON, Term expires 1895. PAST-FEESIDENTS : DR. NORWIN GREEN, 1884.5-6. Pirof. ELIHU THOMSON, 1889-90 FRANKLIN L. POPE, 1886-7. PROF. W. A. ANTHONY, 1890 91. T. COMMERFORD MARTIN, 1887-8. ALEX. GHAHAM BELL, 1891 2. EDWARD WESTON, 1888-9. FRANK J. SPRAGUE, 1892-93. YICE-PRESIDENTS : Terms expire 1895. Terms expire 1896. PATRICK B DELANY, PROF. W 1LLIAM A. ANTHONY, H. WARD LEONARD, PROF. FRANCIS B. CROCKER, WILLIAM WALLACE. JAMES HAMBLET. MANAGERS : Terms expire 1895. CHARLES WIRT, DR. MICHAEL I. PUPIN, ANGUS S. HIBBARD, CHARLES P. STEINMETZ. Terms expire 1896. PROF. HARRIS J. RYAN, J. J. CARTY, CHARLES HEWITT, WILLIAM J. HAMMER. Terms expire 1897. A. E. KENNELLY, CHARLES S. BRADLEY, WILLIAM D. W. LAVER, W. B. WANSIZE, Terms expire 1895. - TREASUR.ER, . SECRETARY : GEORGE M. PHELPS, RALPH. W. POPE, 203 Broadway, New York. 12 West 31st, St. New York. Board of Examiners : GEORGE A. HAM ILTON. Chairman. E. T. BIRDS ALL, C. O. M AILLOUX, J. STAN FORD BROWN. EDWARL) P. THOMPSON. Standing Committees appointed by direction of Counell : Committee on Papers, Meetings, and Editing. FRANCIS B CROCKER, Chairman. J. J. CARTY, JOHN W HOWELL, DR. M. I. PUPIN, GEO. M. PHELPS, Prof. H. J. RYAN, Dr. SCHUYLER S. WHEELER. Sub-Committee on Editing, Sub-Committee on Papers and Meetings. GEORGE A. H A M I LTON, Chairman. T. COMMERFOR D MARTIN, Chairman. C.. O MAILLOUX, HORATIO A. FOSTER, FRANKLIN L, POPE. H. WARD LEONARD, WM. M A V ER, JR., HERBERT LAWS' webb. Library Committee. - . STAN FORD BROWN. Chairman. GEORGES D'INFREVILLE, GEORGE H. STOCKBRIT)GE. Committee on Finance, Building and Permanent Ouarters. GEORGE M. PHEI.PS, Chairman. GEORGE A. HAMILTON, Dr. SCHUYLER S. WHEELER, THOMAS A. Eſh ISON. FRANKLIN L. POPE, FRANCIS R. UPTON, T. COMMERFORD MARTIN, DR. F. BENEDICT HERZOG. Committee on Units and Standards. A. E. KENNF.I.L.Y. Chairman. GEO. A. HAM i LT ( ) N. DR W.M. E. GEYER, FRANCIS B. CROCKER, WILLIAM D. WEAVER. - Committee on Membership etc., RALPH. W. POPE, Chairman THOMAS D. LOCKWOOD, Local Secretary, Boston, Mass., Dr. LOUIS DUNCAN, § { # & Baltimore, Md., CARL HE RING, $$ tº Philadelphia, Pa., • Prof. EDWARD L. NICHOLS, “ {{ Ithaca, N. Y., JOSEPH WETZLER, R. N. BAYLIS, H. A. FOSTER, New York City BION J. ARN old, Local Honorary Secretary. - * 574-576 The Rookery, Chicago, iii. Telephone, Maia-2139. A paper Aresented at the EZezenth General Meet ing of the American Institute of Electrica! Engineers, Philadelphia, May 16th, 1894. Presi- denz Houston in the Chair. TEST OF A CLOSED-COIL ARC DYNAMO. gººmmº-sº BY PROF. R. B. OWENS AND C. A. SEKINNER. That so much has been said and written concerning the design of constant potential machinery, effects of armature reactions, control of sparking, etc., and so little concerning the machinery used for arc lighting, seems rather remarkable considering the fact that by far the larger part of our outside lighting as well as much inside lighting is done by means of arc lamps in series, and I hope a discussion will follow in which more light will be thrown on the principles of design of arc machinery, for at present there seems to be much empiricism in the matter. The immediate object of the present paper is to show some- thing of the nature of the armature reactions which occur in arc light machines of the closed-coil type, maintaining constant current by automatically shifting the brushes to correspond with changes in load in the external circuit, and to point out certain alterations in design which it is believed may be adopted with advantage. Incidentally other points will be noted. Of course there are other well known methods of maintaining the current constant: notably by shunting the field magnets as in the Brush machine, or a combination of this with shifting the brushes as in the new Excelsior machine, or by varying the length of time per revolution during which the armature coils are in series and shunt to each other or short-circuited as in the T.-H. machine, but these will not be considered at present. Nor is it intended here to discuss the relative advantages of the several types, but only to give some results obtained in a test of a closed-coil machine regulating as above mentioned. Such machines are now taking a prominent part in the are lighting industry, and their prominence merits for them more close study. Alternating current dynamos, as the Westinghouse arc light machine, have 525 526 oWENS AND SKINNER on AN ARC DYNAMo. [May 16, TI -----# + + – + – – – – – + – 0• ;; éſ /* * *， Tſ!” (”.$6， \，ŽĀĶĶěêź ---- • • • • • → • • • • • • • = • |||| *...* ºg-º--:-!!!!!！！? T---- 1894.] O WENS AND SHINNER ON AN 24 BC, D Y NAMO. 527 been devised which keep the square root of the mean square of the current remarkably constant through extremely wide varia- tions in load and without any external regulating mechanism whatever. They possess many advantages, but are not now widely used, for are lamps seem as yet to work more satisfactorily on continuous current circuits. We believe it is also possible to build continuous current are machines which by armature reac- tions alone can keep the current very nearly constant throughout a considerable range, but it would seem that their cost would be more, and their efficiency less than in some of the types using an external regulating mechanism, although we have no exact comparative data. The machine on which the following experiments were made is a No. 6, 25-light 2,000 C. P. Wood are dynamo, a scale drawing of which is shown in Fig. 1. From the drawing all dimension as of magnet limbs, yoke pole-pieces armature, etc., are at once seen. Its designer, Mr. James J. Wood, most courteously consenting to my giving the name of the machine tested and its full data. The winding data and other details as furnished by the makers are as follows: The field magnet winding is composed of four coils of No. 10 B. and S. gauge copper wire, single cotton covered. The outside diameter when insulated is 0.114 in. Each coil contains 100 lbs. of wire in 15 layers of 74 turns each. The insulation of the magnet cores, is 1-8 in. thick, and com- posed of one layer of enameled cloth, the enameled surface fa- cing the iron, the remainder being composed of pressboard 0.025 in. thick. The magnet heads are wooden washers 5-16 in. thick, carefully dried and shellaced. The armature core is composed of No. 10 B. and S. gauge annealed, charcoal iron wire. This is wound on a former which is removable, and is composed of 15 layers, 6% in. wide. These wires are held together by interposed strips of linen tape. The core is theninsulated with a layer of asbestos paper, 3 thicknesses of pressboard 0.15 in. thick, one layer of asbestos paper again, and then over this one more layer of pressboard 0.15 in. thick, making a smooth surface for the copper wires to be wound on. The insulations near the spider arms are built up of the same material and in the same manner as the armature core, until they attain a thickness of 4 in. The armature is wound with 100 8. # * : f : . . * * * 528 OWENS AND SKINNER ON AN ARC DYNAMO. [May 16, sections of No. 14 B. and S. gauge double covered cotton wire. Each section is composed of 93 feet, or 57 turns per section, making a total of 115 pounds of wire. The regulator magnet is wound with No. 11 single cotton covered B. and S. gauge wire, in the manner shown on the dynamo. The insulation of the cores being 5-32 in. thick, and FIG. 2.-Showing distribution of E. M. F. with 10 amperes in field and no current in armature. that of the magnet heads 3-16 in. Speed of dynamo, 1000 rev. per minute. CoNDITIONs of TEST. The dynamo was securely bolted to a firm foundation of masonry, and driven through a 7 in. belt by a small 8 in. x 10 in. high-speed automatic Atlas engine making 250 revolutions per 1894.] OWENS AND SKINNER ON AN ARC. DYNAMO. 529 minute. Steain was supplied at as nearly constant pressure as possible. The automatic regulator of the dynamo was removed, together with one pair of opposite collecting brushes, and the re- maining pair reduced one-half in width parallel to the commu- tator bars, to allow of easier manipulation of the exploring brushes, their angular width being of course adjusted for each load to prevent sparking. Q TABLE I. DISTRIBUTION OF E. M. F. AROUND THE COMMUTATOR, WITH FIELDs SEPARATELY ExCITED; No CURRENT IN ARMATURE. BY THE Two-BRUSH METHOD. Current in Fields—8 Amps. Current in Fields—Io Amps. Current in Fields—12 Amps. § § § § # § wd *5 :5 :5 :5 *5 #: § .9 $ g; v 3 || 3 v 3 || 3 ~ 3 || 3: is § | # g-f p. *g § 04 -- § Y. *4 § 2.4 * § p.4 *t #* | 3 ||34 || 3 ||34 || 3 ||34 || 3 ||34 || 3 ||34 || 3 O o.8 50 I. O O O.4 5o O.7 O I. O 5o I. I 2 Io.5 52 II.7 2 9.O 52 I [.. O 2 IO. O. 52 II.9 4. 31.6 54 34.6 4 || 3 I.O 54 35.O 4 3I-3 54 35.O 6 5I o 56 53.O 6 5 1.O 56 54.O 6 51.6 56 53.6 8 55.3 58 57. O 8 55.5 58 $7.4 8 56.o 58 57.o IO 57. I 6o 59.o IO 58.o 6o 59-9 IO 58.9 6o O I2 59-9 62 61.5 I 2 61.6 62 63.5 I2 63.7 62 64.o I4 62.3 64 64. I I4 65.3 64 67.5 £4 68.o 64 69.o I6 64.9 66 66.3 I6 68.9 66 71.o I6 73.o 66 73.o 18 67.1 68 69.o I8 72.6 68 74.O I8 77. I 68 77.9 2O 69.9 7o 7 I.o 2O 75.8 7o 77.o 2O 81.5 7o 81.o 22 71.2 72 72.o 22 78.5 72 78.5 22 83.8 72 82.2 24 7o.8 74 72.o 24 77.5 74. 78.9 24 83.8 74 82.7 26 7o.8 76 71.8 26 77.4 76 78.1 26 83.8 76 82.3 28 69.9 78 7O.3 28 76.o 78 77.o 28 81.o 78 8I.o 3o 67.1 8o 68.5 3O 73.8 8o 75.o 3o 79.o 8o 78.o 32 65.6 82 65.9 32 7O.O. 82 71.3 32 75. I 82 74.O 34 62.5 84 63.o 34 66.3 84 67.o 34 7o. I 84 69.o 36 69.o 86 59.4 36 62.5 86 63.o 36 65.o 86 64.o 38 57.5 88 56.6 38 58.8 88 58.8 38 6o.o 88 59.O 4O 55.2 90 54. I 4O 55.8 Qo 55.o 4O 56.o 90 55.o 42 || 54. O 92 52.5 42 54.O 92 52.7 42 || 54. I 92 53.o 44 || 45.9 94 || 46.3 44 || 45 5 94 || 47 O 44 47.o 94 || 47.5 46 24.O 96 24.O 46 24.O 96 23.o 46 24. I 96 24. I 48 6;o 98 5.7 48 5.2 98 6.o 48 6.4 98 6.o With 8, 10 and 12 amperes the neutral points remained at the positions .6 and 50.6. Check readings taken after each column of observations showed a varia- tion of less than 2 per cent. in all cases. It was at first attempted to use a number of arc lamps as load for the dynamo, but though carefully adjusted and using cored carbons, the variations of potential and current due to their feed- ing was greater than could be admitted, so the lamps were dis- carded for two water rheostats 4 feet X 1 foot X 1 foot, with car- bon electrodes. These latter on the whole were found to work quite satisfactorily, their resistance hot was considerably less than 530 OWENS AND SKINNER ON AN ARC DYNAMO, [May 16, when cold,but it changed so gradually that no trouble was expe- rienced in correcting for it by adjusting the electrodes. The distribution of the induction entering the armature at different loads was obtained by taking the E. M. F. at various points on the commutator between two small pilot brushes moved around and in contact with it. The two brush method, though somewhat more difficult to 2 * * & 7- § sł Pºe FIG. 3.-E. M. F. with 10 ampere current in field and armature, 25-light position. § work than the single brush method, has the advantage over the latter of giving the quantities, sought directly, instead of as a difference between quantities which are large as compared with those desired. In some cases the integral readings of the brush method have been plotted, but curves so obtained do not indicate so clearly what is mainly sought, namely, the distribution of lines of force entering the armature. True, one curve can be 1894.] O WEWS AAWD SAEIWNER ON A W ARC DYNAMO. 531 gº approximately obtained from the other, if electrostatic instru: ments are used, but not, with electromagnetic instruments, for they will give only a mean E. M. F. depending on the relative width of a commutator bar and insulation and distance apart of TABLE II: DISTRIBUTION OF E. M. F. AROUND THE CoMMUTATOR, As SHOWN BY THE TWO- BRUSH METHOD. Position of the toe of collecting brushes. 33.8 and 83.8. Number of segments covered by each collecting brush, 7. Current—8 Amperes. Current—Io Amperes. Current—12 Amperes. * º * º • * ~5 * ~5 tº ro rd . Tº ~5 * & 3 g; s & 2 * $ tº & $ 3 & 3 ºff v š 3 § 04 "S § 04 'S § 24 O § 04 '5 § 24 & § 24 * 3. > || }; $ || 3 > || 3 § - || 3T > || 3 Š o | + 19.7 5o – 2d.o o + 22.5 5o – 22.o o + 24.o || 50 – 23.3 2 | + 33.8 || 52 | – 34.9 2 | + 38.o || 52 — 38.9 2 + 39.9 || 52 - 40.5 4 |-|- 60.6 || 54 – 62.o 4 || + 66.o || 54 — 70.5 4 + 72'o || 54 – 73.o 6 + 85.o 56 — 86.2 6 + 92.o 56 – 93 8 6 +-roo.o 56 —ro1.5 8 + 86.4 58 — 86.3 8 || + 92.9 58 – 94.o 8 +1o 1.4 58 –1oo.9 Io + 82.o 6o — 82.4 Io | + 88.5 60 — 89. I Io + 96.o 6o – 95.7 12 + 78.1 62 — 78.7 12 | + 84.o 62 — 85.2 12 -t- gr.o 62. — 91.6 I4 f 74.7 64 – 75.o 14 || + 8o.o 64 -- 81.4 I4. | -- 87.o 64 — 87.2 I6 7o.o 66 — 7o. 1 I6 + 76.o 66 — 77.4 16 || + 81.6 66 — 82.2 18 + 65.6 68 – 65.4 18 + 7o.2 68 — 72.o 18 + 75.9 68 — 76.5 20 | + 60.7 7o – 60.5 20 + 64.3 7o – 66.6 20 i + 69.2 7o — 70.9 22 | + 54.1 72 | – 54.o 22 || -- 57.r 72 —, 58.7 22 + 59.6 72 — 61.2 24 | + 46.7 || 74 – 46.2 || 24 || -- 46 7 || 74 — 49.3 || 24 : + 48.0 || 74 – 5o.o 26 + 38.o 76 — 38.o 26 |-|- 36.8 76 – 38.9 26 + 37.6 || 76 — 37.6 28 f 29.9 78 — 58.7 28 + 24.5 78 — 27.8 28 + 20.2 || 78 — 24.2 3o 2O.3 8o | — 18.8 3o + 15.2 || 8o — 16.o 30 ; – 6.2 || 8o — Io.2 32 | + 9.9 82 – 9.1 32 || -- 1.5 || 82 - 3.3 32 || – 10. 1 || 82 + 4.7 34 O. O. 84 — o.7 34 o.O || 84 — o.8 34 o.o || 84 + 4.8 36 O. O. 86 O. O. 36 O. O. 86 O.O. 36 o-o. # 86 O. O. 38 f O.3 88 O. O. 38 I I.O || 88 O.O. 38 || + o-4 88 O. O. 4O 5. I || 9o - 3.7 || 4O 8.8 || 9o — 4.0 || 4o f 8.8 || 90 | – , 6.6 42 I4.4 92 || – I2.4 42 f 19.6 92 || – 16. I 42 21.2 || '92 || – 18.0 44 16.4 || 94 | – 15.7 || 44 21.5 || 94 – 19.2 || 44 + 244 || 94 | – 23:o 46 3.o || 96 || – 3.2 || 46 + 5.4 || 96 || -- 4.0 || 46 |-|- 4.3 || 96 || – 6.9 48 – 9.o 98 } + 7.3 48 – 9.1 || 98 || + 9.1 48 – 9.8 i. 98 IO. G. Check readings after each column of observations showed a variation of less than 2 per cent. in all cases. - * * - With 8 amperes the voltage between the collecting brushes was 1160; between neutral points, 1225; the neutral points being at 47.6 and 97.6. With 10 amperes the voltage between brushes was 1190; between neutral points, 1235; the position of the neutral points being 47.6 and 97.6. With 12 amperes the voltage between brushes was 1236; between neutral points, 1319; the neutral points being at 47.7 and 97.7. , * Sparking same as in former positions. the pilot brushes. The results obtained however with a volt. meter of the Weston type, are proportional and for the present purpose are equally valuable. .. 4 - The exploring brushes as finally, used were pieces of steel watch springs firmly held in small fibre holders. These, in turn 532 oWENS AND SKINNER on AN ARC DYNAMo [May 16, were rigidly secured by brass, studs to a graduated sliding ring, moving within another stationary ring, attached to and insulated from the dynamo frame and carefully centered with the commu- tator. - Two brushes were used in each holder to better ensure good contact. Copper, brass and phosphor-bronze exploring brushes were tried at first, but found not as satisfactory as steel. It was also & ; 2. 3- OO sº *Nº. §: te FIG. 4.—E. M. F. with 10 amperes in field and armature, 20-light position. found very necessary at all times to keep the brushes and com- mutator as clean as possible. - The sliding ring was marked off into one hundred divisions, the number of commutator segments,and the exploring brushes made to cover just two commutator bars or one fiftieth of the circum- ference, but the ring might have been divided into degrees if desired. The curves shown in figures 2, 3, 4, 5, 6, and 7 are plotted 1894.] OWEWS AWD SKINNER ON AN ARO DYNAMO. 533 so that the results may be read either in degrees or in divisions of the graduated ring. The inner circle represents the commutator of one hnndred segments, and the 100 divisions of the ring are marked on the outer circle. TABLE III. DISTRIBUTION OF E. M. F. AROUND THE COMMUTATOR, As SHOWN BY THE TWO- - BRUSH METHOD. Position of the toe of collecting brushes, 31.6 and 81.6. Number of segments covered by collecting brushes, 6.7. i } Current—8 Amperes. Current—Io Amperes. Current—12 Amperes. - § § § § g § #5 :3 #5 *5 - #5 *5 & 3 || 3 || v 3 || 3 #3 3 || 2 3 || 3 s: 3 || 3 || v š 3 £4 *4 § 04 "3 cq "S § {Y& "a § p. TC § {Y. q=ſt ; § || } $ || } > || 3. > || } § { }; $ o + 16.9 50 | – 16.1 o + 17.4 5o – 17.2 o + 16.3 5o — 16.7 2 |-|- 32.O || 52 - 33.o 2 | + 33.4 || 52 – 34.6 2 |-H 33.5 || 52 | – 35.2 4 + 58.7 || 54 – 62.o 4 || + 61.7 || 54 — 66.o 4 |-H 64.1 i 54 || – 67.5 6 || -- 82.o 56 – 83.5 6 || -- 87.o 56 – 89.5 6 + 9o.o 56 – 92.5 8 + 83.2 58 – 84.o 8 |-|- 87. 58 – 89.7 8 i 90. I 58 – 91.7 Io —H 78.4 6o – 79.5 1o + 82.5 6o — 84.9 IO 84.5 6o — 86. I I2 —H 74. I 62 – 75.5 12 | + 78.o 62 — 8o o 12 + 79.3 62 — 81.5 I4 + 70. I 64 – 71.5 || 14 + 73.5 || 64 — 75.Q || 14 74.6 || 64 – 76.7 16 + 65.9 66 || – 67.6 16 || –H 68.9 66 — 71.6 16 69.3 66 — 71.5 18 || -- 60.8 68 || – 62.6 18 + 63.o 68 — 65.5 18 62.7 68 – 65.3 2O || -- 55.1 7o - 57.o 2O + 56.3 7o — 58.9 2O 55.2 7o – 58.o 22 | + 48.5 72 — 50.6 22 || -- 48.7 72 – 51.2 22 f 46. I 72 – 49.2 24 | + 39.9 || 74 – 43.2 || 24 |+ 37.9 || 74 – 40.8 || 24 33.o || 74 – 37.6 26 + 31.o 76 — 34.6 26 + 26.5 76 — 29.9 26 + 19.5 76 – 24.o 28 + 21.o 78 — 25.8 28 + 13.o 78 — 18.5 28 + 4.7 78 — 11.2 3o -- 12.o 8o — 16.2 3o + 1. 8o — 5.1 3o – 8.9 8o + 1.5 32 O. O. 82 O.O 32 O O 82 O. O. 32 O, O. 82 + 1.o 34 O.O 84 O.O 34 O. O. 84 O,O 34. O.O 84 O.O. 36 | + 5.4 86 — I o 36 | + 5.7 86 — .3 36 +- 5.3 86 — 1.5 38 I4.2 88 – 9 o 38 f I 5.5 88 — 9.o 38 + 16.5 88 — Io.6 4O 21.8 90 - 17.o 4o 24.O 90 – 19.o 4o + 26.o 90 – 21.5 42 29.O 92 | – 24.5 42 32.4 92 — 27.8 42 + 35.5 92 || – 31.o 44 28.8 || 94 | – 26. 44 33-4 || 94 || - 3O. 4 || 44 35.5 || 94 - 33.o 46 II.7 96 || – 9 8 46 I3. I 96 — I 1.1 46 I5. I 96 — 12.6 48 — 4.7 || 98 || + 4.8 || 48 - 4.0 || 98 || + 4.9 || 48 || – 4.0 || 98 || + 3.5 Check readings taken after the observations in each column showed a varia- tion of less than 1 per cent. With current of 8 amperes the voltage between brushes was 970; between neutral points, 1132; the neutral points being at the positions 48.1 and 98.1. With 10 amperes the voltage between brushes was 976; between neutral points, 1210; the neutral points being at positions 48.2 and 98.2. With 12 amperes the voltage between brushes was 950; between neutral points, 1250; the neutral points being at positions 48.3 and 98.3. With 8 and 10 amperes the sparking at brushes was very slight, but with 12 amperes it increased to destructive sparking. The radial lines are 5 degrees apart, and the radial distance between concentric circles represents 10 volts. If the results had been plotted on a developed diagram, then the areas of the curves would have represented total or integral electromotive * 534 oWENS AND SKINNER ON AN ARC DYNAMO. [May 16, forces, but the circular diagram has the advantage of appealing more quickly to the eye, and though the total E. M. F. is not exactly represented by the area it is proportional to the number of the small approximate rectangles enclosed. In obtaining efficiency measurements, the power delivered to the dynamo was obtained by indicating the engine. The cards were taken with a Tabor / \ \ So Qö ;T 2. / tºº / i FIG. 5.—E. M. F. with 10 amperes in field and armature, 15-light position. indicator, and worked up with a Coffin averaging instrument; the speed was obtained by a speed counter, and stop watch. The electrical instruments used were a Weston 0.15 amperemeter for current measurements. A Weston 0.15 and 0.150 voltmeter for potentials between pilot brushes, and a 0.150 and 0.1500 Weston voltmeter for total electromotive forces. All instruments were previously calibrated. 894.] OWENS AND SKINNER ON AN ARC DYNAMO. 585 RESULTS OBTAINED. Fifteen sets of readings, fifty readings per set, were taken around the commutator with currents in armature and field of TABLE IV. DISTRIBUTION OF E. M. F. AROUND CoMMUTATOR, As show N BY THE Two- BRUSH METHOD. Position of the toe of collecting brushes, 30.1 and 80.1. Number of segments covered by each collecting brush, 4.7. *- ---------- Current—8 Amperes. . Current—ro Amperes. . . Current—-12 Amperes. e l A * • s - 8 : § | # # | # #| : # *5 # . . .'; . . . . ; ; ; ; ; ; ; ; ; ; ; , * 3 * v š fl ºf v š , ; .v Š 2 : s : ; ; ; } & 3 2. º; Oº º §p. 3 ºp. ; as ºp. Tºš : ; p. f. "S ! 3 oz. "S 3. * || 3" | < | #" $ 3 > 3T : ; } }T - : | - | t ſ , , # ‘. o -- 13.2 5o – 13.7 | o + 14.o | 5o – 14.5 o + 12.2 ſ 5o º — 13.8 . 2 || -- 28,8 52 — 3o.o # 2 + 30.7 52 – 32.3 2 + 29.5 # 52 – 32.6 4 + 55.5 i 54 – 58.9 || 4 + 62.3 54 – 64.2 4 : + 66- 6 - 54 – 65.o 6 || -- 79.4 56 – 82.2 | 8 + 86.5 56 – 88.o." 6 Eğ. | 56 – go.o 8 + 8o 4 58 — 81.8 8 + 87.o 58 – 87.7 . . . 8 ' +88.o 58 — 89.o Io —H 76.o 6o — 76.3 Io + 81.7 6o — 82.o. To –– 82. I 60 – 82.7 12 -- 71.0 # 62 — 71.7 : 12 + 76.7 ºf 62 — 76.9 12 + 76.8 || 62 – 77.3 14 + 67.o 64 – 67.0 14 + 72.o iſ 64 – 72 o 14 + 72.2 || 64 – 72.6 16 |+ 62.5 || 66 – 62.o' 16 -i- 67.o i. 66. – 66.7 || 16 -i- 67 o | 66 – 66.2 18 + 57.o 68 – 55.9 18. + 60.6 . . 68 – 60.9. , 18 + 59.9 || 68 ; – 59.1 2d + 51.o 7o – 49.2 20 + 53.3 7o – 52.6 ± 20 i + 51.9. § 7o – 51.o 22 || -- 44.3 72 | — 42.1 ! 22 + 45.o "' 72 — 43.3 22 i-H 41.9 72 – 40.1 24 + 35.4 || 74 - 32.3 24 + 33. 74 - 32.2 24 + 27 9 || 74 – 273 26 – 25.3 76 – 22.2 # 26 +20 4 76 — ig:7 26 + 13.6 || 76 -- 13.8 28 + 13.2 || 78 ; – 11.2 28 + 7.9 78 – 6.7 28 – .3 78 : + 2.2 3o + 3.o || 8o — .8 3o — .8 8o o.o 3o – 5.5 8o + 3.7 32 o.o i. 82 o.o 32 o.o 82 olo 32 o.o 82 o.o 34 + 3.0 || 84 - 5.6 34 + 3.3 84 – 6 o 34 i + 4, | 84 - 6:8 36 + 12.4 86 — 14. I 36 + 14.8 i 86 – 16.o 36 + 16. I 86 – 17.9 38 + 29 8 # 88 – 21.9 38 + 24 o # 88 – 25.1 / 38 : + 26.6 || 88 — 27.6 4o + 28.1 || 90 – 29.6- 4o" + 32.5 | 99. – 33.9 49 + 359 || 99 - 35.7 42 + 35.1 iſ 92 – 35.9 42 + 41.3 || 92 – 4:..o. 42 + 45.2 || 92 * - 44.9 44 + 35. ii. 94 – 36.9 44 + 40.8 94 i – 42.7-i. 44--, + 45.1 || 94 * – 45.7 45 + 16.9 || 96 -- 16.9 46 + 19.2 96 – 20.o , 46 -- 22.0 || 96 – 22.0 48 – 1.9 98 + 1.3 48 – 1.2 98 – 9 º' 48 i – 2 | 68 |. O.O After making the observations in"each column, check readings were taken at numerous positions, and in all cases the variation was less than 1 per cent. ºith current of 8 amperes the voltage between the collecting brushes was With the same current the voltage between the neutral points was 1150; the neutral plane passing through the 48.2 and 98.2 positions on the scale. With 10 amperes the voltage between collecting brushes was 784; the voltage between neutral points was 1183; and the position of the neutral points was 48.9 and 98.9. k With 12 amperes the voltage between the collecting brushes was 740; the volt- #. ºn neutral points was 1200; and the position of the neutral points, 8.I]Cl, 99. With 8 amperes there was slight sparking at the brushes; with 10 amperes there was none; and with 12 amperes there was considerable sparking. - The volts between neutral points varied somewhat, while the volts between . brushes remained constant throughout. 8, 10 and 12 amperes, at positions of the collecting brushes approximately corresponding to loads of 5, 10, 15, 20 and 25 lights. Three sets of readings were also taken with currents in 536 OWENS AND SKINNER ON AN ARC DYNAMO. [May 16, the field of 8, 10 and 12 amperes and no current in the armature The results obtained are given in tables, and for a current of ten amperes are plotted in corresponding plates. The reactions of the armature are so clearly shown by the curves that comment hardly seems necessary. Briefly, we see that the total induction in armature, varies very slightly with lead, and the displacement of the neutral plane decreases with & wº * § re Sº OS &º GO 2S re FIG. 6.-E. M. F. with 10 amperes in field and armature, 10-light position. lead angle, but varies less than 10 degrees from no load to the maximum load used. All electromotive forces on one side of the neutral plane are of the same sign but differ in sign from those on the opposite side. On a developed diagram the electromotive forces between col- lecting brushes would be proportional to the difference between 1894.] OWENS AND SKINNER ON AN ARC DYNAMO. 537 the whole area of curve on one side of the line of commutation and the area of the curve included in the angle of lead. The lead angle being defined as the angular advance of the collecting TABLE V. DISTRIBUTION OF E. M. F. AROUND THE COMMUTATOR, As SHowN BY THE Two- BRUSH METHOD. Position of the toe of the collecting brushes, 28.7 and 78.7. Number of segments covered by the collecting brushes, 4. er Current—8 Amperes. Current—Io Amperes. Current—12 Amperes. 80 80 80 80 80 bo $º ſ: º ſº ſº & #5 * *5 e *5 º ‘g sº *5 e *5 rº & * || 05 $ || } > || 3 $ 3 $ || 3 $ O 8.o 5o - Io.o O i 9.o 5o — Io.8 o |-|- 5.1 5O | – Io.o 2 24.5 52 – 26.9 2 26.8 52 — 28.8 2 | + 24.7 52 – 28.5 4. 52.5 || 54 || - 57.o 4 + 57.5 || 54 – 61.o 4 + 57.o || 54 | – 62.6 6 76.o 56 — 79.o 6 + 84.o 56 — 85.o 6 —H 84.o 56 — 87.o 8 78.o 58 — 79.o 8 —H 84.5 58 — 84.2 8 + 83.8 58 — 86.o IO 72.o 60 || – 73.8 Io + 78.4 6o — 78.3 TO 77.o 6o — 79.1 I2 67.2 62 — 68.9 I2 73.o 62 — 73.o I 2 71.o 62 — 72.4 I4. 63.0 || 64 || – 64. 1 I4. 68. I 64 – 67.9 I4 65. I 64 — 68.o I6 58.3 66 — 58.8 I6 63.o || 66 — 62.o I6 54-4 66 — 62.o I8 52.6 68 - 52.8 I3 f 56.o 68 — 55.2 18 ||—H 51.2 68 – 54.1 2O 46.2 7o — 45.9 2O 48.7 7O | – 47.4 20 | + 43.1 7o – 44.8 22 38.4 72 – 37.4 22 39 O 72 – 38.8 22 + 32.4 72 | – 33.8 24 + 29.8 74 – 27.o 24 27.o 74 || - 24.9 24 | + 16.o 74 – 3- 26 I9.7 76 — 15.9 26 I4.3 76 — 12.9 26 O. O. 76 | –- 3.9 28 + 5.2 78 — 3.o 28 .8 78 O.Q 28 — 5.2 78 I3. I 3o Q, O 8o O.O 3o —- .6 8o O.O So O.O 8o 8.8 32 f 3.8 82 — .7 32 | + 5.o 82 — 3 o 32 —H 2.1 82 — I.o 34 13.o || 84 || – 9.2 || 34 I 15.9 || 84 - 13.7 || 34 |-|- 13.3 || 84 — 13.o 36 I 2.I. 4 86 || — 18.o 36 25.4 86 — 23.3 36 25.o 86 — 23.7 38 29.o 88 — 26.o 38 + 34.o 88 — 31.8 38 f 34-3 88 — 32.9 4o 35.8 90 — 33.2 4O 42.8 go – 39.o 4O 43. I 90 – 41.9 42 42.8 || 92 – 39.9 || 42 5o.7 || 92 - 47.9 || 42 + 52.1 || 92 — 50.7 44 41.3 || 94 | – 4o.6 || 44 49.2 || 94 - 48.9 || 44 |-|- 51.1 || 94 — 42.0 46 2O.3 96 || – 19.o 46 25.4 96 || – 25.3 46 T 25.5 96 || – 26.4 48 |-|- . 98 — .7 48 || -- 2.1 98 || – 2.1 48 + 1.9 98 – 2.5 Check readings taken after the observations in each column showed a varia- tion of less than 1 per cent. in all cases. With current of 8 amperes the voltage between brushes was 654; between neutral points, 1140; the neutral points being at the positions 49.2 and 99.2. With current of 10 amperes the voltage between brushes was 622; between neutral points, 1170; the neutral points being at the positions 49.3 and 99.3. With 12 amperes the voltage between brushes was 552; between neutral points, 1185; the neutral points being at 49.4 and 99.4. With 8 amperes the sparking at the brushes was very slight; with 10 amperes, a minimum; and with 12 amperes it was considerable. • brushes from the neutral plane. An inspection of the curve of total E. M. F. with angle of lead given in Fig. 6, shows that the E. M. F. between neutral points remains nearly constant as lead Varies, which it is believed would not be the case if contracted j38 OWENS AND SKINNER ON AN ARC DYNAMO. [May 16, : « * * . . polar faces were used instead of the extended ones as shown, for then the shifting of the field could not be so easily effected. Of course a machine of the design tested, with extended pole tips, requires an automatic widening of the brush with increased load or independent control of sparking, but it would seem that the waste field at all loads would be less, and its weight efficiency FIG. 7.—E. M. F. with 10 amperes in field and armature, 5-light position. greater or cost for a given output less, than if its pole tips were cut away. Cutting away the pole tips or at least not extending them would have the advantage of allowing the use of collecting brushes of constant width within a certain range, but whether this advantage more than compensates for the decreased range of its output is open to question. Further experimental evidence, is however needed in this regard. 1894.] OVENS AND SKINNER ON AN ARC DYNAMO. 539 Regarding the relative amounts of iron in field and armature, we see no reason for the present practice of using so little iron in the armature, as compared with the field. The necessity of a TABLE VI. DISTRIBUTION OF E. M. F. AROUND THE COMMUTATOR, AS SHOWN BY THE Two- BRUSH METHOD. Position of the toe of collecting brushes, 27.9 and 77.9. Number of segments covered by each collecting brush, 3. 5 A • Current—8 Amperes. Current—Io Amperes. , Current—12 Amperes. º 80 bº 80 # ! 3 tº E .8 .8 f : ; : .E. .5 | o's a o'; ' ', e? | 3 || 3 || 4 || 93 a • 3 a # # || 3 | # || #3 || 3 || #3 # 5 #3 # #3 # Uſ) |- || Uí -> || Cº § { };" | Sº 3 : ; };" & ; ! 2 |+ 5.5 || 52 – 5:3 || 2 |+ 5.5 || 52 – 22 9 |+ 5.9 se - 5.6 2 + 20.5 52 — 21.5 2 + 2I.S + 52 – 24.o : 2 —H. 20.2 52 — 23.o 4 - 41-5 54 - 49. 4 || -- 49.0 || 54 – 54.5 4 -i- 49 4 - 54. 6 || -- 68 56 — 69. 6 + 72.0 || 56 — 75.7 | 6 || -- 71 : : - ; 8 + 67.9 || 58 — 67.9 8 + 71.6 || 58 – 74.3 | 8 || -- 72.9 58 – 74.1 Io —– 62.2 6o — 62.5 Io + 65.8 6o – 68.o iſ Io + 66.4 6o – 67.4 12 -H 57.7 62 — 57.5 12 + 60.3 || 62 – 62.o 12 + 6o I 62 – 61.o I4 -i- 53.5 64 — 52.8 14 || -- 55.5 64 – 56.4 || 14 + 55 o 64 — 55.2 16 –– 48.7 66 — 47. 16 | + ši.ó | 66 – 51.3 16 |+ 56.o 66 — 49.o 18 —H 43 68 — 4o.3 18 + 44.5 68 – 43.4 18 + 42.o 68 – 4 r.o 20 + 36.3 7o – 33.4 20 i + 37.7 || 7o – 35.0 20 | –H 35.1 70 – 31.3 22 i + 28 2 72 — 26. 22 + 29.5 || 72 – 26.o || 22 | + 26.5 72 – 21.o 24 + 20 74 — 16. I 24 —- 18.1 || 74 – I 3.9 24 -- 12.5 74 — 7.o 26 + 9.5 76 – 5.4 26 + 6.0 || 76 – 1.o 26 O. O. 76 + 6.5 28 O 78 — .2 28 o.o iſ 78 O, O. 28 o.o 78 : + 1.o 3o + 2. I 8o — 4.o 3o + 5. I 8o — 5.o 3o -i- 3.5 8o – 6.1 32 |-|- 12.2 82 — 12.4 32 + 16.3 || 82 | – 14.7 i32 |-|- 15.3 82 — 17.8 34 + 20.5 84 — 20.6 34 + 25. I 84 – 24.o 34 |+ 25.1 84 – 27. 36 |-|- 27.8 || 86 — 27.9 36 |+ 32.1 || 86 – 32.o 36 |+ 34.o 86 — 35.4 38 + 34.7 88 — 34.4 38 + 41.o !. 88 – 39.o 38 |- 42.o. 88 — 42.6 4o -f- 4o.9 90 – 4o.2 4o + 47.8 go — 46.o || 4o + 49.3 90 — 5o.o 42 | -i- 47. 92 — 45.8 42 + 54.9 92 – 52.7 || 42 + 57.o , 92 — 57.o 44 || -ī- 45. 94 – 45.5 || 44 |-|- 53.o |, ... I; ; ; # iii.; | 94 – 57.o 46 + 23. 96 — 23.7 46 + 28.9 || 96 – 28.o iſ 46 |+ 36.0 , 96 – 30.8 48 |+ 3.2 || 98 || – 3.1 || 48 |+ 6.1 || 98 || – 5.5 48 |+ 5.5 , 38 – 6.0 l i ; After making the observations in each column several check readings were taken, and in all cases the variation was within 2 per cent., while in most of them it was not more than 1 per cent. - With current of 8 amperes the voltage between the collecting brushes was 390; the voltage between the neutral points, 1110; the neutral plane passing through the positions 49.7 and 99.7 on the scale. S With 10 amperes the voltage between the collecting brushes was 379; the voltage between neutral points was 1160, the neutral plane passing through 49.9 and 99. With 12 amperes the Voltage, between the collecting brushes was 285; the :* between neutral points, 1170; the neutral plane passing through 50.1 and .1. - With 8 amperes there was slight sparking; with 10 amperes there was none; and with 12 amperes there was considerable sparking. y very high field induction or a thoroughly stiff field is apparent; but why when the lines are once generated by the field it is not sought to collect and utilize them all by means of an armature, 540 ownNS AND SKINNER ow AN ARC DYNAMo [May 16, with a generous amount of iron is not so easily seen. The num- ber of commutator segments would of course have to be increased to prevent sparking, but the regulating qualities of the machine Angle of Lead FIG. 8 ^ 7 8 16 Amperes FIG. 9.—Characteristics. would, it is believed, not be impaired. The result would be a larger output and greater efficiency. * Regarding the ratio of ampere turns on field and armature, 1894.] OWEWS AND SKINNER ON AN ARC DYNAMO. 541 such ratio will depend largely on the shape of the pole pieces and desired width of brush, but is in all cases much less than in TABLE VII. CHANGE OF VoITAGE BETweBN NEUTRAL PoinTs witH ANGLE OF LEAD. Angle of Lead. Volts. 74° 116o 69° 117o 62° 1 183 55° I2 IO 44° I235 TABLE VIII. ShowING EFFECT PRODUCED BY SHUNTING THE FIELDs, witH 10 AMPERES IN ARMATURE. Position of Brushes. Current in Fields. Sparking. 28.7 and 78.7 IO. None. $ tº $ $ tº a 9. Too much for good service. 4 * * . & 6 8.7 Excessive. 3o.1 ‘‘ 8o. 1 IO. None. 4 & 1 & # e. 9. I Too much for good service. * * * @ 4 & 8.6 Excessive. 33.8 ° 83.8 IO None. ū tº $ W. 8.7 Too much for good service. {{ { { { * 8. I Excessive. TABLE IX. VARIATION of E. M. F. AT BRUSHES WITH DIFFERENT CURRENTs, AND WITH DIFFERENT PosLTIONS of BRUSHEs. Position of Position of Position of Position of Position of Brushes Brushes Brushes Brushes Brushes 27.9 and 77.9. 28.7 and 78.7. 30.1 and 8o.I. 31.6 and 8.1.6. 33.8 and 83.8. Currents. Volts. Volts. Volts, Volts. Volts. I IOO 7o IOO 245 I95 2 275 2O5 35o 46o 5OO 3 34o 365 42O 652 679 4. 390 445 52O 775 769 5 44O 517 57o 84o 952 6 465 6oo 6ro 960 ro28 7 48o 6oo 630 Iogo I IOO 8 490 590 655 Io:38 II5o 9 48o 582 67o Iočo II55 IO 48o S73 678 IT IO 1177 II 45o 55o 665 II.25 II96 l2 42O 52I 65o Io98 I25o I3 365 474. 590 IO55 I23o I4 3IO 417 53O IOIO IIOO constant potential machines. That in the present instance with the widths of brushes given, the ratio could not be widely de- parted from without violent sparking, is shown in table No. 8, 542 OWENS AND SKINNER ON AN ARC DYNAMO. [May 16, w The characteristic curves shown in Fig. 9, and readings given in table No. 9, were taken at the 5, 10, 15, 20 and 25 light positions of the brushes, and show that with this machine, regula- tion is almost entirely effected by shifting the brushes, as the curves droop too slowly to assist to any material extent. Of 9 0 8 : | 4. 0 l ^- 8 Output in Horse Power FIG. 10. TABLE X. EFFICENCY TEST. Input. Output. Efficiency. H. P. H. P. . Per cent. * 6.86 3.3 49.6 9.7 5.3 54.6 I2.7 9.o 71.o * I5-3 II.6 75.8 2O.5 I7.2 83.9 MISCELLANEOUS. - Constant loss in fields with 10 amperes. . . . . . . . . . . . . . . 1575 watts. Radiating surface of fields . . . . . . . . . . . . . . . . . . . . . . . . 1245 sq. in. Radiating surface of fields per watt loss. . . . . . . . . . . . . .8 sq. in. course they might have been made to droop much more rapidly if the collecting brushes had been moved into sparkless positions for each value of the current, but a curve so obtained is not at all a characteristic. The efficiency curve is given on Fig. 10, and readings in table No. 10. From this curve and from what we have seen of the machine it is evident that it would never 1894.] OWEWS AWD SKIWWER ON AW ARO DYNAMO. 543 pay to run machines of this type underloaded. If a number are used in one station the connections of the external circuits at the switchboard should be so manipulated as to keep the machines actually in use always loaded to as near their full capacity as possible. Our thanks are due to Mr. H. J. Podlesak, who greatly assisted in taking the observations and working up the results. 544 OWENS AND SKINNER ON AN ARC DYNAMO. [May 16, DISCUSSION. MR. C. N. BLACK :—I think that the remark of Mr. Owens, in regard to the iron in the armature is very true. Arc machines as built heretofore have always had enormous field cores and very small armatures. We cannot get a constant current ma- chine by any such arrangement. It is practically impossible. On the other hand if we build an armature with an ample cross- section and work it only just around the bend of the curve, we can build a machine that will be practically automatic, without outside regulation, and which will give a constant current with a very slight variation, . That is the principle on which the latest 125-light Brush machine is built. The iron in the armature is worked at only about 90,000 to 95,000 lines per square inch at full load, and of course at lower loads the ampere-turns on the armature, cuts that induction down proportionally, so that at very low loads we have a very low induction, and we get a character- istic curve that without any regulator does not vary more than two and a half to three amperes, from 6,000 volts to zero. The machine works on the downward slope of the curve, part of which is absolutely vertical; for instance, from 4,500 volts down to 100 volts, there is not one-tenth of an ampere variation in the Current. MR. STEINMETz:—I am of the opposite opinion and at the same time of the same opinion as the last speaker. I am of the opinion that the density of the iron should be very high, but I am inclined to think that the last speaker is so accustomed to the are light dynamo densities of over 100,000 that he considers 95,000 as low density. This is for constant potential machines very high density, though with regard to some old are light machines it is low density. With regard to the problem of building arc light dynamos, it has been said that the worse a machine is, the better suitable it is as an arc light dynamo. But it is not so. The fact is, that the problems to be considered in the design of an arc light dynamo are so essentially different from those of a constant potential dynamo, that a bad design of a constant potential may be a very good design for an are light dynamo, and in general, a good design of a constant potential machine is a bad design of an arc light machine. But it is of just as much theoretical im- portance to investigate and understand the problem of arc light dynamo design, as it is with the constant potential dynamo design. What we want in an are light machine, is a machine which will give constant current automatically, if possible without any regu- lating mechanism at all; or at least so that the regulating mechan- ism is only an additional control to take up secondary actions, but not to do the whole of the regulation—otherwise the machine must be a failure. You can do this in two different ways. The ordinary shunt 1894.] * - DISCUSSION. 545 machine has the tendency to regulate for constant current, be- cause if you have a shunt machine with an ideal characteristic, that is, a machine whose induced electromotive force is propor- tional to the ampere turns in the field, and if the resistance and the armature reaction are negligible, then this machine will at any voltage just give the ampere-turns required to produce this voltage—that means, it will not give definite voltage, but any voltage desired by the conditions of the external circuit. In the machine as it actually is, the excitation of the dynamo must be proportional to the terminal voltage, plus a constant quantity, that quantity which produces the voltage consumed in the armature. Thus a shunt machine with a constant separate excitation, will fulfil the condition of giving a terminal voltage proportional to the external resistance, that is, will act as a con- stant current dynamo for all voltages below saturation, that is, below the bend of the magnetic characteristic. This machine will be a constant current dynamo, but not an arc light dynamo, because it will not regulate quickly enough. If the load is changed suddenly, it is a long time before the mag- netism changes to the altered conditions of load and excitation, and thus either a sudden rush, or a sudden decrease of current takes place. For instance, you cut out half the lights. Then the current will suddenly double its values, and then gradually go down to normal. Such a machine will do very well for a series incandescent dynamo, but for arc light circuits you want machines which, when the load is suddenly varied, do not allow the current to go above or below a certain value. The machine must be one whose armature will regulate auto- matically for constant current, that is, where a small change of the armature current, and thereby the armature M. M. F. will essentially change the field; if need be, destroy it. The effective field, I mean ; for even when short-circuiting the machine, the field may not disappear entirely, but may be turned around in Such a direction as to become ineffective with regard to the ter- minal voltage. - Thus, you require a machine of very large armature reaction, that is, a machine whose armature M. M.F. is of the same magnitude as the field M. M. F., and very large compared with the resultant M. M. F. required to produce the magnetism. In such a machine a Small variation of the armature current, that is, the armature M. M. F., will vary the resultant M. M. F. and thereby the magnetism and the E. M. F. very greatly. For instance, let the ampere-turns of the field = 12,000 at full load, the component of armature am- pere-turns in the direction of the field = 10,000, and the resul- tant or magnetizing ampere-turns = 2,000. When suddenly short-circuiting the machine, the current will rise only so far as to raise the armature ampere-turns to equality with the field am- pere-turns, that is, from 10,000 to 12,000, or by 20 per cent., and thereby blow out the field. 546 OWENS AND SKINNER ON AN ARC DYNAMO, [May 16, This is the principle of a successful arc light dynamo, a dynamo regulating for constant current by its armature reaction. Such a machine will without any outside regulation as shifting of brushes, etc., keep the current practically constant under all loads, whether a continuous current dynamo or alternating. It will, however, require an enormous M. M. F. on field and armature to get very close regulation. Here the external regu- lation comes in. You can get along with very much less M. M. F., just enough not to get too large a fluctuation of current by a very sudden change of load before the regulator can act. Thus the arc light regulator is merely for the purpose of making the inherent reg- ulation of the machine still closer. This is done by short-cir- cuiting or shunting a part of the field, or by changing the E. M. F. of the armature by shifting the brushes, etc. So you have two ways of regulating the are light dynamo, that is, of making a machine which automatically tends to give approximately con- stant current, to yield absolutely constant current. The shifting of the brushes introduces a second difficulty. You must arrange the machine not to spark, that is, to commu- tate at any position where the brushes may stand during the change of load. That means, the field strength at the position where the brushes stand must always be such, that during the time of the reversal of the current in the short-circuited . the E. M. F. of self-induction which is induced by the reversal, is just counteracted and destroyed by the E. M. F. induced by the field magnetism in the short-circuited coil, so that the field has just reversed the current during the time from the beginning of the short-circuit, by the gap entering the brush until the time where the short-circuit is opened by the gap passing and leaving the brush. This requires a low density in the gap. This is secured by large extending pole-pieces, which besides are necessary again to get the large armature M. M. F. and low resultant M. M. F. for automatic regulation. It is theoretically possible to build ma- chines so that the density of the field will be uniform wherever the brushes may stand, and that consequently in a closed circuit armature you can shift the brushes around , the gap without changing the width of the brushes. . Where this is not the case, but the resultant density at the position of brush varies with the shifting of the brush, sparkless commutation can be gotten by varying the frequency of commutation, that is, the width of the brush, or, in other words, using two brushes in parallel and shift- ing the one against the other. Similar considerations hold in the case of regulation by shunting the dynamo field, etc. Another point of importance in arc light dynamos is the amount of iron. Theoretically the amount of iron in the arma- ture is of no importance except that there must be enough iron to carry the flux. But if you have very much iron in the magnetic circuit of a constant current machine of, say, 10,000 ampere-turns 1894.] I) ISO/USSIOW. 547 on the armature and on the field, then if, suddenly, the arma- ture current is broken, the effective or magnetizing ampere-turns rise from 12,000–10,000 = 2,000, to 12,000, the armature M.M.F. being withdrawn, and these ampere-turns being enormous com- . with the ampere-turns that are necessary to send the nor- mal flux through the armature, the density goes up to saturation and the E. M. F. jumps up, as in Mr. Stanley's are light alter- nator—where it was very prettily taken care of by a spark gap short-circuiting the machine at abnormal rise of voltage. This rise of E. M. F. is partially guarded against by running the armature iron at high saturation, so that even the enormously increased M. M. F. in the moment of opening the circuit cannot raise the density, and thereby the voltage seriously. That is the reason why it has been found desirable to restrict the use of iron in the armature of arc light dynamos as far as possible. - MR. BLACK :—I would like to ask Mr. Steinmetz how he would get anywhere near as constant a current from a machine in which the iron in the armature is worked at 110,000 lines as he could get from a machine whose armature is worked just at the bend of the magnetic curve, for the reason that any counter M. M. F. set up in the armature at that point would decrease the flux in armature exactly in proportion to any increase in the current, so that the current would have to remain almost absolutely constant. Further, I cannot understand how he could get a very great in- crease of flux from the field magnets, without at the same time getting a counter M. M. F. in the armature (in the series machine) and the objection that the voltage would go up to double or treble what the machine was designed for, strikes me would not hold good, as any increase of current in the field, would be ac- companied by a like increase in the armature, and if the machine was a constant current series machine the voltage would drop immediately, and not go up. - Mr. Stººz: With regard to the second point, if the line is suddenly interrupted, in a separately excited machine, as an alternator; this means destruction, if the voltage is not kept within limits by magnetic saturation, or some lightning arrester or spark gap is used. In a series machine this danger is greatly reduced, since the field excitation disappears at open circuit. How- ever, in suddenly opening the circuit, the total flux in the field may remain approximately the same as before, but while, due to the counter M. M. F. of the armature, this flux before passed largely around the armature as stray field, now with the with- drawal of the counter M. M. F. of the armature, the total flux passes through the armature, and the E. M. F. jumps up. . All this depends on the length, shape, etc. etc. of the magneto- Circuit and other conditions, and we will therefore choose that density which is high enough to limit the E. M. F., and at the same time low enough not to use too many ampere-turns at normal running. 548 OWENS AND SKINNER ON AN ARC DYNAMO [May 16, MR. BLACK :—I think, as to the first question, that the voltage of the machine would be taken care of under any circumstances. The machine would simply flash at the commutator, which would immediately reduce the voltage. I cannot conceive of any com- bination of circumstances, by which we could keep the current in the field at its normal strength, and have no current in the armature, except in a separately excited machine. MR. STEINMETz:—But it is not necessary to go higher. You can avoid the flashing by not allowing the E. M. F. to rise very much higher. MR. BLACK :—It seems to me, if you have enough turns in the armature to get a back or a counter M. M. F. of any value, and if those ampere-turns are reduced to zero, and the field is kept the same, that the voltage of the machine will rise enormously. Now, in the Brush 60-light machine (3,000 volts) in which the iron is worked to a very high degree of Saturation, if we separately ex- cite the field at the normal current of 9.6 amperes, and take no current from the armature, the voltage of the machine will be practically doubled. In other words, you will get between 5,000 and 6,000 volts, notwithstanding the fact that the armature iron is worked at a very high point of Saturation under normal con- ditions. MR. STEINMETz:—Yes. But in practice you will never get so high a voltage, because if you break the current, the current in the field disappears also, so you are quite within the limits of safety. The proportional increase of º is less with a small amount of iron than with a large amount of iron. THE PRESIDENT:-If there is no further discussion, I will call for the next paper, on the “Relative Advantages of Toothed and Smooth Core Armatures,” by Mr. Alton D. Adams, of Wor- cester, Massachusetts. - In the absence of the author, Professor Anthony read the fol- lowing paper: A £ager Aresented at the Elezenth General Meeting of the American Institute of Electri- cal Engineers, Philadelphia, May 16th, 1894, President Houston in the Chair. RELATIVE ADVANTAGES OF TOOTHED AND SMOOTH CORE ARMATURES. *mºmºsºm-mº BY ALTON D. A.D.A.M.S. The merits of different methods of construction in dynamo electric machinery, as in other lines, must evidently be decided by their comparative costs, all else being equal. Although questions concerning the relative merits of toothed and smooth core armatures have long been discussed, very little seems to have been written to show whether actual saving in cost may be effected by one construction over the other, when employed to produce the same results. The practice of dynamo builders in this country, and abroad, embodies both types, and the history of the art records many changes from each to the other. In view of the above, the inquiry, whether in the light of present facts any saving can be effected by the use of toothed core armatures, seems of interest. The limits of this paper do not permit consideration of this question in connection with all classes of electrical machinery, and its bearing on direct current constant pressure machines only will be taken up. The principal disadvantages of toothed, compared with smooth core armatures, are greater first cost, large change of lead, and excessive sparking, when used with too short air-gaps, and the production of heat in pole-pieces; their advantages are, that induc- tors are positively driven, large solid inductors, protected from eddy currents, and that a reduction may be made in the length and consequent magnetic resistance of the air-gap. Change of lead may be fixed within any desired limits, and sparking abated 549 550 ADAMS ON TOOTHED VS. SMOOTH ARMATURES.. [May 16, by such proportions of air-gap and teeth, as give them sufficient magnetic resistance. Heat in pole-pieces may be reduced by their lamination, by the use of very narrow teeth and slots, by foºms of teeth that present a nearly continuous surface of iron to the pole-pieces, and still more, by the use of openings in core disks which do not cut through their outside surface, or a continuous magnetic sheath outside the teeth. For any given form of tooth, the heating of pole-pieces is less, the longer the air-gap. - The mechanical strength of armature teeth, as usually em- ployed, is far in excess of that required to hold inductors in position, even under conditions of short-circuit, and driving-pins inserted in the core, at proper intervals, are much cheaper and take up less valuable room on the armature circumference. Either teeth or substantial driving-pins are, of course, prefer- able mechanically to the slender bits of hard fibre which have been much used, and frequently give way under the heavy strains to which large generators are subject. When large wires or copper rods are used as inductors, their protection from eddy currents is an important matter, but proper stranding of inductors reduces the eddy loss in them, when used on smooth cores, to a very small amount, and has the further im- portant advantage that inductors may be bent into the proper shape at armature ends, and the joints, necessary when rods are used avoided. The chief possible advantage, then, to be gained by the use of toothed armatures, is through a reduction in the length of the air-gap, and the consequent reduction in the am- pere-turns required on field magnet, weight of copper, or energy in winding, and the length and weight of iron core. To make this advantage available, it must be practical to use air-gaps shorter than are required for insulation, winding and clearance. As is well understood, the armature winding of a dynamo or motor, in operation, has a magnetizing action which is measured in ampere-turns for a bipolar machine, by one quarter the pro- duct of all the inductors of the armature, into the total armature current. The ampere-turns on the armature evidently tend to set up a flow of magnetism, having a complete circuit through the armature core, twice across each air-gap and through the iron of pole-pieces. About half the ampere-turns furnished by the inductors under pole-pieces, evidently act against the field ampere-turns in 1894.] ADAMS ON TOOTHED VS. SMOOTH ARMATURES. 551 each air-gap at the polar tips, and the ratio between the armature and field ampere-turns at this point, necessary to give sparkless reversal there, must determine whether the required magnetic resistance be greater or less than that of an air-gap long enough for insulation, winding, and clearance with a smooth core armature. As an armature coil in an operating dynamo or motor passes under the brush, the current flowing in it must stop, and one in the opposite direction be set up; and if this action is to be ac- complished without sparking, a sufficient electromotive force must be provided in the coil while in direct contact with the brush. In the ordinary dynamo or motor, magnetism forced across the path of the coil, by the field ampere-turns expended in air-gap, must provide this reversing electromotive force. The data of a number of smooth core armature machines of different make, show ratios of field to armature ampere-turns in air-gap, of from about one and one-half to one, to two and one- half to one, and the writer’s experience is that a ratio of two to one will give sparkless operation at full load, with brushes set just outside pole corners. It is a matter of common experience that the ratio between field and armature ampere-turns in the air-gap may be so reduced, even in machines with smooth core armatures, as to require excessive change of lead to secure even approximate freedom from sparking. If it be desired therefore to build machines having an expenditure of field ampere-turns in the air-gap not much greater than those of the armature, we need not resort to toothed cores. Take, for example, the case of a 260-ampere dynamo, with 120 inductors on its armature in one layer; an air-gap induction of 25,000 lines per square inch, and 80 per cent. of inductors under the pole-pieces. An air-gap of .45 inch between the armature core and each pole- piece will be sufficient for insulation, winding and clearance, and the field armature turns expended in each air-gap will therefore be 3523, while the armature ampere-turns, active under each pole tip, will be 3,120. A considerable change of lead and sparking can be readily predicted for this machine. In some types of small machines, the room required by insula- tion, winding and clearance, makes the air-gap longer than neces- sary for sparkless operation, and in such machines the utility of 552 ADAMS ON TOOTHED VS. SMOOTH ARMATURES.. [May 16, teeth seems to depend on their cost, compared with the saving to be effected by their use. As the ampere-turns, furnished by the inductors under any pole-piece grow less, in a machine of given capacity, when the . number of poles is increased, very short air-gaps may be used, if the number of poles is sufficiently large. As, however, an increase in the number of poles usually makes a machine of given capacity more expensive, the question at once comes up, to what extent the number of poles may be increased without a greater expenditure than the saving to be effected. In large multipolar machines of four to six poles, such as are commonly used, the length of air-gap required for sparkless operation, is considerable, and those who have watched the de- velopment of these machines with toothed core armatures during the last four or five years, have seen the air-gaps gradually widen until machines of this character are not hard to find, in which the copper inductors between the teeth could be taken out, wound outside the teeth, and still leave room enough for good clearance. Additional mechanical security, of course, furnishes. a considerable argument for the use of teeth in very large slow speed machines. A number of devices have been suggested from time to time, to enable toothed core armatures to be used with short air-gaps, and the consequent saving in iron and copper effected. No ma- chines with these devices, however, have yet stood the test of time and competition with those of ordinary type, and they have yet to prove their ability to produce results, as at present attained at a less cost. The seeming opportunity to save material by the use of toothed armatures is very attractive, and we cannot but hope it may some day be practical; in the light of present knowledge, however, there seems little to be gained by their use in medium. and large bipolar machines. Worcester, Mass, May 9, 1894. 1894.] DISCUSSION. * 553 DISCUSSION. MR. A. E. WIENER:-After enumerating the advantages and disadvantages of toothed armatures, the author comes to the con- clusion that the chief advantage of toothed armatures over smooth onesis the reduction of the length of the air-gap, and the consequent decrease of the exciting power required. But he left out one very important disadvantage, namely the leakage through the armature core, caused by a portion of the lines entering the teeth, and passing through the armature without cutting the conductors. From a large number of machines I have found that, if otherwise well designed, the disadvantage of this core-leakage just about cancels the advantage of the air-gap reduction; for in order to allow for the waste armature-field due to this core-leakage, the exciting power has to be increased in about the same degree, as the lessening of the magnetic resist- ance of the gap would otherwise decrease it. The chief advan- tage claimed by the author, consequently, is thus only an imaginary one, and, indeed, there are no such striking advantages in either of the two kinds of armatures as to make any one of them super- ior in all cases over the other. On the contrary, it is really a matter of choice, with reference to the special application of the machine to be designed, whether to employ a smooth or a toothed armature. In the case of a slow speed motor, for instance, as used in single-reduction, and in gearless street car motors, where great torque is wanted, a toothed armature core will offer better advantages, and its somewhat higher cost of manufacture has to TABLE I. RATIO FACTOR OF ARMATURE LEAKAGE OF TOOTHED ARMATURES PERFORA red W! DTH OF SLOTS To THEIR PITCH | STRAIGHT TEETH | PROJECTING TEETH ARMATURES ON OUTER & Cl RCU M FERENCE AN %X| /º) \! ɺ |/º-º º - * /. Yºº º tº ſº O.4. 1,4-O to 1.35 1.55 to 1.5C) .45 1.35 “ 1,3C) | 1,50 1.45 .5 1.3O “ 1.25 | 1.45 “ 1.40 1,50 to 1.45 .55 1.25 “ 1.2O | 1.4O “ 1.35 | 1.45 “ i.4O .6 1,2O “ 1.15 | 1.35 “ 1,3C) | 1.4.O “ 1.35 .65 1.35 1.3O .7 1.3O “ 1.25 CoRE LEAKAGE IN Tooth ED AND PERFORATED ARMATURES. be overlooked. When, on the other hand, the machine is to be used as a generator for very low potential (electroplating dyna- mos, etc.), a smooth armature core is preferable. From quite a number of machines I have averaged the follow- 554 ADAMS ON TOOTHED VS. SMOOTH ARMATURES. [May 16. 4200 ing table of armature leakage in toothed, and perforated arma- tures, to appear in a series of articles entitled “Practical Notes on Dynamo Calculation,” and commenced in this week’s issue of the Electrical World." The amount of the core leakage depends upon the ratio of the width of the slots to the width of the teeth, and, if the armature is otherwise properly designed, will vary within the following limits as shown in Table I.: On account of this core leakage, the field-densities obtained in toothed and perforated armatures are considerably smaller than in smooth, core machines, as can be noted from the following table which gives the practical field densities of various dyna- mos, derived from the data and tests of about two hundred of the best modern dynamos: From Tables I and II follows the practical truth of my above TABLE II. * - Field Densities, in Lines of Force per square Centimeter # Bipolar Dynamos Multipolar Dynamos g - § Smooth Toothed Armature Core Smooth 'Toothed Armature Core # ; - * ;3 ºre Straight Teeth Projecting Teeth Arººr© Straight Teeth Projecting Teeth #3 . 3 : g º ton Yºn .8 §§Dº; Tººl ºf ºil, ºil...º.º.º. * * *Polspieceſſ Polepieces Pºſepieces i Polepiecesſ Polepieces [Polepieces Polepies Poiepiecesſ Polepieces Polepieces! Poiepieces Polepieces J1 || 1550 2300 | 1250 1850 | — | – || 2150 || 3100 | 1850 2800 | - — .1 ..e5||1850 |2800 fö50 2300 — — |2500 3700 2150 8250 | – ||-- .23. .5 || 21509. 3100 1850 2800 — — |2800 |4200 2500 |3700 | – || – .5 2300 | 8400 | 2000 | 2950 | 1250 | 1850 2950 4350 2650 | 3850 | 1550 2800 1 5 || 2500 || 3700 2150 3100 1400 2150 || 3100 4500 || 2800 | 4000 || 1700 || 2500 2.5 2650 |3850 2300 3400 | 1550 |2300 |2250 |4700 2950 |4350 | 1850 | 2800 4000 || 2500 || 3700 | 1700 2500 |3400 |5000 || 3100 |4700" 2000 || 3100 7.5 2950 4350 | 2650 || 3850 | 1850 2800 3700 || 5400 || 3250 || 5000 2150 || 3300 10 3100 || 4700 2800 || 4200 | 2000 ſ 3100 | 4000 || 5900 3400 5400 2300 || 3500 25 8400 5100 || 3100 || 4700 2150 3400 || 4350 | 6400 || 3550 5900 2500 || 3700 50 3700 || 5600 || 3400 || 5100 2500 3700 || 4700 | 6800 3850 |6200 2650 3850 || 100 6200 || 3700 || 5600 2800 4200 || 5000 | 7300 4200 || 6500 || 2800 4000 || 200 4700 7000 || 4200 || 6200 3100 4700 || 5400 7750 4500 | 6800 2950 4350 || 300 — — | – || – || 5900 8200 || 4800 | 7200 || 3100 4700 || 500 — — — — | – | — | 6400 | 8700 || 5100 || 7500 || 3400 5000 || 1000 — | – | – | – || 7000 || 9300 | 5400 | 7800 | 8700 || 5400 || 2000 ! 5 28 00 5 smºsºms º ºsmºsº, * f == statement, viz., that about the same exciting power, or same number of ampere-turns will be required in both types of arma- tures; for, also, the reduction of the gap resistance, if the radial depth of the armature core is properly dimensioned, depends upon the ratio of the width of the slots to the width of the teeth. MR. STEINMETz:—I was somewhat astonished when hearing this paper, in-so-far as the conclusions drawn therein. They are to a large part just opposite to what I concluded by theoretical reasoning, and found proved by practical experience. What I intend to say, however, refers only to larger machines, machines of some hundreds of kilowatts. With regard to the 1. See Electrical World, xxiii, p. 675. (May 19, 1894.) 1894.] DISGUSSION. - 555 superiority of the toothed armature in these machines, I may first point to the fact that neither in this country nor in any other country is any large power generator running which will commu- tate sparkless, from no load to full load and overload, without shifting of the brushes, as it is required for instance in railway ſº where, due to the constant and sudden fluctuations of oad, a shifting of the brushes is impracticable. On the other hand, hundreds of thousands of horse power of machines with toothed armatures, which will fulfil this condition of sparkless commutation without shifting of the brushes, are in daily use in this country alone. The reason for this superiority is, that the distortion of the field in a properly designed machine with toothed core is very much less than in the machine with smooth COI’e. You can indeed by shifting the brushes get sparkless commuta- tion in smooth core machines also, and you have in smooth core machines the decided advantage of lower self-induction. But if you have to commutate without shifting the brushes, smooth core machines are out of competition. The advantage of the toothed armature is not so much the lesser ampere-turns consumed in the gap. In larger machines you cannot do anything like what is proposed here, to use .45 of an inch as total clearance from iron to iron. This would give a clearance of about fºr of an inch from the binding wires of the armature to the iron of the field poles, which may be all right for a small machine, but not for a large power generator. In such a machine, with toothed core, the clearance between arma- ture and field is determined by mechanical reasons only, and is from # inch to # inch from the head of the armature teeth to the field poles. The foremost feature of the modern toothed core power gene- rator is the lesser distortion of the field, as the following diagram will show. “º Let, in Fig. 1, be represented the M. M. F. diagram of a smooth core machine. The field pole P and the armature C with the armature conductors are shown in development in drawn lines. The M. M. F. exerted upon the air-gap by the field spools is represented by the dotted line F. The M. M. F. exerted upon the air-gap by the current in the armature conductors (armature reaction), is represented by the dotted line A, which is posi- tive at the trailing, negative at the leading pole-horn, in a gene- rator. Thus the total or resultant M. M. F. acting upon the air-gap is represented by the dotted line T, and proportional thereto, in a smooth core machine, is the magnetic density in the air-gap. As seen, the magnetic gap density is very much less at the leading pole-horn, where it is needed for sparkless Commutation, than at the trailing horn, where it is not needed. At the same time the field has shifted considerably. Now consider the toothed core machine, in Fig. 2. If the 556 ADAMS ON TOOTHED VS. SMoot H ARMATURES. [May 16, total effective gap, that is the space between pole-face and foot of slots, the same M. M. F., F, is exerted by the field spools—that is, the tooth density is appropriately high—the total or resultant . M. M. F., T, is again the same as with the smooth core in Fig. 1. But here the magnetic density B is not proportional to the M. M. F. T, but B varies very much less than F, due to the effect of mag- netic Saturation, and thus the gap density is very much more uni- form, as shown by dotted line B in Fig. 2, and the field has shifted very little. Thus the machine in Fig. 2 will commutate sparkless from no load to full load, without shifting the brushes, while machine, Fig. 1, will spark furiously if the brushes are not shifted with varying load. - On the other hand, due to the small self-induction of the arma- ture conductors, the smooth core machine is very desirable for lighting machines where very large currents have to be commu- tated at low voltage between the commutator bars, and the load does not fluctuate suddenly by hundreds or thousands of amperes. But for railway generators, where you have to use larger voltage between commutator bars, and where you have to leave l P T2. ‘P F 2’ B_ tº ----------- f B2. 24 1 L^ 2^ \ . *. L.' Af Y. I –s *– *: } t C II - II---- Ullmull, ,” C 2’A * - ,’ FIG. 1. FIG. 2. the brushes in the same position under all loads, there you must use the toothed armature. You cannot make a railway generator work decently with a smooth core. º, MR. GANO S. DUNN :—It is true that there must be a definite magnetic resistance in the gap to enable the machine to operate sparklessly, but if you will consider the smooth and the toothed armatures, you will find that with the former the reluctance of the air-gap is constant, and with the latter it increases as a result of armature reaction, with load. This is due to the variable re- luctance of the iron which constitutes the teeth, and which at saturation approaches air, giving a low resistance and a high re- sistance air-gap for light and full loads respectively. To put it a little clearer, the effect is similar to the case of a smooth arma- ture run with an air-gap which as the load increases, lengthens, and thereby preserves sparkless commutation. For the above reasons a toothed armature air-gap can have a lower average reluctance than that of a smooth armature. The reluctance of the latter is constant and always at its maximum value. In small machines however, the above considerations do not 1894.] -- I) ISO/USSION. 557 apply, because sparklessness need not be dependent upon a fringe at the pole tip to reverse the current in the coil. Machines may be lighter and neater which depend on other means for sparkless commutation. If for instance we cause the resistance of the carbon brushes to make the current reversal, then we can greatly diminish the reluctance of our air-gap and use a proportionately smaller field current and weight of copper, and secure important advantages in efficiency and lightness. . point which at present is not of so much importance, is that with dynamotors or direct current transformers, there is practically no armature reaction or tendency to spark, and con- sequently no necessity for reluctance in the air-gap. The toothed armature allows us to take advantage of these conditions in a manner impossible with an armature which of necessity de- mands a high reluctance air-gap. With regard to mechanical advantages, the toothed armature with wires embedded and held firmly in slots, is so superior to the smooth armature wound with wire held on by various devices, that even were the toothed armature more expensive, which I am not ready to admit, it would be preferable. - MR. W.M. STANLEY :—I would like to ask the last speaker if he does not consider that the extra self-induction due to the armature teeth, especially in the larger machines, is the cause of the sparking that we see on the street railway generators, and that if it were possible to arrange the wires on the circumference of the machine—I do not say that it is mechanical to do so— but if it were possible to do it, if the machine would not be more sparkless? Does not the self-induction of the buried wire in the iron core increase the sparking from one commutator bar to another? MR. DUNN:—There is no question that burying the wire in- creases the self-induction, and if the openings at the top of the slot are too narrow, or if as in the case of the Wenstrom arma- ture, there is no opening, this is a very serious defect, but the openings can be so proportioned that the increase of self-induc- tion while a disadvantage, is not serious. MR. STANLEY:—Is it not the principal disadvantage : |MR. DUNN:—Yes, I should consider that it was. The paper alleges that the toothed armature requires more material; that this is true, generally speaking, I do not agree. I think the self-induction is the greatest disadvantage. MR. STEINMETz:—I do not think that the representation of the toothed core by a gap, which widens with the increase of a load quite meets the point. What I wanted to show by the diagram is, that the distribution of the magnetic density at the gap at full load is not proportional to the distribution of the resultant M. M. F., but is very much more uniform, due to the effect of saturation, and therefore the field does not shift seriously, and the brushes can be left in the same position at all loads, in the fringe of the 558 ADAMS ON TOOTHED VS, SMOOTII ARMATURES.. [May 16, reversed field, which is required to overcome the self-induction of the current in the coil which is being commutated. For if you have to reverse hundreds of amperes, backed up by a large E. M. F. of self-induction, you have to have forced commutation. It is to get rid of the shifting of the field, due to the armature reaction, which really constitutes the advantage of the toothed armature, which enables us to get a very much higher efficiency with the toothed armature than with the smooth core. MR. C. N. BLACK :—There is another point I would like to make and that is, it seems to me practically impossible to build dynamos of large units, such as we are building now for railway work, and use a smooth armature, on account of the great losses we would get from eddy currents set up in the conductors them- selves. The size of the conductors is such, that if they are made Solid, that loss could not be neglected and would be a source of a good deal of heat, at the same time decreasing the efficiency of the machine quite materially. If we laminate the conductors it makes a very difficult construction, in fact, almost impracticable. There is one other point that I do not think has been mentioned, and that is in series motors, where we use a toothed armature, we get a much more constant speed. At light loads, the teeth being worked at a low point of magnetization, offer but little reluctance to the flux through the armature, while at heavy loads the teeth become Saturated, and in consequence add a consider- able reluctance to the magnetic circuit, thereby cutting down the induction from what it would be if increased in proportion to the increased number of ampere-turns on the field, consequently we get a motor that is much nearer self-regulating than one with the smooth core armature. - MR. A. E. KENNELLY:-The point has not been brought out, I think, that if you have a toothed armature, you can much more readily ventilate the armature from within, whereby you can carry off the heat from the surface far more efficiently than if the armature is entirely covered by wire. MR. OBERLIN SMITH :—I would like to hear an expression of opinion as to the relative cost of a toothless ring and that toothed I’ll] Q'. . i. STEINMETZ :—I think the question of ventilation is not such a drawback against the smooth core machine, because the modern design of lighting machines, which are smooth cores for the commutation of very large currents, are ventilated also by ventilating spaces between the armature conduction, and even the twisting of the conductors is not by far so difficult, but is done in smooth core armatures. I have some machines being built which will have this stranded conductor, and which will exclude eddy currents almost perfectly—smooth core machines for low voltage, of 400 kilowatts. With regard to the relative cost of both types. of machines, it is difficult to state it, because they are different types of machines for different purposes, and thus cannot be compared properly. - 1894.] DISCUSSION. 559 Smooth armatures are built for lighting where the toothed armature does not offer any advantages, where you have very low speed, large conductors and low voltage from bar to bar, while the ironclad is perfect as a high voltage power generator. Thus you have never built two machines, one smooth core and one ironclad, for the same purpose and of the same dimensions. In general I am of the opinion that the toothed armature is the cheaper one. [The meeting then adjourned for the day.] In the evening the Annual Dinner took place at the Hotel Metropole, at which 76 members and guests were present. A £after fºresented at the EZezenth General Meeting of the American Institute of Electrical Engin- eers, Philadelphia, May 17th, 1894. President Aoteston in the Chair, STANDARDIZING ELECTRICAL MEASURING INSTRUMENTS. (a) By THE PotRNTIOMETER METHOD. (b) AN IMPROVED DIRECT READING PotRNTIOMETER. EY ELMER. G. WILLYOUNG. During the early days of applied electricity, yet easily within the memory of even the youngest among us, so rapid has been its development, electrical devices in general were, as a matter of course, but very poor affairs as compared with those of the present. One machine was a dynamo if it would but produce current no matter how fluctuating, nor at what cost of internal energy consumption; another a motor if one of its parts would but rotate when supplied with electrical energy regardless of the rate of this rotation or whether constant or not under condi- tions of variable load. Having such uncertain quantities to deal with, electrical measuring instruments were, similarly, but few in number and of the crudest possible construction—not measuring instruments at all in any true sense of the word, but merely in- dicators, and very poor ones at that. An instrument was sup- posed to be a non-essential, a decoration for fancy dynamo rooms, and perfectly equivalented by an incandescent lamp for all prac- tical purposes. Indeed, this idea has not yet entirely disappeared, and we may still occasionally find plants running with nothing more than the pilot lamp to go by. In general, however, all this is now changed. Business com- petition and the popular demand for electricity has caused rapid and steady improvement all along the line until now we have much time and study devoted to the problem of how to raise machine efficiencies a fraction of one per cent. or so, how to 560 1894 | WILL YOUNG ON MEASURING INSTRUMENTS. 561, build armatures so as to secure more perfect ventilation and con- sequent reduction of internal heating, how to produce as good results with a little less iron, a little less wire, a little less wear, etc. Losses in joints, switches, etc., hitherto so small as to have been neglected must be guarded against and, if present, reduced to the smallest possible amount. The whole problem of manufac- ture and installation has become one of the gaining of petty victories. . All this has reacted upon the instrument maker. In order to measure these small effects, very perfect and accurate instru- ments are necessary, and great improvements have been made in this direction. The commercial measuring instrument of to-day is, indeed, an entirely new appearance, and demands exactly the same application of mechanical principles and scien- tific methods as is demanded in the construction of bridges and steam engines. The necessity of a complete outfit of proper measuring instru- ments, voltmeters, ammeters, ground detectors, etc., as a factor of economical operation in all kinds of lighting and power systems, is now almost universally conceded, and we find such in- struments all over the country in vast numbers. In the stations we have the station instruments; for general all round testing work, measuring drops, joint and switch resistances etc., the portable instrument is useful. As as at present made, all of these various instruments have in them dangerous elements of change. If the instrument has a permanent magnet, then the strength of its magnet is liable to be seriously affected in time by the perpetual jars and vibrations to which it is subjected; proximity to strong fields, especially if variable, will tend to produce similar results. Any instrument containing springs is also likely to vary in its indications in time through slow changes of elasticity in the springs be they ever so carefully gauged. A hot wire instrument may change on account of the change in radiating quality of the surface of the working wire produced by its slow oxidation; molecular changes in the wire are also liable to go on when continually heated, since our experience with standard resistances shows us that changes of this kind do go on very slowly even with wires kept at normal temperatures. And so of any type of commercial instrument which may be mentioned—none of them can be absolutely trusted not to change. 562 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, This being so, we must, therefore, frequently examine these vari- ous instruments and determine if such changes have taken place, and, if so, what has been their magnitude. As a rule this is done at present not by the owner of the instrument, but by the instru- ment maker, the instrument being taken down and sent back to the maker from time to time for recalibration, or, if it is not, it should be. This, in itself, is expensive—express charges must be paid—time must be spent in correspondence—often, if not always, a charge is made for the work of restandardizing. Not only this, but there is no surety whatever that these restandardized instruments may not again “get out ’’ while on their way back to the owner, as the sharp, “high frequency '' jars of transit are known to be very hard upon magnets and fine mechanism. Consideration of the above, long ago convinced me that this restandardizing should be done by the stations themselves in all cases except when quite small, and that some arrangement of apparatus should be devised which would make the utilization of some absolute standard method inexpensive and convenient, and possible to any one of ordinary intelligence. After a good deal of thought and personal experience, I became convinced that the only method which could be made to at all satisfy these require- ments was the potentiometer method. Before speaking specific- ally of the improved apparatus which I have devised for the commercial utilization of this method I wish to discuss briefly the potentiometer method in general and to outline what I consider its advantages over all other methods. THE POTENTIOMETER METHOD. Broadly, the potentiometer method consists in opposing some known proportion of the drop of an unknown E. M. F. through a given resistance to a definitely known E. M. F., the proportion being so chosen that no current is produced by the latter known source. This condition being established, an equation involving the unknown E. M. F. as the only unknown quantity immediately obtains. The method in general is fairly well known, being variously called the standard cell method, the Poggendorf or Rayleigh-Poggendorf compen- sation method, the Rayleigh method, etc. It is not by any means so widely known, however, as it deserves to be. Diagrammatically the method is represented in Fig. 1. Here A B is a wire of high resistance and any desired length stretched between two fixed points. Ba is the battery whose unknown E. M. F. we desire to know, supposed higher than that of s. c. which 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 563 is a known standard cell. In series with S. C. is a galvanometer, Ga. Ba and s. c. are so placed as to oppose one another so that when the circuits are closed a position, s, of the slider upon the wire may be found such that the fall of E. M. F. of Ba between s and B al s] Bö. | | | | | | | | | | | | | | | | | | | ST S.C. Geo. FIG. 1. will exactly equal the E. M. F. of s. c. There will then be no deflection of Ga, and we will have # = #9 ºn = *se ºff () an equation involving only a known E. M. F., and the ratio of two lengths. The resistance A B should, of course, be chosen so large that the internal instance of Ba is negligible as compared with it. In practice this form of the method is commonly known as the Rayleigh or Rayleigh-Poggendorf compensation method; and instead of a straight wire, A B, this is equivalented by two resistance boxes of about 5,000 ohms each. This arrangement is shown in Fig. 2. Plugs are removed in R and R' so as to have in all a total of, say, 5,000 ohms out. This total is maintained | —Tº- —HH- K Ba. FIG. 2. constant, whatever plugs are taken out of one box, being inserted in another. When a balance is secured, the resistance in the two boxes must be counted up and then equation (1) applied." ... 1, The galvanometer, in both Figs. 2 and 4, has inadvertently been omitted; it should, in both instances, be placed in the “derived” circuit similarly to fig. 1. 564 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, This arrangemenent of the method is very suitable for making comparisons of standard cells, Babeing merely any form of con- stant battery. A balance having been secured for s. c. it is then removed and another standard cell, St. C., substituted ; a new bal- ance is then gotten. By properly choosing Ba and making the total of R + Rſ 10,000 ohms, we may cause each ohm difference in balance between different cells, to signify a difference of 0.01 per cent. If a properly sensitive galvanometer be used a variation of one ohm from balance is very easily seen. This arrangement is also very accurate, and easily used in determining the temperature coefficient of a cell, the cell being surrounded by a water bath, and balance being obtained for different temper- atures. A modification of this method was proposed some years ago by Dr. Fleming, and is shown in Fig. 3." It is, as is evident, ex- actly the same as Fig. 1, save that a resistance, R, is inserted in —[TRTH 1H - E H.L.L.F.L. S Hº– SC. Gºa FIG. 3. the main circuit. Here Ba, instead of being the E. M. F. to be meas- ured, is merely any fairly constant source, such as e. g., a cell of storage battery. The wire, A B, is stretched along a scale uni- formly divided into, say, 150 parts, 100 of which are then made to correspond to a fall of Ba of one volt by adjusting s to a po- ' sition corresponding to balance, if this assumption were true, and then making it true by an adjustment of the variable resistance, R. If A B is so great that the current produced by Ba is small compared with its normal discharge rate, then the difference of 1.5 volts between A and B may be assumed constant for a con- siderable period, especially as the circuits should be closed only long enough for balance. Any inconstancy may be immediately detected by again placing s at the balance point. Balance should 1. See “Short Lectures to Electrical Artisans,” by J. A. ºn; also: “Electrical Measuring Instruments,” by Jas. Swinburne–Proceedings. Institu-- tion of Civil Engineers, Vol. C.X., Session 1891–92, Part IV. 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 565 persist without further adjustment of R. To measure any unknown E. M. F., now, s. c. is simply removed, and the unknown source sub- stituted for it. If this source is less than 1.5 volts then a position of s will be found, at which there will be balance, and the number of parts between s and B will give the E. M. F. directly by pointing off two places of decimals. Should the E. M. F. be higher than 1.5 volts, then it may be placed in series with a high resistance, and the E. M. F. over a portion only of this resistance measured. The two place reading of S multiplied by whole of high resistance portion of high resistance in derived circuit will again be the unknown E. M. F desired. Not only may we thus measure E. M. F. but, by arranging as in Fig. 4, we may also measure current by this method if we know the resistance of shunt S. Similarly, we may measure resistances by comparing the fall of E. M. F. around a known resistance with that Ea |--|--|--|--|--|--|--|--|-- vºy S | shunt | FIG. 4. around the unknown resistance placed in series with it, a con- stant current being maintained through both. The advantages of the potentiometer are: (1.) It is a zero method; a calibrated galvanometer is, there- fore, not necessary. (2.) Accuracy depends only upon a standard cell and a standard resistance, and results obtained by the best authorities over a num- ber of years, show that both of these may be relied upon within extremely small limits of error, with proper treatment, for a prac- tically indefinite time. (3.) It requires but simple apparatus, always obtainable, and ordinary care. It can be used without inconvenience in regions of great mechanical instability and of intense and variable mag- netic fields. 566 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, OTHER METHODS OF STANDARDIZING. The advantages of the potentiometer method can, perhaps, be better appre- ciated by briefly recapitulating the other possible methods. These are but few in number, We have: THE DIRECT INSTRUMENTAL METHOD. Here the values must be obtained by direct measurement with instruments which do not contain elements of change. About the only instruments satis- fying this condition are the tangent galvanometer in some form or other, and the Thomson balance. THE TANGENT GALVANOMETER, Disadvantages:—(a) The instrument must be very accurately constructed and is hence costly. (b) To secure accuracy, the instrument must have a suspended system which is liable to continual break down, and is difficult of repair except by an expert. (c) Accuracy depends upon the constancy of H, the horizontal magnetic com- ponent; this depends upon local conditions and varies with change in position of neighboring magnetic materials and with the temperature of fixed masses of such metals. (d) Indications are greatly affected by variable currents or magnetic fields in the vicinity. - (e) Mechanical stability must be had; hence such an instrument is difficult to use in stations or localities where mechanical vibration is large. (f) The instrument must be very carefully adjusted in the first instance—this requires considerable time and skill. It must, therefore, be permanently set up in combination with the observing telescope or lamp and scale, in a room or part of a room which must not be used for any other purpose in order that the outfit may not be disturbed. THE THOMSON BALANCE, This instrument is much superior to the tangent galvanometer, requiring much less skill in use and practically no adjustment. It is not affected by being moved about from place to place if carefully handled, and is not appreciably varied by magnetic changes of small amount. Disadvantages:—(a) It is affected by fluctuating currents or fields of large value if very near. (b) A large number of instruments is required to cover very much of a range of measurement, any one instrument only measuring within limits of 1 to 100 as e. g., from 1 to 100 centi-amperes, 1 to 100 amperes, etc. THE WOLTAMETER METHOD, This depends upon the maintenance of a steady current for at least 20 minutes or a half hour through an electrolytic solution, usually silver or copper, and an accurate weighing of the amount of decomposition thus produced. Disadvantages:—(a) It is slow, but one value being obtainable in this time. (b) It requires considerable skill in making accurate weighings with a delicate balance; also in adjusting the current values used to the area of the electrodes, since otherwise the amount of decomposition is irregular and unreliable. THE VIENNA SHUNT METHOD, This is an indirect method in which the current is obtained by measuring the E. M. F. produced at the terminals of a suitable shunt by its steady flow. The shunt resistance must, of course, be known. 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 567 Disadvantages:--(a) The E. M. F.'s to be thus measured are usually quite small and must be measured by a very sensitive galvanometer. This galvanometer must itself be calibrated, a work requiring considerable time and skill. This calibration, once obtained, cannot be depended upon from day to day owing to the fact that the slightest change in level in the instrument, irregular loss of magnetism in the needle, if a Thomson galvanometer, or of torsional rigidity in the suspension, if a D’Arsonval galvanometer, will alter it. In a Thomson galvanometer the indications are greatly thrown out by even very small changes in the local magnetic field such as may be produced by keys or a knife upon the person, or active circuits even when some considerable distance away. (b) Great mechanical stability is usually required in order that observations of the reflected beam of light may be possible, (c) Thermal E. M. F.'s are met with which are tedious to eliminate or allow for. (b) AN IMPROVED DIRECT READING PotentIOMETER This instrument, invented by the writer and illustrated in Fig. 5, is capable of being used for measurements of voltage from 0 up to 1,500 volts, and of current from 0 up to any required upper limit, with a maximum error of not over 4'ſ per cent. It is based Eºº Cº-ºº: ſi | i. upon the form of potentiometer originally suggested by Dr. Fleming, which is shown in diagram in Fig. 3. Some good sug- gestions were also obtained from the improved form of Mr. Crompton." 1. See Electrician, (Lon.) May 12, 1893, p. 32. 568 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, A diagram of the arrangement of circuits in my improved form of apparatus is shown in Fig. 6. The wire A B of Fig. 3 is here equivalented by three sets of coils marked respectively Q, M, and s. The regulating resistance (R of Fig. 3) is made up of two parts, one resistance, Ro, consisting of coils, and the other, Rs, being made up of a bare wire of resistance equal to one of the coils of Ro. This wire is laid back and forth upon about 350° of an ebonite cylinder and has a fixed brush, P, so arranged with reference to it that P short-cir- cuits more or less all of the v’s simultaneously, thus giving a large range of variation for a very small angle of rotation. The quick and rough regulation is effected by Ro, while the finer ad- justment is obtained by Rs." The two series of coils, M and s, have at their centers two switches which are in series with the galvanom- eter and unknown E. M. F.; moving these switches over the coils is exactly the same as shifting the points s and B of the derived circuit in Fig. 3. M is the medium movement, each coil being 14, of the entire resistance between A and B, while s is the very slow movement, each of the nine coils in s being equal to fºr of the resistance of one of the coils of M. In order to get a rate of separa- tion of the two derived circuit terminals by steps of 10 times the value of a coil,of M, a third series of resistances, Q, is provided. This is a rather peculiarly arranged affair, its function being to take out resistance from between the derived circuit ter- minals and place it outside, or vice versa, the total resistance between A and B remaining always constant. The construction of this arrangement is shown in Fig. 8; here merely the diagram of circuits can be depicted. It is evident that this change of re- sistance from one part of the circuit to the other accomplishes exactly the same result as is obtained by M and s, viz., the separa- tion or bringing together of the two derived circuit terminals. We have, therefore, the entire resistance, A B, divided into 1,500 parts, and the derived circuit terminals separable along this resist- ance by steps of 100 parts, using Q; ten parts, using M; and single parts, using s. This means an ability to set to 1 part in 1,500 or to Hº; per cent. - In order to make the measurement of any unknown potential convenient and quick, a suitable arrangement of switches is pro- vided. In the lower part of the diagram, R is a high resistance 1. Instead of this form of regulator I have thought of substituting some form of carbon or graphite resistance since all that is needed is invariability for a certain period. E. G. W. - 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 569 connected between two points F and G. To F is permanently joined one derived circuit terminal. The other derived terminal passes, by way of a key, R', through a galvanometer and thence to a switch, w, which plays over a number of contact points con- nected as shown. The two points, s. c.—1 and s. c.–2, are joined each to a terminal of a Carhart one volt cell, the other terminals of which are joined in common to g. The remaining points are connected to points along F g, dividing the whole resistance in the ratio Tºrº, ++o, +, and 4. In this way, with w on one or the other of the standard cell contacts, we may by proper setting of Q, M and s, and adjustment of the regulators Rs and Ro get the E. M. F. be- tween A and B accurately 1.5 volts; we may, also, compare the two cells with one another, and thus detect any possible variations in either, as the probability that both would change alike, in the event of any change taking place, is extremely small. By now setting w on R, any unknown E. M. F. joined to F and G and less than 1.5 volts immediately becomes measurable. Should the E. M. F. be greater than 1.5 volts and less than 15 volts, w is set on R × 10 instead of on R; greater than 15 and less than 150 volts on R × 100; greater than 150 and less than 1,500 volts on R × 1,000. When measuring, current leads are brought to F and G from the shunt terminals and the E. M. F. measured like any other unknown E. M. F. In order to avoid the risk of accidentally getting too large a current through either of the standard cells, a high resistance, H R, of about 10,000 ohms is permanently placed in the galvanometer circuit. A shunt is also placed around the galvanom- eter which may be thrown in or not, as desired, by means of the little switch placed for the purpose. Some of the details of construction employed in this instrument are, it is believed, sufficiently interesting to be worthy of descrip- tion. Fig. 7 shows a novel way of economizing space and material in the construction of the coils and contact points sug- gested by Mr. H. L. Sayen. The contacts instead of being brass rod or portions of rod, as usual, are tubes having a metal end. Into these tubes the coil, wound on a slim spool as usual is slipped, one end of the wire being soldered to the open end of the tube. Holes just large enough to receive these tubes are then drilled into the rubber top of the instrument and the tubes slipped up from below with closed ends uppermost until stopped by a flange which has previously been soldered around the tube at about # inch 1. “A One-Volt Standard Cell,” by Henry S. Carhart. Am. Jour. of Sci- ence, vol. xlvi., July, 1893. - , 570 WILL YOUNG ON MEASURING INSTRUMENTS, [May 17, from its end. A rubber plate, P, about $ inch thick and also drilled through with holes corresponding to the tubes, is slipped over them from below, and screwed fast to the under portion of the top plate. All the tubes are thus firmly clamped in place by means of their flanges. The other ends of each coil are then sol- dered to the next tube, etc. - * - Fig. 8 shows the construction of the resistance exchanging ar- rangement, Q.' There are two concentric circles of segments as pictured, these segments being provided with spring pieces. The coils are joined between diagonal segments. Pivoted at their center is a switch formed of a circular plate of hard rubber, car- rying at its periphery a number of angled brass wedges or knives al F—: -T- K Ba ALL UNKNov/N E.M.F.”s. TO BE CONNECTED HERE, FIG. 6. corresponding to the segments of the coils. Instead of one of these wedges is a pair of contact pieces corresponding to a and b, . of Fig. 6, and joined to the rest of the circuit as shown in that figure; each piece of this pair makes contact with but one seg- ment. It is obvious, therefore, that as the switch rotates, the series is always broken between a and b, while the continuity of all the rest of the series is maintained by the wedges which pass between the segments and keep them metallically joined. In order to get at the standard cells in case either or both of them should show any signs of giving out, all that is necessary is to remove the four screws in the raised block seen in the upper left-hand corner of Fig. 5. This will expose the binding posts to which the cell terminals are joined, the cells themselves being 1894.] WILL young ow MEASURING INSTRUMENTS. 571 contained in two brass tubes passing down through the top. The binding screws are loosened and the cell or cells drawn out, when they can be shipped back to the maker for exchange. E-sº [- & º This form of potentiometer is practically direct reading, the required values of E. M. F., being numerically set down upon the face of the instrument when balance is attained. The manner in which this is effected is very readily seen from inspection of Fig. 9, which shows a composite view of one of the switch devices M or s. Fixed to the switch handle so as to rotate with it and above the contact and contactor itself is a disk, A of Fig. 7, of hard rubber; this has engraved upon its upper surface a series of numbers cor- fºx-s º;:S § wºjº 1 * * 2- ,- º t º ..ſº NY #3 º *S: * * “gis, 2-&lºš $/s &N. º {} { N - %3 tº S-3 & º NY." º C &. d ...Esº Y. 23\\ Sº * ~ * Trºy; C a—tº #ººk oOc :# t I) T ~.e. Yº N} Wº -- $º : “W Š7-33 **ś _X^* Y * t FIG. 8, responding to the coils of the series, and differing in value by an amount equal to the value of the resistance of each coil in terms of the whole resistance between A and B. Thus the disk of Q. 572 WILLYoUNG ON MEASURING INSTRUMENTS. [May 17, having fourteen resistances, each ºr of the whole resistance, is engraved with the series of numbers 0.100, 0.200, 0.300, etc., up through 1.400. s, on the other hand, is engraved 0.001, 0.002, 0.003, etc., through 0.009. M in the same way has its disk, which is engraved 0.010, 0.020, 0.030, etc. In the in- strument these three switch devices are grouped together as shown in the general view and in plan in Fig. 10. A raised metal box, in shape something like a three-leaf clover, covers their operative portions. In each box there is cut a rectangular hole just large enough to expose a single one of the numbers engraved upon the rubber disk below. These numbers are so placed upon the disk that the one visible, indicates the number of parts of the whole resistance, which by virtue of the position of its switch are placed between the points of the derived circuit. The sum of the three numbers displayed is, therefore, the total number of parts of the whole placed between the derived circuit terminals by virtue of the position of all the switches, the number of tenths being taken from one, of hundredths from another, and of thousandths from the third. In practice the operation of the instrument is exceedingly con- venient and speedy. It is first turned to sº and Q, M and s turned until they read 1,000, since the Carhart one-volt cell gives exactly one volt E. M. F. The galvanometer switch being turned to “Galv. Shunted,” K and K' should be depressed for an instant. (In the instrument a single ivory button projecting up through the top operates a double contact below). If the index swings to “R High” the two regulators, R, and Ro, should be turned “Up,” as shown by the arrow engraved upon them ; if to “R Low,” then the regulators should go down. The key being thus alter- nately depressed and the regulators altered, when balance is finally approached the shunt may be removed from the galvanometer by throwing the switch to “Galv. Direct,” which will make the adjustment more sensitive, and the process continued until bal- ance is perfectly attained. This having been done, we know that the points A and B differ in E. M. F. by exactly 1.5 volts. To assure ourselves of this we may turn w to sº and again depress the key; this should also give a balance. To measure, now, any unknown E. M. F., it is joined to the terminals F and g; the switch w should be turned to R, R × 10, R × 100 or R × 1,000, according 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 573 as we believe the E. M. F. to be between 0–1.5, 1.5–15, 15—150, or 150–1,500 volts. If we have no idea what the E. M. F. is, as is very rarely the case, then we may try the points successively. Shunt the galvanometer and depress the key ; if needle swings to “R High '' turn Q, M and s “Down,” as shown by the engraved arrow until the needle swings to “R Low.” If the needle cannot be reversed with w on this point, try the next one, and so on until finally, if the E. M. F. does not exceed 1,500 volts, reversal can be accomplished ; then remove the shunt from the galvanometer and balance as accurately as possible. This done, the reading of the tº: W § ** § A. 5. - gº º {2. | - **asºflºw FIG. 10. dials, R, multiplied by 1, 10, 100 or 1,000, according to which of the points w is on will be the desired E. M. F. If current is being measured, proceed in the same way, only multiplying the E. M. F. thus obtained by the resistance of the shunt in order to get the current itself. The accuracy of the work may be checked at any time by throwing w back on one of the standard cells, and Q, M and s back to 1.000; perfect balance will usually persist, provided the main battery, Ba, has any charge worth speaking of. In order to guard against any possible change in the E. M. F. between A and B, during a series of measurements, due to change 574 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, in the battery, Ba, the latter should be of good size, say with a dis- charge rate of four or five amperes at any rate. The resistance be- tween A and B is 120 ohms, being always constant ; this means a current of about ++}r amperes through A B, while the key is closed; as the key is only closed for an instant at a time, this drain cannot affect even to the most infinitesimal extent the E. M. F. between A and B. ; It may seem as if the large number of rubbing contacts neces- sitated by this device, 28 in ail, was a feature liable to introduce considerable error into the result. This is, however, not the case, for, assuming the largest possible variation in each contact resis- tance to be 0.001 ohms, (the writer has never found it larger than this in switches of ordinarily decent mechanical construction) we have, as the maximum total variation in Q, 0.028 ohms. The total resistance of A B being 120 ohms, this is seen to be less than 4 parts in 12,000 or but a little over 0.02 per cent. In connection with this, it is interesting to note that in adjust- ing the resistances of the coils Q, M, and s the maximum allowable error of adjustment is a constant percentage of the total resistance A B, rather than of the individual coils. Hence if the 8 ohm coils of Q are adjusted to sº; per cent., comparatively easy for coils. of so high value, the 0.8 ohm coils of M need only be adjusted to #}=# per cent. and the 0.08 ohm coils of s to 4 per cent. to se- cure the same accuracy as regards the total of A B, i.e., as regards zesult. The low resistances, therefore, are no more difficult of adjustment than those of the highest value, if indeed they are not easier, so that the resistances as a whole are easily brought within the required limit of not over tº per cent, error in result. The value of this instrument as a convenient and quick way of obtaining absolutely reliable determinations of current and E. M. F. is, we believe, very great. There are scores of engineers, laboratories and stations who constantly find it necessary to secure a standardization of their ammeters or voltmeters. To make a voltameter determination takes a great deal of time, even if but one value is to be gotten, and an amount of skill and painstaking, not always immediately available. The absolutely steady current, suitable solution, chemical balance, etc., are also adjuncts not always at hand. To keep any form of standard instrument about for purposes of comparison is usually not feasible. If the instru- ment has springs, the springs may change. If permanent magnets they are almost bound to change. Other forms of apparatus more 1894.] WILL YOUNG ON MEASURING INSTRUMENTS. 575 free from variable elements, as e. g., tangent galvanometers, are easily affected;by strong fields and mechanical disturbances and require either to be always kept set up absolutely undisturbed, or else to have considerable time spent upon them each time before using, in order to adjust them into good condition. In the po- tentiometer there are practically no variable elements, at least within limits practically infinitesimal in practical measurements. Dependence is placed solely and entirely upon standard resistances and standard cells, both of which have been thoroughly investi- gated by many workers, and the variations of which are well understood. The apparatus is simple and compact, and its mode of use can be successfully learned by a schoolboy in a few moments." Being a zero method it is absolutely unaffected by neighboring currents or magnetic fields and the galvanometer being a dead beat and jewel suspended D’Arsonval, may be used under the most severe conditions of mechanical shock and vibra- tion. On board ship it is believed absolutely the only apparatus which could possibly be used. - 1. The dimensions over all are 11 in. by 14 in. by 5 in. deep; weight less than 10 lbs. j76 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, DISCUSSION. MR. R. O. HEINRICH –Assuming that Mr. Willyoung's intro- ductory remarks in regard to the unsatisfactory constancy of commercial voltmeters and ammeters be true, it should be borne in mind that in the best types of commercial measuring instru- ments this condition of affairs is not due so much to the princi- ples and methods employed in the construction of such instru- ments, as to the very exacting conditions under which they are used. We may safely say that with proper care, instruments employing electromagnetic or permanent magnetic fields are at least as constant as standard cells, and in considering therefore the advisability of adopting one or the other joi for the purpose of comparing and standardizing commercial instruments, convenience and simplicity become the most important factors. I think there is no question that a direct reading instrument is by far the most preferable, under “direct reading,” being under- stood that the instrument gives direct indications which are read on a scale, without any further manipulation than connecting the instrument in circuit. - The potentiometer method in the hands of a skilled person is undoubtedly a very valuable one, being a zero method and entirely independent of surrounding magnetic fields. It is, however, not a direct reading method in the above sense of the word, and it becomes very tedious and even unreliable, if com- parisons with fluctuating currents have to be made. This, I believe, is one very potent reason why all attempts of introducing the potentiometer method in the form of a commercial measur- ing instrument have lacked success. The “dangerous elements of changes” attributed by Mr. Willyoung to all other methods, are in my opinion not at all obviated by the use of a standard cell, at least such cells as are now to be had in the open market. Mr. Willyoung mentions in his paper that his apparatus is capable of being used for measurements of voltage from 0 up to 1,500 volts and of currents from 0 up to any required upper limit with a maazimum error of not over one-tenth of one per cent. Mr. Willyoung is to be highly congratulated if his statements are borne out by actual facts. I have found very great difficulty in obtaining an absolute accuracy of one-tenth of one per cent. working with the best appliances under the best conditions in a laboratory. But assuming that the general construction of the apparatus, the introduction of a complicity of sliding contacts for comparatively low resistances, the adjustment of such resist- ances and finally the sensibility of the galvanometer used in the apparatus will allow such remarkable accuracy after the instru- ment has left the factory, it remains to be proven whether the standard cell employed, and in general any standard cell can be relied upon to such a degree of accuracy for any reasonable length of time. - 1894.] DISCUSSION. 577. On the strength of information collected from various sources and on that of my own experience I am very loath to accept Mr. Willyoung's statement in the affirmative, at least not without a good deal of reserve. Dr. Kahle, of the Imperial Physico-Technical Institute of Berlin, in a most exhaustive treatise on the Clark cell (Zeitschrift für Instrumenten Kunde, vol. xii, p. 117 and (vol. xiii, pp. 191 and 293) mentions (vol. xiii, p. 303) that six Clark cells, made according to the instructions of the Board of Trade, were sent to him from Cambridge, England. Of these six cells two were spoiled in transit. The remaining four were tested at intervals for a period of nine months together with five cells made in Berlin according to the above mentioned instructions. The results of these tests are given in Table I. For the con- venience of comparison I give the differences of these cells from the normal E. M. F. in per centages. Dr. Kahle gives the diffe- rences in hundred-thousandths of a volt. TABLE I. Set up in ºl. and sent to Set up in Berlin. Date of Test, ... - - - - - - - - --- - - - - E1. B2. A’s. Ea. I. II. III. IV. V. Sept. 14, 1892... – o oss |- o.og7 i c.oo7 – o.o.11 + o.o. 6 |+ o.o. 7 — o.o.36 — o.o.39 |+ o.oro ** 15, “ ... — o.o.34 – o.ozo o.Orr — o.o.o.9 -H o.o.16 -H o.or 5 — o.o.38 |— o.o.41 |+ o.or 2 Oct. 31, “ . . |— c.o.o.4 |+ o 13 |Hz o.o.14 |-|- o.oro + o-oo:2 – o.o.o.9 — o.o.29 — o.o.o.4 — o.o. 4 Nov. 1, “ ... — o.o.o.4 |+ o.o. 7 | No test.]+ o.oro |+ o.o.o.2 – o.oog – o.o.29 — o.o.o.4 – o oró { { , “ . . [-o, 178 O. OOO { * – c. 116 |+ o.o.o.4 – o.o.70 – o.o.91 – o. 11o |— o. 1 oz. ** 12, “ . . – o. 142 – O.og8 { { – oozo |+ o.o.o.8 – o.o.5o – o.o.5o |— o.ozo – o.o.67 April 19, 1893... — o. 184 – o.370 |+ o.o.o.4 |— o. 104 o.Ooo — o.o.92 – oozo |— o.362 |No test. une 14, “ ..]— o 131 — oog5 |+ o.oos – o oë7 |+ o.o.o.2 - o.obo — o.c22 – o.191 • * “ 17, “ . . [- o.252 – o.ogo + o-oo7 — o.oS5 ||Nº test.— o.o.64 — o.o.25 – o. 167 (, i. It will be seen from this table that of the four English cells only one, and of the five cells prepared in Berlin only three would answer Mr. Willyoung's requirements. Dr. Kahle ascribes the desultory and sometimes very consider- able variations to the general construction of these cells, since the variations were shown when the cells had never been dis- turbed and had been kept at almost constant temperature during the entire period of the test. In the same article he says: . “The E. M. F. of the Feussner cell (a Clark cell of somewhat “large dimensions with mercurous sulphate and mercury elec- “trode retained in a porous cup) and especially of the English “ cells, even at constant temperature, depends entirely upon the “conditions of temperature to which the cell was exposed dur- “ing the previous day. This uncertainty of E. M. F. surpasses in “the Feussner cell 0.001 volt (0.07 per cent.) and may amount “to 0.003 volts (0.21 per cent.) to 0.005 volts (0.35 per cent.) in 578. WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, “the English cells. * * * * On account of the large and “indefinite changes with change of temperature of the E. M. F. “of the Clark cells, it has been tried to replace it with others “which are claimed to behave more favorably in this respect. “Prof. Carhart has reduced the temperature coefficient of the “Clark cell by using a zinc sulphate solution which is concen- “trated at 0°C. The advantage gained by this is, however, an- “nulled by the disadvantage that such cells according to the “experience collected here, cannot be reproduced with such “exactness as the cells with zinc sulphate crystals in excess. It “is very difficult to make a solution which is saturated at exactly “0°C. If it is saturated for a temperature deviating only a few “tenths of a degree from zero, a deviation of the E. M. F. “amounting to several ten thousandths of a volt from the normal “will be the consequence.” - However this may be for the reproduction of these cells by any person skilled in the arts, my experience has been that Professor Carhart knows how to reproduce them with admirable agreement. Their portability seems also to be very satisfactory. Of the 19 Carhart cells which have passed under my observa- tion I have a definite knowledge of the condition when received, of only eight. Seven of these showed a very good agreement amongst themselves in a test made about two weeks after they were received. Cell 332 was tested two days after receipt, and showed an E. M. F. 0.075 per cent. above the normal of 1,440 volts. Tested two months later its E. M. F. had dropped 0.117 per cent. below its original value. In point of constancy the results have been less satisfactory, the changes being most likely due to leakage. It is quite evident that in Professor Carhart's modified Clark cell, the slightest leakage must be detrimental since this would at once alter the concentration of the zinc sulphate solution. Although there seems to be a marked improvement in the cells received lately from Professor Carhart, it will be seen from Table III. that in five of the ten cells a continual dropping of TABLE II. I 2 3 4. 5 & Testº * | Difference in | Difference in No. 284. 284 Standard. 21o Standard. Nº. 2O2. . . . . . . . Sept. º: 1891 Feb. #2, 1892 ... — o.24 – o.o.9 { { 2O3. . . . . . tº e 4 [. 39, { { { i ; : § { ... – O. I9 * O.O4 2O4. . * * * * * ( * { { £ { * tº 4 { % O.99 3 O. 17 - O O2 A { 2O5 s & * * { { .. * { { { * * ...? - O.2 I * o.o.6 § { 2O7. . . . . . . $ - $ tº { { { { { % { { . – 3:4 + o or ... 299... ... -- * { { { { { § { a tº $ 4 .998.7 O. I3 + o.o.2 2IO. . . . o.9985 — o. 15 O.OCO “ 275.... ...] Nov. 19, 1892 August, 1893 O.9998 – O O2 “ 284. . . . . . “ 24, “ { % * { I.OOOO # # TABLE III. .. 㺠### Date of Test, 3II 312 313 31.4 315 316 317 275 284 332 É § §§ 3 Average E.M.F. # 3 || 3: cr) *—º-— Nov. 7, 1893 I, COOO I.OOOI T = OOO. I I - OOOI 1.cooz 1.oooo I.O.O.O.I. No test No test No test I4.9 1. oooo.6* Dec. 7, “ 4 & I.OOOO o,9999 o,9998 O.9997 O.9997 o.9998 O.9992 O.9997 { { 18.75 O.99999 1.44021.v. Dec. 14, “ { { I.OOOO I, OCOO O.9999 o,9997 o,9997 o,9997 O.9993 O.9997 s { % I9.oo o 99999 I.44O2 Dec. 18, “ { % I. OOOO O.9999 O.9999 o.9996 o.9996 O.9999 O.9992 o.9996 (, . 18.8o 9.99989 I,44O2 Bec. 20, “ { % I • OOOO O.9999 O.9999 o,9996 o.9996 o.9998 O.9992 o. 9997 { { 19.60 o.99988 I.44O2 Jan. 16, 1894 { % O.9999 o.9999 |, o,9999 o.9996 o.9995 O.9999 No test No test { { 20.5o o.99987 I.44OI Jan. 24, “ { { I.OOOO o 9999 O.9999 O.9994 O.9993 O.9997 { % * { { { 19.8o o,99982 1.4401- Mar. 21, “ { { I.OOOO O.9999 O. 9999 O.9994 o.9990 O.9997 { { * { 1.oOo.5 18.3o o,99979 I.4409 May 7, “ { { O.9999 o.9999 O.9999 O.9993 o,9987 o.9998 § { { { I.oOo.5 19.85 o.99975 1.4400- May 9, “ § { l.oOoo o.o.999 o,0099 O.9993 o.9987 o,9998 { { { { 1.ooos 19.60 o,99976 I.44OO l May 25, “ { { 1. ooooo o.99984 o.99990 o.99927 o.99862 o.99973 o.999.19 || 0.99953 o.99933 19.51 o.9997.36 1.4439-1- May 1o, “ § { o 99997 | o 09987 o.99987 o.99929 o.99869 o.99972 | No test o.99953 || o.99933 19.85 o.999741 1.4430+ June 5, “ { { o.99995 || o.99999 o.99990 o,99927 o.99857 o.99.972 o,999.18 o.99951 o.99933 20.40 o.99974o | 1.4439-H The comparisons were made taking 311 as standard. The E. M. F. of 311 was determined by five silver voltmeter tests and gave an average of 1,44031 inter. volts. Prof. Carhart's figures for the same cell 1.4402, satisfactory proof that this cell remained very constant. The figures in the last column show that the average E. M. F. of the cells 311 to 317 differs not more than 0.014 per cent, from the normal 1.4402 intern. volts whilst cells 315 and 316 have reached very nearly the ſº per cent, limit. Another F. that a large number of cells should be used to obtain accordant results. It will be interesting to investigate further how the cells showing tendency to change will behave during the hot summer weather, since this seems to me to be critical to the seals of most cells. * The first horizontal line are Prof. Carhart's figures. 580 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, the E. M. F. has taken place. . These cells were kept continually in an oil bath covered completely by oil and were subjected to only very small variations of temperature. Cells 275 and 284 had been kept in open air in the laboratory from August '93 to November '93. , Cells 147, 150, 202 to 210 were also kept in open air in the laboratory and had to undergo changes of tem- perature during the year between 15° and 30° centigrade, the same would be the case for cells used in an apparatus as proposed by Mr. Willyoung. . Remarks to Table II.-Cells 202 to 275 were compared with 284 as standard. Assuming that at that time 284 was very nearly correct, since it was just received and still shows in Table IV a fair agreement with the normal E. M. F., the figures in column 4 would give the percentage difference from the normal E. M. F. Cells 202 to 210 were returned on account of these changes, therefore no further test could be made. The figures in column 5 are rather interesting, as they show that a number of cells of TABLE IV. Test, May 25, Correct & Carhart-Clark. Set up. Received. 1894. E. M. F. Value at º: - at 15° C. 15° C. in per cent, Cell No, I47 Mar. 22, 1890 1891 I. 43O I .44 I. — o.75 I5O ** 2 { { $ tº I-43 I I.44 I. – o 69 %; Nov. 16, 1892 August, 1893 I.438 I. 44O *-º § 2 “ 24, “ º § { I . I. 44C) - O, O : [ { 4 8 November, 18 : :. O,OI 3 ... 7, 1893 moer,1993 44O4. 44 4. 312 { { .. { % § { 6 t I.44O4. I 44O3 o.oo7 3I.3 I.44O2 I .4403 — o.oo7 3I4 { { { { { { § { * { I.44O2 I.44O3 — o.o.o.7 3 15 * { { { { * { { { I. 4390 : I.44C4 - O, IO 316 { % * { { * * { { % 1.4384 . I.44OI — O. I 2 317 * { § { { { { { tº ſº I.44OO I.44O3 - O.O2 322 Dec. 15, 1894 March, 1894 I. 439 I 44O — o.oS * TABLE V. Test, May Correct Differ- Clark Cells. Set up. Received. 25, 1894, E. M. F. ence in Remarks, at 15° C. 15° C. per cent. wirt-Clark, 252 #. : April, '91. I.422 1.434 — o 85 |Signs of leakage. º 252 D.. sº º I.4I5 ł - I-35 |... (, i. 265 A . 2 { * { % I. 37 I { % — 4.4 |Signs of leakage. { { 265 H. . ? { % { I 390 º * 3.6 § { * Weston-Clark, 1..., |May, 1891|\ g o.986 – 24.2 |Apparently in good S * condition. . . $ $. 2.... ‘‘ “ § 2, I 432 § i. – o 14 |Glass cracked in seal- > s ing, leaked, $ 8. 3.... “ { % } = *: J. 433 § { — ooz Apparently in good f s 5 condition. * { ( , 4. . . . * { § { 2-3 1.432 § { — o. 14 ſº tº $ 5. . . { { { { §- I.43O $ tº — o,28 { { - { { . 6... º º J 9 .# . – o. 14 C º º g t 7- . . % { P+ I.38 I — 3.7 |U1acked in seating, leaked. Feussner–C'ark, 457|Begin. '93|July, 1893] 1.371 * { — 4.4 |Leakage, spoiled in tranSlt. 1894.] DISCUSSION. 581 the same batch may compare very well and still differ consider- ably from the normal E. M. F. A very good proof against the assumption that two standard cells, kept under the same condi- tions, are correct ºf they agree with each other. Cells 147 and 150 (Table IV.) are now almost dried up, the seal being completely covered by effloresced zinc sulphate ; they had shown signs of leakage already in the early part of 1892. Cells 202 to 210 showed whitish spots between the seals and the lass. A yellowish white coat on the seal was explained by ; Carhart, as silicate of sodium acted upon by the air. Table V gives the results of tests of Clark cells of various origin. With very few exceptions the cells have changed con- siderably more than one-tenth of one per cent. The Wirt-Clark cells were contained in two Wirt voltmeters, 8. e., direct reading potentiometers. Instrument 265 when re- vived gave the following results on April 14th, 1891: Standard 100 volts. . . . . . . . . . . . . 100.2 265 A. +0.2 per cent. 100.35 265 B. +0.35 6 & 10 volts. . . . . . . . . . . . . . 10.35 265 A. +3.5 º 10.70 265 B. --7.0 On May 25th, 1894: Standard 100 volts. . . . . . . . . . . . . . . 77.0 265 A. —23.0 per cent - '79.0 265 B. —21.0 é & 10 volts . . . . . . . . . . . . . 9.73 265 A. — 2.7 * & 9.53 265 B. — 4.7 & S. On Table V the cells are shown to differ from the normal — 4.5 and – 3.6 per cent. at May 25th. It is evident that the sliding contacts and changes in the resistances have in the course of time introduced a much larger error than the cells. The instruments were not used, but had been standing in the laboratory for three years. Weston Clark cell. 1 is a remarkable case, in so far as no sign of leakage could be detected, and that the cell was apparently in faultless condition. There is then a record of 31 standard cells, of which 21 have given out at this date. It would be difficult to say what the useful life of these cells has been, since no record was kept at sufficiently close intervals. My experience with the Calomel cell has been too limited to allow of forming a definite opinion. With two Calomel cells the following results were obtained by silver voltameter deter- mination. Cell 803. April 3d. . . . . . . . . . . . . . . . . . . . 1.00001 intern, volts at 20° C. April 6th. . . . . . . . . . . . . . . . . . . 1.00009 § { & 4 & C April 16th. . . . . . . . . . . . . . . . . . 1.00002 “ & & • & May 10th. . . . . . . . . - * * * * g º a º ºs 1,00010 & & & 4 { { One test made May 8th gave the E. M. F. of the same cell as 0.99922 intern. volts at 20° C. Previous to this test the cell was used very continually during one hour, a grounded circuit 582 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, giving trouble in adjusting. Although the circuit contained resistances, considerably more than 100,000 ohms in series with the cell, it is thought that the continual use caused the drop in E. M. F., the more so as a comparison with Carhart-Clark cell 311, made shortly after the experiment indicated also a lower E. M. F. than usual. A silver voltameter test made two days later gave a result agreeing well with previous determinations. These determinations would make the E. M. F. of this particular cell ().99961 intern. Volts at 15° C. Carhart, Calomel cell 5 loaned through Professor Carhart's courtesy for comparison with cell 303 showed by comparison 1.00018 intern. volts at 15°C, a difference of 0.06 per cent. be- tween the two cells. These two cells seem to have stood trans- portation well and make a very satisfactory showing. How they will behave under more exacting conditions with an occasional abuse is a question yet to be determined. It is evident, however, that the standard cell which Mr. Willyoung proposes to use has to be a very much superior article to anything which we now have, in order to fulfil the require- ments of remaining for a reasonable time within an accuracy of one-tenth of one per cent. Moreover, allowing for occasional abuse of the apparatus and taking it into consideration that a multiplicity of sliding contacts is used in connection with com- paratively low resistances, I should consider an accuracy of 0.2 per cent. quite remarkable. On the other hand I know from experience and from carefully kept records extending over five years, that there is no difficulty whatever in maintaining an accuracy of 0.2 per cent. with direct reading instruments as defined previously, and employing electro- magnetic or permanent magnetic fields, and affording the same flexibility in range as the potentiometer described. The use of the potentiometer method for commercial measur- ing instruments dates back quite a few years. The Wirt and Howell, voltmeters were constructed on this principle. Dr. Feussner describes a potentiometer in 1890 in Zeitschrift für Instrumenten Kunde and points out, how the instrument may be made direct reading in substantially the same way as Mr. Will- oung describes. Mr. Crompton's potentiometer is referred to in Mr. Willyoung’s paper. It is rather significant that, in spite of these various attempts, the actual use of such instruments is very limited indeed. For the commercial calibration of a large number of instru- ments the method is altogether too slow. For occasional com- parisons of instruments in daily use a direct reading instrument of known standard qualities seems preferable, the accuracy at- tainable with such instruments being amply sufficient for all practical purposes. For laboratory use, where time is usually a minor considera- tion, the potentiometer would be commendable; but when it 1894.] A. I) ISO/USSION. 583 comes to accuracies as high as one-tenth of one per cent, I should always take the silver voltameter and a standard resistance as a last resort for a check on the standard cell. |-www-(3), _–= ſ - |8 ,7° G - ki UNITS ‘TENS HUN DREDS THOUSANDS - © . .% ºf 3 Q 6-3-4-3 O 6.3-4-3 O 6-4-3-3 8 º ×2 7 3 ºx2 73°W, 2 7&T. ×2 * Nº,...}^\Sºlº’ \'º, º \'ºs ſº 9 9 : .* º 0 º |E|sº tº, }+. Pºº-ºººº- Tº dº T- 10 SCN.C.C. Jº-H, 3. Tº 3 - 0 w - 2' 6 a. JTsūTitº Lº JöT, º 9 & C SF1 8 2. & 1. - fºr 1. º c. 371 º C £: 8 * C 8 - . Yº # , º.º.º. º.º.º. b iº...” *.ſ.l…” * 6 5 4 6 5 4 3 6 5 4 3 6 : 3 * FIG. 1.-Rheostat for Rayleigh's Compensation Method. In regard to one detail of construction I would say that one idea used also by Mr. Willyoung occured to me some time ago. Mr. Weston designed a potentiometer which was to shorten the tedious adjustment of resistances in Lord Rayleigh's method. Fig. 1 shows its general arrangement. A resistance of 10,000 ſº 2- --|-- Qhms is kept in circuit continuously with an auxiliary battery. It will easily be seen from the diagram that by moving the cranks of any of the four dials, resistance cut in on the circuit 584 WILL YOUNG ON MEASURING INSTRUMENTS. [May 17, containing the standard cell C (on the a side) is cut out on the opposite side (b side). This potentiometer necessitates, how- ever, the adjustment and use of 80 resistance coils. In the modification shown in Fig. 2, the number of resistance coils is reduced to 40 although the same number of steps from one to 10,000 is obtained. The identity with Mr. Willyoung's idea will be found in the arrangement of dials C and D. These two dials are identical in their arrangement, taking dial 0 for a descrip- tion; the two halves a and b of the . carrying the sliding contacts serve to make a short-circuit between the segments of E, F and G, H. The upper part of these two dials forms always up to the position of the crank, counting from left to —||1|||| | 0. Ó | º g 2 FIG. 3, right, a part of the circuit containing the standard cell, whilst the lower part is up to the position of the crank in series with the auxiliary battery. Fig. 3 will show this more clearly. a + b + c + d is then the resistance of the circuit containing the standard cell, whilst the total resistance is always kept con- stant at 10,000 ohms. Such an arrangement may of course be made direct reading in the sense taken by Mr. Willyoung, by proper adjustment of the current through the total resistance of 10,000 ohms; it has the advantage of very much higher resistances which I believe essen- tial for accuracy whenever sliding contacts are used. In summing up my remarks I would say that I do not wish to appear opposed to the use of standard cells, or to that of the 1894.] I) ISOUSSION. 585 potentiometer method. I consider both in the hands of an experienced and careful man extremely valuable and useful. I do not believe, however, that the use of the potentiometer method avoids “dangerous elements of change” any more than any other instruments of standard qualities. * I should consider it an injustice to the user of an apparatus to make him believe that he can measure to a certain percentage of accuracy when the chances are so very great that he does nothing of the kind. I am not a believer in “universal portable instruments,” with which anything and everything can be done ; usually they are crowded into much too small space. My doubts about sliding contacts in connection with low re- sistances have been expressed before. From a superficial inspection of Mr. Willyoung's apparatus I should expect difficulty and trouble in regard to proper insula- tion, especially if higher voltages are to be measured. If the galvanometer used is of the same sensibility as the one contained in Queen and Company’s portable testing sets, I should consider its sensibility jº for the attainment of an accuracy of one-tenth of one per cent., as claimed. A paper presented at the Eleventh General Meet. ing of the American Institute of Electrical Fngineers, Philadelphia, May 17th, 1894. Presi- dent Houstozz in the Chair. A * AN OPTICAL PHASE INDICATOR AND SYNCHRONIZER. *- BY PROF. GEORGE S. MOLER AND DR. FREDERICK BEDELL. In starting a synchronous alternating current motor, it is usual to bring the motor up to speed by some external means, and to switch it into connection with the generator when the motor and generator are running synchronously but are in opposite phase. Various devices have been employed to indicate synchronism, and to show when the motor is in opposite phase to the generator, one of the simplest of these devices consisting of an incandescent lamp used as a pilot lamp. The lamp is connected directly in the circuit supplying the motor so that all the current through the motor armature passes through it. Before the motor is started the lamp glows steadily. As the motor attains considerable speed, the lamp suddenly flashes up and dies out alternately according to whether the electromotive force generated by the motor, and the electromotive force from the alternator are in the same or in opposite phases. Beats are thus produced which occur at longer . intervals as the motor approaches synchronism with the alterna- tor. When the intervals are long enough to be quite marked, the motor is connected directly to the generator circuit by cutting the lamp out at a moment when it is dark, indicating that the machines are in opposite phase. At the same time the external power, which has driven the motor to synchronism, is removed. Instead of one lamp, several lamps or a lamp together with dead resistance may be used where required. - This device is simple and efficient. It does not, however, indi- cate the moment when exact synchronism is reached, nor does it show whether the motor is running at a greater or less speed 586 1894.] MOLER AND BEDELL ON A PHASE INDICATOR. 587 than that corresponding to the generator. It does not show the exact phase difference between the motor and generator, and does not indicate the phase relations after the motor has been connected to the alternator and is being driven by it. The following instrument has been devised by the writers to give definite information in regard to the relative speeds and phase-positions of the motor and generator in laboratory investi- gations. It shows: (1.) When the machines are synchronous: (2.) Which machine is running the faster when they are not synchronous. (3.) The angle by which the motor lags behind the generator. FIG. 1. FIG. 3. We will first describe the simplest form of the phase-indicator. The motor and generator are placed together, with shafts in line and abutting, but not quite touching. The two machines must have the same number of poles so that a revolution of the arma- ture of each, represents the same number of alternations. The abutting ends of the shafts carry two disks, one connected rigidly with the motor armature, the other similarly connected with the armature of the generator, as shown in Fig. 1. In these disks are curved slits, one slit for each pair of poles of the machines. These slits are shown in Fig. 2 for an eight-pole machine. The two disks are in every way similar; the one being the reverse of the other. The two disks are practically superimposed and to- 588 MOLER AND BEDELL ON A PHASE INDICATOR [May 17, gether form one disk with four holes where the slits of one disk cross over the slits of the other. Evidently the distances of these four holes from the center depends upon the relative posi- tions of the two armatures; they move in and out as the arma- tures shift their relative positions. From the symmetrical ar- rangement of the slits, if one armature is stationary and the other is moved past two pole-pieces or through 90° of arc (cor- responding to a complete period of alternation or 360° of phase) the intersection of the slits will be the same distance from the center as before. The curvature of the slits is such, that the dis- tance to or from the center that the intersections of the two sets of slits move, is proportional to the change in relative position of the two armatures. When the two armatures are running at the same speed in the GeneRAJOR sº MOTOR /* 2^ FIG. 2. same direction, and there is a source of light on one side of the disks, the intersection of the slits, as seen from the other side, appears as a continuous ring of light. A slight difference of speed causes this ring of light to move outward or inward, accord- ing to which disk is revolving the faster. The more rapidly the ring moves in or out, the greater the difference in speed of the two disks. If the ring is moving out, a new ring starts at the center when one ring reaches the edges, and these rings keep following one another outward. If the difference in speed is the other way, the successive rings move inward. In Fig. 3, the heavy dotted line represents the ring of light for a particular position of the two disks. The position of the ring of light indicates the relative position of the two armatures. The disks may be secured to the shafts so 1894.] MOLER AND BEDELL ON A PHASE INDICATOR. 589 that when the armatures are in the same positions with reference to the pole-pieces (i. e., the machines are in the same phase) the ring of light will be at the inner or outer ends of the slits. The concentric rings in Fig. 3 represent the phase differences cor- responding to positions of the ring of light in this case. For convenience in operation, the arrangement of the apparatus which has thus far proved satisfactory, has been as follows: On one side of the pair of disks is placed an incandescent lamp en- closed in a box. One side of the box is close to the disk and has a slit in it about half an inch wide extending from the shaft to the circumference of the disk. This slit is covered with a piece of oiled paper so as to give a diffused light upon the disks. A complete ring of light is no longer seen from the other side, but only a small portion corresponding to the width of the half inch slit. A stationary scale is fixed so as to extend from the shaft to the edge of the disks on the opposite side from the lamps, so that the distance of the changing line of light from the center, may be read so as to give the phase difference of the two machines by direct reading. To enable one to see the scale and line of light most conveniently, a mirror is arranged at forty-five degrees with the disks, so that the line of sight is at right angles to the shaft. The disks may be arranged in the manner just described upon the abutting ends of the motor and generator shafts, only in case the two machines have the same number of poles. Where such is not the case, one or both of the disks can be driven by gears which will give the proper relative speeds to the two disks. In operation, the instrument has proved quite satisfactory, giv- ing exact and definite information concerning the changes in the armature lag of the motor. The fluctuations in this lag are usually quite marked, and the conditions which cause them can be readily investigated by this apparatus. For instance, this fluctua- tion is small with proper field excitation; as the field current of the motor is diminished, this fluctuation increases, the line of light moving rapidly back and forth through a greater and greater distance which finally becomes so great as the excitation is weakened that it goes a distance beyond which it cannot re. cover; i. e., the motor gets out of step and stops. It would be possible to make a more detailed investigation of these fluctua- tions by means of a revolving mirror, and they may be photo- graphed and made of permanent record by means of a moving plate. 590 MOLER AND BEDELL ON A PHASE INDICATOR. [May 17, The apparatus can be applied to other lines of work involving an investigation of phase differences and synchronism, and may be modified to meet the requirements of the problem in hand ; but it is peculiarly suited for use in synchronous motor work for which it was designed. The scope of the present paper admits. only of a general description of the apparatus here given. A paper presented at the Elezenth Annual Meeting of the American Institute of Electrical Engin- eers, Philadelphia, May 17th, 1894. President Houston in the Chair. A RELIABLE METHOD OF RECORDING WARIABLE CURRENT CURWES. BY DR. ALBERT C. CREHORE. INTRODUCTION. A practical problem that has in more recent years presented itself to the electrician and physicist alike is: “How shall we measure the exact current which flows in a conductor at any instant of time, and record all the irregular changes to which it is subject 7” Probably every one who has thought of such mat- ters at all has considered this problem in some of the phases which it presents. The importance of the question, since the introduction and extensive use of the alternating current, has emphasized the fact that we need a “reliable method” of measur- ing the instantaneous values of a variable current, which is not a “method by points,” but “a method which continuously records the current.” Under “a method by points” is included any method in which the current is obtained from readings (usually of an electrostatic voltmeter) due to the charge of a condenser which may be con- nected in at any point of time. The essential characteristic of the method is that the current is supposed to repeat itself exactly during successive periods, or more generally when the conditions are exactly repeated. There can be no doubt that the current does repeat itself under exactly similar conditions, but can we be sure that those conditions are exactly repeated 2 By this method a number of points are found, the time occupied being at least several minutes, and the collection of points properly arranged is a representation of the current during as short a time as the one- hundredth of a second, perhaps. Yet this method has proved 591 592 CREHORE ON RECORDING CURRENT GURVES [May 17. to be a very useful and practical one, and has given us informa- tion concerning the currents and potentials of generators and transformers which is of paramount importance. Yet all will agree that this “method by points” is too limited in its applica- tion, and does not show us any sudden temporary change taking place in a current which does not repeat itself. Such, for in- stance, as a sudden “make,” or “break,” or “change” in an alternating current would not be easily shown by this method. The second method, previously designated “a method which con- tinuously records the current,” is the one to which this paper more particularly refers. Under this head are included all methods which attempt to record the current by causing it, either directly or indirectly, to move a material “something” so that its displacement is some single valued function of the current. As an example of this method may be mentioned the well-known experiments of Frölich in which a telephone is used, upon the disk of which is mounted a mirror that permits a beam of light to be reflected from it. Any vibration of the disk gives an angular motion to the ray of light, and this motion is in turn recorded upon a moving photographic plate. Other examples might be mentioned in illustration of this method, for instance, a wire which is deflected in a magnetic field, or stream of mercury so influenced; but it will be noticed that in all of these cases an appreciable amount of ponderable matter is required to be moved backward and forward during each reversal of the current. When the current reverses hundreds of times per second, the unavoidable difficulty is introduced that the forced oscillations of this ponderable matter, no matter how small in amount, become so superimposed upon those of the current which it is desired to measure that they are inseparably mixed together; and the record does not show the true current, but the resultant vibra- tions of the instrument. That this is the case with the method of the telephone above referred to, has been established beyond a doubt it seems, by experiments conducted at Cornell University by Mr. Henry Floy. The current furnished to the telephone was carefully measured by the “method by points,” and care was taken to see that the current as measured by points was the same as that used in the telephone. The vibrations of the tele- phone did not even approximately agree with the current as measured by well-established methods. Bearing these points in mind, and remembering the high fre- 1894.] OREHORE ON RECORDING OURRENT OUR VES. 593 quency of some of the oscillations which it is desired to record, may we not with some degree of certainty predict that any of these methods requiring the rapid motion of ponderable matter will be open to precisely the same objections which are noticed in the case of the telephone? Without answering this question, probably all will agree that the difficulty may certainly be avoided by using as a vibrator, instead of this so-called “ponder- able matter,” a vibrator that has no weight. It is to this ques- tion of finding a form of vibrator without weight that I invite your attention. THE WEIGHTLEss WIBRATOR. The idea of the weightless vibrator is perhaps already sug- gested in the beam of light. But how shall we cause a beam of light to have a change in direction simply by means of a current flowing in a circuit without the intervention of some moving material? A way of influencing a beam of light directly by an electric current (or more properly by its magnetic field) is that discovered long ago by Faraday. It is by means of the dis- covery of the rotation of the plane of polarization by an electric current that I propose a method of obtaining a weightless vibra- tor. The explanation will be made clearer by reference to the diagram of apparatus (Fig. 1.) A beam of light is passed through a polarizer (Nicol prism), so that the vibrations of the beam take place in only one plane upon emergency. If it is then passed directly through an analyzer (Nicol prism) the latter may be set at such an angle as to prevent all light from passing through it, and thus produce darkness beyond the analyzer. Faraday’s discovery was, that if a beam of polarized light is passed through some substance in the direction of the lines of magnetization within that substance, there is a rotation of the plane of polarization in a direction which is the same as the direction of the current required to produce such a magnetic field. The direction of rotation is unaltered, therefore, whether the light beam advances in the same or the opposite direction to the magnetization, so that a beam reflected back and forth through the substance several times, has its rotation increased by equal amounts each time. If the direction of the ray of light be at right angles to the lines of magnetization, there is no rotation produced. The amount of this rotation has been carefully in- vestigated by Verdet, who announced laws by which it may be .594 CREHORE ON RECORDING OURRENT CURVES. [May 17, expressed. They are summed up in the following statement: “The rotation of the plane of polarization for monochromatic “light is in any given substance proportional to the difference in “magnetic potential between the points of entrance and emer- “gence of the ray ”; that is, it is equal to a constant times this “difference of potential, and is expressed by the formula 6 = w V, (1) where 0 = angle of rotation, W = difference in magnetic poten- tial, and v for a given wave-length is constant in any one sub- \ ACTUAL ARRANGEMENT OF APPARATUS #Eft-le: *—v2.1 ſ−1 a S {t+1. ~~Tle=TZ. º * \\ DIAG RAM OF APPARATUS N tº:= ===#EEEEE::=#Eß-E §NāšāH=###########v= K-2 sº Ni ###### =N===s ſº -- | [-. ºw-ºx- º §§ LENS O or = * & > ; Sè-2 Qº ºf 92 § 2 # XX ſº 2 N 0. N N ſº H- Orº Z! > tº 3 n H $ 0- I m. \ º “ - <ſ <ſ ~! (ſ) W § 2 9 5. <ſ = W. 2. 2. PHOTOGRAPHIC ^, * PLATE & * C. FIG. 1. stance. This constant is known as Verdet's constant. If now " the light is passed through the polarizer and then through a tube containing the substance used, around which is wound a coil of wire, and thence through the analyzer, an observer would find complete darkness upon looking through the analyzer, when set in the crossed position. But if without moving the analyzer a current is sent through the coil on the tube, light appears to the observer. This is because the plane of polariza- tion has been rotated by the current, and practically the prisms are no longer crossed. Now let the analyzer be rotated while the current is still flowing, and the observer will see a series of 1894.] OREHORE ON RECORDIWG CURRENT OUR VES. 595 beautiful colors through the analyzer, a different one for each position of it; but as long as the current flows, he cannot pro- duce darkness again by any amount of rotation of the analyzer. The effect suggests what is known to be a fact, that the differ- ent wave-lengths composing white light are rotated by the current in different amounts, so that when the analyzer is turned to the angle corresponding to the yellow light, say, only the yellow light is prevented from passing through the analyzer. All the other rays, being rotated by different amounts, pass through the analyzer, and there being mixed together they give rise to the series of beautiful complex colors above mentioned. A different color is seen for each position of the analyzer, be- cause in each position a different color is subtracted from white light, and the observer sees what is left, or merely the comple- mentary color, The law, which tells the amount of rotation given to the differ- ent colors is pretty accurately known ; and theory in this case is in close accord with the observed facts. The equation which closely expresses the amount of the dispersion for the different wave-lengths may be written:- 3 * C 70, Ž d n, 2 Q) – *(1 -- - }) (2) A° n d A * where w is the so-called Verdet’s constant, 7 the wave-length, and m the index of refraction of the medium : c is a constant for any one medium, which is, however, for different media, in- versely proportional to the permeability of the medium. This is a formula at which Maxwell arrived from his theory of molec- ular vortices, and we shall see how closely it is in accord with observation. We see by this formula that Verdet's constant de- pends not only upon the wave-length, but upon the index of refraction corresponding to that particular wave-length, and also upon the rate of change of the index with respect to the wave- length. If this rate of change of n with respect to A is small, as would be the case with a substance where the dispersion is small, and the index of refraction regarded as approximately constant, then it is seen that the formula reduces to an extremely simple form, viz.:- * = } (3) Here Verdet's constant is inversely proportional to the square of the wave-length. Using this approximate form for the present, we see from Verdet's law, equation (1), that 596 CREHORE ON RECORDING OURRENT CURVES. [May 17, V () = Q, W = e, , . . (3) ve * ſº . 4 T S : But the difference of magnetic potential, V, is TOT” where S i is ampere-turns, and thus we have 6 = 4 z o. S 6/10 X* = e, º/X*, (5) where ce = 4 to, S/10. (6) |-> 1O mm. * FIG. 2. A reference to Fig. 2 will show this relation between angle of rotation, wave-length, and current. Several spirals are shown, corresponding to the several lines of the spectrum, known as A, B, D, F and G. The radii of the circles which intersect these spirals are proportional to the current flowing in the circuit, while the angle, which the radius, drawn to any point of inter- section, makes with o P, represents the rotation for that particu- 1894.] OREHORE ON RECORDING CURRENT OUR WES. 597 lar wave-length and current. The spiral OA is in the extreme red, and O G in the violet of the spectrum, and the diagram thus indicates that the red rays are not rotated so much as the blue. The direction of rotation in the diagram is as indicated by the arrow. Now, returning to the observer looking through the analyzer, if he could resolve the light there seen into the pure colors of the spectrum, what he should expect would be, with no current, a complete spectrum, since all rays are rotated by the current. But let him rotate the analyzer, and he finds that first one color and then another disappears, and a dark band is seen to move across the spectrum as he rotates the analyzer. Again, let him rotate the analyzer to a certain angle and leave it there while he varies the current. He should expect that the band would move, but would vanish entirely with zero current, and thus prevent observation for small currents. Fortunately we have substances which naturally rotate a beam of polarized light, for by means of this aid we may obviate the difficulty that the band vanishes with no current. For instance, a parallel plate cut from a crystal of quartz perpendicular to the optic axis has this property of rotating the plane of polarization. Quartz is selected for the material used because of its great transparency and high specific rotary power. The law of the rotation is similar to that already mentioned for the rotation by the current. The approximate law is, that the rotation is in- versely as the square of the wave-length, which may be ex- pressed :— - % = Cs é / 29, (7) where p is the angle of rotation for the wave-length X, cs is a constant, and e is the thickness of the plate. The thickness of the quartz plate is seen to correspond to the current in equation (5). Fig. 2 represents the actual rotation for different thick- nesses of quartz, each circle corresponding to a plate one millime- ter thick. The equivalent of a quartz plate one millimeter thick is represented approximately by 35,700 ampere-turns wound upon a tube containing carbon bisulphide. This latter is the substance used, being selected on account of its high transparency and specific rotation. If a quartz plate be placed between polarizer and analyzer, the effect is the same as if the current circulated around the tube of carbon bisulphide, and we may, by rotating the analyzer, move the dark band completely across the spectrum by means of the 598. CREHORE ON RECORDING OURRENT GURVES. [May 17, quartz plate without any current. But suppose we set the analyzer so that the dark band remains in the center of the spec- trum, and then pass a current through the coil. We observe a motion of this dark band back and forth through the spectrum as the current is repeatedly reversed. For any given current its position is always the same, so that its motion may be calibrated by passing known currents through the coil. Have we not in this, found a weightless vibrator that is sure to move in unison with the currents, if the term is allowed ? Before passing on to the more practical side of the question, it may be asked, will this band move back and forth so that its dis- placement is approximately proportional to the current? The answer to this question lies so near at hand that your attention is invited to it for a moment. The rotation of the plane by quartz is approximately represented by the formula:— ‘p = Cs eſ?” The rotation by the current is represented by 6 F C2 & / X*. If both these rotations take place together, the resultant is merely the sum of the components, and x = 2 + 9 = (a, -e, , . (8) The position of the dark band depends upon the position of the analyzer. Let the analyzer be set at some convenient angle, a, with the position of complete darkness, and let it remain there. Then the wave-length or color where the dark band occurs for the quartz plate (being called Āo) is given by (7) above, and we have (Z = 63 # (9) The wave-length corresponding to this constant angle, a, when both quartz and current are used, is given by (8), and we have a = (es é + c, i)} (10) in which A is that wave-length corresponding to a certain current, l, and therefore i and 2 are co-ordinate variables. Equating the values of a, we have & e = * *-H & ! º, (11) 1894.] CREHORE ON RECORDING OURRENT CURVES. 599 This may be written --- • Go ?? . . . . X* = 3 to i + 2., (12) C3 & and in this form the relation between wave-length and current is seen to be represented by a parabola. In Fig. 3 are represented two sets of parabolas obtained from equation (12) by assuming that X, and e take in succession different values. When e = 2 mm. the set of parabolas marked I is obtained, and where e = 6 mm. set II is obtained. By giving 2 different values we merely vary the parameter of the parabola without changing the origin. It will be remembered that Å, represents that wave-length corres- 8000 –40 —'SO - 20 -10 0. +10 —#20 Amperes, i. FIG. 3. ponding to the positions of the dark band for no current. It is therefore the value of A when i is equal to zero, as appears from the equation independently. The axis of A is the vertical line to the right of the figure, upon which the letters A, B, etc., are written. These letters show the positions of the various Fraun- hofer lines, and one parabola is drawn for each line. Each parabola then corresponds to one setting of the analyzer and the dark band is found at these lines of the spectrum for zero cur- rent. The upper parabola is at the red end, and the lower at the blue end, of the spectrum. The axis of current is the base line of the diagram, and currents to the left of the vertical line are 600 CREHORE ON RECORDING CURRENT CURVES, [May 17, called negative, while those to the right are called positive. The axes of all the parabolas coincide with each other and with that of the current, and for a given quartz plate they all intersect this axis at the same point, so that taking different settings of the polarizer is equivalent to changing the parameter only of the parabola. The interpretation of these results may be put as follows: If we have a spectrum in which the wave-lengths are proportional to the distances along the spectrum (which is the case with Pro- fessor Rowland's arrangement of a concave grating), then the displacement of the dark band to one side or the other, due to the current, will be exactly according to the shape of these parabolas near the zero point; that is, near the vertical line lettered A, B, etc. Since it appears that each parabola at such a great distance from the origin is nearly a straight line, the dis- placement in such a spectrum will be nearly proportional to the Current. - A noticeable feature, easily revealed by the graphical construc- tion, is that in the red end of the spectrum, where the inclination of the parabola to the 7 axis is the greatest, the motion of the band will be the greatest for a given current. - Of course it is understood that this construction has to do with the relation between the wave length and the current, and not between the displacement and current, unless the wave-length and displacement are proportional. It does not apply, for instance, to the displacement in the spectrum of most prisms. In the prisms used, the red rays were so crowded together that the motion as observed was nearly the same in the red as in the blue. The width of the band, however, is for this reason narrower in the red than in the blue—a consideration of considerable practi- cal importance. --- DESCRIPTION OF SOME OF THE APPARATUs. The tube upon which the coil carrying the current was wound, was a glass tube 1.4 cm. internal, and 1.8 cm. external, diameter, and 70.15 cm. long. The tube was filled with carbon bisulphide, which was confined in the tube by means of two plane parallel plates of glass, each 1.3 cm. thick, fitted tightly upon the ground ends of the tube. Upon this tube was wound six layers of No. 18 double cotton copper magnet wire, occupying a length on the tube of 61.5 cm. The wire was wound so that 100 turns occu- 1894.] orkhore ow RECORDING OURRENT 00 RVES. 601 pied 12.7 cm. Thus the total number of turns, 2,900, is very large considering the size of wire. - - The light used was sunlight reflected from the mirror of the heliostat. The Nicol prisms are two fine specimens which were obtained by Dartmouth College at a time when larger specimens could be obtained than may now easily be found. The slit does not need to be very narrow. A width of a quarter to a half-millimeter will do better than a narrower one, because more light is admitted to the photographic plate, and in passing through so many different substances even sunlight is rendered comparatively feeble by the time it strikes the photographic plate. A further description of the apparatus is hardly deemed to be necessary, inasmuch as no claim is made to having obtained more than the most crude of first results, which may be the results ob- tained by apparatus arranged in a comparatively poor manner for the end sought. Yet the results obtained seem to be so promis- ing for the future, that the subject is presented to you at this early date in the experiment, in the hope that it may soon receive an impetus from other experimenters who have better facilities than those at my disposal, and thus become a fruitful source of extending our knowledge of instantaneous current flow in con- ductors. The objections which most naturally suggest themselves against this method of taking current curves are perhaps the following. The photographic plate must move so quickly that the time of exposure of any one part of the plate is extremely short. To meet this demand the most sensitive plates that can be made shonld be used. The width of the band with any given plate depends largely upon the time of exposure. Then, too, a plate is to be desired that will photograph toward the red end of the spectrum as well as in the blue. The band does not possess very sharp outlines, but gradually shades off from dark to light. These objections do not have so much weight, however, in cases where the general direction of the variation of the current is what is wanted, more than any exact measurement of its amount, and in the majority of cases this is really what is required, yet it cannot be said that in these preliminary experiments the band used was nearly as sharp as may be obtained. Another objection of a different nature that seems difficult to avoid is the fact that the coil, which is wound upon the tube, 602 CREHORE ON RECORDING CURRENT OUR VES. [May 17, must necessarily possess a small amount of self-induction. It may be said, however, that even though we are prohibited from measuring certain currents on account of this self-induction, we are always sure that we are measuring the exact current which is flowing through the coil. A MoRE ExACT ExPRESSION of THE RELATION BETwFEN THE WAVE-LENGTH AND VERDET’s CoNSTANT. The approximate relation between the wave-length and Verdet's constant used above was that Verdet's constant varied inversely as the square of the wave-length. It is considered of sufficient interest to inquire just how nearly this is an approximate formula. By reference to equation (2) it is evident that if we only knew the relation between the index of refraction and the wave-length, we might obtain the relation between the wave-length and Verdet's constant in terms of these two quantities alone and GOnstants. Such a relation is afforded by Briot's formula, which is a modi- fication and improvement upon the well-known formula of Cauchy. This is 1/n} = k X* + A + Bj X* + C/X* + . . . . , . (14) where n is the index of refraction corresponding to the wave- length 2, and k, A, B, etc., are constants for the given substance. Assuming that all terms beyond B/X* are negligible, we may differentiate with respect to Å and obtain the equation #. = m” (£ — k r). - (15) Upon eliminating B/X” between (14) and (15), we obtain ** = 1–2% ºr - A w. (16) Substituting in (2) the expression thus obtained, we have w = e n° (2 k + A/X”). (17) But by (14) - # nº = (AE A*-i- A + B/?”) ; (18) Hence t w = e (2 k + A/2") (k X* + A + B/2") (19) This formula represents to a high degree of accuracy the observed values of Verdet's constant for carbon bisulphide. It 1894.] CREHORE ON RECORDING OURRENT OUR WES. 603 probably would for any other substances, but carbon bisulphide is the only one to which it has been applied by me. The con- stants k, A, and B may be found by means of equation (14) and the observed values of the refractive index for known wave- lengths. The values used are those observed by Messrs. Gladstone and Dale. (See Glazebrook’s Physical Optics, page 243.) º Index of refraction - Index of refraction Line of spectrum. for carbon bisulphide. Line of spectrum. for carbon bisulphide. A 7621 1.614. E 527o 1.6465 B 687o 1.6207 F 4861 1.6584 C 63.63 I.6240 G 4308 1.6836 D 5893 I.6333 H 3969 1.7090 These values give curve I, in Fig. 4. The lines A, F, and 1. 6 9 .06 1 .0 C iſ B. | | | | 1.61 4000 - 5000 - 8000 Wave Lengths in tenth-meters A FIG. 4. H were selected and three simultaneous equations formed from (14), so that the resulting curve II should pass through these three observed points. The values * k = — 1.98 × 10-9, (20) A = .41384, (21) B = 1076250, (22) were obtained by the determinant solution of these three simul- taneous equations. The resulting black curve may not appear to coincide very closely with the red, but it must be remembered that the origin of coördinates is a long distance below the paper, 604 CREHORE ON RECORDING OURRENT GURVES. [May 17, and the apparent differences are but a very small fraction of the whole. The unit is the tenth meter for wave-lengths. Having these constants, they may now be substituted in (19) 3. 2k+42 J-12 x 1.98 x 16"-- –4.03 k 10' A H-. l 4000 6000 - * Wave Lengths in tenth-meters A. FIG. 5. and 6 determined from the observed values of Werdet's constant. These observed values are: Line of Spectrum. (%) Verdet's Constant for Carbon Bisulphide. (z) C 6563 c.o319.' D 5893 - o.o.415' E 527o o.os37' F 4861 o of 67' G 4308 o,0920' { The constant thus determined, where a minute is the unit of angle, gives G = 310243. (23) 1894.] 4. J) ISO/USSION. 605 Using these constants for equation (19), we obtain curve 1, in Fig. 5. The points marked X are observed values, and the cal- culated curve practically passes through them all. Curve II in this diagram represents the approximate law that Verdet's constant is inversely as the square of the wave-length, and the degree of the approximation may be observed. - - DISCUSSION. MR. STEINMETz:—I have listened to this important paper with a very great interest. As you remember, some years ago Dr. Fröhlich, of Germany, proposed a method of taking indicator cards of alternating currents. His method, however, had the serious defect of all former methods to employ moving parts. Now here, in this method, we see a beam of light, which has no inertia whatever, trace the picture of the alternating current, so that we can expect here to get a true picture of the alternating current wave or any other electric current, not by a series of complicated and tedious instantaneous readings, but with almost the same ease as a steam engine indicator card. This, I think, is a very important step in advance. For practical use, it is of great im- portance to get the values—the amplitude of oscillation of the black band in the spectrum, proportional to the intensity of the current, so that the photograph need not be reduced. The use of the glass prism gives the amplitude, in the red, larger than in the violet part of spectrum. However, this is not unavoidable in this method, because by replacing the glass prism by a refrac- tion grating, at the expense of a large amount of light, indeed, you can get proportionality between the current and the ampli- tude of the black band. So it is a question of the intensity of the picture against proportionality to the current. It is especially interesting to note from the parabolic equation, that is the dependence of the current on the amplitude of oscil- lations of the black band, that that part of the parabola which is within the range of the spectrum, is very nearly straight, that is to say, the motion of the black band in the spectrum is almost proportional to the intensity of currents. All this goes to make the tracing of the instrument the direct picture of the wave, and not merely a picture which has to be reduced to get the exact value. Though not so important for the physical laboratory, this is very important for the practical use of such an instrument. I think, therefore, that this method is exceedingly valuable, and will perhaps, give us one of the most important instruments of electrical engineering when worked out in detail, of the same usefulness as the steam engine indicator. PROF. ANTHONY:—I do not care to spend time, at this late hour, in the discussion of the paper. I merely want to say that this has been an extremely interesting paper to me, and I be- lieve that the ingenuity displayed in bringing out the results here 606 CREHORE ON RECORDING OURRENT OURVES [May 17, is something that we ought fully to recognize. I believe that this instrument will be a most important instrument in the investiga- tion of alternating currents. [The meeting then adjourned for the day.] The afternoon was devoted to a trip down the river, a visit being made to Cramps' shipyard. Gloucester, N. J. was next visited and after an excursion on the electric railway, and a visit to the power-house, a “planked-shad” dinner was served, through the courtesy of the Engineers and Manufacturers of Philadelphia, and under the management of the Sub-Committee on Entertainment. The party returned to Philadelphia by a special steamer up the Schuylkill river. A £ager £resented at the Eleventh General Meet- ing of the American Institute of Electrical Engineers, Philadelphia, May 18th, 1894, Presi- dent Houston in the Chair. RESONANCE ANALYSIS OF ALTERNATING AND POLY PHASE CURRENTS: BY M. I. PUPIN, PH. D. I. INTRODUCTION. The presence of upper harmonics in an alternating current wave is a fact which deserves careful consideration, both on ac- count of the purely scientific interest which is attached to it, and also on account of the technical bearing of electrical resonance upon the construction of conductors possessing appreciable dis- tributed capacity. That alternating current and electromotive force waves of a great variety of forms can be produced by properly designing the pole-pieces of the field magnet, and the iron core of the armature of an alternator, is a fact nearly as old as the discovery of electro-magnetic induction. Fully as old is also the know- ledge that a great variety of alternating current and electromotive force waves can be obtained by means of the induction of an intermittent current. - A careful investigation of these waves was first made more than forty years ago by Lenz' and Koosen,” who employed alternators with iron in the armature. They plotted these waves from the instantaneous values of current and electromotive force obtained by means of the now well-known revolving sliding contact. Em- ploying the same method of investigation Joubert” showed in 1880 that the electromotive force wave obtained from an eight pole Siemens alternator without iron in the armature is very nearly a pure sine wave. The method is now known as Jou- * 1: Pogg Ann. 76 p. 494, 1849;-92 p. 123, 1854. 2. Pºgg Ann. 87 p. 386, 1852. 1é Comptes Rendus, Vol. xci, p. 161, 1880 ; Ann. de l'ecole super. 10 p. 131, 1. - - 607 608 PUPIN ON RESONANOE ANAI, YSIS. , [May 18 bert's method of sliding contact. In 1888, Dr. L. Duncan' showed how successfully this method can be employed in the study of alternating current waves produced by commercial machines in actual operation. The same method was considerably elaborated by Professor H. J. Ryan” in an investigation of the action of transformers. The name, “indicator diagram,” has been ap- plied to wave curves of current and electromotive force obtained by Joubert's method, and very properly, I think, because they do very clearly indicaté the action of alternating current ap- paratus. The process of taking these indicator diagrams has been shortened very much by Dr. L. Duncan's four dynamometer method. º Our knowledge of the action of alternating current apparatus has been extended considerably by these indicator diagrams. For instance, we are now much more certain of the limitations which must be imposed upon the simple harmonic wave theory of alternating currents than we were a few years ago, and it looks very much as if progress in this direction, even more than in any other, meant progress towards a complete theory of the working of alternating current apparatus. Hence the desirability of as large a number of workers in this particular region of electrical research as possible. There is no doubt that a simpler method would increase this number: for though much must be said in favor of the sliding contact method of obtaining indicator diagrams, yet it must also be acknowledged that the method is a very laborious and unin- teresting process of investigation. A great many attempts have been made to devise some optical or some automatic method, but with little success. There is another reason why a new method of studying alternating current waves seems desirable. It is this: The method of sliding contact is not sufficiently sen- sitive to detect small deviations from a true sine wave, and con- sequently it is not capable of following up the causes of these deviations, when the effects seem to be absent. For instance, the primary current of a transformer can differ very much from a true sine form when the secondary circuit is open, but when a large current is flowing through an approximately non-self-inductive secondary circuit, then the primary can be made to differ inap- preciably from a true sine wave. The question arises now, 1. See article by Duncan, Hutchinson and Wilkes in the Electrical World, March, 1888. 2. TRANSACTIONS, vol. vii, p. 1, Jan., 1890. 1894.] PUPIN ON RESONANCE ANAI, YSIS, 609. what has become of these causes when the secondary carries a heavy load? & - This question is of deep scientific interest; it is also of con- siderable technical importance. For, if these causes are present at all loads, and only hidden by the principal wave, then, consider- ing that these hidden small causes can produce large effects when conditions favoring resonance arise, it is evident that they must be carefully watched and guarded against in the construction of long lines possessing distributed capacity. I do not think that indicator diagrams obtained by the method of sliding contact are capable of giving a definite answer to this important question. The method of analyzing alternating current waves by electrical resonance which I employed in the following investigation was suggested by me a year ago". It is the object of this paper to describe this method at some length, and to illustrate, by some of the more definite results so far obtained, the simplicity, sen- sitiveness and reliability of the method. I shall also point out that this method of resonance analysis works quite satisfactorily even in those cases alluded to above, where the sliding contact method would, in all probability, fail. II. DESCRIPTION OF THE METHOD. Consider the following arrangement of circuits:—A non-self- inductive resistance ab Fig. 1a is inserted in the circuit of an alternator A and the primary B of a transformer. In shunt with ab is a circuit, a, c, d, b, consisting of an inertia coil, o, of a large number of turns of copper wire of low resistance, about 10 ohms, but containing no iron, and a con- denser, d, divided into subdivisions ranging from .001 M. F. up. In shunt with the condenser, d, is an electrostatic voltmeter, e. The self-induction of the coil, c, can be varied by throwing a larger or smaller number of its sections into the circuit. The resistance can be varied by a rheostat, f. Suppose now that the self-induction of c is kept constant, and that the capacity of the condenser is gradually increased from zero up. Whenever a capacity has been reached which, with the self-induction of the circuit a, c, d, f b, a, produces resonance with one of the har- monics in the main circuit, then the resonant rise of potential will produce a large deflection in the voltmeter. In this manner all 1. M. I. Pupin, “Electrical Oscillations of Low Frequency and their Reso- nants, American Journal of Science, vol. xlv., p. 429, May, 1893, 3610 PUPIN ON RESONANOE ANALYSIS. [May 18, the harmonics which are present in the current of the main cir- cuit can be detected in the course of a few minutes. If the reso- nator circuit, a, c, d, f. b. is placed in shunt with the non- self-inductive circuit (this circuit is denoted in Fig. 1a by a line, beaded with asterisks and running from one pole of the alter- nator to the other) consisting of a bank of incandescent lamps, then the harmonics of the impressed electromotive force can be detected in the same manner. The ratio of the amplitudes of these harmonics to that of the fundamental can also be de- termined by this method, if desirable, provided the conditions of &-A i. f º e FIG. 1d. the experiment are properly arranged. For let the current in the main circuit be a = a, sin pt + as sin 3 pt + . . . . -- a, sin a pt + . . . then the drop between a and b can be represented by \ e = b, sin pt + ... + ba sin a pt, where b. = a, r, and * = ohmic resistance between a and b. Denoting now by L the self-induction of the resonator a c d.f b a. R the resistance of the resonator a c d ºf b a. O the capacity of the resonator a c d f b a, 1894.] PUPIN ON RESONANOME ANA I, YSIS. 611 then it can be easily shown that the current in the resonator will be * b 0. '->v.; 1 1) + iº * ŽTCT If, therefore, the capacity 0 is adjusted in such a way that— sin (a pt – p.). 1. a go-Z = 0, then the circuit will be in resonance with the harmonic of fre- quency a p, and if L is sufficiently large and IP sufficiently small (two conditions which are very easily fulfilled) then the current y is to within a small fraction of a per cent. given by ba. = — sin a pt $/ Aº p The amplitude of the potential difference in the condenser which is measured by the voltmeter e is given by P. = ****. In the same way we obtain for the fundamental frequency P = *# bi. Hence Pa ba 0%, — E 0 – F O. — “ P, bi Q1 This gives the ratio of the amplitude a, of the harmonic of frequency a p to that of the fundamental. Let a = 5, then, *= mºmsºm, sºme *= a . The voltmeter readings which give P, and P. magnify that ratio five times, in the case of the fifth harmonic, and it can be easily seen that a similar relation holds true for other harmonics. This is a very desirable feature of the method, considering that the amplitudes of the upper harmonics are generally small in com- parison to the amplitude of the fundamental. When quantitatively very accurate results are desired, then a low resistance, say one ohm, should be used for the section a b, 1. For further information see the authors's paper cited above, 612. PUPIN ON RESONANOE ANALYSIS. [May 18, and an electrometer capable of giving a large deflection for about ten volts. - The principal interest, however, in the study of the distortion of alternating current waves, is centered not so much in the exact ratio of the amplitudes of the harmonics to the amplitude of the fundamental wave, as it is in the causes producing these har- monics, and the conditions which modify the effects of these causes. Hence a quantitatively less accurate arrangement will do, provided that it is very sensitive, simple and easily manageable. Such an arrangement is given in Fig. 16. It differs from that given in Fig. 1a in the substitution of an air core transformer coil a’ bºfor the non-self-inductive resistance a b. The secondary of this coil forms a part of the resonator e’ FIG. 15. circuit. For every harmonic of the inducing current we shall have a harmonic electromotive force of the same frequency in the resonant circuit. By varying the capacity in the resonator and watching the voltmeter needle, we can tell, by the deflection of the needle, whenever we have reached the capacity which, with the self-induction of the resonator brings this circuit into resonance with one of the harmonics. A reference to Fig. 2 will explain this more clearly. - - In this figure the lower horizontal row of figures refers to the two-peaked curve, the upper row refers to the dotted flat-peaked curve. The vertical column denotes the voltmeter readings in volts. Consider now the two-peaked curve. It expresses the law of variation of the voltmeter readings when the capacity of the re- 1894.] PUPIN ON RESONANOF, ANAL. YSIS. 613 asonator circuit is varied from 0 to 2 microfarads, the self-induction being kept constant. The readings are recorded in Table I. TABLE I. Capacity in M. F. º Voltº. ºdiºs, .18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 .181 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 .182 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.5 .188 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 .184 . . . . . . . . . . . . . . . . . . . . . . . . . • e º 'º e e s = e º e º is sº e º º º 89 .185 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 .186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 .187 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 .188 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 .189 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 .190 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 .191 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 194 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 .198 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 .202 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Very low 1.65 ... . . . . . . . . . . - * tº º º te tº e º tº º is tº $ tº e & e º & & gº © tº gº tº gº tº e ºs 69 1.70 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 1.75 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 1.80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 1.808 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • * * * * * 146 1.817 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 1.897 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 1.976 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . (50 The voltmeter employed in all these experiments was a Sir William Thomson's multicellular voltmeter with a range from 60 to 240 volts. The curve was obtained from a 10 H. P. Fort Wayne eight pole alternator with smooth core armature feeding a 5 K. wi Stanley transformer (closed magnetic circuit), the secondary being open. It is seen that resonance took place at .190 M. F. and 1.8 M. F. The capacity of the inertia coil cº Fig. 1b, and of the volt- meter as gathered from all experimental data was about .011 M.F., so that the real capacities at which resonance took place were .201 M. F. and 1.81 M. F., that is, in a ratio to each other as 1:3°. It will be seen, however, that a very accurate knowledge of capac- ity is not required in the following experiments. The frequencies detected by the two-peaked curve, which I shall call the resonance diagram, were the fundamental and the first odd harmonic, that is, the harmonic of three times the fre- quency of the fundamental. The resonance diagram has, of course, as many peaks as there are frequencies in the inducing 614 PUPIN ON RESONANCE ANALYSIS. [May 18, current." The dotted curve (flat-peaked) in Fig 2 was plotted on an enlarged scale from the readings taken in detecting the first harmonic, represented by the sharp peak of the resonance dia- , rep y p p gram, and represents this peak spread out, so as to show how the various readings fit into a well defined and symmetrical curve such as required by theory. It also shows that a condenser of small sub-divisions must be employed in order to detect higher harmonics. But it should be observed that these higher har- monics can also be detected with coarser sub-divisions, provided the self-induction of the inertia coil is made small enough. 0. I 2 3 4. 5 6 7 8 9 10 11 12 13 14 15 16 17 187 19 20 - 1ö’Faradº arads FIG, 2. DESCRIPTION OF EXPERIMENTs. The resonance diagram obtained by the method of Fig. 15 gives the number of harmonics which are present in the indu- cing current. It does not give the exact value of the amplitudes of these harmonics. It would be somewhat premature to discuss the theory of the resonance diagram obtained by this arrange- 1. I have never detected an even harmonic in alternating current waves pro- duced by ordinary commercial alternating current apparatus, and conclude, therefore, that such harmonics do not exist there. In machines of perfectly symmetrical construction, even harmonics should of course not appear, asobserved Some time ago by Prof. Ayrton. Alternators with slotted armatures give waves in which all the odd harmonics up to the harmonic of nine times the frequency of the fundamental can be easily detected. As a rule the first odd harmonic is the strongest. - 1894.] . . . . PUPIN ON RESONAWCE ANALYSIS. 615 ment, and to show how the ratio of the amplitudes of the har- monics to that of the fundamental frequency of the inducing - current, that is the exact color of this current, could be calculated from the ratio of the height of the peaks in the resonance dia- gram. Suffice it, for the present, to mention only that the peaks of this diagram represent the amplitudes of the harmonics, mag- nified about proportionally to the square of the frequency. For instance, the resonance diagram in Fig. 2 tells us that the ampli- tude of the first odd harmonic in the inducing current is about one-ninth of the amplitude of the fundamental. The determi- FIG. 3. nation of the exact value of this ratio was not the object of the Jollowing eaſperiments. Their aim was to detect the presence of harmonics, to trace their origin and to study their variation with the variation of the load, and of other elements of the circuit on which these harmonies seem to depend. Preliminary Tests.-In order to form an estimate in how far the experimental data obtained by the arrangement of Fig. 15 agreed with the theory, the following tests were applied. a. Study of the damping effect of the dielectric in the con. * , denser, 616 PUPIN ON RESONANCE ANALYSIS. [May 18 Let L = self-induction of the resonator circuit. Let R = resistance of the resonator circuit. Let P = amplitude of the difference of potential in the con- denser when point of resonance has been reaehed. Let E = amplitude of impressed electromotive force in the resonance circuit. then according to theory p 1, P = Tº A. - Hence if the Æ is varied, P will vary also, but in such a way that P AE = constant. That is to say, if we vary the resistance of a resonant circuit, and tabulate the voltmeter deflection for every particular resist- ance, and then plot a curve taking the resistances for abscissae, and the voltmeter readings for ordinates we should, according to theory, obtain an equilateral hyperbola. Curves II and III, Fig. 3, were obtained that way, the frequency employed was that of the 10 H. P. alternator, that is, 130 periods per second. -- TABLE II. - * Resistance in Voltmeter Reading with Voltmeter Reading with Theoretical Value of hms. a Mica Condenser. a Paraffin Condenser. Voltmeter Reading. 38 183 17o 225.6 48 I55 I48 178.9 53 144 I37 I61.8 58 I34 128 147.8 63 I25 I2O 136 68 118. II3 126 78 IO 5 IOI I IO 88 Q4 9I 97.4. 98 85 83 87.5 1 ob 78 76 79.4 I 18 72.5 7o -- 72.6 128 67 65 65.5 138 62 6o 6o The experimental data from which they were plotted are given in Table II. Curve II was plotted from voltmeter readings ob- tained with a mica condenser. Curve III represents the corres- ponding readings obtained with a paraffin condenser and given in the third column of Table II. Curve I represents the theoretical curve, which would have been obtained if the law of variation of the voltmeter readings with the resistance had been the same through- out as it was at low readings. On account of the damping effect due to dielectric viscosity in the condenser, a deviation from the above 1894.]" PUPEN. ON RESOAAAWCH* AAVAI, YSIS, 61? mentioned hyperbolic relation was, of course, expected, but it was quite a pleasant surprise to find a perfect regularity of these deviations. . These curves indicate a rapid increase in the dielec- tric damping with the voltage, and also the superiority of mica to paraffin, especially at higher voltages. They also suggest that at low voltages and at frequencies over a hundred periods per second, this difference between the two substances is inappreciable. Similarly the damping effect of the magnetic viscosity of iron is small at low magnetizations, such, for instance, as would be pro- duced by a telephonic current, and at frequencies which are well within the range of higher telephonic frequencies, say 750 periods per second. It is well to point out here that electrical resonance C 3 a tº º Jº) offers a very convenient method for studying the viscosity of iron and of dielectrics, Similar curves and similar results were obtained with higher har- monics. This experimental test shows, therefore, that the relative values of the amplitudes of the harmonics to that of the funda- mental frequencies are not seriously distorted by the dielectric damping of the condensers, especially when one operates with moderate voltages as was the case in the following experiments. (b). Second Test of the Resonator Indications.—This test is represented graphically by diagram Fig. 4. Two transformers o and D had their secondaries connected in series. The primary of the air-core transformer E formed a part of their circuit. The 618 PUPIN ON RESONANOF ANAL.YSIS. [May 18, : secondary of this transformer, was a part of the resonator F. The transformer C, a Stanley 5 K. w. (closed magnetic circuit) was fed by the 10 H. P. alternator mentioned above (180-P. P. s.), the transformer D, of induction coil type with a cylindrical core, of fine iron wire, was fed by a 1. H. P. alternator with slotted arma-. w ture (278 P. P. s.). Both alternators were run simultaneously at . full excitation. First, the primary circuit of the large alternator was broken so that the current in the circuit C D E was due to the action of the small machine alone. The resonator detected a . resonant rise of 240 volts at capacity .407 M. F., and another of 150 volts at capacity .044 M. F. These were evidently the funda- mental and the first odd harmonic. Then the circuit of the small machine was broken and that of the large machine closed, so that the current in the resonator was due to the action of the large machine alone. The resonator detected a resonant rise of 220 volts at capacity 1.78 M. F. This corresponded to the fundamen- tal frequency (130 P. P. s.) of the large machines. Finally both circuits were closed, so that the current in the resonator was due to the simultaneous action of the two machines. The same fesonant rises of potential were detected by the resonator and at the same capacities as before, in perfect agreement with theory. This experiment afforded another opportunity of testing the theory which underlies this resonance method of studying the wave curves of current and electromotive force. It is this: If two or more electromotive forces of different frequencies are im, pressed upon the resonator circuit and their resonant rises of po- tential are determined for a given resistance in this circuit, then, according to theory, the ratio of these rises should remain the same for all other resistances within the limits within which the . periodicity of the circuit is practically independent of the ohmic resistance. Accordingly, the resistance of the resonator, F., Fig. 4, was varied gradually from 100 to 250 ohms, and the resonant rises of potential produced by the fundamental frequencies of the , two machines (130 and 278, P. P. s.) were carefully determined for each particular resistance. The ratio of these rises remained constant to within five per cent., but the deviations were now in one direction and now in the other, and they were undoubtedly due to the variation in the excitation, and the speed of the small machine, both of which depended on the potential of the electric mains of the College plant, which, of course, could not be kept very constant for so long an interval of time as is necessary for : this experiment, which was about 15 minutes. 1894.j PUPIN ON RESONANCE ANAL YSIS. . . 619 | It is interesting to observe here that three air-core transformers ; like E, with three resonators like F, when placed in the circuit, C DE, and each resonator tuned to one of the frequencies of the circuit represent an exact, analogy of Helmholtz's well-known arrangement of accoustical resonators which he employed in the analysis of vowel sounds. The variety of exceedingly instructive experiments which one can perform with such a multiplex reso-, nance circuit is very large and most interesting. It has long formed my favorite subject for an extended series of experiments whose results, however, are beyond the limits of this paper. In all experiments of this kind the voltmeter, which is attached to each resonator, performs the same office as König’s sensitive manometric flames in the well-known experiments on acoustical resonance, and, it should be noted here, that they are just as sen- sitive. In fact, in electrical resonance experiments one is con- tinually impressed with the striking resemblance between reso- nance phenomena in electricity on one hand and those in sound on the other. This resemblance is a trusty and suggestive guide. - (6). Sympathetic Resonance.—Now, an acoustical resonator tuned to a certain pitch will respond feebly, to be sure, but dis- tinctly, to a simple sound of a frequency which is an exact sub- multiple of its own frequency. A similar phenomenon might exist in electrical resonance, though ordinary alternating current . theory does not lead us to expect anything of the kind. But some experimental results, which will be given below, led me to suspect that a sort of sympathetic resonance might exist, that is to , say, a simple harmonic current might perhaps be capable of pro- ducing by induction a resonant rise of potential in a resonator, which is tuned to a frequency which is an exact multiple of the frequency of the inducing current. If that were the case, then a resonant rise of potential in a resonator would not necesarily mean that an upper harmonic in the inducing current has been detected, and, therefore, the indications of an electric resonator might be misleading. To investigate this point the air-core transformer E with the resonator F, Fig. 4, was connected to the secondary of . the 5 K. W. transformer and the current gradually increased by varying gradually an electrolyte resistance. The feeding machine was the above-mentioned 10 H. P. alternator, with smooth core armature. Here I must disturb somewhat the logical sequence of 62ö’ - PUPIN ON RESONājyº AyALYSIS. [May 18; this paper by stating that the secondary current, produced by this machine and transformer; when flowing through a non-self-induc- tive resistance in the external circuit or through a coil of small self-inductance possessing no iron core, showed under ordinary tests no distortion worth mentioning. But when the secondary current was increased, and with it the electromotive force induced. in the resonator, the harmonics began to appear more and more distinctly. When the secondary current was 11.5 amperes and the electromotive force induced in the resonator was 133 volts, the resonant rise of potential was as follows: For the harmonic of: 3 times the frequency of the fundamental the potential rose from 133 to 155 volts. 5 & 4 { % & 4 “ & 6 {{ 133 to 139 , ( & 7 & & { % & 4 4 & & & & 4 faintly. 9 6 & { { & & & & § 6 ( & not perceptibly. ... The resonant rise with the fundamental frequency would have been with the initial potential of 133 volts several thousand volts, so that the resonant rises obtained for the upper harmonics were extremely small in comparison. The conclusion is, therefore, that if such a thing as sympathetic resonance really exists, it is so feeble at small initial voltages in the resonator as to escape de- tection. It could, therefore, in no way modify the results recorded in this paper, since these were obtained almost invari- ably with resonant rises of potential which started from very small initial voltage. These preliminary experimental tests demonstrate clearly that a resonator of the type given in Fig 1b is quite capable of detect- ing all the frequencies that may exist in an alternating current wave, that its indications are in good agreement with the theory as far as the fundamental frequency is concerned. and that it gives: us a fairly approximate idea of the relative strength of the har- monics. Additional evidences proving the correctness of its indications will be found among the results of the following ex- periments. IV. Location of THE ORIGIN OF UPPER HARMONICs. A. EXPERIMENTS WITH ALTERNATOR OF SMOOTH CORE ARMATURE. 1st Series.—The first set of experiments in this direction was . . performed with the 10 H. P. Fort Wayne 8-pole alternator with smooth core armature, and the Stanley 5 K. witransformer (closed magnetic circuit). The secondary circuit was open and a 1891. PvPry, ow. RESONAworia MALysis. 624. Cardew voltmeter indicated the secondary voltage. The current which excited the field of the alternator was gradually increased. The secondary voltage measured the strength of this excitation. The air-core transformer with the resonator was inserted into the primary circuit as indicated in Fig. 1b. The resonant rise of po- tential, recorded by the multicellular voltmeter e', was carefully determined at every excitation for the fundamental frequency and the first odd harmonic. Higher harmonics were present, but very faint. The results are given in Table IV. and plotted in Fig. 5. The initial voltage in the resonant circuit was small, just perceptible in the multicellular voltmeter. TABLE IV. Resonant Rise in Volts Due | Resonant Rise in Volts Due Secondary Voltage. to the Fundamental. to the F1 st Odd Harmonic. 43 I22 58 48 I3o 65 53.5 I36 72 56 138 73 62 146 80.5 66.75 I 52 86 75 16.5 94 83 17o IO4 88 T75 I IO 97 185 I 17 | IO4 I95 128.5 ... ; The curves in Fig. 5 were plotted from this table by taking the readings of the first column for the abscissae and the cor- responding readings of the second and third columns for ordi- nates. The upper curve corresponds to the fundamental and the lower curve to the harmonic. The two curves are two straight Jºnes parallel to each other, which means that the fundamental and the harmonic increase at the same rate from nearly one third excitation to full excitation of the alternator. This result I did not expect, but its correctness was verified beyond all reason- able doubt. - The same series of experiments was extended to lower excita- tions of the alternator, but, since I had no low reading alternating current voltmeter, the excitation was measured by measuring the exciting field current. This current was 10 amperes at full excita- tion and the series of experiments extended down to 1.5 amperes, hence to nearly one-seventh of the full excitation. To bring the readings of the resonant rises of potential within the scale of the multicellular voltmeter at low-excitations the number of turns in 622 PºſN tºyzºtºrs. [May 18 : the air-core transformer was suitably increased. Within all these , limits of excitation, both the fundamental, and the harmonic in- creased at the same rate and proportionally to the excitation. This curious relation I mistrusted at first and suspected the existence of something like sympathetic resonance mentioned above. But all experimental evidence is in favor of its correctness. . *Aſh. AVA.J. sº fº ſº. AsſW 2 180 P. 21 130 120 110 1001 Pº 90 23 ------- 80 Pº 2^ 70 J.T Pº Volts in Secºndary * 45 50 55 60 65 70 75 80 85 90 95 100 105. FIG. 5. 2d. Series.—To determine whether the presence of the har-, monic was due to the action of the transformer or to that of the alternator, the transformer was disconnected, and two series of in- candescent lamps, connected in parallel, were substituted in its place. Each series consisted of 13 lamps, each about 24 c. P. The . resonator, with its air-core transformer, remained in circuit as be-, 1894.] PUPIN, ON RESONAWCF, ANAL, PSIS, 623 fore. First one series of lamps was placed in circuit. . The rise due to the fundamental was stronger than in the preceding ex- periments, but that due to the harmonic was exceedingly faint. . When both series of lamps were thrown in, the harmonic ap- peared a trifle stonger, but still very weak. Hence the inference that the harmonic was due almost exclusively to the action of the transformer. It should be observed here that the alternator armature, though well laminated, runs fairly hot in a short time, hence it must be the seat of a decidedly strong hysteretic process. On the other hand, the transformer does not heat nearly as much as the alternator armature, and yet its action produces the harmonic. This certainly seems to speak strongly against the view that harmonics are due to hysteresis. Other evidences against this view will be given below. 3d Series.—A series of experiments with open magnetic circuit transformers of induction coil type in place of the lamps showed the harmonic much stronger than the lamps did, but weaker than the experiments with the transformer of closed magnetic circuit. Although I have not succeeded in ob- taining accurate numerical comparisons between the two types of transformers in this respect, one thing is certain, and that is, closed magnetic circuit transformers distort under similar condi- tions the primary current considerably more than transformers with open magnetic circuits; on the other hand, in the first case . the distortion is confined almost entirely to the primary circuit, when the secondary is closed by a non-self-inductive resistance, whereas in the second case it is felt in the secondary circuit also, though considerably less than in the primary. The general conclusion of this group of experiments may be summed up as follows: I. A ferric self-inductance in circuit with an alternator which gives a simple harmonic electromotive force,"distorts the current by introduciug higher odd harmonics, principaliy the harmonic of three times the frequency of the fundamental. II. This harmonic (and in all probability all other harmonies) increase at the same rate as the fundamental when the excitation increases, the rate of increase being up to 4000 c. G. s. lines of force per sq. cm. proportional to the intensity of magnetic induc- tion in the core of the ferric inductance. 62&N PUPIN ON RESONANUE AWAL.YSIS, [May 18; III. When this ferric induction is a transformer, then the dis- tortion appears, but not seriously, in the induced secondary electromotive force; if the transformer has an open magnetic cir- cuit, it does not appear there to any extent worth considering if the magnetic circuit is a closed one. IV. A practically simple harmonic electromotive force is pro- duced by alternators with smooth core armatures, even if the ma- chine is worked at considerable degrees of magnetization of the armature COre. B. EXPERIMENTS WITH ALTERNATOR OF SI.OTTED CORE ARMATURE; TYPE. The machine employed in these experiments was the 1 H. P. alternator mentioned above. It is a 16-pole machine; its arma- ture is a Crocker-Wheeler 1 H. P. motor armature wound for 500 volts. It gives at full excitation, and the speed at which I usu- ally ran it in these experiments about 1,500 volts. The trans- former connected with it was of induction coil type with a cylin- drical iron core made up of very carefully insulated thin iron wire. The same series of experiments were performed as under group A. The first series in this group gave exactly the same results as the corresponding series in group A. The excitation varied from one-seventh of the full to the full excitation ; the amplitude of the fundamental and the first odd harmonic” varied at the same rate during the whole interval, so that a parallel pair of straight lines like those in Fig. 5 could be plotted in this case also. The second series resulted in the conclusion that the har- monic was very strong and due in a very large measure to the action of the armature, and not to that of the transformer as in the other case, although the transformer, also, contributed a dis- tinct but small measure to the strength of the harmonic. The third series showed that the harmonic appears in the secondary of an open magnetic circuit transformer, although considerably weaker, but does not appear there to any appreciable extent when the magnetic circuit is a closed one. To the four conclusions given at the end of the series of experi- 1. A more complete description of this machine and the transformer will be found in Amer. Jour. of Science, June, 1893, p. 510, etc. Owing to the accident which somewhat impaired the insulation of the armature the machine was run last year at low excitation, and hence low voltage, although the speed was then considerably higher. 2 The second odd harmonic, that is the harmonic whose frequency is five times that of the fundamental, was there but weak. 1894.] PUPIN ON RESONAWOE AWAT, PSIS, 625. ments under group A we may, therefore, add the following addi- tional conclusions:— a' W. An alternator with slotted core armature produces a com- plex harmonic electromotive force in which the upper harmonic of three times the frequency of the fundamental is generally by far the strongest. VI. The amplitudes of the fundamental and the harmonic increase at the same rate with the increase of excitation ; this rate is proportional to the excitation, that is to say proportional to the magnetization of the armature. VII. A ferric inductance in circuit with a slotted iron core armature introduces no new harmonics. It seems to strengthen those already existing in the electromotive force, that is odd har- monics, especially the first odd harmonic. The same conclusions will evidently hold true for alternators of ordinary types, that is alternators whose armature is made up of coils wound on iron cores which are bolted to a cylindrical iron drum common to all of them. W. EFFECT of THE LOAD UPON THE HARMONICs. It is a well-known fact that the distortion of the primary cur- rent disappears gradually with the increase of the secondary load, that is when the external part of the secondary circuit is a non- self-inductive resistance. The question arises now, what becomes of the harmonics which produce the distortion in the primary when the secondary current increases? The following experi- ments seem to answer this question definitely. The arrangement of circuits was that given in Fig. 1 b. The secondary circuit of the large 5 K. W. transformer contained an electrolyte resistance and the secondary current was measured by means of a Siemens electro-dynamometer. For every particu- lar value of the secondary current the resonant rises of potential due to the harmonic and the fundamental were carefully deter- mined by means of the multicellular voltmeter. Table W. con- tains the observations relating to the harmonic of three times the frequency of the fundamental; Table VI. relates to the funda- mental (130 P. P. s.). The apparatus employed was the large alternator and the 5 K. w. transformer. Table VI. requires explanation. When the secondary current was over 3.6 amperes the resonant rise of the fundamental was too high for the voltmeter employed, and also too risky for the {{26 PUPIN ON RESONANCR 4NALYSIS. [May 18, { TABLE V. Secondary Current in Resonant Rise of the Har- mperes. monic in Volts. O 65 3.6 4 65 4.8 66 6.9 68 8.5 | 7o II.5 | 76 I 5.7 | 85 2O | 97 28 I2O 4O I62.5 56 2O2 TABLE VI. Resonant Rise of the Auxiliary Resistance Resonant Rise of the S y - - seº Cºlent Fundamental in Volts 1n the Resonator Fundamental in Volts mperes. (observed). in Ohms, (calculated). O 8o O 8o 36 24O O 24O 5.o I 22 5C. 5O3 6.7 150 5o 616 9 O 2OO 5O 825 I7.3 2OO IOO I,450 27.o I 35 2 IO 2,613 44.O I 55 4IO 4, 127 $6.o 6o 5 IO 5, IOO condenser. An auxiliary resistance had to be introduced into the resonator to bring the resonant rise down to the limits of the voltmeter. These auxiliary resistances are given in the third column. The readings that would have been obtained without these auxiliary resistances were then calculated, roughly, as fol- lows:—According to theory which was verified by experiments described in the beginning of this paper, the resonant rise multi- plied by the resistance of the resonator gives a constant product for all resistances as long as the period of the resonator is prac- tically independent of these resistances. The resistance of the resonator coils was 16 ohms. Hence if, for instance, a denote the rise which would have been obtained without auxiliary resist- ance in the resonator when the secondary current was 5 amperes, then since with an auxiliary resistance of 50 ohms the resonant rise was 122 volts we have with a rough approximation. f a — 122 × 66 16 In this manner the figures of the fourth column were obtained. They are only very rough approximations, but still they give a = 503 volts. 1894.] . PUPIN ON RESONANCE ANAL Y SIS. 627 ... very fair idea of the ratio of the fundamental to the upper har- monic at various loads. Curves I and II, Fig. 6 were plotted from these data. The secondary amperes were taken for the abscissae and the corresponding resonant rises in volts for the ordinates. Curve III represents Curve II plotted on a different scale for the 32 34 36 38 40 42 44 2 4 6 8 10 12 14 16 18 20 22 24, 26 28 |FIG. 6. volts of the resonant rise of potential. These are given in the right hand vertical column of the diagram. This curve gives a better picture of the gradual apparent increase of the harmonic. An inspection of I and II shows clearly how much more rapidly the fundamental increases than the harmonic. In reality the increase 628 PUPIN ON RESONANCE ANAI, YSIS, [May 18, is even more rapid; for according to Table V it appears as if the strength of the harmonic increased with the secondary current, only much less rapidly than the fundamental. For instance, at open secondary the voltmeter indicated 65 volts for the resonant rise of the fundamental; and at 56 amperes in the secondary this rise was indicated by 202 volts. But it must be noted that in the first case the voltmeter needle went from practically zero at no resonance, to 62 when resonance was reached; whereas in the second case it went from 135 volts at no resonance to 202 volts when resonance was reached, so that the real resonant rise was practically the same in both cases. Similarly for all other loads in the secondary. It follows, therefore, that if the harmonic increased at all with the increase of the load, this increase was much smaller than appears at first sight from the data of Table W. The more import unt conclusion, however, which follows from this eageriment, and which I wish to point out more par- ticularly, is that the harmonic which manifests itself in the dis- tortion of the primary current when there is no load in the see- ondary is present at all loads, if not stronger, then certainly with about the same strength. At full load this harmonic could not possibly be detected by Joubert's method of sliding contact; it is so eacceedingly small ºn comparison to the fundamental. This persistence of harmonics at all loads even when com- pletely hidden by the fundamental wave holds true also when their origin can be traced to the action of the armature of the generator as in the case of the machine with slotted iron core armature. In all cases their strength seems to depend upon the mean intensity of magnetization of the magnetic circuits to ſwhich #hey owe their origin and upon nothing else. Another somewhat more difficult but very instructive way of proving the persistence of the harmonics is represented in Fig. 7. In circuit with the primary of the large machine and transformer described above are two equal air-core trans- formers, a b and a' bº. By means of a double switch either one of the two can be made a part of the resonating circuit, c, d, f. A number of condensers, D, in series, are counected across primary circuit as indicated. The two air-core transformers, a b, and a' b', will be equivalent when the resonator voltmeter, e, gives the same indications, no matter which one of the two trans- formers be connected to the resonator. This balanced arrangement having been obtained, the balance will be disturbed as soon as 1894.] PUPIN ON RESONANOE ANALYSIS. 629. the condenser, D, is plugged in, and it will be disturbed in agreat variety of ways, according to the capacity plugged in. But when the transformer, B, is of closed magnetic circuit type, then the resonator indications remain practically the same as long as the resonator is switched on the air-core transformer aſ bº. no matter what capacity is plugged in the condenser, D. When the resonator is switched on the air-core transformer, a b, then its indications will be different for every particular capacity in D. FIG. 7. In fact the circuit A, a, b, D, A, can be treated as an entirely sepa- rate circuit from the circuit A, a', b’, B, A. This statement needs practically no modification in order to cover that case also in which the self-inductance of the prim- ary of B is diminished by putting a non-self-inductive load on the secondary. This utter disagreement between theory and experi- ment deserves a closer discussion, but since its connection with the subject of this paper is only an indirect one I prefer to reserve it for some other time. That which has a direct bearing upon the present discussion is the method which the above men- tioned relation offers for observing the variation of the harmonics. 630 PUPIN ON RESONANCE ANALYSIS. [May 18, with the load without the disturbing inductive effect of the large primary current. It is this: Connect the air-core transformer a b (and with it the resonator,) in series with the condenser. Add to this series an auxiliary coil 6 (no iron core). By the combination, thus obtained, bridge the primary circuit, so that in place of the simple condenser bridge D given in Fig. 7 there will be a bridge consisting of condenser D, the air-core transformer a b and the auxiliary coil c. The office of the auxiliary coil will be explained presently. The secondary C being open, tune the circuit consisting of the alternator armature, the primary conductors up to the bridge, and the bridge, to any one of the harmonics. The tuning is done by means of varying the capacity of the condenser and the self-inductance of the auxiliary coil. Then close the secondary circuit by means of an electrolyte resistance and vary the second- ary current. It will be found that the harmonic diminishes only slightly with the increase of the secondary load. As an example I give the following: The circuit just mentioned was tuned to the harmonic of five times the frequency of the fundamental, that is 650 P. P. s. At no load the resonator indicated a rise of 108 volts, at full load the rise was 94 volts. But this drop, small as it was, might have been caused by armature reaction. Whatever the ultimate meaning of the appearance and the per- sistance of the odd harmonics in an alternating current wave may be, I am not quite prepared to state with any high degree of con- fidence. One thing is certain, and that is that they are present at all loads with almost undiminished strength. Their presence is hidden by the fundamental wave at heavy loads, but when con- ditions favoring resonance with any one of them arise they will certainly come out and do all the mischief they can to the insula- tion. The self-induction of a motor or that of a closed magnetic circuit transformer has practically no bearing upon the conditions of their resonance. These conditions depend in such circuits solely upon the self-induction of the alternator on the one hand, and the self-induction and static capacity of the line on the other. According to the experiments just described, the resonant current is confined entirely to the alternator and the line, the di-electric forming a part of its circuit. These observations will be modified in the case of transformers with open magnetic circuits and their equivalents, that is, closed magnetic circuits possessing considerable magnetic leakage, especially when the conditions of the line favor resonance with the fundamental frequency, this frequency being t 1894.] PUPIN ON RESONA. WCE AWAL. YSIS. 631 low; such magnetic circuits possess much less magnetic sluggish- mess and can influence considerably the conditions of resonance with a low frequency. VI.-DISTORTION OF THE SECONDARY CURRENT. It was pointed out that the superposition of harmonics upon the fundamental wave was confined to the primary circuit when the secondary is closed by a non-self-inductive resistance, that is, if the transformer is of closed magnetic circuit type. With an open magnetic circuit transformer, the deviation of the primary current wave from the simple harmonic form, due to action of the generator or the transformer or both, is felt more or less in the secondary current also. If, however, the secondary is closed by a ferric self-inductance, then odd harmonics will appear in this circuit also in both types of transformers. In fact, the secondary circuit should now, as far as the harmonics are con- cerned, be considered as a separate circuit, in which the second- ary coil of the transformer and the ferric inductance in the secondary circuit play the same part as the armature of the alter- nator and the transformer play in the primary circuit. The series of experiments which related to the origin and growth of harmonics in the secondary circuit was exactly the same as the one described above, by means of which the so-called distortion of the primary current was studied. The results were the same. The presence of harmonics is due to the action of the ferric inductance; their strength increases proportionally to the intensity of magnetization of the iron in the ferric induc- tance. They seem to be entirely independent of hysteresis, that is, if by hysteresis the process be understood by means of which most of the heat is generated in a very finely laminated, well in- sulated and well amnealed iron core, when such a core is sub- jected to rapid reversals of magnetism. I shall describe briefly an experiment bearing upon this point The secondary circuit of the five K. w. transformer was closed by an electrolyte resist- ance, and a short cylindrical coil having about 120 turns coarse copper wire. A short cylindrical core made up of very fine (No. 26 B. and S.), and well annealed iron wire could be inserted into this coil. The core was 40 cm. high and 5 cm. in diameter. The wires were fairly wellinsulated from each other. A layer of fine copper wire surrounding this coil formed part of the reson- ator circuit. First, the secondary current was passed through 682 PUPIN ON RESONANOF, ANAI, YSIS. [May 18, the coil before the iron core was inserted. The resonator could , detect no harmonic worth mentioning even when the current was increased almost to full load. But as soon as the iron core was introduced the odd harmonics appeared, especially the third harmonic ; its strength increased proportionally to the current. Placing now another similar iron core on the top of the first, and adjusting it in such a way that it allowed a small rocking motion . the two cores could be set into violent vibration by the induc- tive action of the current which gave a very loud note corres- ponding in pitch to the frequency of the alternator. The vibration could be stopped by pressing the top core against the lower core and against the table. The vibration produced no ap- preciable difference in the strength of the harmonic; if anything it seemed to make it stronger. This experiment seems to me to render the theory, which ascribes the origin of harmonics to the hysteretic action of iron, completely untenable. I do not think that the proper time has arrived yet for the for- mulation of a physical theory which will give a complete account of the peculiar behavior of iron, by means of which it superposes odd harmonics upon the wave of a simple harmonic current. The view which irresistibly suggests itself to my mind is simply this: Upper harmonics will be generated whenever more or less abrupt changes of the magnetic state in any part of the magnetic field through which an alternating current flows occur. A slotted core armature or an armature made up of coils with iron cores distributed over a drum common to all of them will introduce such abrupt changes. An alternating current motor, especially when it is not of a smooth core armature type, will also cause abrupt changes of magnetism and hence cause strong deviations of the feeding current from the simple harmonic form. But if this view be correct, then every complete cycle of magnetization to which iron is subjected when under the inductive action of a simple harmonic current must be accompanied by some abrupt changes in magnetism, and that, too, whether the mean magnetic intensity of the cycle be large or small. A great many things may be suggested which could account for such cyclic abrupt changes. One thing is certain and that is, that hysteresis, as commonly understood, will not account for them; for these peculiar abrupt cyclic changes, if they really exist and are the cause of harmonics, are not affected by mechanical vibrations by which, as is well known, all hysteretic effects are influenced very much. But ,1894.] PUPIN ON RESONANCE ANALYSIS, 633 whatever the real theory underlying these upper harmonics may be, the bare fact which the engineers have to face is: There is no cure against harmonics as long as the cºrcuits contain iron. Hence construct your lines in such a way that conditions favor- &ng resonance with the frequency of the fundamental or with one of its odd upper harmonics will seldom occur, and whenever they do occur the resonant rise of potential should not be capa- ble of producing any damage. Avoid slotted armatures and armatures with projecting pole-pieces and keep the magnetization down as much as possible. VII. FLUCTUATIONs of THE ROTARY FIELD. Before closing this paper I will describe briefly the applica- tion of the resonance method of analysis to the study of the in- tensity fluctuations of a rotary magnetic field. The investiga- tion was carried out by two students of the Electrical Department of Columbia College, at my suggestion, and will be published in the near future. The method, briefly stated, is this: A suita- ble number of turns of wire are subjected to the induction of a rotary magnetic field. These turns form part of a resonator. Whatever fluctuations there be in intensity of the rotary field they will be periodic, their period bearing a perfectly definite ratio to the periodicity of the current which produces the rotary field. For instance, in a three-phase combination of alternating currents, the intensity of the rotary field will, according to theory, show six maxima and six minima during each complete revolution, the maxima differing from the minima by about 14 per cent. A circuit, subjected to the inductive action of such a field should have a periodic electromotive force induced in it whose frequency will be either three or six times the fre- quency of the fundamental, according to the shape of the curve of fluctuations. Similarly in a rotary magnetic field produced by a two-phase combination of alternating currents. If such elec- tromotive forces were induced the resonator would detect them, and from the resonant rise of potential the extent of the fluctua- tions producing these electromotive forces could be estimated. No electromotive forces of this type were detected in either a tri-phase or a two-phase combination. Hence the inference: Rotary magnetic fields produced by reasonably well constructed machines are not accompanied by fluctuations in their intensity. In conclusion I wish to thank my friend, Professor H. A. 634 PUPIN ON RESONA.N.C.E. A. NAL YSIS. [May 18, , Storrs of the University of Vermont, who during his whole stay at my laboratory this year was always anxious to aid me in my work in a most ready and disinterested way. His most efficient assistance was of the greatest value to me. 1894.] CORRESPONDEWOE. 635 SMOOTH AND Tooth ED Core ARMATUREs. [Reply to Discussion, by A. D. Adams, see page 549 et seq.] The statement that “In order to allow for the waste armature- field due to this core-leakage, the exciting power has to be in- creased in about the same degree as the lessening of the mag- netic resistance of the air-gap would otherwise decrease it” seems to be entirely at variance with the known facts. There is some leakage from tooth to tooth, the amount vary- ing with the type, but a toothed armature can readily be so de- signed that with given number of armature inductors and given field magnet, the ampere-turns required on field magnet for given speed, are much less than when a smooth core armature is used; in fact the question usually is, how far the ampere-turns on field may be reduced, and excessive sparking avoided. It is no doubt possible to build generators with either toothed or smooth core armatures, that will not spark under extreme changes of load with the brushes in one position, but it is not hard to find many of both types in operation which do not meet this condition. The .45-inch air-gap from iron to iron, cited as an example of what may be done in a smooth core armature machine of about 30 K. wi would not of course remain the same in similar machines of several hundred K. W. capacity. As the total energy used in field winding of even smooth core armature machines of 100 K. W., or more capacity is usually not more than 1% per cent. it is hardly possible that a “very much higher efficiency” can be obtained by the use of toothed armatures in such machines. The main question for which answer was sought in my paper is whether the same results can be obtained in bipolar machines, more cheaply with toothed or smooth core armatures. To those engaged in the manufacture of these machines as a money mak- ing enterprise, the answer to this question is much more than a mere matter of taste. The toothed armature for the same capac- ity must cost more, for while about the same amount of copper, and only a little more iron are required, the additional labor to form the teeth, and cost of tools for same is a considerable item. Unless the toothed amature can effect some saving in other parts of these machines to offset its own greater cost, the smooth core will have the preference. In machines under 10 K. w., at about 1500 revolutions per min- ute, the air space required by winding and clearance is usually greater than that necessary for sparkless operation, and the sav- ing in metal of field core and winding will probably more than Offset the greater cost of toothed armatures in these machines. In bipolar dynamos of 20 K, w, or more capacity, at 1200 to 1500 revolutions per minute, the air space required for winding and clearance is usually less than that necessary for sparkless opera- tion. Good builders in this country and Europe are in the main $636 CORRESPONDENCE, using smooth core armatures in medium and large. bipolar dyna- mos and we can hardly expect to see this practice reversed unless some means not now in use is provided to produce sparkless com- mutation. Troy, N. Y., Oct. 3d, 1894. º [The proceedings of the Philadelphia meeting will be continued in the No- vember issue.] THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS. New York, September 19, 1894. The 89th meeting of the Institute was held this date at 12 West 31st Street, and was called to order at 8:20 P. M. by Vice- President Crocker. THE CHAIRMAN (Vice-President Crocker):—The first business is the reading of the names of the associate members elected by the Council this afternoon. The Secretary read the list, as follows:– Name. Address. Endorsed by. BAKER, GEO. O., Local Superintendent, General J. C. Bennett. Electric Co., 44 Broad St. ; resi- D. McF. Moore. dence, 450 W. 23rd St., New W. G. Whitmore. York City. BERG, ERNST JULIUS, Engineer, General Electric Co.; C. P. Steinmetz. residence, 540 Liberty St., H. M. Hobart. Schenectady, N. Y. H. G. Reist. BLANCHARD, CHARLEs M., 714 Girard Building, Philadel- E. J. Houston. hia, Pa.; residence, 4565 E. G. Willyoung. ulaski Ave., Germantown, Pa. A. E. Kennelly. BoILEAU, WILLARD E. Superintendent and Electrician, A. M. Schoen. rush Electric Light & Power A. E. Worswick. Co., Columbus, Ga. Ralph W. Pope. BRADY, E. D. A., . Consulting and Constructing En-H. Ward Leonard. ineer ; Lock P. O. Box 132, F. A. Pattison. aterbury, Conn. Ralph W. Pope. BRowN, EDWARD D., District Inspector, American Tele- F. A. Pickernell. hone and Telegraph Co., 18 G. A. Hamilton. 8.n. St., New York City: A. N. Mansfield. residence, 75 Hicks St., Brook- lyn, N. Y. CHASE, HARVEY STUART, Electrical and Mechanical Engi- H.Ward Leonard. neer, 136 Liberty St., New A. S. Wance. York City. Ralph W. Pope. CoMPAGNIE, GEORGE Boune, Chief Engineer, Antwerp Hydro- A. G. Inrig. Electric Supply Co., Ralph W. Pope. Antwerp, Belgium. G. Succo Albanese. CREws, J. W., Manager, Southern Bell Tele- C. E. McCluer. phone and Telegraph;Co., Tele- M. B. Leonard. phone Exchange, Norfolk, Va. E. W. Trafford. 637 638 ASSOCIATE MEMBERS HI, ECTED. [Sept. 19, CUSHING, HARRY CookE, JR., Electrical Inspector, Boston Caryl D. Haskins. Board of Fire Underwriters, 55 Geo. F. Curtiss. Kilby St. ; residence, 259 Bea- S. Dana Greene. con St., Boston, Mass. DARLINGTON, FREDERIC W., Consulting Electrical and Me- C. A. Bragg. º chanical Engineer, 5'3 Girard Iſouis Duncan. Building, Philadelphia, Pa. E. G. Willyoung. DELANCEY, DARRAGH, Manager of Works, Eastman Francis R. Hart. Kodak Co., Rochester, N. Y. J. P. B. Fiske. Leonard C. Wason. DRYSUALE, WILLIAM A., Consulting Electrical Engineer, E. J. Houston. Hale Building, Philadelphia, W. J. Hammer. Pa.; residence, Overbrook, Pa. A. E. Kennelly. DYER, FRANCIS MARON, Associate Engineer with Chas, L. F. Broadnox. Eidlitz, 10 W. 23rd St.; resi- L. Stieringer. dence, 160 W. 129th St., New J. C. Hatzel. York City. w EDEN, MoRTON EDWARD, Electrical Inspector, the Under- E. Braddell. writers’ Association of the L. Knowles Perot. Middle Department, Philadel- T. C. Martin. phia, Pa.; residence, 83 Fourth Ave., Pittsburg, Pa. BGLIN, WM. C. L., Chief of Electrical Department, W. D. Marks. Edison Electric Light Co., C. W. Pike. 909 Walnut St.; residence, 4230 E. G. Willyoung. Chester Ave., Philadelphia, Pa. EIDLITZ, CHAs. D., 10 W. 23rd St. ; residence, 1125 F. Broadnox. Madison Ave., New York L. Stieringer. City. J. C. Hatzel. FLLICOTT, EDWARD B., Superintendent of Construction, E. M. Barton. 'estern Electric Co., 4438 C. D. Crandall. Ellis Ave., Chicago, Ill. T. D. Ilockwood. ERICKSON, F. W.M., Flectrical Engineer, with C. L. E. G. Waters. Livingston, 713 Penn Ave. ; S. B. Paine. residence, 5812 Parker St., R. W. Pope. Pittsburg, Ta. FULLER, FRANK G., Salesman with W. R. Brixey, G. M. Phelps. 203 Broadway, New York City; F. R. Colvin, residence, Meriden, Conn. W. R. Brixey. GERSON, LOUIS JAY, President, The Gerson Elec- C. W. Pike. trical Co., 4303 Walnut St., Carl Hering. Philadelphia, Pa. E. J. Houston. GRISSINGER, ELWOOD ARISTIDEs, Electrical Engineer, E. J. Houston. Mechanicsburg, Pa. A. E. Kennelly. W. E. Geyer. HoDIERITH, HERMAN, Washington, D. C. T. C. Martin. Jos. Wetzler. R. W. Pope. HUBLEY, G. WILBUR, £lectrical Engineer, Louisville C. F. Scott, , Electric Light Co., L. B. Stillwell, ouisville, Ky. Alex. J. Wurts. HUNT, ARTHUR L., Electrician, Utica State Hospital, T. C. Martin. Utica, N. Y. W. W. Nicholson. R. W. Pope. KAMMEYER, CARLE., Western Manager the Electrical Charles Wirt. Hºngineer, 1439 Monadnock B. J. Arnold. Block, Chicago, Ill. Geo. B. Shaw. LA ROCHE, FRED. A., President and Manager, La Roche E. G. Willyoung, 4. Electric Works, American and E. J. Houston. º Diamond Sts. : residence, 2235 A. F. Kennelly. N, 16th St., Philadelphia, Pa. 1894.] 639 ° ASSOCIATE MEMBERS ELECTED. Alex. J. Wurts. C. F. Scott. B. Shallenberger. Fred. Bedell. H. J. Ryan. E. L. Nichols F. F. Barbour, C. L. Cory. J. A. Lighthipe. T. C. Martin. Gilbert Wilkes. Jos. Wetzler. R. B. Owens. E. G. Willyoung E. J. Houston, G. A. Hamilton G. M. Phelps. R. W. Pope. W. E. Geyer G. A. Hamilton. H. A. Reed R. H. Pierce, B. J. Arnold. Edw. Caldwell. J. A. Cabot- T. J Creaghead A. I. Searles. C. P. Steinmetz F. R. Upton. LYMAN, CHESTER Wolcott, Manager, Herkimer Paper Co., LYMAN, JAMES, MEDINA, FRANK P., MYERs, L. E., PoTTER, HENRY NoFL, PRICE, CHAs. W.. REED, HARRY D., RICHARDSON, ROBERT E., RoPERTs, WM. H., ROLLER, John E., ROWLAND, ARTHUR John, SHIELDs, W. J., SLADE, ARTHUR J., SMITH, FRANK E., STEVENS, J. FRANKLIN, TAIT, FRANK M., WARLEY, THOMAS W., Total, 44. Herkimer, N. Y. O Student in Electrical, Engineer- ing at Cornell University, 39 Eddy St., Ithaca, N. Y.; resi- dence. Middlefield, Conn. Electrician, Pacific Postal Tele- graph Co., 534 Market St., San Francisco, Cal. Secretary and Treasurer. Elec- trical Installation Co., Monad- nock Building, Chicago, Ill. Electrician, Laboratory of West- inghouse Electric and Mfg. Co., Pittsburg, Pa. Editor the Electrical Review, 13 Park Row, New York City: residence, 223 Garfield Place. Brooklyn, N. Y. Electrician, Bishop Gutta Percha Co., 420 E. 25th St., N.Y. City: residence, 88 N. 9th St.. New- ark, N. J. Electrical Engineer. Pierce & Richardson. 3827 Forest Ave., Chicago, Ill. Assistant Engineer, South Cov- ington and Cincinnati Street Railway Co., 15 Harrison St., Cincinnati, O. Lieut. U. S. N., in charge of In- spection and Installation, U. S. Navy Yard, New York: resi-F. Tischendoerfer dence, 515 Clinton Ave., Brook- lyn, N. Y. Professor of Electrical Engineer- ing, Drexel Institute ; resi- dence, 4007 Powelton Ave., Philadelphia, Pa. Professor of Electrical Engineer- ing, University of Vermont, Burlington, Vt. Student Electrical Fngineering, Columbia College ; residence. 62 E. 66th St., N. Y. City. Chief Electrician, Edison Light and Power Co., 229 Stevenson St., San Francisco, Cal. Secretary and Treasurer, La Roche Electric Works, American and IDiamond Sts. ; residence, 1419 Walnut St., Philadelphia, Pa. Superintendent CatasauqualElec- tric Light and Power Co., 731 3rd St., Catasauqua, Pa. Electrician, The Okonite Co., Tutd., Passaic, N. J. II. S Hering E. J. Houston Louis Duncan E. L. Nichols Fredk. Bedell. C. P. Matthews F. B. Crocker. M. I. Pupin. W. H. Freedman F. F. Barbour. C. L. Cory. J. A. Lighthipe, E. G. Willyoung. E. J. Houston. A. E. Kennelly. R. W. Pope. H. A. Foster. J. W. Lattig G. A. Hamilton, G. W. Gardanier Jas, Hamblet, \ , 640 SPERRY ON THE ELECTRIO BRAKE. [Sept. 19, THE CHAIRMAN:-The time is somewhat limited, and we will pass directly to the reading of the papers. The first paper is entitled “A Study of the Residual &: of Condensers and their Dependence upon Temperature,” by Frederick Bedell and Carl Kinsley. This paper is to be read by title only, in the ab- isence of the authors, as it has been printed and in the hands of the members for some time before the meeting. The paper is now open for discussion, if there are many remarks to be made up- on it. The subject is rather in the line of pure physics, but is nevertheless of considerable practical importance nowadays as condensers are coming more and more into use in connection with alternating current apparatus. However, if there is no dis- cussion, we j pass to the next paper, which is entitled “The Electric Brake in Practice,” by Elmer A. Sperry, of Cleveland, Ohio, whom I now take pleasure in introducing to you. MR. SPERRY:-In connection with this paper, I wish to thank the Excelsior Electric Company, who have kindly loaned us the series-wound motor before you, and also the Weston Electrical Instrument Company, who have furnished us with these two beautiful illuminated ammeters by means of which we are all able to so easily observe the current furnished the motor in accelerat- ing, and also the current produced in the brake circuit by the transformed motor after it is converted into a dynamo. 1894.] DISCUSSION 641: DISCUSSION. [See page 495, August and September issue.] THE CHAIRMAN –I consider Mr. Sperry’s paper very impor- tant, as all electrical engineers must feel it has been a reproach to our profession, that electric cars have killed so many people in the last few years. In fact, such accidents have been much more fatal than those due to the direct effect of the electric current; that is to say, the number of persons killed by electric current, strictly speaking, is probably far less than those killed by electric cars which were not stopped in time. It seems to me that anything in the direction of alleviating this trouble is welcome, and something which seems to be so effective as this, is particularly welcome. Discussion of the paper is now in order. MR. Joseph WETZLER:-I would like to ask Mr. Sperry if he has noticed any additional wear on the teeth of the gear, due to the action of the brake? In ordinary braking by hand, when the current is shut off the wear practically ceases. But with the motor acting as a generator, the teeth would again come into action, the wear, of course, being on the opposite flanks of the gear teeth. MR. SPERRY:-In response to the gentleman’s question I would say that we have noticed no wear whatever, and the rea- son for it is this, and it is made quite apparent in Table III. If you will notice, in this, table the currents mentioned are really the currents used in the braking application, and they hardly more than consume the stored up energy of the moving masses of the motor. You can see that the watts delivered to the brake are very small indeed. The ordinary braking current employed to de-energize both the car and the trailer is only about fourteen amperes; it is hardly anything, you see, compared with the cur- rent used to accelerate the same car and trailer, which would probably require 40 or 50 amperes. MR. C. S. BRADLEy:-Mr. President, Mr. Sperry has brought this out so well that I do not dare to criticize it, but I would like to ask him a question that occurs to me, and it is this: Does the motorman ever get rattled and throw that switch clear over and throw off his brake, and bring in the motor current, and then throw it back again, and in that movement undertaking to stop the car, when really he is throwing the motor on ? MR. SPERRY-Is your question this: Does the motorman throw the lever off a little way, and then throw it on again without go- ing clear over, thus 3 ſillustrating]. My experience is that an ex- cited motorman will try to throw the lever over too hard and through the end of the controller box if he could. Mr. BRADLEY:—But a motorman, in the event of a great emergency and under excitement, is sometimes apt to make two motions, one forward and one backward in succession. **. x; 642 SPERRY ON THE ELECTRIC BRAKE. [Sept. 19, MR. SPERRY:-I should think it possible, but I never knew it to occur, however. MR. W. J. HAMMER —I would like to ask Mr. Sperry a ques- tion. Mr. Sperry speaks of the braking effect of the Foucault currents on the generator. I would iike to ask him what his estimate is of the percentage which is due to the Foucault cur- rent. A little over two years and a half ago, when I was in England, I had the pleasure of witnessing some experiments made by Mr. Henry E. Walter, a member of the INSTITUTE, and formerly Chief Electrician of the Edison Machine Works, in Goerck Street, and afterwards at Schenectady. He made a brake in which he employed nothing but the Foucault currents gene- rated, and in the experiments referred to, magnets were sus- pended underneath the cars, placed close to the rail, and by passing a heavy current through them he produced Foucault currents which he proposed to use solely for the braking effect on the car. That seems somewhat in line with the experiments which Mr. Sperry has been making, and, as he refers to the importance of it, I would like to ask him about what percentage of the braking effect he considers is due to that in his brake. These experiments of Mr. Walter's that I saw were only preliminary, and were con- ducted on a small scale. MR. SPERRY:-I would ask the gentleman, in the experiments referred to, was the air-gap open There was no contact. MR. HAMMER:—No sir. MR. SPERRY:-Of course the resistance there is something enormous. We have found that the reduction of the resistance at the air-gap is a great point in fully utilizing these induction cur- rents. Table III, in the paper, will give the exact percentage of any point on the curve that you may want. Taken at the knee, which occurs at 16 to 18 amperes, the pull due to magnetic ad- hesion is 160, and the pull actually obtained from both was 2,584. You can readily see that the Foucault currents here were by all manner of means the greater component. Just what per- centage I have not figured. THE SECRETARY :—I would like to inquire of Mr. Sperry as to the reception which such a radical change in the form of brake-shoe has received at the hands of the railroad men who have been using the ordinary brake-shoe for so many ears? y MR. SPERRY:-I could better answer that inquiry by referring you to our sales department. The reception of it at the hands of engineers, wherever they have been found, has been very enthusi- astic ; but as to the average railroad purchasing agent, he looks upon it as a brake-shoe that is liable to cost more than the ordin- ary brake-shoe, and he is a little afraid of it on that account, los- ing sight of the saving in wheels which is from two to three fold. The reception of the brake at the hands of the motormen has been very enthusiastic. There has, however, been one ex- 1894.] * A) ISO/USSION. 643 ception. A motorman by the name of Wm. Kerslake, thought it was a dangerous thing, because if they put this kind of a brake on all the cars the company would be hiring women to run them. It must of course be remembered that it takes the place of two brake-shoes and a lot of brake mechanism. MR. Joseph SACHs:—I would like to ask Mr. Sperry some- thing in reference to Table III. I notice in looking through that table that the effects obtained from magnetic adhesion, or attraction of the brake-shoe to the magnet is but a small part of the entire retarding effect. It would seem to be possible to en- tirely brake the car by means of a non-magnetic armature, and simply use the currents generated therein to brake with. Ap- parently the greatest retardation is due to the brake magnet and shoe, acting as a dynamo. It would seem from your experi- ments that the friction due to magnetic attraction could be dis- regarded. MR. SPERRY:-I should say that such a thing would be per- fectly possible. Suppose these two circles were upon the two sides of the core, and suppose that was a non-magnetic material, where would you get your lines, to commence with ? You will be obliged to have enormous current to get any circulation, and of course it is the lines of force that do the business after all. The air-gap there would be so great that it would be putting a coil of wire down against a magnet and expecting a heavy flux. Of course there would be hardly any appreciable magnetism. But as to the question, given the flux, and of course the retardation would certainly be there, as has been shown. MR. MAX OSTERBERG :—I would like to add one, to the ad- vantages pointed out by the speaker which seems of rather strik- ing commercial value. The authorities in a great many cities limit the maximum speed of the cars in the business districts to eight miles per hour, as with a higher speed sudden stops in cases of emergency become impossible. It would not be long be- fore the maximum limit would be raised, if we could convince those entrusted with framing the laws that with an electric brak- ing system, cars running at ten miles an hour can be stopped quicker than at present running at eight. There are about 2,600 cars running in New York, and if every car can run ten instead of eight miles, that is 25 per cent. faster, then 20 per cent. or 520 of the total number of cars can be done away with. Count- ing the wages of motorman and conductor at $5.00 per day, it amounts to $2,600.00 a day, or $955,000.00, pretty nearly one million dollars per year, which the car companies in New York City alone would save. MR. SACHs:–The point I wanted to bring out is in regard to the wear of the gears, as Mr. Wetzler asked before. I notice that the actual braking energy, supplied by the motor, is very Small. The brake acts like a separately-excited dynamo, the ex- citing current being furnished by the motor. 644 SPERR Y ON THE ELECTRIC BRAKH). [Sept. 19, The braking effect of the motor through the gears, when act- ing as a dynamo, is very small, compared with the braking energy of the brake magnet and shoe, acting as a dynamo. I believe I am right in that supposition. - Mr. BRADLEY :—Mr. President; this magnet seems to be something that I never have heard of before. I have often though of such a magnet. I would like to ask Mr. Sperry exactly how the winding runs; where is the coil located and where are the terminals? % MR. SPERRY :-The coil is first wound in a large hoop, then folded back upon itself and made to surround the crescent- shaped core. The recess is contracted at the face, the coil is secured in place by a plastic material surrounding same, the upper portion of the slot being filled with metal forming a smooth metallic surface. The terminals are brought to the surface in the form of flexible wires one of which is usually again reimbedded. wº MR. Robert MoA. LLoyD:—Mr. Sperry has given us this evening the result of an able research, and º us some ingen- ious devices; but, Mr. President, they do not satisfy me that the brake problem is solved, and for three principal reasons. First, it seems to me that this residual magnetism does not offer any security while holding a car on a steep gradient. Second, Mr. Sperry has said that this apparatus is much less liable to disorder than the familiar mechanical brake, but it is not clear to me why electrical devices should be any more free from fault than me- chanical devices, and so I do not see why this brake should be more perfect than a windlass brake. There may be some trou- ble in the switch box, or some difficulty in the motor itself, or a brush might be injured so that there would be no exciting cur- rent in the magnet. Then, in the third place, when you stop the wheels you have not necessarily stopped the car, and a great many of the accidents which occur in our cities are because the tracks are covered with a soapy kind of mud that will let a car slide along fifty feet. It is true, as Mr. Sperry has said, that most brakes are not capable of locking the wheels, but even if the wheels are locked on such a rail as we have in many of our cities, a car will slide a considerable distance, leaving grade out of account. So that in order to help ourselves, we may have to pay more attention to the track, and to the wheels themselves; — a turned steel tire is of course better for traction purposes than a chilled wheel. Then we ought to have both a mechanical and an electrical brake on a car, because in going down a hill if any- thing should happen to such a brake as this, you would be lost, and the same would be true also of a mechanical brake. It seems to me that pressure might be applied to these disks by a windlass, or some other mechanical contrivance, and make the brake just as efficient as if it were held by magnetism. On the other hand, I would like to say in answer to one of the previous 1894.] DISCUSSION. 645 speakers, that I do not think it would be practicable to use a com- bination of that sort as a generator, besides if you are going to do that, you might as well as well use the armature of the dynamo or the motor as a brake, and brake through the gears. Of course, that presents a great many difficulties, and it is not a good way of braking a car, the gears, however, not being the greatest source of difficulty. Then I would like to say that an improvement might be made in putting the disks on the armature shafts where there is gearing. I have tried some of these disk brakes and think this is by far the best one I have ever seen, and I believe Mr. Sperry will work it out to much greater perfection. MR. SACHs:—I would like to answer the previous speaker in regard to using the motor and braking the cars by means of the gears. I think that is just the point that has been tried at var- ious times, and the point that Mr. Wetzler brought out. I think if a car were braked by means of simply short-circuiting the motor, or using it as a dynamo and retarding the car through the teeth of the gear, that in a very short time you would have no gears. I think, therefore, the principle that Mr. Sperry has brought out is a much superior one. If the retarding effect of a current in a magnetic field is used, it is certainly better to obtain this effect as Mr. Sperry does, than by the motor itself through the gears. I think that the experience with the electric motor, used as a braking dynamo, has not been very successful and I believe one of the principal reasons has been that the wear and tear upon the gears has been so great that your gears would not last. MR. FRANKLAND JANNUs :—Mr. President; I have understood all through the paper of Mr. Sperry that his device was intended to bring a car to a stop, and there it ended. I supposed that he intended to have a mechanical brake in addition to this. For example, if a long hill is to be traversed, the electric brake will stop the car, but then of course the motorman will want to use his hand-brake in order to hold the car. Is not that the idea 2 If there is any way of using this device to let the car down, I think a little explanation of that would be very inter- esting. . SPERRY:-Mr. Lloyd mentioned tracks covered with a soapy kind of mud and the wheels of the car sliding along fifty feet, etc. I would like to call attention to the fact, that in all large cities where these conditions are likely to exist, the railway companies usually use sand to give the wheels better adhesion and this incidentally helps on the brakes. For instance, to-day, when the rainfall has been constant for twelve hours, I have no doubt, but that the Broadway cable road near us, has used a num- ber of tons of sand. Now of course their cars are propelled without traction of the wheels in any sense, still they use sand for the purpose of making their $º effective. This is a remedy commonly adopted for slimy rails, and without it there 646 SPERIRY ON TELE BLECTRIC BRAKE. [Sept. 19, are conditions of track where no brakes would be of service. The ordinary hand-brake may be used as a duplicate brake apparatus if required. I have, however, yet to see the first man who will wear himself out on the hand-brake, when he can brake the car by simply pushing the lever and allowing electricity to do his work. As to the certainty of its acting, as I said in my paper, I do not see how anything can be more certain; every time you apply the current you necessarily test its capacity for the next brake application. In the thousands of miles per day that this brake is now running in this country, I do not know of a single failure. If a car .# not run, it should be put in order, but if it runs, it brakes. As to coming down hills, that is doubtless a point that I have not made clear. The brake will not make a full stop unless you want to stop. We are operating on a long and steep hill (a mile and a quarter, I think) in Waterbury, Connecti- cut, not far from New York City, and if anyone is sufficiently interested in its operation he may go up there and ride all day up and down the hill, and he will see that it performs its work well. The point that I have not made clear, I believe [illustrating with the apparatus, and one which you can readily understand, is that I can hold the amperage in the brake circuit anywhere I choose by simply manipulating the lever thus. When I apply the brake I will now cause it to hold the amperes at some given place, and that means that the car is retarded at a certain rate or pace. [Il- lustrating]. Now you see I hold it right there. MR. JANNUs:—Suppose the car has come to a full stop on the hill, what then Ž MR. SPERRY:—As I said in the paper, the residual magnetism producing current, will hold the car for a time as you can see, and perhaps you did see the last time; this is very much more marked on a large motor than on this one. . [Illustrating.]. Of j the hand-brake is on the car if you wish to hold it inde- nitely. MR. E. A. MERRILL :-I would like to ask as to one point. About two weeks ago I was in an Eastern city where there are a number of grades. They were running two motor cars, pulling three trailers all in one train. Near the top of an eight per cent. grade the fuse blew on one of the motor cars, and the other motor car was not able to hold the train, which started back down hill. Now I would like to ask Mr. Sperry what would be the action of the electric brake in a case like that ? MR. SPERRY:-The electric brakes work equally well after the fuse has blown. The blowing of the fuse in the case cited would not have made any difference whatever with the electric brake. MR. MERRILL :-In the case I refer to, they caught the train and held it by the ordinary hand-brake. This was an eight per cent. grade, running up to nine per cent. at the top. There were three trailers attached to two motor cars, the two motor cars act- 1894.] 1) ISOUSSION. 647 ing in conjunction. My question is, what would have been the result if they had had your electric brakes and found that they were useless to hold the train } Mr. BRADLEY :—The motion of the cars in itself applies this brake. - MR. MERRILL :-My point is this. This electric brake will undoubtedly stop the train, but how are you going to hold the train on a grade like that after you have stopped it & - - MR. SPERRY:-That depends on how long you wish to stop, and has been before explained. - MR. MERRILL :-Also, can that brake be used on an ordinary emergency stop? There is a great difference between the emer- gency stop and the ordinary stop. In an ordinary stop it is of reat advantage to have the adhesion increased as the speed ecreases; that is, to have the brake pressure decrease. In an emergency stop it is very necessary for that adhesion to re- main constant or to increase. Now with the electric brake the stop is very gradual; the retardation is practically uniform. With the hand-brake or with the air-brake you can hold the brakes set, and the stop becomes relatively more rapid as the speed decreases. MR. SPERRY:-In reply I would say that it is in emergency ser- vice that the full beauty and effectiveness of the electric brake is brought out. By its use the car can be brought almost to rest before the motorman can get the slack out of his hand-brake chain. There is nothing more instantaneous than the electric brake. There is no appreciable time lost. You see, the motor- man puts it on instantly, and there is no time lost in winding up the slack chain as in a hand-brake as stated. MR. SACHS:—I should like to ask another question: What would happen if the motorman suddenly stopped his car on a down grade, stopping the wheels, so that the motor generated no more current, would not the retardation cease and the car start again : I would like to know whether the hand-brake would not then have to be applied, or whether the electric brake would take care of itself? - - MR. SPERRY:-Such a condition cannot exist. If the wheel stops, very little or no current is then circulating in the brake circuit and the wheels start again to roll and the generator to produce the braking current. MR. SACHs:–Under the above condition, if the speed is very low, perhaps the motor would not generate current enough to energize the brake sufficiently, and the car would continue mov- ing down grade slowly. R. SPERRY:-It is º automatic. It will generate and stop itself at very low speed, hardly moving. MR. SACHs:—Is it not possible for the wiel, to skid along for a few feet? 648 SPERRY ON THE ELHOTRIO BRAKE. [Sept. 19, MR. SPERRY:—No sir. MR. SACHS:—Then I understand you to say that you cannot hold the car on a down grade with your electric-brake alone. MR. SPERRY:-Oh, yes, we can. I illustrated that a few mo- ments ago. THE CHAIRMAN –I think that this point has been pretty well discussed, and the hour is quite late. But if there are any fur- ther remarks on some new point that has not yet been brought out, we should be glad to hear them. - MR. MERRILL :-I would like to ask one more question. There are a great many statistics showing the space within which a car can be stopped with various brakes. I would like to ask Mr. Sperry if he has any statistics of that sort by which his system can be compared with other systems in use. MR. SPERRY:-The Westinghouse air-brake people from their latest tests, give data showing that they only utilized about four- teen per cent. of the available adhesion of the rail, whereas we utilize it nearly up to the limit. I judge from this that with a given speed we could stop in say less than one-fourth of the distance that they require, or did require in the tests named. THE CHAIRMAN –If there are no further remarks, a motion to adjourn will be in order. [On motion the meeting then adjourned.] CoMMUNICATIONS RECEIVED AFTER ADJourn MENT. MR. E. A. MERRILL :-It is to be regretted that Mr. Sperry has made no tests to determine in what distances cars can be brought to a stand-still under given conditions of weight, speed and track, and especially for emergency stops, for this would, in the minds of practical men, go far in determining the merits of the system as compared with other methods. Also that we have no definite information as to its ability to control cars on steep grades, as this question is one of the first to arise wherever grades occur. Ithink Mr. Sperry has failed to make proper allow- ances, in his comparisons with the Westinghouse tests, for the two principal factors of weight and speed. In stopping the car, a certain amount of energy must be dissipated, and it is evident that there is a limiting rate per ton weight, which cannot be ex- ceeded without ſºil. the safety of the car and passengers; it is quite possible not only to reach but to exceed this rate with the Westinghouse air-brake for any speed we meet in street rail- road practice; therefore, speed for speed and weight for weight an electric car cannot safely be stopped in a less distance. The present limit for an 800-ton train from 30 miles per hour, is about 325 feet on an emergency application; with a correspond- ing rate of energy dissipation per ton weight, an allowance of one second for shutting off the current and applying the brakes. The distance required for bringing an 8-ton electric car to a full stop. 1894]. - CORRESPONDENCE. 649 from an initial speed of 12 miles per hour is 39 feet, or a little less than one-eighth the former distance; such a comparison, however, is manifestly unfair, for the 800-ton train can also be stopped in 39 feet under similar conditions, and the 8-ton, elec- tric car will require 377 feet for a full stop, from an initial speed of 30 miles per hour; if the rate of energy destruction were greater, of course this distance would be less. MR. SPERRY:-Having noted the above communication, I would add that the tests mentioned in connection with emer- gency service are given in the general statement found on top of page 498. The limiting rate of energy dissipation does nºt seem to trouble railway managers very much for strictly emergency purposes, and certainly cannot be more severe than reversing the motor under full speed, which is almost a universal practice in cases of the most urgent necessity. The statement that electric cars cannot be safely stopped in less distance than ordinary rail- way cars I have found not to be true, and probably for the rea- son that the strain is not required to be transmitted through the swiveling bolt, or bolster of the truck high above the wheel con- tact upon the rail, which has been found to be the first place to give way in emergency stopping in railway service. On the street car the masses are more resiliently supported, especially on the four-wheel car, where the stripping of the car body from the truck is a far more difficult matter than with the swiveling truck. I have found in practice that an emergency stop with the elec- tric brake can be made under the conditions and within practi- cally the distances named in the paper. The easing off of the curve of retardation at both ends, making it an o. G. curve rather than a straight line at a declining angle gives by far the easiest stop. This curve I have found is the one naturally produced by the electric brake, and is probably the condition which yields the sensation of a cushioned stop. MR. W. E. HARRINGTON:—I think without peradventure of a doubt that the paper as read by Mr. Sperry is one that covers a subject vital to the interests of every electric railway manager. The question of the proper braking of a car should really be viewed from an emergency standpoint, and further, the form or method of braking employed, should be such that it be always in use and not known as an emergency brake' The present method of reversing a motor in case of an emergency is absurd, and usu- ally results in opening the magnetic circuit-breaker at the power station controlling the particular division the car may be on, or breaking gears and probably springing shafts. The above results are so usual, that particular instructions are given to motormen never to reverse, except in cases of extreme emergency, as, for instance, where life is in danger. The recent and established principles of electric railway engineering, which now make it necessary to place, magnetic cut-outs on the feeders leading out from the switchboard of our power stations, has rendered it abso- 650 SPERRY ON THE ELECTRIC BRAKE.. [Sept. 19, lutely necessary to have other methods of stopping our cars with- out depending on the power station for so doing. An accident occurred recently at York, Pa., where a life was lost, simply be- cause the magnetic cut-outs opened at the power station when the motor circuit was reversed. I mention this case particularly as it had the rather peculiar effect on the local management of their considering the advisability of going back to the unreliable and station-destroying fuse-wire of ancient history. The facts are so numerous and so convincing that the braking of a car should be self-contained and entirely independent of the power station that it may be considered axiomatic. The above position is further emphasized when we consider the fact that in the next two years it will be as common to see magnetic cut-outs on our cars, as it is at present to see such devices in our power stations. I think that the plan and method as employed by Mr. Sperry are correct and practicable, and after a few minor details not insur- mountable, are overcome, or rather remedied, the system will be commercially successful. MR. Joseph SACHs :—There is one point in reference to the form of electric brake, described by Mr. Sperry, which would appear to be more or less of an objection under certain condi- tions; that is the fact that it is impossible to completely stop the car for any length of time on a down grade by simply using the electric brake as herein described. During the discussion at the meeting of the INSTITUTE I attempted to bring out this point, but it appears to me from the answers made by Mr. Sperry to my Questions, that I was not properly understood. I assumed a con- dition where an obstruction made it necessary for the motorman to stop his car instantly and hold it on a down grade, but I could not see how this could be accomplished with the form of brake described. It is true that the car can be brought to a stop by the arrangement Mr. Sperry describes, but I can see no way in which it can be held on a down grade without the use of some addi- tional device. After the car has been brought to a stop by changing the motor into a dynamo, and throwing it across the brake magnet, the retardation of the brake will also be stopped, as no more current will then be generated by the motor. %. à, natural consequence, therefore, the car will start again and stop, start again, and stop, and so on until it gets to the bottom of the grade, or, perhaps, after the first stop, will run down the grade at perhaps such speed as to prevent enough current being gen- erated by the motor to effect sufficient retardation in the brake to hold it. It would seem therefore, to me, that in case of an accident under the conditions given, that it would become an absolute necessity to provide some means whereby the car can be held any length of time. It is true that this can be ac- complished by applying the hand-brake after the car has been brought to its first stop, but this would seem to be objectionable. It would seem to be a simple manner to so arrange the brake 1894.] CORRESPONDEWOME 651 that current could be supplied to it to hold the car under any conditions. While I think that Mr. Sperry’s device of the reatest interest and value to electric traction, it would seem that the feature which I have described would be an objection but one which could no doubt, readily be obviated, even without the use of the hand-brake. 5 MR. SPERRY:-The gentleman is referred to previous answers in the discussion. [The report of the discussion of Mr. Sperry’s paper at Chicago, has been delayed in the mail, and could not conveniently be printed in this issue.] NOTICE. Written discussions of the papers contained in this issue, if acceptable will be printed in the November number if received before November 1st. The Secretary will esteem it a favor if his attention is called to any errors in either papers or discussion, in order that they may be corrected before printing the sheets for the annual volume. The Institute as a body is not responsible either for the statements made, or for the opinions expressed, in the TRANSACTIONs. A £after to be £resented at the Nintieth Meeting of the American Institute of Electrical Engi- neers, New Pork and Chicago, October 17th, 1&24. [ADVANCE COPY.-SUBJECT TO REVISION.] THEORY OF TWO AND THREE PHASE MOTORS. |BY LIEUT. SAMUEL REBER. The complete mathematical solution of the two and three phase motors with the coefficients of self-induction as variables, and the effect of magnetic leakage taken account of, is extremely difficult, if not impossible. But an approximate solution in which the change of magnetic properties of the iron and mag- netic leakage are neglected, the coefficients of self-induction considered constant, while the mutual-induction between the armature and field circuits follows a sine law, and the field sup- posed to be without projecting pole-pieces, is quite easy. We will then proceed to the solution with these assumptions, remark- ing that the two-phase formulae are those of Professor H. A. Rowland, while the three phase formulae and tables are our own. Use the following notation: - J. . . . . . Coefficient of self-induction of one armature circuit. — e. e. e. e. e Coefficient of self-induction of one field circuit. c’ c’’ 6” Field currents. c. c., c., Armature currents. F. . . . . . Maximum E. M. F. applied to field circuit. p and p' are Maxwell’s electro-kinetic momenta of one armature and one field circuit. 0 . . . . . . 2 it times the complete periods of field circuit. .f. . . . . . 2 it times the complete periods of armature circuit. * . . . . . . Angular position of the armature. M. . . . . Maximum value of coefficient of mutual-induction be- tween a field and an armature circuit. V. . . . . . Velocity of rotating field ?) . . . . . . Velocity of rotating armature. 652 1894.] REBER ON TWO AND THREE PLIASE MOTORS. 653 * . . . . . . Length of one complete wave of magnetization or .* angular distance subtended by four (or six in the case of three-phase) poles. I. . . . . . Impedance of one armature circuit. I'..... Impedance of field circuit. 0 c. ... Maximum currents in one field and armature circuit. Jº Jº"... Armature and field resistance. 9 and p. Lag in the two circuits. We may write at once the following equations: Two-phase. Three-phase. c' = 0 cos (b t + 9). c' = 0 cos (b t + 9). c’ = 0 sin (b t + 9). c" = 0 cos (b t + 9 + 120). c, - 6 cos (f t + ºp). c" = 0 cos (b t + p + 240). c) = e sin (f t + p). 6, = c cos (f t + p). c. = c cos (ºf t + p + 120). 6, = e cos (ºf t + p + 240). The angular position of the armature at any moment will be a 9 where a = º, and in the case of the two-phase motor the mutual-induction between one armature circuit and the two field circuits adjacent will be M cos a } and M sin a 9, and for the other armature circuit will be — Jſ sin a 9 and M cos a 9. For the three phase they are M cos a 9, M sin (150 — a 9), M sin (210 — a 9), and M cos (a 3 + 120), M sin (210 — a 9), M sin (270 — a 9). - For p and p" we have for the two-phase p = L 6, + M. c' cos a 3 + Mo" sin a 9, p' L' c' –– M c, cos a 3 — Me, sin a 9, substituting and reducing since b t – f t = a 9. p = L c cos (ºf t + p) + M C cos (f t + 9), p' = Z/ C cos (b t + 4) + Mo cos (b t + p). For the three-phase p = 1, 6 cos (f t + £) + š M C cos (f t + g), p' = L C cos (b t + ft) + # Me cos (b t + p). For the two-phase motor, the equations for the other two circuits are the same as the first except sine is substituted for cosine. In the three-phase the values will differ by 120 degrees in the cosine functions. Passing to the exponential form, and in the two-phase system multiplying the sine values by i, the imaginary unit, and adding, Maxwell’s equations become .654 REBER ON TWO AND THREE PHASE MOTORS.. [Oct 17, * (f t + p) d - • . - * G & + # = 0. . . . (1) * (b t + 4) , i b t - Aº’ O’ s +%= E's . (2) If a condenser of capacity q be added in series to the armature circuit, L will be changed to Z — * Substituting, differentiating and reducing equations (1) and (2) for the two-phase reduced to & 1 * p . . 0 & 9 R+:(1. –2.) + i f M ‘’ s = 0. 3 [ J-74, f iſ . @ & 9 6 & (R' + i b //) e + 2 iſ "e". (4) O O 2 divide (3) by e and reduce we have % (9 – p) G 1 - — 2 * ---------> & gzºrolºr (zy #)] (9 – ?) tº c SII) Cé & = cos (9 – p) tº sin (§ – p) we have at once 1 G º cos (; — = -(1. –2.) 5 5), Ø — p) Vº) Wººd (5) sin (§ – p) = R y; or (6) an e-e, --—“– aIl 9-0--zz-I. (7) j q Squaring and adding (5) and (6) and reducing, we may write G M f - M f 4. R* + (1. * –) - J-7, d - Eliminating e from (3) and (4), and writing for { - 1 - Jº R' + b [*— I (1-2)] = 4, f f* q * I R +/ F (1–2)= B. 1894.] REBER ON TWO AND THREE PHASE MOTORS. 655. we have -- A 7. ºf d # /) B –H & A). p O E – A* – Bº hence, -- & A.' - ... – #47 A. * * = #F# = — witH. A.' _ – † "4 B , * * = +H = -74.H. tan p = 4. B Squaring (10) and (11), and adding and reducing E VAZ-E B. o ––7– Solving (5) and (6) by aid of (10) and (11) 1 47(4–74)—a ſº, sin ſ = I WA*-E Bº: A R + (ºf –?) ºf cos ſ = ſq 5 I WA” -- Bº Af(4–7: ) – B R tan 9 = f*q 1 \ . A Fê –– f B (1,– $). ) + f f* q For the three-phase by the same method of solution 2 6 Hº Aº in (9-0) = sº? – ? – 2 1 * & -2 = sº, (ºf-?) tan (; — p) = — (9) (10) (11) (12) (13) (14) (15) (14) (15) (16) (17) 656 REBER ON TWO AND THREE PHASE MOTORS.. [Oct 17, A = E R + [*#– Z (z-jº) f*q 1 JB = b // R + f Ję' | L — -a; ). + f ( zº) E' ! ~! #4 I A , (18) sin # = − 4 ++ = — witH. F' 7, BI B (19) • * = - 74-H = - VAH-B. tan * =# (20) E WAZ-ETº z – —7– (21) 1 A f | L – —zº- B Hº sin ſ = f( #) * (22) I WA*-E Bº g 1 A R + B f ( L — — — cos Q = ( º) (23) I WAATE B Aſ (4–2 ) – B I. tan Q = g 1 \' (24) A R + ºf (n-:) In the case of the two-phase motor the total work done on the motor will be 1 ro-º-º: *:::::A; wº. (25) cºrº (−4) The current heating in the field circuits is *==== *== Tr 0 2 AD/ f 2 AD/ 2 b */ ***** / ...” 7, tºº-ºº: 7, * = - b 2. b = } 0° R' + 3 O' R = 0° R'. 1894.] REBHR 6.V TWO AWD THREE PEIASE MOTORS, 657. Likewise for the armature circuits the heating is 0° R. / AP M2 A” I? o, e - R = c(a^r, Fºr) = r(******) A*-H Bº The total energy transformed into mechanical work less the hysteresis loss in the fields is: A z's ſº M* f (b —f) ſ — ſcº 2 = }^2 EC cos 9–(6* R -- 0° R') = É A* -- Bº (27) 02 FM".ſ () —ſ) I? The ratio of this to the cº R loss of the armature is b * (26) Q) V — v , when hysteresis loss in the field is neglected. (when no condenser is used) or , hence the armature effi- 9. V In the three-phase motor the work done by the currents on the motor is: ciency is w- A R + ºf (4–2) # E 0 cos ſ = } E A*-H Bº Q 1 A R + B f(z-jº) = 3 Cº I? ſº aſ The current heating is: / 2 / 2 4 / 72 * @ R.I. o. Rye o (ºr ºf tº 1) 3A% (*******) - 3 A* -- Bº The total energy transformed in the armature less the hystere- sis loss in the fields is: # E 0 cos / — ; (6* R + C* R') = 27 E, ſº Mºſ (0– f – 27 gº F M f ( – f.) 8 A*-H Bº 8 I? and the ratio of this to the 6° ſº loss in the armature is as b —f before e f 658 REBER ON TWO AND THREE PEIASE MOTORS.. [Oct 17, The angular torque is equal to the work divided by the veloc- ity, and is in the case of the two-phase motor A2.2 T R M*.ſ on 27 A' Mº.f 2 A* -- Bº Å 73– and for the three-phase 27 2 7 ºn R M* f 27 On 27 R M*f § - “ TTE. T. s. Å I? The starting torque can be increased by changing either the resistance or condenser; representing the quantities as starting by the sub o, we have the ratio of the starting torque to the run- ning torque as follows for both cases: T, E. R., b (A* -- Bº) C. R., b /* T - BºM.I.B.) - ºf 77. At a certain speed the torque is a maximum, and the motor, if pushed in its work beyond this speed will stop. To prevent this, the motor should not be pushed to a point more than half the maximum torque. This speed will be given by finding what value of f will make T'a maximum, and there will be two solu- tions depending on whether E or C is constant. To simplify the solution make the following abbreviations: 1 1 ! = L — — — !. = * –- f* q a = I, #7 R Fo 3 M* Iz, R' R = f; K. =#; m = #P. K. = K = 5%, then A*- B = W fºr L*[(K K – 1 + my + K. -- Kº I* = AE fº (Kº -- 1). I.” – A fº (K.” + 1). _ 2 t as M* K. T = tº o Tº Ti = ** E. Aſ m? X * L. [(K K – 1 + m3) -- Kº-E Kºji _ Zºº K M*(b – f') W (work) = 0 7 (K. -- 1) – Elº K m” b — f L' [(K K’ — 1 + m”)" -- K* + K*] bº 9 M3 For the three-phase the same solution, except m” = 4.777° 1894.] RH/BER ON 'I' WO AND THREE PHASE MOTORS, 659 the torque reduces to this form 27 2 7 on M* K_ 8 A ! K* + 1 27 27 E. A m? 8 A WZTICK. KZLTTºy Ikº Ikºj It is evident from the similarity of the formulae that the two and three phase motors have the same properties and differ only in the constants, hence what follows will apply to both kinds of motorS. CoNSTANT CURRENTs. T is a maximum when Fº 1 3 1 A” \? f = ′, -7, E V 72 + (; ; #). If there is no condenser we have at once the condition for maximum torque R = f' L. Consequently the armature resistance must be adjusted till the condition is fulfilled to obtain the maximum torque. The maxi- mum torque can be obtained at starting by a proper resistance, as at starting f = b. The armature velocity for maximum torque in terms of the rotating field velocity is: V (1–3 Vº, ––– + Vº-º-;) b 27 Z 7 A q* L q 2 / .” When b L—R=0 the torque is a maximum at the start and will decrease rapidly as the speed increases, likewise when b Z ~ R the torque at the start is greatest and will decrease rapidly as the speed goes up. Such motors will start well, will have a low efficiency and will regulate poorly as the decrease of torque will increase if speed is too slow. When b D > R the point of maximum torque comes near the point of maximum speed, giv- ing good regulation but they will have poor starting qualities unless resistance is introduced at the start and then cut out. The maximum value of the torque when f L = R is 2 : 0° M. A 2 L 27 2 7 C° M. 3 T T2 Z for the two, and 660 REBER on Two AND THREE PHASE MOTORS. ſoot 17, for the three-phase motors which is independent of the speed, and depends only on the proper adjustment of the armature re- sistance. - The equations of torque with no condenser reduce to 2 TT 2, M* AC T = * “ O* * * * Å ! K* + 1 i : for the two-phase, and for the three-phase. The variable part of which is zé 1. which may be put in the form 1894.j REBER ow TWO AND THREE PHASE Motors. 661 - | Q) K. (1–3) — 1 - 2 1–3) _A, 1 — ” Kº--( V. If 4. ' |W. - y A., Representing the value of V by unity, and expressing the torque in terms of the maximum as unity we have the fol- lowing table: - TABLE I. Q) Ko = 1 Ko = # Ko = *, Ko = # Ko = "o Ko = 2 y T T T. T T T O,O I.O.O. .8o .55 .38 .2O .8o • I .99 .85 .6o -42 .22 .75 .2 .98 .90 .66 47 .25 .69 •3 -94 .95 .72 -53 .28 .62 •4 .88 .98 .8o .6o .32 .55 •5 .8o I.O. .88 - 38 , 47 .6 .69 .98 .96 .8o .47 .38 .7 .55 .88 I.O .92 .6o .29 .8 .38 .69 .92 I.O. .8o .2O .9 .2O .38 .6o .8o I.O ... [O I.O .OO .OO . OC •O . OC) .OO Taking the safe working torque at .5 the maximum torque, the value of i. will be for the various values of K, as follows: K. = 2, ... = 48; K = 1, y y K. = ** = .92; K = } The ratio †. likewise gives the armature efficiency and conse- quently K, should be as small as possible, and ought not to be greater than about fºr, even in small motors. The diagram shows the necessity of a starting resistance in high efficiency motors and the way they regulate. Fig.2 shows some curves of three phase motors built by Steinmetz, and described by him in the March TRANSACTIONs of this year. If the condition of maximum torque is satisfied, the ratio of starting to working torque with constant current does not depend on the frequency, but only on the working out-put which can only be increased by change of size and not design. - - 662 REBER ON TWO AND THREE PHASE MOTORS. [Oct. 17, If the motor is forced beyond the point of maximum torque it is not only liable to stop, but to make the starting torque by comparison smaller. For a given current the maximum torque and work depend on the ratio of * If there is no magnetic 1,0 T i | | |\|| i. \ | \ | V |\ / /\ \- / ^ V\ W © Č 4 Zy &\ /\||7|WVA | "pºt-N-y ׺ -1 - k1– * ^ \ N N - :0 .1 .2 .8 .4 .# i–F–F–F–r, - - SPEED . . . FIG, 2. . . . . s leakage M* = L L", L' being that part of the field self-induc- tion interior to the machine, Z therefore cannot be diminished without decreasing the output or increasing L" at the same time. If the field be increased, the same output can be obtained with a smaller value of L, but this increases the electromotive 1894.] REBER ON TWO AND THREE PHASE MOTORS. 668 force and does not change the properties, as these depend on the ratio K, and not on the self-induction and resistance alone. If ºthere is leakage as there always is, M* < D. D." which reduces the output. CoNDENSER IN ARMATURE CIRCUIT. The ratio of the torque of a motor with a condenser in the armature to one without, is R* + L2 fº 1 2 R -- f'(1 – #) fº f q / . whose maximum value is 1 + #. This maximum by proper adjustment of the condenser can be thrown at any value of the armature velocity. The value of f which makes the above ratio a maximum is f* - #, (1 + V2 R*L*q =FIA), hence by TABLE II. () Ro = }. n = 1. * = 2. n = 4. n = 16. n = 32. V 77 – 8 O. O. IO. O.O. I. 37 .66 49 43 4O f 4.21 2.25 .83 57 49 •4I 2 I.32 4.54 I. I5 .7o .57 .52 3 .48 6.95 1.77 .9o .67 59 4. .2O 2.48 3.24 I.23 83 69 5 • Og 7o 5.of I.95 I. (O 88 6 .O.4 2 I 1.76 3.36 1.6t I, II § .O.I. O5 -47 2.24 2.47 I-54 .Oo3 Ol .o'7 .36 I.52 I.91 9 .oOo.4 ood .O3 • I2 46 92 I.O. . OCO OOO .O.O. OOC) OO OCO adjusting the value of g, f can be made anything we please. Calling the maximum starting torque without a condenser l, the starting torque with a condenser is 2 b /, He * + r( –?) times as great, and will be a maximum when L = + which re- duces the factor to *—. This can have a large value if the resist- O w ance of the armature is small. Thus we see that the starting torque can be increased without changing the resistance, and 664 REBER ON TWO AND THREE PHASE MOTORS.. [Oct. 17, this increase of torque is obtained, not by increasing the current in the field circuits, but only in the armature. When the con- dition L = * is satisfied, the torque at any velocity with a condenser is using the same unit as before 2 AT K? -- (1 •º- #) : i FIG, 3. where - - = K_* K. • VLT.' b? q}} 7 * ty—y and 1884s REBER ON TWO AND THREE PEIASE MOTORS. 665 To illustrate, let us take the case where K. = }, and compare it with the same case without a condenser, the general formula 70, b” L is in writing for q, 2 AT AT2 + ( - 1. %). 70, Table II. is calculated by this formula. The curves show that the condenser has only a local effect on the torque and a small change in velocity renders it useless, though this defect could be overcome by a variable condenser. The advantage is that the motor can be run at a slow speed with increased torque without overheating. As the field current has TABLE III. 4) CURRENT. TORQUE. y K' = }. K’ = 1. K’ = 2. || K' = 4. K' = 1. K’ = 2 O O 1.81 I.O.O. . So • 33 .24 •39 ... I I.8o .99 .5O • 35 .26 .45 •2 1.78 -99 . So .4O • 3r .5I • 3 1.76 .99 .5o .46 .36 .58 •4 I.73 .98 .5O . So .4 I .65 •5 1.64 .97 .5O .56 .5o • 74 .6 1.58 .97 .5O .6o .6o .85 .7 I.4. I .94 • 49 .65 ... 79 •94 .8 I , 22 .88 .48 .75 I, OO I, O.O. •9 I. OO 22 44 I.O.O IO 66 I.O. C, OO • OO • OO • OO ...O.O. • CO been supposed to be constant there is no extra heating of the field circuits; this will require special means for keeping the field current constant. By use of a variable condenser the speed can be made to increase to any extent up to synchronism and there is no overheating at low speeds, or waste of power by the insertion of resistance to increase the torque. A variation of the capacity from one to four, changes the armature speed from zero to one-half of the rotating field velocity and an increase of con- denser capacity to 25 varies the armature to 80 per cent. of synchronism at the point of maximum torque. CoNSTANT E. M. F. Neglecting the change of the magnetic properties of the iron at high magnetization, the torque and work of the motor vary at 666 REBER ON TWO AND THREE PHASE MOTORS. [Oct. 17, the square of the field current. With constant E. M. F., when the motor is at rest or just starting, the current is very large and if there are other motors or lamps in the exterior circuit, they are rendered unsteady at the moment of starting of the first motor, this however may be corrected by a secondary trans- former. The formulae for the current and torque for E constant 3.I’ê c - A.A/ A3 - 1 b L' ' (K K – 1 + m3) -- KA-E K?' TWE's (ATKTTºy Tkº Tkº for the two-phase, and sº - . : º .2 SPEED FIG, 4. T = 37 E * : 1 A’ –- 1 T is 2 b" Z” (K K – 1 + m2) -- KA-E A* for the three-phase. - - To keep down the heating of the fields, the field resistance must be small, hence K' must be small compared with unity. When the self-induction external to the machine in the field cir- cuit and the magnetic leakage are small, mº is very nearly equal to unity. There is always some self-induction in the dynamo or transformer so that m” is rarely less than }, for a transformer equal in self-induction to the motor mº = }. If there is no condenser, >n 2 2 2 *###" in r the torque is a maximum for K = 1894.] REBER ON TWO AND THREE PHASE MOTORS. 667 must vary from 0 to #, which gives R varying from 0 to # f L. as the condition of maximum torque. The added starting resist- ance must be less than in the case of constant current. - Table III. and curves, show the variation of current in the field circuits and the torque when the field resistance is changed, but K. - # for the armature: ms is taken at .75 the torque is expressed in terms of the maximum as unity. To show the effect of changing the armature resistance I have taken the case where K* = .2 m” = .75 and calculated for Ko = Tºr, ºr, fºr and 1. The value of K, = fºr gives the maxi- mum at the start (see Table IV. and curves). We may conclude that the two and three phase motors have in general the same properties, and that the most important rela- tion is that of R to f L. The lower the field and armature TABLE IV. Q: pr Rºo = 'o Ko = 'o Ro = *, Ko = 1 ... O 5S .89 3ſ. CC, 53 ... I 56 .94 - 99 5o .2 65 97 .98 54 •3 74 -99 .95 38 • 4 8o I.O.O. , 88 32 • 5 89 QS .8o 26 .6 .97 .89 .7o . 22 .7 I.O.O. .74 .54 . I 8 .8 91 53 .37 o6 •9 53 28 . 1 7 oo:3 I, O OO CO • OO OOO resistance are, the higher the efficiency of the armature and the nearer to synchronism is the point of maximum torque. We see that high efficiency motors require a starting resistance, and that in such motors the torque can be readily regulated by adjustment of the armature resistance and we are enabled to throw the point of maximum torque at any speed we desire. It is likewise apparent that the smaller the magnetic leakage the more efficient the motor. If the frequency is supposed to vary, the speed and output are greatly changed. K., varies inversely as the frequency, so the motor is improved for higher frequencies as far as this relation effects it. Increasing the frequency n times in a motor without a condenser, the velocity will be increased n times, R., decreased n times, the maximum torque is not affected, while the hysteresis 668 REBER ON TWO AND THREE PHASE MOTORS.. [Oct. 17, is increased n times nearly, the output of the motor will be increased nearly n times if the motor is run at a given percentage of the maximum torque. Hence it is an advantage to increase the frequency till the hysteresis heating becomes too great, or the motor runs too fast. If the efficiency is to be kept constant, the work will then vary as n° and the field and armature currents will be increased Wn times. Hence increase in speed gives an advantage in output till the machines begins to overheat. With a condenser the same facts hold, but with this advantage that an increase in the frequency greatly reduces the size of condenser necessary. A high frequency motor will weigh less than a low frequency one. When the clearance is large, the advantage of high frequency motors is not so decided, and if very large the low frequency motors are better if weight is no consideration. The higher frequency motor will contain less iron and more copper. If we vary the size of the motor, keeping the magneti- zation constant, output and hysteresis vary directly as the weight, the heating of the field and armature circuits, directly as the increase of size. A paper to be Aresented at the Wintieth Meeting of the American Znstitute of Electrical Engin- eers, Mezw York and Chicago, October 17th, 1894. [ADVANCE COPY-SUBJECT TO REVISION.] THEORY OF THE SYNCEIRONOUS MOTOR. f IBY CHARLES PROTEU'S STEINMETZ. The following theory of the synchronous motor was written somewhat over a year ago, but was not intended for publication. Since, however, through Prof. S. P. Thompson’s paper, entitled “Some Advantages of Alternating Currents,” read before the British Association, the synchronous motor has been brought into discussion again, it may be of interest to communicate this sketch. While by the use of the method of complex quantities, the analytical treatment may be shortened somewhat, I consider it preferable to give the theory essentially in its original form. I shall discuss one circuit only; the results apply however to the polyphase synchronous motor as well. In the latter case the volts, amperes, watts, etc., are these quantities per phase of the system, so that for instance in a three-phase synchronous motor the total power is three times the value per phase, introduced in the discussion. Let u = Wrº-H s” = impedance of the circuit of (equivalent) resistance r and (equivalent) reactance s = 2 T N L, containing the impressed E. M. F. e., " and the counter E. M. F. ei of the syn- chronous motor, that is the E. M. F. induced in the motor armature by its rotation through the (resultant) magnetic field. Let c = current in the circuit (effective values). 1. If eo = E. M. F. at motor terminals, u = internal impedances of the motor; if eo = terminal Voltage of the generator, w = total impedance of line and motor; if eo = E. M. F. of generator, that is, E. M. F. induced in generator armature by its rotation through the magnetic field, w includes the generator impedance also, 669 670 STEINMETZ on THE SYNCHROYoUS MOTOR. (Oct 17, The mechanical power delivered by the synchronous motor (including friction and core loss), is the electric power consumed - by the C. E. M. F. e., hence: - p = c e cos (c. e.), (1) thus: cos (e, e.) = + 3. * 6 €1 - (2) sin (c. e.) = V 1 — (# ). C 61 The displacement of phase between current c and E. M. F. e = u c consumed by the impedance u is: - (3) | - Since the three E. M. F.'s acting in the closed circuit: eo = E. M. F. of generator, e1 = C. E. M. F. of synchronous motor, cos (6 e) = sin (c e) = : e = w c = E. M. F. consumed by impedance, form a triangle, that is, e, and e are components of eo, it is (Fig. 1): e = e,” + e” + 2 e el cos (eſ, e) (4) hence, 2 2 2 2 2 2 2. €n" — 61" — 6 e.” — e.” — wº gº - cos (e1, e) = * 1 – ‘Q 1 (5) 2 e, e 2 w c el since, however, by diagram : cos (eſ, e) = cos (c, e—6, e.) (6) = cos (6, 6) cos (6, e) + sin (6, e) sin (c, e.) substitution of (2), (3) and (5) in (6) gives after some transposi- tion : wº. e.” — e.” — wº cº – 2 r p = 2 s Woº eſ” — pº (7) the Fundamental Equation of the Synchronous Motor, relating impressed E. M. F., eo; C. E. M. F., e, ; current, 6 ; power, p, and resistance, r ; reactance, s; impedance, u. This equation shows, that at given impressed E. M. F. e., and given impedance u = Wrº-Hº, three variables are left, ei, e, p, of which two are independent. Hence, at given e, and u, the current c is not determined by the load p only, but also by the excitation, and thus the same current c can represent widely different loads p, according to the excitation ; and with the same 1894.] STEINMETZ on THE SYNCHRONous Motor. 671 load, the current c can be varied in a wide range, by varying the field excitation e1. The meaning of equation (7) is made more perspicuous by some transformations, which separate e, and c, as function of p and of an angular parameter p. - Substituting in (7) the new coordinates: * +” ºf ſ a * + y 03 F — W3 4/2 *—e ºf Or, Ø — (8) 42 J - 4/2 we get *- - & A /a:” — 2 * //TM as- "A - éo" — as wº-2, p = 2; V gº — wº, (9), substituting again ed” E (I, | 2 u p = b w 7? - e Q0, | (10) hence, s = u V1 — s” 2 7 p E & b J €1 --~~% \ _2~~~7. \ SC e=uck-ase \ e-ues---ºf-------> º | 60 | \ | | \ | | \ | | \ | | \ | X re'.< A. >e rcké w > C ed FIG. 1. FIG, 2. we get a — a V2 – e b = W(IE *) (2 × 2 y-W), (11) and, squared - - * (1–sº 1–e h\? s” aº-H(1–s”) y”—a W2 (a–s *º-º-º: ; b) =0, (12) substituting s a (a – e b) V2 Q) | 2 e ; (13) y VI-F = w, gives, after some transposition, 1 — e.") , * + º-'gºla (, –2 = } (14) 672 STEINMETZ ON THE SYNGHRONO US MOTOR. Oct 17, hence, if * - VEH.M. (15) Q)” + w” — Jº, (16) the equation of a circle with radius /ē. Substituting now backwards, we get, with some transpositions: }* (e.” + w” cº — w” (e.” – 2 r p)}” - + $7 s (e.” — wº Gº)}* = sº wºe.” (e.” – 4 rp). (17) the Fundamental Equation of the Synchronous Motor in a modified form. The separation of e, and c can be effected by the introduction of a parameter p by the equations: * (e.”—wº cº–w” (e.”—2 r p)=s we, Veº—4 r p cos p | 18) it is 7 s (e.”—wº cº–s u e, Veº—4 r p sin ºp These equations (18), transposed, give - 1 w” tº *-*-*. •=V2 | (ex-2, p)+ **(ºos e-Hsing) We’—4 rp | 7° == i (19) 60 *V;( **) (; o–L’s ..) Hº! ––. 2 1 + Q!, COS g-Hsing V l e.” e.” Tl * *–-- •=Vºº-ººp-Hº (; cº-inº) wº € - e 47, 70 l (20 —ºvº (1–4)+(; COS 9– S1 Il ..)MHz | ( ) The Parameter Equations of the Synchronous Motor:- The parameter p has no direct physical meaning, apparently. These equations (19) and (20), by giving the values of e, and 6 :as functions of p and the parameter p enable us to construct the Power Characteristics of the Synchronous Motor, as the curves relating e, and c, for a given power p, by attributing to p all different values. • Since the variables v and w in the equation of the circle (16) are quadratic functions of e, and c, the Power Characteristics of the Synchronows Motor are Quartic Curves. They represent the action of the synchronous motor under all conditions of load and excitation, as an element of power trans- mission even including the line, etc. - Before discussing further these Power Characteristics, some special conditions may be considered. 1894.] STEINMETZ ON THE SYNCHRONO US MOTOR. 673 A. MAXIMUM OUTPUT. Since the expression of e, and c [equations (19) and (20)] contain the square root We...”—4 rp, it is obvious that the maximum value of p corresponds to the moment where this square root disappears by passing from real to imaginary, that is, e.” — 4 r p = 0, e.” 4 r This is the same value, which represents the maximum power transmissable by E. M. F. e., over a non-inductive line of resistance r, or more generally, the maximum power which can be transmitted over a line of impedance u = Wr” + s” into any circuit, shunted by a condenser of suitable capacity. Substituting (21) in (19) and (20), we get, Or, p = (21) _ !!! Y 61 F 2 7 60 | 22 e = * | (22) 2 ” J and the displacement of phase in the synchronous motor, — ? — ” COS (61. 6) E →- E — (e., 6) 6 €1 70 hence, tan (ei, c) = — 8. (23) 7° That is, the angle of internal displacement in the synchronous motor is equal but opposite to the angle of displacement of line impedance, (el, c) = — (e, c) = — (u, r) (24) and consequently, (eo, 6) = 0 (25) that is, the current c is in phase with the impressed E. M. E. e. If u < 2 r, e, 3 eo that is, motor E. M. F. 3 generator E. M. F. If u = 2 r, e = e, that is, motor E. M. F. = generator E. M. F. If u > 2 r, e, X eo that is, motor E. M. F. P. generator E. M. E. In either case, the current in the synchronous motor is leading. B. RUNNING LIGHT, P = o. When running light, or for p = 0, we get, by substituting in (19) and (20), - - *674 STEINMETZ ON THE SYNCHRONOUS MOTOR. [Oct 17, 61 *Vºi Hºmº | (26) * = % #1 * cos o – " in a | G 7. 2 +. ‘p ; si Ø Obviously this condition can never be fulfilled absolutely, since p must at least equal the power consumed by friction, etc., and thus the true no load curve merely approaches the curve p = 0, being however rounded off, where curve (26) gives sharp COI"Ile I'S Substituting p = 0 into equation (7) gives, after squaring and transposing, e;*-Heº-Hwº cº-2 e.” e.”—2 w? Gº eº-H2 r" cºe,”–2 s” o” e.”=0. (27) This quartic equation can be resolved into the product of two quadratic equations, - e.” -- wº cº — e.” -- 2 s 6 e = 0 generator. | (28) e.” -- wº gº — e.” — 2 S 6 e = 0 motor. which are the equations of two ellipses, the one the image of the other, both inclined with their axes. º g - wº € The minimum value of C. E. M. F. ei is, e1 = 0 at c = N N \ .N.IN \ * 5000 4000 3{\{)0 20 - Af× ÆR f\- f-w\* }\ŽA* ;|*- sº p* ** * ** ** / /. - A A 2' - ( A. 2 ) NJZ ~~ - 240 sº Z— FIG. 3, - - and the interior space c and exterior space D, whose points do not represent any actual condition of the alternator circuit, but make the dependence et, c imaginary. * A and A', and the same B and B', are identical conditions of the alternator circuit, differing merely by a simultaneous reversal of current and E. M. F., that is, differing by the time of a half period. * 676 STEINMETZ ON THE SYNCHRONO US MOTOR. [Oct 17, Each of the spaces A and B contains one point of equation (22), representing the condition of maximum output of generator, viz., synchronous motor. - C. MINIMUM CURRENT AT GIVEN Pow}ER. The condition of minimum current, c, at given power, p, is de- termined by the absence of a phase displacement at the impressed E. M. F. 60, * - (e), c) = 0. This gives from diagram Fig. 2, • e” = e,”-- 6° w” – 2 c e : (33) * º/, or, transposed, e = W(eo — a r)” – gº sº +. (34) This quadratic curve passes through the point of zero current and zero power, C = 0, €1 = 60 through the point of maximum power (22), 60 €0 t/ — F-3 61 F - 2 ” 2 7. and through the point of maximum current and zero power, 62 €n S * 7° and divides each of the quartic curves or power characteristics into two sections, one with leading, the other with lagging cur- rent, which sections are separated by the two points of curve (34), the one corresponding to minimum, the other to maximum Current. It is interesting to note, that at the latter point the current can be many times larger than the current which would pass through the motor while at rest, which latter current is, * 60 * - 6 F — 36 QM, (36) while at no load, the current can reach the maximum value, 66 * º 7° (35) the same value as would exist in a non-inductive circuit of the same resistance. - 1894.] STEINMETZ OW THE SWYCHRONO US MOTOR. 677 The minimum value at C. E. M. F. e., at which coincidence of phase, (e), c) = 0, can still be reached, is determined from equa- tion (34) by, de, - esºmºmº d 6 aS, 7, S. * 6 = €o La é = €o - 37) (?!, 2/, - The curve of no displacement, or of minimum current, is shown in Figs. 3 and 4 in dotted lines." D. MAXIMUM DISPLACEMENT OF PHASE. (60, c) = maximum. At a given power p the input is, h po = p + 6 r = e, c cos (co, 6) (3S) ence, 2 ..., cos (, ) = * tº (39) é0 C At a given power p, this value, as function of the current c, is a maximum when d (p + & !) = () d c \ a, a this gives, * p = Gº r (40) o–V7. (41) That is, the displacement of phase, lead or lag, is a maximum, when the power of the motor equals the power consumed by the resistance, that is, at the electrical efficiency of 50 per cent. Substituting (40) in equation (7) gives, after squaring and transposing, the Quartic Equation of Maximum Displacement, (e.” – e’)” – e' alº (wº + 8 r") + 2 o’ e.” (5 r" — alº) — 2 & eº (A + 3 rºy – 0 (42) Or, 1. It is interesting to note, that the equation (34) is similar to the value, e, = V(eo – cr)* – cºs”, which represents the output transmitted over an inductive line of impedance u = Vºr” + 8° into a non-inductive circuit. Equation (84) is identical with the equation giving the maximum voltage e1, at current c, which can be produced by shunting the receiving circuit with a condenser, that is, the condition of “complete resonance ’’ of the line & = 'Wr” + s” with current c. Hence, referring to equation (35), e, - e, * is the • q' maximum resonance voltage of the line, reached when elosed by a condenser of reactance, — s. - 678 STEINMETZ ON THE SYNCHRONO US MOTOR. [Oct 17, The curve of maximum displacement is shown in dash-dotted lines in Fig. 3 and 4. It passes through the point of zero current —as singular or nodal point—and through the point of maximum power, where the maximum displacement is zero, and it inter- sects the curve of zero displacement. E. ConstANT COUNTER. E. M. F. At constant C. E. M. F., e = constant, If, 61 < 60 V1 –º 240 2" 2 tº an 22 * 2021 2^2 , / Z- 7\ A-47 2' 2^ - ººº- Jºvºv 2^ 21 Jºv ; / / 120 ( / * ºn *VV N / ſ 2’ _^ …” A Y N. ¥ // 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 FIG. 4. the current at no load is not a minimum, and is lagging. With increasing load, the lag decreases, reaches a minimum, and then increases again, until the motor falls out of step, without ever 1894 STEINMETZ ON THE SYNOEIROWO US MOTOR. 679 coming into coincidence of phase. —-a If, • V1- * < e < c, the current is lagging at no load; with increasing load the lag decreases, the current comes into coincidence of phase with éo, then becomes leading, reaches a maximum lead; then the lead decreases again, the current comes again into coincidence of phase, and becomes lagging, until the motor falls out of step. If e, < el; the current is leading at no load, and the lead first increases, reaches a maximum, then decreases, and whether the current ever comes into coincidence of phase, and then becomes lagging, or whether the motor falls out of step while the current is still leading, depends, whether the C. E. M. F. at the point of maximum output is > e, or < e. F. NUMERICAL INSTANCE. Figs. 3 and 4 shows the characteristics of a 100 K.w.. motor, supplied from a 2500 volt generator over a distance of 5 miles, the line consisting of two wires, No. 2 B. and S. G., 18 inches apart. In this case we have, en = 2500 volts constant at generator terminals. \ 'r = 10 ohms, including line and motor. | 43 s = 20 ohms, including line and motor. } (43) hence, w = 22.36 ohms. | Substituting these values, we get, 2,500*— e.” – 500 & – 20 p = 40 We” e.” –p (7) {e,” + 500 & – 31.25 × 10' + 100 p?” + $2 e.” – 1,000 cº" = 7.8125 × 10" — 5 + 10° p. (17) e1=5590 (19) Wº;(1–3.2×10−p)+(894cose-H447sing) V1-6.45x10 "p}. C =559 (20) '#(1–3.2×10−ºp)+(894cose-447sing VI-64x10º. Maximum output, - p = 156.25 K.w. (21) at, 61 = 2.795 volts 6 = 125 amperes | (22) Running light, e.” -- 500 cº – 6.25 × 10' + 40 c e = 0 28 e1 = 20 c + 4/6.25 × 104 – 100 cº | (28) 680 STEINMETZ on THE SYNCHRONous MotoR. [Oct 17, At the minimum value of C. E. M. F. e. ={0, is, c = 112 (29) At the minimum value of current, c = 0, is, e = 2500 (30) At the maximum value of C.E.M.F. e. = 5590 is, c = 223.5(31) At the maximum value of current, c = 250, is, e = 5000 (32) Curve of zero displacement of phase, e = 10 W(250 – dy-F4 & (34) = 10 W/6.25 × 104 – 500 g + 5 o' Minimum C. E. M. F. point of this curve, e = 50 e = 2240 (35) Curve of maximum displacement of phase, p = 10 & (40) (6.25 × 10% – e.”)? --.65 × 10° c – 10" Gº = 0 (42) Fig. 3 gives the two ellipses of zero power, in drawn lines, with the curves of zero displacement in dotted, the curves of maximum displacement in dash-dotted lines, and the points of maximum power as crosses. Fig. 4 gives the Motor Power Characteristics, for, p = 10 K. W. p = 50 K. W. p = 100 K. w. p = 156.25 K. w. together with the curves of zero displacement, and of maximum displacement. G. DISCUSSION OF RESULTs. The characteristic curves of the synchronous motor, as shown in Fig. 4, have been observed by me frequently, with their essen- tial features, the V-shaped curve of no load, with the point rounded off and the two legs slightly curved, the one concave, the other convex; the increased rounding off and contraction of the curves with increasing load; and the gradual shifting of the point of minimum current with increasing load, first towards lower, then towards higher values of C. E. M. F. e. The upper parts of the curves however I have never been able to observe experimentally, and consider it as probable, that they correspond to a condition of synchronous motor running, which is unstable. The experimental observations usually extend about over that part of the curves of Fig. 4, which is reproduced in Fig. 5, and in trying to extend the curves further to either side, the motor is thrown out of synchronism. 1894.] STHINMETZ ON THE SYNCHRONO US MOTOR. 681 It must be understood, however, that these power character- istics of the synchronous motor in Fig. 4 can be considered as approximations only, since a number of assumptions are made, which are not, or only partly fulfilled in practice. The foremost of these are: 1. It is assumed that e, can be varied unrestrictedly; while in reality the possible increase of e, is limited by magnetic saturation. Thus in Fig. 4, at an impressed E. M., F. e., - 2,500 volts, e, rises up to 5,590 volts, which may or may not be beyond that which can be produced by the motor, but certainly is beyond that which can be constantly given by the motor. 140 | L: LZ / l 00 a 3; N 2. / // |NLC/ { A 20 sº Volts I 50) 1000 1500 3000 2500 3000 3500 4000 4500 5000 FIG. 5. 2. The reactance sis assumed as constant. While the reactance of the line is practically constant, that of the motor is not, but varies more or less with the saturation, decreasing for higher values. This decrease of s increases the current e corresponding to higher values of et, and thereby bends the curves upwards at a lower value of e, than represented in Fig. 4. It must be understood that the motor reactance is not a simple quantity, but represents the combined effect of self-induction, that is, the E. M. F. induced in the armature conductor by the cur- rent flowing therein, and armature reaction, that is, the variation of the C. E. M. F. of the motor by the change of the resultant 682 STEINMETZ ON THE SYNCHRONO US MOTOR. [Oct 17, field, due to the superposition of the M. M. F. of the armature current upon the field excitation. 3. These curves in Fig. 4 represent the conditions of constant electric power of the motor, thus including the mechanical and the magnetic friction (core loss). While the mechanical friction can be considered as approximately constant, the magnetic fric- tion is not, but increases with the magnetic induction, that is with el, and the same holds for the power consumed for field exci- tation. Hence the useful mechanical output of the motor will on the same curve p = const. be larger at points of lower C. E. M. F. e., than at points of higher ei, and if the curves are plotted for con- stant useful mechanical output, the whole system of curves will be shifted somewhat towards lower values of e1, hence the points of maximum output of the motor correspond to a lower E. M. F. also. It is obvious that the true mechanical power characteristics of the synchronous motor can be determined only in the case of the particular conditions of the installation under consideration. To BE issued OCTOBER 20, 1894. AMERICAN INSTITUTE OF | ELECTRICAL ENGINEERS. Members' Wºº Year-Bºk, |Revised to SEPTEMBER 1st, 1894. CONTENTS: *AGº- Officers, Members of Council, C R.A.-- i tº List of Honorary Members and Members.----...............— ....... I - * Associate Members.... . 1 ºf Summary of Memb hip 4. It Past Officers ... ... ... <-2 Geographical Distribution...... 43 Definitions of New Units... 58 Rules of the Institute . .--, ...... 57 Classified List of Papers Published 62 calendar of Meetings. - HEADQUARTERS OF THE INSTITUTE. 12 WEST 81st STREET, New Yobs. TELEPHONE, 1512 38TH. | All Members and Associate Members, who have paid their - dues for the current year are entitled to a copy of the MEMBERs' Pocket YEAR-Book. - Revised to September 1, 1894. The above plate is an exact fac-simile of the title page. RALPH. W. Pop E, Secretary. ****, r*.*.*|American ElectricalWorks, PROF. W.M. A. AWTHowy, Manufacturers of TEMPLE COURT, . . NEW YORK, [BARE & /MSULATED ELECTRſc W/RE, CABLES, &c. United States and Foreign Patents, Electrical Specifications, Expert Advice and Testimony. P rovid € Y) Ce, - R m I is DAY'S KERITE Highest Grade of Insulation for - ºf Flºriº Wilts and Calls, —GRANTED :- - Two Highest Awards World’s Fair, W. R. BRIXEY, T = - Chicago, Ill., 1893. Sole MANUFACTURER, J. E. H.A.M., 203 Broadway, - New York. General Agent EXPERIMENTAL AND MODELVORK, Electrical Apparatus and Fine Machinery, Special Tools, Patterns, Gear Cutting, Specialties, Repairs, Etc. E. V. BAILLARD, 106 Liberty St., N. Y. TRANSACTIONS WANTED. I have orders on file for volumes 3 and 4 (1886 and 1887) Transactions A. I. E. E., wanted by new members and libraries to complete their sets. The following prices will be paid for copies in good Order. - - Volume 3, - E- - m . $2. Volume 4, - tº tº a sº - $3. Address, RALPH. W. Pope, Secretry. McINTOSH, SEYMOUR & CO. | AUEURN, N. Y. —BU ILIDERS OF- . Engines". Electrical Purposes. OPE, READ & ROGERS. ! * | CO RT L.A. N. DT ST, N.Y. atents for Electrical Inventions THE AMERICANBFILTELEPHONE COMPANY 125 MILK STREET, BOSTON, MASS. This company owns Letters-Patent No. 463,569, granted to Emile Berliner November 17, 1891, for a combined telegraph and telephone, and controls Letters- | Patent No. 474,231, granted to Thomas A. Edison May 3, 1892, for a speaking telegraph, which Patents cover fundamental inventions and embrace all forms of micro- phone transmitters and of carbon telephones. * American Institute of Electrical Engineers. Members of the Institute, who have been transferred from associate to full membership, can now receive the official Certificate issued by the Institute, upon applying to the Secretary, and enclosing the sum of two dollars ($2.co) to cover cost of same, and the engrossing of names, necessary dates, etc. In ordering a certificate, the name of the applicant should be plainly written, exactly as he desires to have it appear. These Certificates are printed upon heavy parchment paper, from an engraved steel plate. Associate as well as Full Members are entitled to receive the Official Badge of the Institute which is now prepared in the following forms and at prices stated: Pin, $3 ; Scarf-pin, $3 ; Lapel Button, $3 ; Watch Charm, $3 ; Locket for single picture, $8; 1 ouble Locket for two pictures, $10. THE OFFICIAL BADGE ADOPTED BY THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS EMBODIES THE FOLLOWING CHARACTERISTICS FRANKLIN'S KITE, which demonstrated the identity between Lightning and Electricity, and represents static electricity. It is a recognition of America’s. first Electrician and Phi- losopher, Benjamin Franklin. A diagrammatic representation of Wheatstone’s Bridge, one of the most im ortant pieces of electrical testing apparatus THE GALVANOMETER, another equally important piece of test- ing apparatus and which represents Magnetism and Induction. - THE AMBER of which the galvanometer is made represents the first conception of electricity, dating back to 6oo years B. C., when Thales, the Greek philosopher, recorded the fact that amber, when rubbed, attracted light particles to it, and the Greeks worshipped it, be'ieving the gods had endowed it with life, and that it possessed a soul. -- In 16oo A. D., Dr. Gilbert, court physician to Queen Elizabeth, coined the word Electricity from the word Elektron, the Greek name for Amber. , L. E. E. represents the initials of the American Institute of Electrical Engineeers. # , C-É represents represents Ohm's I aw—a fundamental law in electrical work. ~. The badge is made of white enamel, with the lettering and front, portions, of 18 karat gold, and ºthebacking in 14 karat gold. Apply to the Secretary, 12 W. 31st St, New York jº., 's, •ºt st & Contents of Vol. X. 1893. REPORT of Committee on ProvisionAL PROGRAMME for CoNGREss of 1893. ELECTRICAL REcoRDING METERs. (Illustrated.) By Caryl D. Haskins. No. 1, January 1893. ELECTRICAL RECoRDING METERs. (Discussion). SUPPLEMENT TO REPORT of SUB-COMMITTEE on PROVISIONAL ProgRAMME. NoTE on DISRUPTIVE DISCHARGE THROUGH DIELECTRICs. (Illustrated.) C. P. . Steinmetz. THE Most EconoMICAL AGE OF INCANDESCENT LAMPs. (Illustrated.) Carl Hering. No. 2, February, 1893. THE COST OF STEAM Power PRODUCED witH ENGINES OF DIFFERENT Types UNDER PRActicAL CoNDITIONS; witH SUPPLEMENT RELATING To WATER Power. By Chas. E. Emery, Ph. D., of New York City. THE Most EconoMIcAL AGE of INCANDESCENT LAMPs. (Communications and Discussion.) , NoTE ON DISRUPTIVE DISCHARGE THROUGH DIE- LECTRICs. (Communications and Discussion.) No. 3, March, 1893. THE COST OF STEAM Power, Etc. (Discussion.) IMPEDANCE. (Illustrated.) By A. E. Kennelly. No. 4, April, 1893. IMPEDANCE. By A. E. Kennelly. (Discussion and Correspondence.) ON THE BEHAvio R OF FUSE METALs in DIRECT AND ALTERNATE CURRENT CURCUITs. (Illustrated.) By Chas P. Matthews. A MoDIFIED DEPREz D'ArsonvaL GALVANOMETER. (Illustrated.) By Chas. D. Parkhurst. AN AUTomi ATIC PRINTING SPEED-CountER For DYNAMo SHAFTING. (Illustrated.) By Geo. S. Moler. THE WARIATION IN EcoMony of THE STEAM ENGINE, DUE to VARIATION IN LOAD. (Illustrated.) By Prof. R. C. Carpenter. APPENDIX IV. Report of Sub-Committee on Provisional Programme World's Electrical Congress. No. 5, May 1893. ANNUAL MEETING, May 16, 1893. REPORTs of Council AND TREASURER. REPORT OF TELLERs. ON THE BEHAVIOR of FUSE, METALs. (Discussion.) A MoDIFIED DEPREZ-D’ARSoNVAL GALVANOMET R. (Discussion.) THE WARIAt Ion IN EconoMY of THE STEAM ENGINE. (Discussion.) HEATING OF ARMATUREs. (Illustrated.) By A. H. and C. E., Timmerman. PRACTICAL ASPECTS OF ELECTRIC VL-FESONANCE. (Illustrated.) By Dr. M. I. Pupin. CoMPILATION OF DISCUSS ONs, SUGGESTIONS AND CRITICISMs, APPEARING IN THE TECHNICAL AND ScIENTIFIC PRESS UPon THE REPORT AND PROVISION L PRO- GRAMME of THE SUB-COMMITTEE APPoſNTED BY THE AMERICAN INSTITUTE OF ELEC RICAI. ENGINEERs, PROGRAMME of WoklD's ELECTRICAL Congress. (Discussion.) ON THE No TAtion Proposed By M. HospitaLER. By Prof. Alex. Macfarlane. Comtm ENTs on THE REPORT OF THE CoMMITTEE ON THE PROvISIONAL PROGRAMME FOR THE Congress. By Dr. John Sahulka. Nos. 6 and 7, June and July, 1893. A NEw METHOD FOR THE CONTROL of ELECTRIC ENERGY. (Illustrated.) By D. McFarlan Moore. EMERY os THE CoST of STEAM AND WATER Power. (Comm nicated Discussion.) By L. B. Stillwell. PARKHURST ox GALVANOMETERs. Reply to Discussion Communicated by the Author. Nos. 8 and 9, August and September, 1893. DISCUSSI N of “A NEw METHop For th & CoNTRol of ELECTRIC ENERGY.” THE INTERNATIONAL ELECTRIC CoNGREss, AND World's FAIR OF 1893. INAUGURAL ADDRESS. By Edwin J. Houston. REPORT of THE CHAMBER OF ID ELEGATEs. Month LY MEETINGs of THE INSTITUTE: THEIR ORIGIN AND PROPosed DEVELOPMENT. By Ralph W. Pope. HEDGEHog TRANSFORMER AND Cow DENSERs. Illustrated.) By Frederick Bedell. No. Io, October 1893. A BRIEF GLANCE AT ELECTRICITY IN IEpicine. (Illustrated.) B v. W. J. Morton. No. 11, November, 1893. REPort of CoMMITTEE on Local MF ETINGs. THE PRActicABL, ITY OF FILECTRIC CONDUIT RAILwAys. By Albert Stetson, REPORT of CoMMITTEE on UNITS AND STANDARDs. No. 12, December, 1893. Contents of Vol. XI. 1894, as far as Published. CATALOGUE OF MEMBERSHIP. PROPOSED REvision of ELECTION RULE. PRACTICABILITY OF ELECTRIC ConDUIT RAILwAys. (Illustrated.) (Discussion.) No. 1, January, 1894. PRACTICAL PROPERTIES of PolyPHASE APPARATUS, (Illustrated.) By Louis Bell, Ph. D. REPORT OF CoMMITTEE ON REvision of ELECTION RULE. How SHALL we OPERATE AN ELECTRIC RAILway roo MILES FROM THE Power STATION. (Illustrated.) By H. Ward Leonard, CoNCERNING A CHANGE IN Policy IN THE ADMINISTRATION OF THE PATENT OFFICE. By Philip Mauro. No 2. February, 1894. ON THE EFFECT OF HEAVY GASEs IN THE CHAMBER of AN INCAND ESCENT LAMP. By Prof. Wm. A. Anthony. CIRCULAR OF COMMITTEE ON JNcompi.ETED Congress WoRK. No. 3, March, 1894. ON THE EFFECT of HFAvy GASES IN THE CHAMBER of AN INCAND Escº NT LAMP. (Discussion). Conce RNING A CHANGE of Policy IN THE ADMINISTRATION of the PATENT OFFICR. (Communication). DEstructive EFFECT of ELECTRICAL CURRENTs on St BrFR." ANRAN MiBTAL PIPEs. (Illustrated). By Isaiah H. Farnham. No. 4, April, 1894. DiscRIMINATING LIGHTNING ARRESTERs, AND RECENT PRocRESS IN MEANS For Protection AGAINST LIGHTNING. (Illustra ed.) By Alex. J. Wurts. ON THE SUBDIVISION AND DISTRIBUTIon of ARTIFICIAL Sources of JLLUMINATION. Illiistrated.) By Prof. William A. Anthony. No. 5, May, 1894. A REVIEw of THE PROGRESS OF THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERs, (illustrated ) By President Houston. Some StoragE BATTERY PHENoMENA. (Illustrated.) By W. W. Griscom. UNIPOLAR DYNAMos For ELECTRIC I.IGHT AND Power, (Illustrated.) By Prof. Francis B. Crocker and C. Howard Parmly. DISEASEs of DYNAMos. By Lieut, C. D. Parkhurst. No. 6 and 7, June and July, 1894. ALTERNATING CURRENTS AND FUSEs. (Illustrated.) By D. C. Jackson and R. J. Ochsner. "A STUDY OF THE RESIDUAL CHARGES of ConDENSERs, AND THEIR TEPEND. ENCE Upon TEMPERATURE. (Illustrated.) By Frederick Bedell and Carl Kinsley. THE ELECTRIC BRAKE IN PRACTICE. (Illustrated.) By Elmer A. Sperry. Nos. 8 and 9, August and September, 1894. TEST of A CLosäD Coil Arc DYNAMo, (111ustrated.) By Prof. R. B. Owens and C, A. Skinner. RELATIVE ADVANTAGES of Tooth ED AND Swooth Col. E ARMATUREs, By A. D., Adams. STANDARDIzıNG Electrical MEASURING INSTRUMENTs. (Illustrated.) By E. G. Willyoung. AN OPTICAL PHASE INDICATOR AND SYNCHRONIzER. (11 ustrated.) By Prof. Geo. S. Moler, and ſ}r. Frederick Bedell. A NEw METHOU of RF corp ING ANY KIND of VARIABLE CURRFN'r, (lilustra' ed.) By Prof. A. C. Crehore. ResonANCE ANALysis op ALTE NATING AND PolypH ASE CURRFNTs. (Illustrated.) By Prof. M. I. PUPIN. TH F or Y F Two AND THREE PHASE Morok's (! Ilustrated.). By Lieut. Samuel Reber. THEoky of THE SYNCHRON ous Motor. (llustrated.) By Chas. P. Steinmetz. No. ro, October, 1894. f With the Compliments of the Author, [FROM THE AMERICAN Journal, OF SCIENCE, WoL. XLVIII. Nov., 1894.] RESONANCE ANALYSIS OF ALTERNATING CURRENTS. By M. I. PUPIN. ART. LIII.-Resonance Analysis of Alternating Currents;* [FROM THE AMERICAN Journal or ScIENCE, Vol. XLVIII, Nov., 1894.] by M. I. PUPIN, Ph.D., Columbia College. I. Introduction. THE presence of upper harmonics in an alternating current wave is a fact which deserves careful consideration both on . account of the purely scientific interest which is attached to it, and also on account of the technical bearing of electrical reso- nance upon the construction of conductors possessing apprecia- ble distributed capacity. - That alternating current and electromotive force waves of a very great variety of forms can be produced by properly design- ing the pole-pieces of the field magnet, and the iron core of the armature of an alternator is a fact nearly as old as the discov- ery of electromagnetic induction. Fully as old is also the knowledge that a great variety of alternating current and elec- tromotive force waves can be obtained by the induction of an intermittent current. A careful investigation of these waves was first made more than forty years ago by Lenzt and Koosen, who employed alternators with iron in the armature. They plotted these waves from the instantaneous values of current and electromo- tive force obtained by means of the now well-known revolving sliding contact. Employing the same method of investigation Jouberts showed in 1880 that the electromotive force wave obtained from an eight pole Siemens alternator without iron in the armature is very nearly a sine wave. The method is now known as Joubert’s method of the sliding contact. The name “indicator diagram ” has been applied to the wave curves of current and electromotive force obtained by Joubert’s method, and very properly, I think, because they do very clearly indi- cate the action of alternating current apparatus. Our knowledge of the action of alternating current apparatus has been extended quite considerably by these indicator dia- Taſſl S. Although much must be said in favor of the sliding contact method of obtaining indicator diagrams, yet it must be also acknowledged that the method is a very laborious and uninter- esting process of investigation. Many attempts have been made to devise some optical or some automatic method, but * Read before the Annual Meeting of the American Institute of Electrical Engi- neers at Philadelphia, May 17th, 1894. + Pogg. Ann. lxxvi, p. 494, 1849; xcii, p. 128, 1854. # Ibid., lxxxvii, p. 386, 1852. § Comptes Rendus, vol. xci, p. 161, 1880; Ann. de l'école super. 10, p. 131, 1881. 2 Pupin—Resonance Analysis of Alternating Currents. with little success. There is another reason why a néw method of studying alternating current waves seems desirable. It is this: the method of sliding contact is not sufficiently sensitive to detect small deviations from a true sine wave, and conse- quently it is not capable of following up the causes of these deviations, when the effects seem to be absent. For instance, the primary current of a transformer can differ very much from a true sine form when the secondary circuit is open, but when a large current is flowing through an approximately non- self-inductive secondary circuit, then the primary current can be made to differ inappreciably from a true sine wave. The question arises now, what becomes of these causes when the secondary carries a heavy non-self-inductive load? This question is of deep scientific interest; it is also of con- siderable technical importance. For, if these causes are present at all loads and only hidden by the principal wave, then, con- sidering that these hidden small causes can produce large effects when conditions favoring resonance arise, it is evident that they must be carefully watched and guarded against in the construction of lines possessing appreciable distributed capacity. I do not think that indicator diagrams obtained by the method of sliding contact are capable of giving a definite answer to this important question. The method of analyzing alternating current waves by elec- trical resonance which I employed in the following investiga- tion was suggested by me a year ago.” It is the object of this paper to describe this method at some length and to illustrate, by some of the more definite results so far obtained and relating principally to the causes which produce distortions in simple harmonic waves, the simplicity, sensitiveness, and reliability of the method. I shall also point out that this method of reso- nance analysis works quite satisfactorily even in those cases, alluded to above, where the sliding contact method would in all probability fail to detect any distortion whatever. II. Description of the Method. Consider the following arrangement of circuits:—The non- self-inductive resistance, ab, fig. 1°, is inserted in the circuit of an alternator A and the primary B of a transformer. In shunt with ab is a circuit acdb consisting of an inertia coil c of large number of turns of copper wire of low resistance, about 10 ohms, but containing no iron, and a mica condenser d divided into subdivisions ranging from .001 M.F. up. In shunt with the condenser d is an electrostatic voltmeter e. The self-induc- tion of the coil e can be varied by throwing a larger or a smal- * M. I. Pupin, “Electrical Oscillations of low frequency and their Resonance,’ this Journal, vol. xlv., p. 429, May, 1893. . - Pupin—Resonance Analysis of Alternating Currents. 3 ler number of its sections into the circuit. The resistance can be varied by a rheostat f. Suppose now that the self-induction of c is kept constant, and that the capacity of the condenser d is gradually increased from zero up. Whenever a capacity has been reached which with the self-induction of the circuit acdf'b 1a. © produces resonance with one of the harmonics in the main cir- cuit then the resonant rise of potential will produce a large deflection in the voltmeter. In this manner all the harmonics which are present in the current of the main circuit can be detected in the course of a few minutes. If the resonator cir- cuit acdf b is placed in shunt with the non-self-inductive cir- cuit g (this circuit is represented in fig. 1" by a line beaded with asterisks and running from one pole of the alternator to the other) consisting of a bank of incandescent lamps then the harmonics of the impressed electromotive force can be detected in the same manner. The ratio of the amplitudes of these har- monics to that of the fundamental can also be determined by this method, ºf desirable, provided the conditions of the experiment are properly arranged. For let the current in the main circuit be a:= a, sin pt--a, sin 3pt + . . . . . +aza + 1 sin(2a+ 1)nt-H . . then the drop between a and b can be represented by e=ö, sin pt-- . . . . --ó2a+ 1 sin(20 + 1)pt + . . . where b2a+1=aza 4 17’ and r = ohmic resistance between a and b. Denoting now by : L the self-induction of the resonator aeſha - R the resistance “ & & C the capacity && “ “ 4 Pupin—Resonance Analysis of Alternating Currents. then it can be easily shown” that the current in the resonator will be : 3 *rī - 3/=a l 0 2 I 2 ... 2 *===ºmºmºsºm-mº-ms- L 2 R” Węa Dº tºot";" If, therefore, the capacity C is adjusted in such a way that –– — L- 0 (2a+1)^p"C then the circiut will be in resonance with the harmonic of fre- sin [(2a+1)pt + p.2a+1] Quency (ºr ; and if L is sufficiently large and R sufficiently T small (two conditions which are very easily fulfilled) the cur- rent y will in general to within a small fraction of a per cent be given by b 2a 4- 1 . v= -R- sin (2a+ 1)nt The amplitude of the potential difference in the condenser which is measured by the voltmeter e is then given by P2a+1_(2a+1)pſ 1)pL R %2a+1 In the same way we obtain for the fundamental frequency L P, =#5, Hence P2a+ I , %22+ I P F. (2a. + 1) b l l This gives the ratio of the amplitude aza * of the harmonic of frequency (ºr to that of the fundamental. Let a-2, then, 27T The voltmeter readings which give P, and P. magnify that ratio five times, in the case of the fifth harmonic, and it can be easily seen that a similar relation holds true for other har- monics. This is a very desirable feature of the method, con- sidering that the amplitudes of the upper harmonics are gener- ally small in comparison to the amplitude of the fundamental, ºnly when the secondary circuit of the transformer carries a load. & * * For further information see author's paper cited above. Pupin—Resonance Analysis of Alternating Currents. 5 When quantitatively very accurate results are desired then a low resistance, say one ohm, should be used for the section ab ". an electrometer capable of giving a large deflection for ten VOltS, The principal interest, however, in the study of the distor- tion jº. current waves, is centered not so much in the exact ratio of the amplitudes of these harmonics to the amplitude of the fundamental wave, as it is in the causes pro- ducing these harmonics and the conditions which modify the effects of these causes. Hence a quantitatively less accurate arrangement will do, provided that it is very sensitive, simple, and easily manageable. , Such an arrangement is given, fig. 1". It differs from that given in fig. 1" in the sūbstitution of an air core transformer coil a'b' for the non-self-inductive resist- ance ab. The secondary of this coil forms a part of the resonator circuit. For every harmonic of the inducing current we shall have a harmonic electromotive force of the same fre- quency in the resonant circuit. By varying the capacity in the resonator and watching the voltmeter needle, we can tell by . the deflection of the needle, whenever we have reached the capacity which with the self-induction of the resonator brings this circuit into resonance with one of the harmonics. A refer- ence to fig. 2 will explain this more clearly. 2. * - . af In this figure the lower horizontal row of figures refers to the two-peaked curve; the upper row refers to the dotted flat-peaked 0 1 2 3 5 & 7 8 9 10 11 12 13 14 15 16 17 18, 19 20 1ö’Farade 2 º 6 Pupin—Resonance Analysis of Alternating Currents. curve. The vertical row denotes the voltmeter readings in volts. Consider now the two-peaked curve. It expresses the law of variation of the voltmeter readings when the capacity of the resonator circuit is varied from 0 to 2 microfarads, the self-induction being kept constant. The readings are recorded in Table I. TABLE I. Capacity of the condenser Woltmeter readings in microfarads. in volts. • 18 62 • 181 68 * - 182 73°5 • 183 & 79 *184 89 • 185 96 ‘186 - 104 • 187 110 • 188 - 120 • 189 126 • 190 127 • 191 125 • 194 99 •] 98 71 •202 very low I-65 69 1-70 89 1.75 120 1 '80 146 I '808 146 1.817 145 1-89.7 96 I '976 60 The voltmeter employed in these experiments was a Sir Wil- liam Thomson's multicellular voltmeter with a range from 60 to 240 volts. The curve was obtained from a 10 H. P. Fort Wayne 8 pole alternator with a smooth core armature feeding a 5 K. W. Stanley transformer (closed magnetic circuit), the secondary circuit being open. It is seen that resonance took place at 190 M. F. and 1.8 M. F. The capacity of the inertia coil cº, fig. 1" and of the voltmeter as gathered from all experi- mental data was about 011 M. F., so that the real capacities at which resonance took place were 201 M. F. and 1.81 M. F., that is in a ratio to each other as 1:3°. It will be seen, how- ever, that a very accurate knowledge of capacity is not required in the experiments described in this paper. The frequencies detected by the two-peaked curve, which I shall call the resonance diagram, were therefore the funda- º Pupin—Resonance Analysis of Alternating Currents. 7 mental and the 1st odd harmonic, that is the harmonic of three times the frequency of the fundamental. The resonance dia- gram has, of course, as many peaks as there are harmonics in the inducing current.* The dotted curve (flat-peaked) in fig. 2 was plotted on an enlarged scale from the readings taken in detecting the first harmonic represented by the sharp peak of the resonance diagram, and represents this peak spread out, so as to show how the various readings fit into a well defined and symmetrical curve such as required by theory. It also shows that a condenser of small subdivisions should be employed in detecting higher harmonics. - III. Description of Eageriments. The resonance diagram obtained by the method of fig. 1" gives the number of harmonics which are present in the induc- ing current. It does not give the exact value of the ampli- tudes of these harmonics. It would be somewhat premature to discuss the theory of the resonance diagram obtained by this arrangement and to show how the ratio of the amplitudes of the harmonics to that of the fundamental frequency in the in- ducing current, that is the exact color of this current, could be calculated from the ratio of the height of the peaks in the resonance diagram. Suffice it for the present to mention only that the peaks of this diagram represent the amplitudes of the harmonics magnified about proportionally to the square of the frequency. For instance, the resonance diagram of fig. 2 tells us that the amplitude of the 1st odd harmonic in the inducing current is about one-ninth of the amplitude of the fundamen- tal. The determination of the exact value of this ratio was not the object of the following experiments. Their aim was to detect the presence of harmonics, to trace their origin and to study their variation with the variation of the load, and of other variable elements of the circuit on which these harmonics seem to depend. Preliminary Tests. In order to form an estimate in how far the experimental data obtained by the arrangement of fig. 1" agreed with the theory the following tests were applied: *I have never detected an even harmonic in alternating current waves pro- duced by ordinary commercial alternating current apparatus, and conclude, there- fore, that these harmonics do not exist in such cases. For asymmetrical machines this would obviously not hold true. Alternators with slotted armatures give waves in which all the odd harmonics up to the harmonic of nine times the fre- quency of the fundamental can be detected. As a rule the first odd harmonic is the strongest. 8 Pupin—Resonance Analysis of Alternating Currents. a. Study of the damping effect of the dielectric in the condenser. Let L = self-induction of the resonator circuit. R = resistance of the resonator circuit. P = amplitude of the difference of potential in the condenser when point of resonance has been reached for a given frequency. - E = amplitude of impressed electromotive force in the reso- nant circuit. then according to theory _pL P = R. E. Hence if R alone is varied P will vary also but in such a way that P R = constant. That is to say if we vary the resistance of a resonant circuit and tabulate the voltmeter deflection for every particular resist- ance and then plot a curve taking the resistance for abscissae and the voltmeter readings for ordinates we should, according to theory, obtain an equilateral hyperbola. , Curves II and III, fig. 3, were obtained in this manner, the frequency employed was that of the 10 H. P. alternator, that is 130 p. p. S. 3. Pupin—Resonance Analysis of Alternating Currents. 9 TABLE II. Woltmeter readings Woltmeter readings Theoretical Resistance with a mica with a paraffin value of volt- in ohms. condenser. condenser. meter readings. 38 183 170 225-6 48 155 148 -- I 78-6 53 144 1.37 16 1-8 58 134 128 147-8 63 J 25 I 20 | 36 68 1 | 8 II 3 126 78 105 10 1 1 1 0 88 94 91 97.4 98 . 85 83 87-5 108 78 76 79°4 118 72°5 70 72.6 128 67 65 - 65°5 138 62 60 60 The experimental data from which these curves were plotted are given in Table II. Curve II was plotted from voltmeter readings obtained with a mica condenser, Curve III represents the corresponding readings obtained with a paraffin condenser and given in the third column of Table II. Curve I repre- sents the theoretical curve, that is the curve which would have been obtained if the law of variation of the voltmeter readings with the resistance had been the same throughout as it was at low readings. On account of the damping effect due to dielec- tric viscosity in the condenser a deviation from the above mentioned hyperbolic relation was of course expected, but it was quite a pleasant surprise to find a perfect regularity of these deviations. These curves indicate a rapid increase in the dielectric damping with the voltage and also the superiority of mica to paraffin, especially at higher voltages. They also suggest that at low voltages and frequencies over a hundred periods per second this difference between the two substances becomes less and less marked. It was also found in a similar way that the damping effect of the magnetic viscosity of iron is small at low magnetizations, such, for instance, as would be produced by a telephonic current in a telephone receiver, and at frequencies which are well within the range of higher tele- phonic frequencies, say 750 periods per second. Similar curves and similar results were obtained with higher harmonics. These experimental tests show, therefore, that the relative values of the amplitudes of the harmonics to that of the fundamental frequency are not seriously modified by the dielectric damping of the condensers, especially when one operates with moderate voltages as was the case in the follow- ing experiments. - * 10 Pupin—Resonance Analysis of Alternating Currents. b. Second test of the resonator indications. 4 - e º * CD w” ºf ** **, ~ *, *, *3. * * - C .G.) (2). Aº This test is represented graphically by diagram fig. 4. Two transformers C and D had their secondaries connected in series. The primary of the air-core transformer E formed part of their circuit. The secondary of the transformer E was a part of the resonator F. The transformer C, a Stanley 5 K.W. (closed magnetic circuit), was fed by the 10 H. P. alternator mentioned above (130 p. p. s.), the transformer D of induction coil type with a cylindrical core of fine iron wire was fed by a 1 H. P. alternator with slotted armature (278 p. p. s.) Both alternators were run simultaneously at full excitation. First, the primary circuit of the large alternator was broken, so that the current in the circuit CDE was due to the action of the small machine alone. The resonator detected a resonant rise of 240 volts at capacity .407 M. F. and another of 150 volts at capacity '044 M. F. These were evidently the fundamental and the first odd harmonic. Then the circuit of the small machine was broken and that of the large machine closed, so that the cur- rent in the resonator was due to the action of the large machine alone. The resonator detected a resonant rise of 220-1 volts at capacity 1.78 M. F. This corresponded to the fundamental frequency (130 p.p.s.) of the large machine. Finally both circuits were closed, so that the current in the resonator was due to the simultaneous action of the two machines. The same resonant rises of potential were detected by the resonator and i. the same capacities as before, in perfect agreement with theory. * - + * & # i. ". experiment afforded another opportunity of testing the theory which underlies this resonance method of studying the Pupin—Resonance Analysis of Alternating Currents. 11 wave curves of current and electromotive force. It is this: If two or more electromotive forces of different frequencies are impressed upon the resonator circuit and their resonant rises of potential are determined for a given resistance in this circuit, then according to theory the ratio of these rises should remain the same for all other resistances within the limits within which the periodicity of the circuit is practically independent of the ohmic resistance. Accordingly, the resistance of the resonator F, fig. 4, was varied gradually from 100 to 250 ohms (the self-induction of inertia coil in the resonator circuit was about 75 Henrys) and the resonant rises of potential produced by the fundamental frequencies of the two machines (130 and 278 p. p. s.) were carefully determined for each particular resist- ance. The ratio of these rises remained constant to within five per cent but the deviations were now in one direction and now in the other. They were undoubtedly due to the varia- tion in the excitation and the speed of the small machine, both of which depended on the potential of the electric mains of the College plant which, of course, could not be kept very con- stant for so long an interval of time as is necessary for this ex- periment, which was about 15 minutes. These preliminary experimental tests demonstrate clearly that a resonator of the type given in fig. 1" is quite capable of detecting all the frequencies that may exist in an alternating current wave, that its indications are in good agreement with the theory as far as the fundamental frequency is concerned and that it gives a fairly approximate idea of the relative strength of the harmonics. 12 Pupin—Resonance Analysis of Alternating Currents. IV.- Location of the Origin of Upper Harmonics. A. Experiments with alternator of smooth core armature. 1st Series.—The first set of experiments in this direction was performed with the 10 H. P. Fort Wayne 8 pole alterna- tor with smooth core armature and the Stanley 5 K. W. trans- former (closed magnetic circuit). The Secondary circuit car- ried no load and a Cardew voltmeter indicated the secondary voltage. The current which excited the field of the alternator was gradually increased. The secondary voltage measured the strength of this excitation. The air core transformer with the resonator was inserted into the primary circuit as indicated in fig. 1". The resonant rise of potential, recorded by the multi- cellular voltmeter e', was carefully determined at every excita- tion for the fundemental frequency and for the first odd har- monic. Higher harmonics were present but very faint. The results are given in Table IV and plotted in fig. 5. The initial voltage in the resonant circuit was small, just perceptible in the multicellular voltmeter. TABLE IV. Resonant rise in volts Resonant rise in volts due to the first odd Secondary voltage. due to the fundamental. harmonic. 43 122 58 48 130 65 53.5 136 72 56 138 73 62 146 80°5 66.75 152 86 75 160 94 83 - 170 104. 88 175 110 97 185 117 104 195 128'5 Pupin—Resonance Analysis of Alternating Currents. 13 5. *H 2 1ſo ~~ © 1% 2 H 21 189H2 J21 |: J2^ aft: 2.1–1. i. J21 tº: 2" 199 - 99 Lºr .* J^ Q& P- | º (50 Volts in Secºndary • 45 § $ $º 6; 70 ($ 80 $ 90 95 100 105 The curves in fig. 5 were plotted from this table by taking the readings of the first column for the abscissae and the cor- responding readings of the second and third columns for ordi- nates. The upper curve corresponds to the fundamental and the lower curve to the harmonic. The two eurºesºe two straight lines parallel to each other, which means theißhe fun- damental and the harmonic increase at the same rate from nearly one third eaccitation to full eaccitation of the alternator. This result was not expected, but its correctness was verified beyond all reasonable doubt. e The same series of experiments was extended to lower exci- tations of the alternator, but, since I had no low reading alter- nating current voltmeter, the excitation was measured by measuring the exciting field current. This current was 10 amperes at full excitation and the series of experiments ex- tended down to 1-5 amperes, hence to nearly one seventh of 14 Pupin—Resonance Analysis of Alternating Currents. the full excitation. To bring the readings of the resonant rises of potential within the scale of the multicellular voltmeter at these low excitations the number of turns in the air-core transformer was suitably increased. Within all these limits of eaccitation both the fundamental and the harmonic increased at the same rate and proportionally to the magnetization of the transformer core. This magnetization extended between about 600 and 4000 C.G.S. lines of force per square centimeter. 2d Series.—To determine whether the presence of the harmonic was due to the action of the transformer or to that of the alternator the transformer was disconnected from the alternator and two series of incandescent lamps, connected in parallel, were substituted in its place. Each series consisted of 13 twenty-four candle power lamps. The resonator with its air-core transformer remained in circuit as before. First one series of lamps was placed in circuit. The rise due to the fundamental was stronger than in the preceding experiments, but that due to the harmonic was exceedingly faint. When both series of lamps were thrown in the harmonic appeared a trifle stronger but still very weak. Hence the inference, that the harmonic was due almost exclusively to the action of the transformer. - It should be observed here that the alternator armature, though well laminated, runs fairly hot in a short time, hence it must be the seat of a decidedly strong hysteretic action. On the other hand the transformer does not heat nearly as much as the alternator armature and yet its action produces the harmonic. This certainly seems to speak strongly against the view that harmonics are due to hysteresis. Other evi- dences against this view will be given below. 3d Series.—A series of experiments with open magnetic circuit transformers of induction coil type in place of the lamps. showed the harmonic much stronger than the lamps did, but considerably weaker than the experiments with the transformer with closed magnetic circuit. Accurate numerical comparisons between the two types of transformers in this respect was not attempted. It sufficed to establish that, closed magnetic cir- cuit transformers distort the primary current considerably 'more than transformers with open magnetic circuits under equal degrees of magnetization ; on the other hand, in the first case the distortion is confined almost entirely to the pri- mary circuit when the secondary is closed by a non-self-induc- tive resistance, whereas in the second case it is felt in the secondary circuit also, though considerably less than in the primary. Pupin—Resonance Analysis of Alternating Currents. 15 The general conclusions of this group of experiments may be summed up as follows: I. A ferrio self inductance in circuit with an alternator which gives a simple harmonic electromotīve force distorts the current by introducing higher odd harmonics, principally the harmonic of three times the frequency of the fundamental. II. This harmonic (and in all probability all other harmon- ics) increases at the same rate as the fundamental when the ea citation increases, the rate of increase being up to 4000 C. G. S. lines of force per sq. centºm proportional to the intensity of magnetic induction. III. When this ferrie inductance is a transformer then the distortion appears in the induced secondary electromotive force, if the transformer has an open magnetic circuit, it does not appear there (to any eatent worth considering) if the magnetic circuit is a closed one. IV. A practically simple harmonic electromotīve force is produced by alternators with smooth core armatures when symmetrically wound, even if the machine is worked at con- siderable degrees of magnetization of the armature core. B. Eacperiments with alternator of slotted core armature type. The machine employed in these experiments was the 1 H. P. alternator mentioned above. It is a 16 pole machine with slotted armature core. It gives at full excitation and the speed at which it was usually run in these experiments about 1500 volts.” The transformer connected with it was of induction coil type with a cylindrical iron core made up of very care- fully insulated fine iron wire. The same series of experiments were performed as under group (A). The first series in this group gave exactly the same results as the corresponding series in group (A). The excitation varied from one-seventh of the full to full excitation; the amplitude of the fundamental and the first odd harmonict varied at the same rate during the whole interval, so that a parallel pair of straight lines like those in fig. 5 could be plotted in this case also. The second series resulted in the conclusion that the harmonic was very strong and due, in a very large measure, to the action of the armature and not to that of the transformer as in the other case, although the transformer, also, contributed a distinct but * A more complete description of this machine and the transformer will be found in this Journal, June, 1893, p. 510, etc. Owing to an accident which somewhat impaired the insulation of the armature the machine was run last year at low excitation and hence low voltage although the speed was then considera- bly higher. . ' ' . . , # The second odd harmonic, that is the harmonic whose frequency is five times that of the fundamental was there but weak. 16 Pupin—Resonance Analysis of Alternating Currents. comparatively small share to the strength of the harmonic. The third series showed that the harmonic appears in the Secondary of an open magnetic circuit transformer although considerably weaker, but does not appear there to any appreci- able extent when the magnetic circuit of the transformer is a closed one. - To the four conclusions given at the end of the series of experiments under group A the following additional conclu- sions may, therefore, be added: - W. An alternator with slotted core armature produces a complea harmonic electromotive force in which the upper har- nonic of three times the frequency of the fundamental is generally by far the strongest. VI. The amplitudes of the fundamental and the harmonio &ncrease at the same rate with the increase of eacitation; this fate is within the limits of magnetization mentioned above proportional to the eaccitation, that is to say, proportional to the magnetization of the armature. VII. A ferrie inductance in circuit with a slotted iron core armature introduces no new harmonics. It strengthens those already easisting in the electromotive force, that is odd har- nonics, especially the first odd harmonic. The same conclusions will evidently hold true for alter- nators of ordinary types whose armature is made up of coils wound on iron cores which are bolted to a cylindrical iron drum common to all of them. - * High degrees of magnetization of the transformer core pro- duce a strong deformation of the primary current wave. With inductions of over 12000 C. G. S. lines of force per sq. cm. it is possible to make the amplitude of the 1st odd harmonic even greater than the amplitude of the fundamental. It is evident, therefore, that the parallelism of the lines in fig. 5 ceases as soon as the magnetization curve of the transformer core begins to approach the knee. Experiments relating to this point will be described in the near future. The experi- ments described in this paper were limited to conditions met with in the operation of commercial alternating current appa- ratus. & V. Effect of the load upon the harmonics. It is a well known fact that the distortion of the primary current disappears gradually with the increase of the secondary load, that is when the external part of the secondary circuit is a non-self-inductive resistance. The question arises now, what becomes of the harmonics which produce the distortion of the Pupin—Resonance Analysis of Alternating Currents. 17 primary current when the secondary current increases. The following experiments seem to answer this question definitely: The arrangement of circuits was that given in fig. 1". The secondary circuit of the large 5 K. W. transformer contained an electrolyte resistance and the secondary current was meas- ured by means of a Siemens electro-dynamo-meter. For every particular value of the secondary current the resonant rises of potential due to the harmonic and the fundamental were care- fully determined by means of the multicellular voltmeter. Table V contains the observations relating to the harmonic of three times the frequency of the fundamental; Table VI relates to the fundamental (130 P. P. S.) The apparatus employed were the large alternator and the 5 K. W. trans- former. - TABLE W. Resonant rise of the harmonic Secondary current in amperes. in volts. 0 65 3-6 65 4-8 66 6-9 68 8-5 70 I 1 -5 76 15.7 85 20 97 28 120 40 I 62-5 56 202 TABLE WI. e Resonant rise of Resonant rise of Secondary the fundamental Auxiliary resistance the fundamental current in in volts. in the resonator in in volts. amperes. (Observed.) ohms. (Calculated.) O 80 0 80 3-6 240 O 240 5-0 122 50 503 6-7 150 50 613 9-0 200 50 825 17.3 200 - 100 1,450 27-0. *. 185 2 | 0 s 2,613 44-0 I 55 - 410 4, 127 56-0 t | 60 - 5 10 5,100 Table VI requires explanation. When the secondary cur- rent was over 3-6 amperes the resonant rise of the fundamental was too high for the voltmeter employed and also too risky for the condenser. An auxiliary resistance had to be introduced into the resonator to bring the resonant rise down to the limits 18 Pupin—Resonance Analysis of Alternating Currents. of the voltmeter. These auxiliary resistances are given in the third column. The readings that would have been obtained without these auxiliary resistances were then calculated, roughly, as follows: According to theory which was verified 6. 2 To 8 to 12 tº W \, :) 22 & 49 & 8) ; # 85 & 40 & a by experiments described in the beginning of this paper the resonant rise multiplied by the resistance of the resonator is within certain limits mentioned above independent of these resistances. . The resistance of the resonator coils was 16 ohms. Hence, if, for instance, a denote the rise which would have been obtained without auxiliary resistance in the resonator when the secondary current was 5 ampères, then since with an Pupin—Resonance Analysis of Alternating Currents. 19 auxiliary resistance of 50 ohms the resonant rise was 122 volts we have with a rough approximation, 122 X 66 Q = º = 503 volts. In this manner the figures of the fourth column were obtained. They are only very rough approximations, but still they give a fair idea of the ratio of the fundamental to the upper harmonic at various loads. Curves I and II, fig. 6, were plotted from these data. The secondary ampères were taken for the abscissae and the corresponding resonant rises in volts for the ordinates. Curve III represents Curve II plotted on a different scale for the volts of the resonant rise of potential. These are given in the right hand vertical column of the dia- gram. This curve gives a better picture of the gradual apparent increase of the harmonic. An inspection of I and II shows clearly how much more rapidly the fundamental increases than the harmonic. In reality the increase is even more rapid : for according to Table V it appears as if the strength of the harmonic increased with the secondary current, only much less rapidly than the fundamental. For instance, at open sec- ondary the voltmeter indicated 65 volts for the resonant rise of the fundamental; and at 56 ampères in the secondary this rise was indicated by 202 volts. But it must be noted that in the first case the voltmeter needle went from practically 2ero at no resonance, to 62 when resonance was reached; whereas in the second case it went from 135 volts at no resonance to 202 volts when resonance was reached, so that the real resonant rise was practically the same in both cases. Similarly for all other loads in the secondary. It follows, therefore, that if the har- monic increased at all with the increase of the load this increase was much smaller than appears at first sight from the data of Table W. The more important conclusion, however, which follows from this experiment and which I wish to point out more particularly is that the harmonic which manifests itself in the distortion of the primary current when there is no load in the secondary is present at all loads, if not stronger, them certainly with about the same strength. At full load this harmonic could not possibly be detected by Joubert's method of sliding contact ; it is so exceedingly small in comparison to the fundamental. - This persistence of harmonics at all loads even when com- pletely hidden by the fundamental wave holds true also when their origin can be traced to the action of the armature of the generator as in the case of the machine with slotted iron core armature. In all cases their strength depends upon the mean intensity of magnetization of the magnetic circuits to which they owe their origin and upon nothing else. 20 Pupin—Resonance Analysis of Alternating Currents. Another somewhat more difficult but very instructive way of proving the persistence of the harmonics is represented in fig. 7. In circuit with the primary of the large machine and transformer described above are two equal air-core transformers, a b and a' b'. By means of a double switch either one of the two can be made a part of the resonator circuit, c d.f. A number of condensers, D, in series, are connected across pri- mary circuit as indicated. The two air-core transformers, a b and a' b', will be equivalent when the resonator voltmeter e gives the same indications, no matter which one of the two transformers be connected to the resonator. This balanced arrangement having been obtained, the balance will be dis- turbed as soon as the condenser D is plugged in, and it will be 7. Al Z2. I. * c tºº...? (2. & ce" &Z º disturbed in a great variety of ways, according to the capacity plugged in. But when the transformer B is of closed mag. netic circuit type, then the resonator indications remain prac- tically the same as long as the resonator is switched on the air-core transformer a b', no matter what capacity is plugged in the condenser D. When the resonator is switched on the air-core transformer, a b, then its indications will be different for every particular capacity in D. In fact the circuit A, a, b, & Pupin—ſeesonance Analysis of Alternating Currents. 21 D, A, can be treated as an entirely separate circuit from the circuit A, aſ b', B, A. This statement needs practically no modification in order to cover that case also in which the self-inductance of the pri- mary of B is diminished by putting a non-self-inductive load on the secondary. This utter disagreement between theory and experiment deserves a closer discussion, but since its con- nection with the subject of this paper is only an indirect one I prefer to reserve it for some other time. That which has a direct bearing upon the present discussion is the method which the above mentioned relation offers for observing the variation of the harmonics with the load without the disturbing induc- tive effect of the large primary current. It is this: Connect the air-core transformer a b (and with it the resonator) in series with the condenser. Add to this series an auxiliary coil o (no iron core). By the combination, thus obtained, bridge the primary circuit, so that in place of the simple condenser bridge D given in fig. 7 there will be a bridge consisting of condenser D, the air-core transformer a b and the auxiliary inertia coil c. The secondary C being open, tune the circuit consisting of the alternator armature, the primary conductors up to the bridge, and the bridge, to any one of the harmonics. The tuning is done by means of varying the capacity of the condenser and the self-inductance of the auxiliary inertia coil. Then close the secondary circuit by means of an electrolyte resistance and vary the secondary current. It will be found that the harmonic diminishes only slightly with the increase of the secondary load. As an example I give the following: The circuit just mentioned was tuned to the harmonic of five times the frequency of the fundamental, that is 650 p. p. s. At no load the resonator indicated a rise of 108 volts, at over- load (56 ampères) the rise was 94 volts. But this drop was in all probability caused by armature reaction. Whatever the ultimate meaning of the appearance and the persistence of the odd harmonics in an alternating current wave may be I am not quite prepared to state with any high degree of confidence. One thing is certain and that is that they are at present at all loads with almost constant strength. Their presence is hidden by the fundamental wave at large loads, but when conditions favoring resonance with any one of them arise they will certainly come out and do all the mischief they can to the insulation. The self-induction of a motor or that of a closed magnetic circuit transformer does not neces- sarily affect the conditions of their resonance. These condi- tions may depend in such circuits solely upon the self-induction of the alternator on the one hand and the self-induction and static capacity of the line on the other. According to the 22 Pupin—Resonance Analysis of Alternating Currents. experiments just described the resonaut current is then con- fined entirely to the alternator and the line, the di-electric forming a part of its circuit. These observations will be modi- fied in the case of transformers with open magnetic circuits and their equivalents, that is, closed magnetic circuits possess- ing considerable magnetic leakage, especially when the condi- tions of the line favor resonance with the fundamental fre- quency, this frequency being low; such magnetic circuits possess much less magnetic sluggishness and can influence con- siderably the conditions of resonance with a low frequency. VI. Distortion of the secondary current. It was pointed out that the superposition of harmonics upon the fundamental wave was confined to the primary circuit when the secondary is closed by a non-self-inductive resistance, that is, if the transformer is of closed magnetic circuit type. With an open magnetic circuit transformer the deviation of the primary current wave from the simple harmonic form, due to action of the generator or the transformer or both, is felt more or less in the secondary circuit also. If, however, the secondary is closed by a ferric self-inductance then odd har- monics will appear in this circuit also in both types of trans- formers. In fact, the secondary circuit should now, as far as the harmonics are concerned, be considered as o separate cir- cuit, in which the secondary coil of the transformer and the ferric inductance in the secondary circuit play the same part as the armature of the alternator and the transformer in the primary circuit. The series of experiments which related to the origin and growth of harmonics in the secondary circuit was similar to the one described above, by means of which the so-called dis- tortion of the primary current was studied. The results were similar. The presence of harmonics is due to the action of the ferric inductance; their strength increases proportionally to the intensity of magnetization of the iron in the ferric inductance. They seem to be entirely independent of hysteresis, that is, if by hysteresis the process be understood by means of which most of the heat is generated in a very finely laminated, well insulated and well annealed iron core, when such a core is sub- jected to rapid reversals of magnetism. I shall describe briefly an experiment bearing upon this point. The secondary circuit of the five K. W. transformer was closed by an electrolyte resis- tance, and a short cylindrical coil having about 120 turns coarse copper wire. A short cylindrical core made up of very fine (No. 26 B. and S.), and well annealed iron wire could be inserted into this coil. The core was 40" high and 5* in diameter. The Pupin—Resonance Analysis of Alternating Currents. 23 wires were fairly well insulated from each other. A layer of fine copper wire surrounding this coil formed part of the resonator circuit. First, the secondary current was passed through the coil before the iron core was inserted. The resonator could detect no harmonic worth mentioning even when the current was increased almost to full load. But as soon as the iron core was introduced the odd harmonics appeared, especially the third harmonic ; its strength increased proportionally to the current. Placing now another similar iron core on the top of the first and adjusting it in such a way that it allowed a small rocking motion the two cores could be set into violent vibra- tion by the inductive attraction between them. This vibration manifested itself by a very loud note corresponding in pitch to the frequency of the alternator. The vibration could be diminished very much by pressing the top core against the lower core and against the table. The vibration produced no appreciable difference in the strength of the harmonic; if anything it seemed to make it stronger. Mechanical vibration produced by striking the cores produced no appreciable change in the harmonic. These experiments seem to me to render the theory which ascribes the origin of harmonics to the hys- teretic action of iron completely untenable. I do not think that the proper time has arrived yet for the formulation of a physical theory which will give a complete account of the peculiar behavior of iron, by means of which it superposes odd harmonics upon the wave of a simple har- monic current. The view which irresistibly suggests itself to my mind is simply this: Upper harmonics will be generated whenever more or less abrupt changes of the magnetic state in any part of the magnetic field through which an alternating current flows occur. A slotted core armature or an armature made up of coils with iron cores distributed over a drum com- mon to all of them will introduce such changes. An alternat- ing current induction motor, especially when it is not of a smooth core armature type, will also cause abrupt changes of magnetism and hence cause strong deviations of the feeding current from the simple harmonic form. But if this view be correct, then every complete cycle of magnetization to which iron is sub- jected when under the inductive action of a simple harmonic current must be accompanied by some abrupt changes in mag- netism, and that, too, whether the mean magnetic intensity of the cycle be large or small. One thing seems certain and that is, that hysteresis, as commonly understood, will not account for these abrupt cyclic changes; for, if they really exist and are the cause of harmonics, they are certainly not affected by mechanical vibrations by which, as is well known, all hysteretic effects are influenced very much. But whatever the real / 24 Pupin—Resonance Analysis of Alternating Currents. theory underlying these upper harmonics may be, the bare fact which the engineers have to face is: There is no cure against harmonics as long as the circuits contain iron. Hence, con- struct lines in such a way that conditions favoring resonance with the frequency of the fundamental or with one of its odd upper harmonics will seldom occur, and whenever they do occur the resonant rise of potential should not be capable of producing any damage. Avoid slotted armatures and arma- tures with projecting pole pieces and keep the magnetization down as much as possible. * VII. Analysis of rotary magnetic fields. Before closing this paper I will describe briefly the applica- tion of the resonance method of analysis to the study of the intensity fluctuations of a rotary magnetic field. The investi- gation was carried out by two students of the Electrical Department of Columbia College, at my suggestion, and will be published in the near future. The method, briefly stated, is this: A suitable number of turns of wire are subjected to the induction of a rotary magnetic field. These turns form part of a resonator. Whatever fluctuations there be in intensity of the rotary field they will be periodic, their period bearing a perfectly definite relation to the periodicity of the current which produces the rotary field. For instance, in a three- phase combination of alternating currents the intensity of the rotary field will, according to theory, show six maxima and six minima during each complete revolution, the maxima dif- fering from the minima by about 14 per cent. A circuit, sub- ject to the inductive action of such a field should have a periodic electromotive force induced in it whose frequency will be either three or six times the frequency of the funda- mental, according to the shape of the curve of fluctuations. Similarly in a rotary magnetic field produced by a two-phase combination of alternating currents. If such electromotive forces were induced the resonator would detect them, and from the resonant rise of potential the extent of the fluctua- 'tions producing these electromotive forces could be estimated. No electromotive forces of this type were detected in either a triphase or a two phase combination. Hence the inference : Ičotary magnetic fields produced by reasonably well constructed machines are not accompanied by fluctuations in their intensity. Electrical Engineering Laboratory, School of Mines, Columbia College, New York, May 10, 1894. **. wr- sº Rºxxºs zººsºrº: Rºº. > * ~ * gººgººk" *> # * , - * ~ * -- ** Pupin’s System of Multiplex Telegraphy by Electrical Resonance. Reprinted from The Electrical Engineer, New York, June 13, 1894, pp. 509–510. It is now fifty years since the first commercial telegraph message was sent by the Morse system, but the make and break, and dot and dash of Morse, still hold the field against all comers. The modifications and extensions which the Morse sys- tem has undergone have been the subject of not a few volumes and have engrossed the attention of some of the greatest inventors of the past and pres- ent. Among the methods for increasing the trans- mitting capacity of telegraph lines that of syn- chronism early attracted attention, and we need only recall the work of Meyer, Farmer, Gray, La Cour, Delamy, Patten and others, not to men- tion the type printers of Hughes, Phelps, Edison Baudot, and a host of others in this particular field, to indicate how fascinating this principle has been and the various ways in which it has been applied. In all the systems mentioned above, however, the under-lying principle has been to cause a reed, wheel or other mechanical device at the receiving end of a line to move in synchronism with another apparatus sending electric impulses from the trans- mitting end. The synchronous movements at each end have invariably been obtained through the in- tervention of moon ng devices which almost with- jº 2 out exception require a high degree of adjustment and usually embodied some “correcting” device to maintain the moving parts at the two ends in Syn- chronism. Recent investigations in electrical res- onance, however, would appear to have made all moving synchronizing mechanism unnecessary and its application to multiplex telegraphy is one of the results of the researches of Dr. M. I. Pupin, whose work in this and in other branches has been recently noticed in our columns. - * In order to understand the working of Dr. Pu- pin's new system, it may be well to recall that among the multiple systems proposed, such as the Gray, a number of impulses are simultaneously sent over the line by a set of reeds vibrating at different periodicities, which impulses are indiv- idually picked out at the distant end by reeds tuned to respond respectively to the transmitting reeds. In the Pupin system, the impulses, instead of be- ing picked out by corresponding vibrators are picked out by a combination of an inductance coil and condenser, “tuned” in the well-known way to that particular vibration, that is, having the same time constant as the initial vibration. Instead, also of employing reeds, alternating currents produced by alternators of different periodicities are em- ployed. The accompanying diagram shows the method and apparatus employed by Dr. Pupin in a test made last week at Columbia College in the pres- ence of a number of gentlemen interested in tel- egraphy. At the transmitting station, shown at the left, the alternators, I, II, and III, send impulses into the line through transformers, a -key in the circuit of each serving to send the impulses in the form of dots and dashes, as usual. The alternators, I, II and III, respectively, send alternating currents of 70, 130 and 250 periods per second into the line. At the distant end, the circuit first passed through three incandescent lamps of 350 ohms each, in Series, indicated at 7, , i., is, and then 3 three taps were taken off and the current in each passed through an inductance coil Li, and a con- denser C, and a sounder S, the others being let- tered to correspond; and thence to ground. The alternator IV illustrates the transmission in the opposite direction. PUPIN's SYSTEM OF MULTIPLEX TELEGRAPHY. Now it will be understood that if the inductance coil I, , and the condenser C, are adjusted or tuned to respond to the periodicity of the alternator I it will allow the impulses from that alternator alone to pass through and operate sounder s, and will remain opaque to all other impulses coming over the line. The same is the case with the other combinations L, O, S, and L, Cs, Ss. During the test Dr. Pupin showed how, by vary- ing the inductance or the capacity, the tap lines would be thrown out of tune, but when once ad- justed remained so indefinitely. Three circuits were shown in operation, and were worked simul- taneously, singly or in pairs, without mutual interference. In discussing the probable limits to which this system could be worked Dr. Pupin expressed the opinion that, beginning with 25 periods per sec- ond, the separate impulses sent over the line could be increased in steps of 25 up to 1,000 periods per second, so that 40 messages could be transmitted simultaneously, all in One direction or divided in any desired manner from either end. Electrical Consonance. By T1. I. Pupin. Reprinted from THE EZZCZ'RICAL WOA' LD, Feb. 9, 1895. Electrical Consonance. By T1. I. Pupin. The question has often been asked whether there is any dif- ference between neutralization of self-induction by capacity and resonance. A similar question is invariably put by young stu- dents when they first attempt to grasp the distinction between consonance and resonance in the case of sound. Consonance means strengthening of sound emitted by a vibrating body by connecting this vibrating body to a sounding-board, as for in- stance, when a tuning fork 1s put upon a table. Resonance means equality of periods of vibrations, and therefore syn- chronization. So in electrical circuits ; the apparent self-induction of a circuit may be neutralized and a 1arge current produced in it by a given impressed electromotive force, although the nat- ural period of the circuit is not the same as that of the impressed electro-motive force. This will happen, just as in the case of sound, when the circuit is electromagnetically connected to another secondary circuit capable of electrical vibrations. The name electrical consonance might well be applied to phenomen a of this class. I propose to discuss a case of this kind : In Fig. 1 1et A be an alternator, B a transformer, C a con- denser in series with the secondary of the transformer, and D an inertia coil of adjustable self-induction. F is an electro- dynamometer, and E is an electrostatic voltmeter. Let L be the self-induction of the primary circuit. Let R be the resistance of the primary circuit. 2 Let N and S be the corresponding quantities of the secondary circuit; let, finally, C be the capacity of the condenser. Fig. 1. Denoting now by 3 and y the primary and the secondary cur- rent, respectively, we shall have by the generalized form of d d Ohm’s law:— L #+M #4-re =E sin pt dy dºr Nå--Mir-i-Sy +P=O where P is the potential difference of the condenser at any Imoment. By elimation we obtain (ºw-ºr); (&x-se); +(As4%); +...+- = p^ (; ; –A)* sin pt-H pSE cos pt Hence the solution _ E *. * ~#####, sin (pt-º) *M (; – wy * (; – & ) is ri-r-ţ ‘M’s. 2 *( zº-w)+s 2 Where L' = L-H Tan •=+% 3 The zero value of the phase difference of a is evidently obtained when Z', the apparent self-induction of the primary circuit, is zero. We shall have then : - # * pt To obtain this neutralization of the apparent self-induction of the primary circuit, we can vary any one of the four quantities, viz: L, p, C, N. If, however, for a given periodic speed p 1 #CT then no value of L will reduce L’ to zero for that speed. N > * Then either C or M must vary. The values of C and N which will reduce LZ to zero, can be determined as follows: 1 Let ŽC —N-Z. 2 M22. I./=o when Z+###= –– * * +v/2, 373–472 Sº = ′ – or Z= ; }* p°M4–4L*S }=, c AV Hence, for a given frequency, a given primary co-efficient of self-induction, and a given secondary resistance there are two values of the capacity and also two values of the secondary co-efficient of self-induction at which the apparent co-efficient of self-induction of the primary circuit will be neutralized. A case may arise, however, in which no value of C or W can reduce LZ to zero. This will evidently take place when p°M 4 × 4L*S* for in this case the expression for 1 e tº t— —N becomes imaginary. p'C g y * It will also be readily seen that for given values of the electrical constants of the two electromagnetically connected circuits 4 there will be two frequencies at which L' will be equal to zero. For from the relation *M (; -w) L+ -b =O p” 1 M 2 + S2 (;c- ) We obtain 24–24%-4* - 4.3% pa - º L NC (LN – M*) NC*(LN–M*) ... Pe =2/ N–M3–LS C+v/(2ZW-WWIZSCW-47. WCZW = Maj 2NC(LN–M*) Hence there are two distinct frequencies at which the apparent inductance of the primary circuit will vanish. It is plain, how- ever, that the electrical constants of the two circuits may have such values that the neutralization of the primary apparent inductance will be impossible at any frequency. These considerations show, first, that the neutralization of the apparent inductance of a circuit has nothing whatever to do with resonance or synchronization, and secondly, that the ex- perimental adjustments necessary to produce this neutralization are very much more difficult and uncertain than the adjustments necessary to produce electrical resonance. This explains why this phenomenon has not received that attention which at first glance it would seem to merit. It is interesting and instructive to examine carefully the two values of the secondary apparent self-induction which will neutralize the apparent self-induction of the primary circuit. We have seen that at the point of neutralization a is given by : =#|sin ot *=z, sin p 2 M2 S Where A2/= A2 –– ſº p” (;a —w)--sº 5 - 2 But since L = ——a A M2 (; c. —w) p (º-w)--s we can also write R-R-_** 1. _t –N (..**) 1. Hence, since zº-W) can have two values for which L/=o we shall also have two values of Aº’ and therefore, the current a can have two values when the primary apparent self-induction is neu- tralized. Denoting these two values by subscripts we shall have A. º 2: 1+ sin pt pM 24-v'pºſſ-47%.S. 22 at- A. g z + 22/*S sin pt pM2–vºn Mºº- 47.25° These two values of the primary current can and will gener- ally differ considerably. For it is possible, theoretically, at 1east, to make 3:1 as many times as large as 2:2 as we choose. So, for instance, by making pl/*—v/?" M*-4 ZºS’ very small ar, will become very small indeed, whereas ºt, may be very 1arge if we choose to take the trouble to make it so. A numerical example will assist one to see this interesting relation more clearly. Let N=1 Henry. M=.5 & & A =2 £ 6 S =20 ohms. AC =50 6 & p =2 TX110=700 (very nearly) The capacities in the secondary circuit at which the apparent self-induction of the primary circuit is neutralized will be C =2.3 microfarads. Co-2.03 microfarads. 6 There is only about 12 per cent. difference in the two capacities. But if we examine the corresponding apparent resistances of the primary circuit we find A3/1=358 ohms. R/2=5945 “ Hence, the ratio of the two possible currents in the primary circuit when its inductance is zero will be 1: 16.6 (about). We see, then, that the neutralization of the inductance does not necessarily increase the primary current. On the contrary, it may diminish it very much and it will do that whenever this neutralization increases the impedance of the primary circuit. In fact, a moment’s reflection will convince us that the physical meaning of the existence of the two values for each the secondary self-induction, the capacity, and the frequency each of which will neutralize the primary apparent reactance is simply this. One value will make the primary impedance a maximum and the other will make it a minimum. There is, therefore, a radical difference between the following two distinct methods of neutralizing the self-induction of a cir- cuit by means of a capacity. The first method consists in placing the condenser in direct connection with the self-induction which is to be neutralized. It gives the circuit a definite period- icity, and neutralization takes place at the point of resonance or synchronism. The capacity acts upon the self-induction alone and upon nothing else. The second method consists in placing the condenser in a secondary circuit, so that its capacity acts indirectly upon the self-induction which is to be neutralized. It modifies, however, not only the self-induction but also the resist- ance of the circuit, so that although it may sometimes reduce the reactance it will not always reduce the impedance, but on the contrary, it may increase it very much. The neutralization does not take place at the point of resonance or synchronization; and it is quite natural that it should not; for a circuit which has no 7 direct connection to a capacity can no more have a definite period of oscillation than a body can have which is devoid of elasticity, and in the absence of such a period there can be no resonance effects. It is, therefore, not at a11 surprising that for any given values for the electrical constants of the circuit and its secondary there should be two frequencies, if there is any at a11, at which the reactance of the primary circuit is reduced to zero. One fre- quency, however, will give the minimum and the other the maxi- mum impedance. The following experimental method was employed for the pur- pose of testing the validity of the theory just given. An alternating current of 133 p. p. s. was sent through the primary turns (No. 12 B. & S.) of a small hedgehog trans- former B. (Fig. 1) The secondary was connected to a coi1 D of adjustable self-induction and to two large condensers C in series with each other. The extreme poles of the condenser bat- tery were connected to a Thomson electrostatic voltmeter E. A Siemens electrodynamometer F was employed to measure the primary current. The capacity was gradually varied and for each particular capacity the primary current and the difference of potential in the condenser were read and recorded. The fol- 1owing table records the results of one of the series of these ex- periments. The rise of the primary current is gradual just as the theory indicates it. I have not been able to produce a very 1arge in- crease, although I have taken considerable pains to do it. The capacity at which the primary impedance is reduced to a mini- mum is always greater than the one at which the impedance is made a maximum. Both these capacities are always greater than the capacity which produces resonance in the secondary circuit. The two capacities can be made to approach each other as near as we choose to make them. When p?//*=4L*S2 then the two capacities coincide. In this case, however, there is neither a maximum nor a minimum in the impedance when the phase Capacity in Difference of Potential in Microfarads. Primary Current. the Condenser. 4.94 11.3 Below the lowest reading. 4.36 11.4 { { { % 3.68 $ 11.45 ! { • { { 3.10 12.00 { { § { 2.48 11.95 {{ € $ 2.12 11.6 {{ { { 1.96 11.2 500 1.49 9.5 1.19 2.5 1,135 .48 6.5 Below the 16west reading. difference of the primary current is reduced to zero by the varia- tion of the capacity. As a rule the capacity which makes the impedance a maximum is near the capacity which produces resonance in the secondary circuit. Such a case is illustrated in the table given above. This class of capacity effects does not present those very inter- esting features which electrical resonance presents. I have observed them several years ago, but failing to detect in them any purely scientific interest or technical importance I have never paid very much attention to them. This brief note, however, seemed necessary in order to draw a clear distinction between them and electrical resonance. As a phase-changing device this method of 1modifying the reactance of a primary circuit by a con- denser in the secondary will no doubt do very good service some time, especially in the case of high tension primary circuit where a direct introduction of condensers into the primary circuit would be neither advisable nor perhaps very effective. The American Automatic Telegraph. Reprinted from “Electricity and the Electric Telegraph " by George B Prescott, New York, D. Appleton & Company. 1877. pp. 724–728. An automatic system was patented in the United States in 1869 by G eorge Little, of New Jersey, in which the perforating apparatus was operated by electro- magnetism. The paper strip was fed to the cutters by a feed wheel, carrying a revolving armature upon its axis, which was driven by an electro magnet, forming a small motor. The punch and die were also actuated by electro-magnets. The perforator was manipulated by a tablet formed of non conducting material with the telegraphic characters inlaid in metal, and a style or cir- cuit closer attached to one pole of the battery by a flexible conductor, the other pole being in connection with the inlaid characters of the tablet. When the person composing the message drew the style at a uni- form rate of speed over one of the inlaid characters upon the tablet, alternate pulsations of electricity were pro- duced for feeding the paper and perforating it by the action of the electro magnet. The transmitting machine was similar to that of Bain, except that it was driven by an electro-magnetic motor, while the record was made by electro chemical decomposition, a platinum roller being employed in place of the iron stylus of Bain. In 1869 a telegraph line was constructed from New York to Washington, about 280 miles in length, which was intended to be operated by this system. It was soon discovered, however, that the transmission at high speeds was very materially retarded by the effects of induction, which caused the dots and dashes to run into each other and become indistinct and illegible. The perforating apparatus was also found to be totally inadequate to the 2 The American Automatic Telegraph. requirements of an efficient service. Little, in 1870, suc- ceeded in partially overcoming the effects of inductive action by means of a shunt passing around the receiving instrument in which an adjustable rheostat was inserted. This device rendered the recorded signals much more distinct, but still fell short of what was required. Soon afterwards it was discovered that, by the insertion of an electro-magnet in the shunt passing around the receiving instrument, the signals at high speeds and on long lines were vastly improved. This effect is owing to the oppos- ing induced currents set up by magneto-electric action within the short circuit formed by the shunt and the re- ceiving instrument. A keyed perforator upon the same general principle as that of Siemens— (fig. 430) was also introduced, by which the transmitting slip could be pre- pared at a rapid rate. The perforations, as made by this machine, are arranged in two lines and grouped to form the dots and dashes of the telegraphic characters in the manner shown in fig. 435. The lower row of perfora- O O O O O O O O O O O O O O Fig. 435. tions are of comparatively small size, and by themselves each represent a single dot. The dash is formed by two of these smaller perforations in the lower line combined with a single large perforation in the upper line. The circuit closer of the transmitting machine consists of two small rollers running side by side and electrically con- nected together. As one of these rollers runs over the upper and the other over the lower line of perforations, the effect produced by passing over a group of two small performations and one large one is to close the circuit three times as long as for a single small perforation, so that, as transmitted, one dash is equal to three dots. The arrangement of circuits shown in fig. 436 is the one which has been adopted for long circuits. A repre- * The American Automatic Telegraph 3 sents the transmitting and B the receiving station. At the transmitting station two equal batteries, E and E, are placed in the main circuit with their like poles towards each other, and normally produce no effect upon the line. When, however, the battery E, is shunted by the closing at the transluitter of the short circuit, 1, 2, 3, 4, the current of the battery E passes over the line to the receiving station. When the circuit at the transmitter is broken the flow to line ceases, and the return or static charge is neutralized by the magneto-electric discharge - LINE É) A 4 | from the induction coil M, which consists simply of an electro-magnet with its armature permanently in con- tact with its poles. The recording instrument at the re- ceiving station is shunted with a series of helices Mī ar- ranged upon iron cores, the former being continuous while the latter is divided into sections which may be connected or disconnected by the insertion or withdrawal of iron contact plugs, so as to increase or diminish the length of core under a single inductive action. In this way the duration of the discharge from the helices may Fig. 436. 4 The American Automatic Telegraph. be adjusted to correspond with that of the line. It is obvious that the discharge from the helices Mi, which oc- curs at the termination of each signal passing over the line, will be in the reverse direction to the primary cur- rent, and will therefore tend to neutralize and destroy that portion of the inductive discharge from the line which tends to pass through the receiving instrument at B. This effect is greatly augmented by means of the ad- justable condensers C, which are arranged in connection with resistances r r r, so that the time of the discharge may be graduated to produce the best effect. On very long circuits it has been found advantageous to connect the main line with the earth at one or more interme- diate stations, including in this derived circuit an electro- magnetic coil of very great resistance, as shown in fig. 436. On circuits of moderate length the battery E, is dispensed with and an adjustable rheostat is placed in the wire 3, so that the current passing through M may be regulated to produce the proper inductive effect. The condensers C are not used except upon very long circuits. The above described improvements in the American sys- tem are nearly all included in the patents of T. A. Edison. General Theory of Electrical Oscillations. Reprinted from “The Theory of Electricity and Magnatism,” by Arthur Gordon Webster, London, Macmillan & Co., Limited, 1897 pp. 491–502. We shall now consider the question of electrical oscil- lations in the most general case of a network of linear FIG. 95. conductors, conducted with any number of conductors A which may carry electrostatic charges. These may be grouped in pairs to form condensers, as in the last section, or they may be entirely independent of one another. Of the linear conductors, any one may form a closed circuit unconnected with the others, and affected only by current induction, or may end at points of em- branchment with other conductors, or upon any of the conductors K. For brevity we shall call the linear con- ductors wires, and the conductors K accumulators. We shall suppose that the net contains p points of em- branchment, k of which are connected with accumula- tors, for all wires which end on the same accumulator are to be considered as meeting in an embranchment. Let the number of wires be l. Then if all the wires form a part of the same net, the number of independent meshes is l—p-i-1, for we see at once that the smallest umber of lines that can join p points to form a closed 2 General Theory of Electrical Oscillations. net is p, giving one mesh, and that after the first mesh every additional line adds a mesh.* For every wire r between points a and b we have an equation (1) M., ºff-Mºr...+M.; HRJ.-P.+V.-W. where Eag is the impressed electromotive-force from a to b and V, and V, are the potentials of the points a and b. There are l equations of this sort. For every point of embranchment a we have an equation (2) Ila+/a+ * tº tº º +1.=} the currents being now marked with double suffixes to denote the points between which they run, as in § 171, and e, denoting the charge of the accumulator connected with the point, or zero if there is no accumulator. These p equations are not all independent, for adding them all together, every current appears in both directions, so that the left-hand side in the sum - is identically zero, giving de, des de, () (3) 7; +. + . . . j; T‘’’ which is merely the statement that the total charge of the system is unaffected by the flow of currents. There are accordingly p—-1 independent equations (2). For every accumulator K, we have an equation, § 138 (10), 7. (4) Vaspiae-Hpºses-- tº gº º & +pksek _2 W ôea *- From the equations (1) the V's may be eliminated by *By independent meshes we mean such that circulation about any one is not the resultant of circulation about any number of others. For instance the outer boundary of a plane net is not independent of its meshes. General Theory of Electrical Oscillations. 3 Kirchhoff's principle, § 179. If, traversing any closed circuit, we add the equations (1) for each wire, every V appears with both signs, so that on the right we obtain the sum of the É's around the circuit. We shall thus obtain as many equations as there are independent meshes in the net, l—-p+1. Other equations may be obtained in the same manner by traversing any un- closed circuit ending on two accumulators. All the po- tentials at embranchments passed over are eliminated ex- cept those of the two ends. The number of equations to be obtained in this manner is one less than the num- ber of accumulators, or 3–1. We thus obtain in all l—p-HK–n equations, and there are the same number of independent variables. We may take as parameters to characterize the system a set of currents, one circu- lating in each mesh, so that the actual current in any wire is the sum or difference of the currents in the two meshes to which that wire is common. The time- integral of any mesh-current shall be taken for one of the parameters g. Besides the l—p-H1 q’s thus de- fined, we will choose k—1 others, denoting the integral currents along any series of wires joining the accumu- lators two and two, the whole series forming a chain with two ends. The charge of any accumulator is thus the difference of the two q’s of this sort whose wires it separates. The whole number of q's is now jnst equal to n, the number of degrees of freedom of the system. The current in any wire is the sum of two or three of q's with the proper signs, and as the electrokinetic energy is a homogeneous quadratic function of the currents, it becomes one also of the q’s. The derivative — #(#) dt\ög', is the electromotive-force of induction around the cir- cuit s, for 37 y 6T6/, §7,TT'37, 37,' and every 61./ög', is zero except in the case of the cur- rents which bound the circuit, for any of which 31,767', 4 General Theory of Electrical Oscillations, is either plus or minus unity. The dissipation function, § 64. (7) F=#| | RI,”--R, I.'... R, Iº;, becomes also a homogeneous quadratic function of the q's in which the product terms will in general appear. The dissipative force will also be represented by * #. for 3F_ x 62’6/, 37, "37,57. which is again the sum of the products R1 around the circuit. The terms d (#. ) lº d;\57./' 37.’ are accordingly what we get by adding the equations (1) for all the wires bounding the mesh s. Since any charge is equal to plus or minus one of the q’s of the second sort, or to the difference between two, W, the electrostatic energy, becomes a homogeneous quadratic function of these q’s. Again —º is the Qs electrostatic electromotive-force belonging to q, for 6 W_y. 3 Woe. 30, TT" de óz, Now by (4), ºſ- |W, while º: is zero except for the &r Q's accumulators at the beginning and end of q, where the derivative has the values minus one and plus one re- spectively. We shall write our three functions T— #2r 2.• Mººg',4', *- (5) F=#2.2, Rºq'.g', W= # 2. 2. Prºgs, where the M’s are linear combinations of the inductan- ces of the wires, the R's linear combinations of their re- * General Theory of Electrical Oscillations. 5 sistances, and the p’s linear combinations of the coeffi- cients of electrostatic potential of the accumulators. The values of the coefficients of the three functions are such that each of the functions is positive for all possible choices of its variables. We may now apply Lagrange's equations for any parameter ge. 6. /37’ \ , ÖA' , ) W (6) #(º) # =& where E, is the total external electromotive-force around the circuit. Performing the differentiations this be- COIOleS dºg, dºg, dºg, Mis #+M,...} +- • * * * * M...} (7) dq, dq, dq, +R.;--R. dź +. tº º º R.: +pig-Hººgs. . . . --page=E. a linear differential equation of the second order with constant coefficients. We have one such equation for each parameter ge. We shall first find the free oscillations, that is the solutions with every E.-0. As in the case of the sim- ple examples of § 237, a particular solution may be ob- tained by assuming for every ge, (8) gaa." y where A is the same for all the q’s. Inserting these values in (7) we obtain (Muſſº–H Riº+pi.)al-H . . . . --(M mº-H.Rink-Hpin)an=0, (Mºº-H.R.13+psi)ai-H. . . . --(Mºº-Hº-Hpon)an=0, as a e is tº Q tº e º e º e º ºs e º e \! t e º e º w e º º ºs e º 'º º e e º ºs e º ºs e & º º a set of linear equations to determine the ratios of the 6 General Theory of Electrical Oscillations. a's when X is known. If these are to be satisfied by other than zero values of the a’s, however, the deter- minant of the coefficients must vanish, namely Muſſº-H.R.1%+pu, .... Minº-H Rink-Hpis =0. (10) || “... . . . . . . . . . . . . . . . . . . . . . . . . . . . • e º is a e s ∈ E e º e o 'º e º is e e º 'º e º e s tº t e º e º e º e ºr • e º sº tº e º e º 'º e º e º 'º e s is e s s s a s e e º e º e s e º e Malžº-HIºni?-Hpil, . . . . Man?--Ran}+pan This is an equation of order 2, in A, from which the odd powers are absent if F=0. We shall denote its roots by Wi. %, • * * * *n. If we multiply the rth equation (9) by ar, and take the sum for all r's, we obtain (1 1) X? 2. 2, Mr.a.a.--A2.2, Rºsa,a,-H2, 2-pººd, = 0. The double sum by which X* is multiplied is the value of the function 27 when for every q', is substituted a.. We shall denote this by 27 (a). Similarly the coeffi- cient of A is 2F'(a) and the term independent of X is 2 W (a). But by the fundamental property of the three functions, each must be positive. The equation (11), X*T(a)-HAF(a)-- W(a)=0, shows us at once that A can not be real and positive, for that would involve the sum of three positive terms be- ing equal to zero. Secondly, if F =0, that is, if the resistance of every wire is zero, _ W(a) *— X*— T(a)” and 2 is a pure imaginary. In this case * and e-" are trigonometric functions, representing an undamped oscillation of the same period for all the parameters q. Thirdly, if F is large enough, Ā can be real and nega- tive. In this case each parameter q gradually dies away General Theory of Electrical Oscillations. 7 to zero, the relaxation time being the same for all. This corresponds to Case I of § 239. Fourthly, if either W or T is zero, instead of a pair of roots we have a single one, which is real and negative, the cases corresponding respectively to § 237 or § 207. Fifthly, in other cases, that is when neither T, F, nor W vanish, and F is not too large, X is complex. We shall prove that then the real part of A is negative. When any value of X is determined, the equations (9) determine the quantities a except for a common factor. If complex values enter, since any equation which in- volves i will also hold good if be changed to — i, changing any root A to its conjugate A' causes every a to change to its conjugate a'. We shall denote the a’s cor- responding to the conjugate roots A and A' by a and a' where sºsºms * y * -º-º-º tº R= p +?v, A' =/1 —iv, 0s- o,+73, a's - a,—iff, Let us now apply the process that gave us equation (11), except that we multiply the equations (9) contain- ing A by the a”s belonging to A', obtaining (12) A*2,2's Misa,a's-HA 2.2. Rºsa,a's-H2.2, p.a.a. =0, In this equation, any coefficient Man appears in the terms for which r=a. S=b, and r=b, s—a, so that the sum is Man (a,a'b-i-aba's), or substituting the values of the a's, Mabſ(a+ić,) (3,-73)+(G+78) (a,-78)]= -- 2 Mab (a,as-HB,3). Using a notation similar to that before employed, equation (12) is (13) *[T(a)+T(3(+]/[F(a)--F(3)]+ W(a)-- W(3)=0. S General Theory of Electrical Oscillations. Now performing the same process on the equations (9) with X', and multiplying by the a's we obtain (14) "[7(a)-7(8)]+[F(a)+P(S)]+ W(a)+ W(5)=0. so that X and A’ are roots of the same quadratic. We have therefore for their sum * / F'(a) -- F(3) 15 A + A =20 = — Yº! I : \f2. (15) + =% =-º-Hº Accordingly g is negative. The solution therefore represents a damped vibration, as in the second case of § 239, the period and damping being the same for all the q’s. *- Since for every root X we obtain a set of values of the a's, we shall distinguish the values for the different roots by a second set of suffixes, so that are means the coefficient of "in the coordinate q, for the sth period. The theory of differential equations tells us that for the general solution we must take the sum of the terms o,” for all the roots, so that we obtain q=aue”--aue”-- s tº e º +ause"92nt qs=ase”-Haqe^*-i- ....+ause”, e sº e g º e s ∈ e º e e e º e s e º & a tº e º e º 'º, º e s tº q.-a, e^*-i-a.e.”-- • * g e +a,e”. We may now replace the exponentials by trigono- metric terms. The appearance of the terms with con- - jugate imaginaries Å / *- a..." + aſse *= 22* f (a, cos vt—3, sin vt) leads to the disappearance of imaginaries from the re- sult, so that we obtain, General Theory of Electrical Oscillations. 9 g; = 2 [*(al, cos vit—Busin vit) + . . . . -- + gºat (on cos vat — 3 m sin va!)], q: = 2 [e” "(... cos vit — 3, sin vit) + . . . . –H (17) + e/4 *(a. cos vot–Baa sin vat)], a tº e e º a tº e s a s e º e s is ~ * * * * * * e s e s = e < e < * s s e º 'º e º e s - a s e e s e e º e e s e e s • e e s - e. e. e. e. e. e. e s e e º 'º e e º 'º s a e s m e º ºs e º 4 e e e qn = 2 ſe”(a, cos vić – 3al sin vit) + . . . . -- + e”(a, cos vºt — 3an sin vnt)]. The ratios of the a's or of the 3's in any column are given by the equations (9), being different for the different colums. Since the ratios of the gº of any column are the same as those of the a's we may otherwise write the equations as q = 2 [An epit cos (vit — ri) + Ais e”cos (v,t—rº).. + +Ame” cos (vat-ra)], t So q, = 2 [A, "cos (vt-r) + 42 º'cos (vº-r). -- (18) +4..."cos (v.t-rºl, * e º e º 'º e e º e º e º e º e e º e º e º e º e º e º e s e n e º t e is e e ºs e e s e a e e º e a e º ºs e s tº e º ºs e e º 'º e º e º 'º e º 'º e º e º 'º e s a º e s e º sº e s e a º e a e qa = 2 [Ani 24*cos (vit—r) + Ans gº! cos (vst–rº).. + +Ame” cos (v.t-r)], where Ar.” = Cºrs + 8. - ſarº, (19) r, = — tan" tº = — arg are: Cºrs We accordingly may state the general result:-The [0 General Theory of Electrical Oscillations, free vibrations of any electrical system consist, for each electrical coordinate, of the resultant of a number of damped harmonic oscillations of different periods, the number of different terms being n, the number of de- grees of freedom of the system. The phase and damp- ing of any particular simple oscillation are the same for all the coordinates, and the n factors of the amplitudes and the n phases are to be determined from the initial values of the q’s and of their first time derivatives. We will now consider the case of forced vibrations. On account of the linearity of the equations, if we find a solution q,” for a particular set of values E." of the right-hand members of our equations (7), and a sec- ond solution q,” for a second set E.”, then the sum q,” + q,” will be the solution when the right-hand members are E." —H E.”. We shall, therefore, consider the effect of each impressed force by itself. Suppose first then that in each circuit there is impressed a harmonic elec- tromotive force, E, cos ot, all of the same period. Then we have the equations of which the sth is M.4%+,+M,”--R4+...+R.4: (20) “” dº Oſº dt *d, +p.4-4 p.m.-E." Assuming q = a.” these reduce to (—Mao”—H Ružo-Hpt.)al-H.... + (21) + (–Mino”--Iºnio-Hpin)a,-E, • * c e º s e s ºr & s e e º f ºf a s s e e a e s a s e e º s & e < * * * * * * * * * * * * g e e s e < e < * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ~ * * * (—Maio"—HRaičo-Hpni)a,-H * {} + +(—Mano”-H Rania-Hpan)aa-E, a set of linear equations to determine the a's If we call the determinant of equation (10), D (R), and General Theory of Electrical Oscillations, 11 D., (2) the minor of the element of the rth column and sth row, we have as the solution of (21), 2, Dr.(to).E. 2 r= ********. (22) 0, D(ia) Since D (X) = 0 is the determinantal equation for the free vibration, whose roots are 21, 22. . . . Man, we have (23) D(A)= O(2–Å) (2—A.)....(?--—ºn)= CII.(?--A,). Accordingly the denominator D (ia) is (24) D(ia)= CII,(io—A)= CII, [–g,-Hi(0––v.)]. The minors D., (iw') are rational integral functions of io, and the numerators are therefore complex quantities, which reduce to real ones if the R's are zero. Calling the modulus of a numerator B, and its argument 6, * y ...A in p 30, (25) X, Dr.(io) E. = B.e", 6, is a small angle if the resistances are small. We thus have B.'"; A.'(0,-2.4) (26) a = CII.E.Lio-v)] T TO II.A.T.’ where (27) As=[p,”—H·(a)—v)*]%, tan a,——*-*. As Retaining now only the real parts, we have for the solution (28) _ B, cos (ot + 6, -2, a.) * CIITVºI (JL); Thus if the resistances are small, all the oscillations are in nearly the same phase. If the frequency of the impressed force coincides with that of any one of the free oscillations, a -- vs = 0, and one factor of the de- nominator reduces to ps, so that if the damping of that 12 General Theory of Electrical Oscillations. oscillation is small, the amplitude is very large, or infin- ite if there is no damping. This is the case of resonance. (Resonance may also be defined in a slightly different manner as occurring when io is one of the roots of the equation D (X) = 0 in which all the R's have been put equal to zero. This corresponds with our example in § 240. In practical cases the difference is very small.) If now we have a system acted on by electromotive forces each one of which is the sum of any number of harmonic components of different periods, any com- ponent may cause resonance with any free oscillation of the system, so that resonance may occur in a large num- ber of ways. Examples. Two Circuits. We shall illustrate the principles of the preceding section, aside from the examples that have already been given in §§ 239, 240, involving one degree of freedom, by an example of two circuits. Consider an induction coil in which both the primary and secondary contain a condenser in series. This is the case of the so-called Tesla high-frequency coil, in which a Leyden jar produces an oscillatory dis- charge through the primary, while the ends of the secondary are usually connected with a small capacity, say a pair of knobs. We shall take for q1 and q, the charges of the two condensers, so that the currents 8,I’é *º-e dq, dº (1) J-ºff, A= } We accordingly have T=#|L, Iſº-HMI. I.--, L, Iº, (2) F=# R.I."+#R, I.”, 2 2 1 2 and the differential equations for the free oscillations 8,I'ê General Theory of Electrical Oscillations. 13 02 02 d 1 L*Z--M*A*--R, 421-L_*. o. = #+Mºº-ºº-Hºº-0. (3) 67% dº? dq, 1 M% 71 || L.922 *{3–1––t- a. = #1, ######4–0. The equation for the frequencies is | Lº-º-H. M;2 =0, (4) 1. M* , Lº-Rºt- 2 Or (5) (L. L.-M*)2++(L, R,+L, R)}^+ (####RR)* R; #) ––– +(;+%)+zz-0. As this equation is of the fourth degree, we shall treat only the case of no damping, which as we have seen, will not cause a large error in the determination of the frequencies. Putting then R = R = 0 the equation becomes Li Ki-HL, Kº ; 1 6 A4 > 1–4–1–1 24 M-2 ë 22 =0, (9) “Hººf, "t Kºkºzz-Z, or, as we may otherwise write, () --(LR,+LK) --KKXL-M')=0. If the two roots of this quadric are 1 1 Wº X.” we have for the periods, 27t, , 27t. – “”, 7'' – “. X, ' 2. ' so that 14 General Theory of Electrical Oscillations. T=rV2[L. K.--L,R,+ W(L.K.EZ, KY-HK.K.M., (8) Tezyżſz Kº LL.A. W.R.L.I.F.H.R.R.W. If we introduce the periods of the two circuits alone T=27 W.K. L., T – 27t 4/A, L., and a quantity 6 which is nearly a mean proportional between them • 0–2 VM Wºº, these periods become 7 A/T2+Tº-H W(78–75-Hö 2 (9) z_A/7′E73–WTF7FºHº 2 In case T = T, ^. T*=Tº-H6*=4t"(K. L.--M 4/K. K.), (10) T*=T.”—ff"–4t"(K, L,-M W.K. K.). This is a case of so-called resonance, though not the one that we have examined. We see that one of periods is greater and the other less than the common period of the separate circuits. If the period of one of the circuits is much greater than that of the other, so that both T-T, and Tº–Tº 26°, we have, developing the square roots by the binomial theorem, the approximation, 64 7–74 zº-ſº (11) Tº-Tº- " * T 7-7; In this case the longer period is nearly that of the General Theory of Electrical Oscillations. 15 { longer individual period, being somewhat longer, while the shorter period is somewhat shorter than the shorter individual period. This is probably the usual case of the Tesla coil, where only the longer oscillation plays much part. For a further treatment of this example, the reader is referred to articles by Oberbeck” and Blümcket. We shall now consider the forced oscillation. Let there be an impressed force E, cos at in the primary circuit, there being none in the secondary. Then we have for the secondary tot q2 = 0.26 (12) *I n = E. Mo? 2 – -wºo'-9-1-1-4's * - " - 3 J – 3_L(R1-L Ra)., (L.I.-Mºº-ººrººzzº } (º, sº The amplitude of the secondary current I."=w. as is 13) I., (C)= (13) Is E. Mos - § -Mºo-91.44% a , 1 \ ^ (Ril Fe), * }; |}º. M*)0 #####, Rºe * K.K. | ++(u, R. L. Rºt}}} We get resonance when o’ is one of the roots of the quadratic L. , L. 1 (14 L.J.-M* o'-(# #)* —=0. (1) (1,1,–Mº'-(+%)*Hººk In case there is no condenser in the secondary, we have ’ — 2=OO } and there is then but one frequency for resonance, * Oberbeck. “Ueber den Verlauf der electrischen Schwingungen bei den Tesla'schen Versuchen.” Wied. Ann. 55, p. 623, 1895. ł Blümcke, “Bemerkung zu der Abhandlung des Hrn. A. Oberbeck.” Wied, Ann. 58, p. 4U5, 1896. 16 General Theory of Electrical Oscillations. K(L. L., M*) (15) o” This is the practical case of a transformer or induction coil, and is treated by J. J. Thomson in his Recent Re- searches in Electricity and Magnetism, Chapter VI., to which the student is referred for further examples of this subject. For a treatment at length of the subject of oscillations, the student may consult Rayleigh, Theory of Sound, Chapters IV, V. and X.B, and Routh, Advanced Rigid Dynamics, Chapter II. UNITED STATES PATENT OFFICE. MICHAEL ID WORSKY PUPIN, OF NEW YORK, N. Y. APPARATUS FOR TELEGRAPHIC OR TELEPHONIC TRANSMISSION, SPECIFICATION forming part of Letters Patent No. 519,346, dated May 8, 1894. Application filed December 14, 1898, Serial No. 493,651. (No model.) To all whom it may concern: Be it known that I, MICHAEL IDWORSKY PUPIN, of the city, county, and State of New York, have invented a new and useful Method 5 of and Apparatus for Electrical Transtnis- sion, of which the following is a specification. The invention is one by means of which I can, on the one hand, overcome the imped- ence which electrical cables possessing con- Io siderable self-induction, electrostatic capac- ity, and electrostatic absorption offer to va- rying, and especially to rapidly varying, elec- trical currents, and on the other hand vary the time constant of the circuit. \ By “impedence” as everywhere herein em- ployed, I do not mean yelectro magnetic im- pedence, but the combined reaction of the ohmic resistance, self induction, electrostatic absorption and the attenuating effect of dis- 20 tributed capacity of a long cable. By “time constant” I mean the number of I5 seconds during which an electro-motive force' practically completes its process of charging the circuit. - The transmission of rapidly alternating, intermittent, or any other kind of variable currents over long cables, especially subma- rine cables, is a problem which has not yet received a-satisfactory solution. The conse- quence is that on the one hand the present limit of the rapidity with which telegraphic messages can be sent over such cables espe- cially over submarine cables, is very low, and, on the other hand, it appears to most electrical scientists of the present day that the transmission of telephone currents over submarine cables of considerable length, say over fifty miles, is practically impossible. It is well understood that the difficulty of trans- 4o mission of alternating, intermittent, or any other kind of variable currents over such ca- bles is owing to the physical fact that the combined action of the self induction, the electrostatic capacity, and the electrostatic 45° absorption of the insulation, of such cables when constructed according to methods which now prevail offer an insurmountable barrier to these currents. My theoretical and experi- mental investigations, some of the results of 5o which were published in various scientific 25 30 35 periodicals (American Journal of Science, April, May and June, 1893, proceedings of the American Institute of Electrical Engineers, May, 1893, and others), lead me to the con- clusion that alternating, intermittent, or va- rying currents of any kind, even when their rate of variation or frequency is high, can be easily transmitted over land or submarine ca- bles of even very considerable length, as for instance the length of a transatlantic cable. I will first state the physical facts and principle upon which my invention is based: First physical fact.—Every electrical cir- cuit behaves, in consequence of its self-induc- tion and capacity toward a periodically vary- ing electro-motive force, just as a heavy elas- tic body, in consequence of its inertia and elasticity, behaves toward a periodically vary- ing disturbance. For just as stich a body has a definite period of vibration, so an electrical circuit has a definite period of its own, that is to say, when its electrical equilibrium is disturbed by an external impulse a periodic electrical current will result. This period depends not only as heretofore supposed on the self-induction, the electrostatic capacity and the ohmic resistance, but also as I have discovered on other frictional resistances of the circuit, such as magnetić and dielectric hysteresis for instance. The ohmic and other frictional resistances can, however, generally be reduced in such a way that they would practically have no influence on the period of the circuit. This may be done by avoid- ing closed magnetic circuits, by reducing the amount of iron to a minimum and by laminat- ing and annealing iron. In such cases the period depends on the self induction and the electrostatic capacity of the circuit alone so that by a suitable change of these two the periodicity of the circuit can be changed in any way that may be desirable. The process of changing the period of a circuit by a suit- able change in either its co-efficient of Self- induction, or in its electrostatic capacity, or in both, I shall denote herein by the expres- |sion “tuning the circuit.”. * - -" electro mag- Second physical fact.—The netic impedence which such an electrical cir- cuit as above described in which the other 55 6o 65 7o 75 8o 85 90 95. 1oo. 2 519,346 frictional and magnetic resistances have been reduced offers to an impressed simple har- monic electro-motive force diminishes gradu- ally with the approach of the periodicity or 5 pitch of this electro-motive force to the pe- riodicity or pitch of the circuit. It is a mini- mum, and equals the ohmic resistance of the circuit when the two periodicities are the same; that is, when the impressed electro- 10 motive force and the circuit are in resonance. I have found that if a complex harmonic electro-motive force acts upon such a circuit and if the periodicity of the circuit is con- siderably above the highest periodicity of the 15 harmonics contained in the complex electro- motive force, then the electro-magnetic im- pedence which the circuit will offer to the various component harmonics of the electro- motive force will be very nearly inversely 20 proportional to the periodicity of these com- ponents. I believe that I have been the first to call attention to the portions of these two physi- cal facts which have been especially empha- 25 sized above, and more especially that I have been the first to discover that the influence of magnetic and dielectric sluggishness varies with the period of the impressed electro-mo- tive forces and more especially with high pe- 30 riods. I certainly consider myself the first to have practically applied these principles for the purpose of electrical transmission. I have also found that these two physical facts and the principle underlying them can be ex- 35 tended in such a way as to include circuits divided into Sections by interposed condens- ers which connect in series the several sec- tions of the circuit, that is to say I have found that all the rules of tuning a circuit can be 4o applied to Such a circuit as to the whole or to any part of it. This extension is my own discovery and it is disclosed now in this speci- fication for the first time. It enables me to regulate the time constant and the electro- 45 magnetic impedence of a long conductor and at the Same time also to diminish the attenu- ating effect due to distributed electrostatic capacity and also diminish the electrical ab- Sorption in the insulation of such conductor. 5o I now proceed to set forth the principle of this method: v } If the parts into which the circuit is divided act upon each other by electrostatio induc- tion, then the period of the total circuit is 55 equal to the period of any one of its parts, if Said parts are equal and essentially similar. IIence, according to the first physical fact and the extension of this fact mentioned above, if the ohmic and other frictional re- 6o sistances in such a circuit due to dielectric and magnetic hysteresis are reduced in each part in such a way that the period of any part depends practically on the self induć- tion and the electrostatic capacity of that 65 part, then the period of the whole circuit, no matter what its length may be, will depend on the Self-induction and the electrostatic ca. * pacity of any one of the parts, and on noth- ing else; but if said parts are not equal nor similar to each other, then the circuit may be said to contain as many periods as it has parts. I call these the partial periods of the circuit. Thére will, however, be one period for which the electromagnetic impedence of the circuit is a minimum. This period I call the period of the circuit; it lies between the shortest and the longest partial periods. Then the conditions of resistances above mentioned, being fulfilled, both the partial periods and the resultant period will depend on the coefficient of self-induction and the electrostatic capacity of the various parts, and on nothing else. This relation of the partial periods to the total period of a Sec- tional conductor just described will hold true even if these partial periods are not independ- ent of the ohmic and other frictional resist- ances, provided that these frictional, resist- ances are not beyond the limits.outside of which they render the several parts of the con- dućtor aperiodic. - ‘. In carrying my method into practical effect, I prefer to proceed as follows, and by the aid of the following means: '. 2 Let a long electrical cable be divided into any number of parts, and let condensers be interposed between these parts, so that the Various parts of the cable connect the various condensers in series. To illustrate this, con- sider a cable six thousand miles long having a total electrostatic capacity of five hundred microfarads. Dividing it into six thousand equal parts, making thus each part one mile long, we shall have an electrostatic capacity of one-twelfth microfarad per mile. Inter- posing six thousand condensers of twenty microfarads each, I shall have for the total effective electrostatic capacity of the cable 20 + 1-1 2 – 1 1 º o #########-F####7 microfarads. That is, I Shall have reduced the effective electrostatic capacity of the cable to nearly one one-hun- dred and fifty thousandths part of its origi- nal value before division, and I shall also have the line capacity of the cable very small in comparison to the electrostatic capacity of the interposed condensers. Therefore, I may construct the cable so that the statical charge of the line at any moment during the variable flow of an electrical current along the cable, can be made small in comparison to the static charge in the interposed condensers; hence the electrostatic absorption of the whole cable can be made practically independent of the dielectric properties of the insulation of the Cable, and be confined entirely to the dielec- tric properties of the insulator employed in the interposed condensers. Hence, if con- densers, possessing no electrostatic absorp- tion are used, as for instance, carefully con- Structed mical condensers, then the electro- Statio absorption of the total cable can be re- º to any practical limit that may be de- S11'60ſ. The foregoing, which is based upon careful 7o 75 8o 85 90 95 IOO IOS I [O I I5 I 2 O I 25 I 30 IO 15 2O 25 3o 35 4O .45 5o 55. 6o 65 519,346 3 investigations and experiments made by my- self, is of extreme practical importance in view of the present well-known difficulties arising from electrostatic absorption by the insulation of cables as now constructed. I also prefer in practice to place in shunt with each condenser a coil cf wire of many turns surrounding an iron core, which core forms a closed, or nearly closed, magnetic circuit. When such a coil is shunted by a condenser and placed into a circuit in which a periodically varying electro-motive force acts, then as long as the frequency of the electro-motive force is over about fifty periods per second, the effect of the condenser ca- pacity upon the current through the coil will be inappreciably small. This is a novel fact and apparently contradictory to all experi- ences in telegraphy; but the contradiction is only apparent. Referring now to the accompanying draw- ings, Figure 1 is an electrical diagram Sym- bolically representing a conductor divided into parts and having interposed condensers, constructed and arranged in accordance with the foregoing. Fig. 2 represents the same with shunt coils added. & Similar letters of reference indicate like parts. Suppose it is required to construct a cable to connect two places three thousand miles distant from each other, the cable to have six thousand ohms resistance and a periodicity of eighteen hundred periods per second. Fig. 1 indicates a preferable construction of a part, X Y, of such a cable, according to my method. The cable is divided into equal Sec- tions, A, B, C, D, E, and the return Sections, A’, B', C', D', E'. A A', B B', &c., act upon each other through electrostatic induction by means of the condensers a a', b b', c c', d d", &c., or in other words, the condensers are con- nected in series to each other by means of the sections of the cable. Let the capacity of each condenser be twenty microfarads, and let there be three thousand pairs of con- densers so that two Successive pairs are at the distance of one mile from each other. The sections A A', B B', &c., will therefore be each one mile long. To simplify the de- scription, I shall assume that each of these sections consists of a thick cylindrical copper wire 0.5 centimeters in diameter. It is evi- dent, however, that wire ropes or flat strips of a conductor can be used as Well. Well an- nealed copper being used I shall have for each mile about one ohm resistance (see Stewart and Gee, Practical Physics, Vol. II, p. 116), hence for six thousand miles six thousand ohms. Let the adjacent cylindrical conductors be parallel to each other, and let the distance between their axes be 2.72 multi- plied by their radius. According to Maxwell (Electr. and Mag. Vol. II, p. 294) I shall have for the self-induction of the conductor connecting two successive condensers, denot- ing it by L: Lºz.000396 Henrys, Since each | cable suitable to the transmissign 6f tele- conductor is connected to a capacity of twenty microfarads, we shall have for the period of each part of the cable: 7o 27 — T=# VLC = rºw (about) where T is the period of any one of the equal parts of the cable, measured in seconds, I., is 75 self-induction, measured in Henrys, and C, its capacity, measured in microfarads. The resistance has a very small effect upon the per riod, as a simple calculation will show. The electro-magnetic impedence of this cable to a simple harmonic current of eighteen hundred periods would be six thousand ohms, that is to say, a simple harmonic electro-motive force whose period is one eighteen hundredths of a second and whose mean amplitude is say one *5 thousand volts, would serid through Such a ca- ble a current whose mean value will be one- sixth ampèrereversing three thousand six hun- dred times per second. This is true of course on the supposition that the alternating effect 9° of the distributed capacity of the cable be neglected. This form of cable I call a “high pitch cable,” because it has a high periodic- ity, much higher than the periodicity of the notes in the average human speaking voice. 95 It is evident that a periodicity of two hun- dred complete periods per second would more than suffice for telegraphic purposes in which case it would be necessary to have only sixty pairs of twenty microfarad condensers, which *** would, of course, reduce the cost of the cable very much. The high pitch cable, however, which I am describing would be a form of 8c phone-currents, through cables "possessing **5 large distributed capacity, as for instance, a trans-Atlantic cable, for reasons which can now be stated briefly. The range of notes in the average human speaking voice is about between one hundred ‘’” and twenty and six hundred complete periods per second. To show the advantage of this form of cable it is well to calculate the elec- tro-magnetic impedence for periodicities ly- ing between the two limits just mentioned. **5 Let 712o stand for electro-magnetic impedence to an electro-motive force of periodicity 120, and let igno stand for the electromagnetic im- pedence to an electro-motive force of peri- odicity 600, then: I 2 O $120 = 400000 ohms • I V7 too = 80000 ohms } very nearly. The lower periodicities would therefore be 125 Iendered somewhat weaker; the rendering - would be very nearly inversely proportional to the number of periods per second. To illustrate this result, I now assume that two suitable telephones, G. H., one at the station 130 Y and one at the station Y, three thousand miles distant from X, form a part of this cir- cuit, and that a note is sung into the tele- phone at X. Supposing that the note is com. 4 519,346 IO [5 2O 25 3o 35 40 45 5o 55 6o 65 posed of a fundamental note having one hun- drod and twenty periods per second and of four upper harmonics having two hundred and forty, three hundred and sixty, four hun- dred and eighty and six hundred periods per second. It is well known that the vibrating telephone diaphragm at X will induce in the circuit a complex electro-motive force con- sisting of the fundamental simple harmonic electro-motive force having one hundred and twenty periods per second and also of the upper harmonics having the periodicities of two hundred and forty, three hundred and sixty, four hundred and eighty, and six hun- dred periods per second. A perfect tele- phone diaphragm would produce these har- monic electro-motive forces in such a way, that their amplitudes would be in the same ratio to each other as the amplitudes of the sound harmonics in the note which is uttered into the telephone. If, however, the dia- phragm of the telephones G and H are of low pitch, then the induced electro-motive force would be stronger in its lower harmonics than, the sound waves which set the diaphragm into vibration. It is evident, therefore, that the tendency of the telephone diaphragm to | strengthen the lower harmonics of the sound can be counterbalanced as nearly as desirable by the tendency of the cable to strengthen the upper harmonics; so that a long distance transmission of telephonic currents by a cable of the description just given is not necessarily accompanied by a distortion of the sounds transmitted. * I assume now that the mean value of the sº induced simple harmonic component electro- motive forces with a perfect telephone dia- phragm would be: one volt for the funda- mental harmonic; one-half volt for the first upper harmonic; one-third volt for the sec- ond upper harmonic; one-fourth volt for the third upper harnionic, and one-fifth volt for the fourth upper harmonic. This ratio of the amplitudes represents the ratio of the mean values of the amplitudes of the harmonics in the Sound vibrations which agitate the tele- phone diaphragm. The mean values of the component simple harmonic currents would be one four-hundred thousandths ampères for every harmonic. Iſence the color of the Sound would be Somewhat changed. But it can be easily seen that with a telephone dia- phragm favoring lower notes the above ratios of the induced electro-motive forces could be changed so as to give Say: one volt for the fundamental harmonic; one-fourth volt for the first upper harmonic; one-ninth volt for the second upper harmonic; one-tenth volt for the third upper harmonic, and one twenty- fifth volt for the fourth upper harmonic. In this case the mean Values of the component harmonic currents would be: i ** 1:10, monic, ampères for the fundamental har- *Iºw ampères for the first upper har- monic. 1. **15:10, monic. ampères for the second upper har- # X rºw ampères for the third upper har- monic. 1 #*45. 105 monic. ampères for the fourth upper har- That is to say, the intensities of the compo- nent simple harmonic currents would be to each other in the same ratio as the intensities of the simple harmonic sounds of which the sound uttered into the telephone is composed. Hence there would be no discoloration in the transmitted sound. It should be observed here that every one of the above eurrents is very much stronger than the currents which can produce audible sounds in the telephone, for, according to trustworthy investigations, 109 ampères produce Sounds in the telephone that can be heard very easily. But these numeri- cal values of the currents just obtained will be modified if the hypothesis on which the calculations So far have been made is dropped, the hypothesis, being, namely, that the elec- trostatic capacity of the conductor of any one section of the cable is infinitely small in comparison to the capacity of the terminal condensers of that section. A brief discussion of that modification will bring out clearly another very great improvement which I can obtain by constructing a cable embodying my present invention. Consider the instantaneous electrical state of the cable at any moment when an alter- nating current is flowing through it. Com- mence at the first pair of condensers nearest to the transmitter. One condenser will be on the positive side of the transmitter at that moment and the other on the negative side. I shall confine now my attention to the series of condensers which are at the moment con- sidered on the positive side of the transmit- ter. This series consists of three thousand condensers distributed equidistantly between the two stations. One side of the first con- denser of the series will have, at the particu- lar moment under consideration, a charge m, This charge induces a charge —m, on the opposite side of the condenser. In the sec- ond condenser I have charges m, and –ms, and So forth until I reach the last condenser. In this one I have charges mn-, and —ma. An exactly similar distribution of charges will take place in the Series of condensers on the negative side of the transmitter. In my case n=3000. The charges m and mi, mi, and mg, &c., are not numerically equal to each other because the capacities of the conduct- currents of the order of magnitude of 7o 75 8o 85 9C 95 IOO IoS II 5 I 2 O I 25 I39 IO I5 2 O 25 3O 35 4O 45 5o 55 6o 65 519,346 01's 90nnecting the various condensers are not infinitely small in comparison to the ca- pacities of the condensers. Let the capacity of half the conductor Connecting two con- secutive condensers be the lºh part of the ca- ©acity of one of the condensers—then I shall have Tn4 = i –– l 777 ' m. 'mo = —#4– = —tº * = Hi-Hº &c. nº = –“ — * (l +. !)n In the cable described above we have 77 = 3000 ! — Hence Tºw —*— 777, t Tºln E 1 \* =# (very nearly). 1 + —t- y y ( +iº) 500 The currents in the various sections of the Cable would vary in very nearly the same ratio, that is to say, the value of the current at the receiving station would be only the one five-hundredth part of the theoretical Value, deduced on the supposition that the line capacity of the conductors of the varibus Sections is infinitely small in comparison to the capacity of the condensers. To show now the numerical value of these currents at the receiving station, I shall point out the value of the weakest one among them. It will be 1 *X →= +a ° C 4 × 105 × 500T TOP mperes. As observed before, this current is, according to Very trustworthy investigations, over a thousand times stronger than the weakest Current that can be heard in a telephone. It should be also remarked that the telephonic current which, could be sent over the cable just described would be much greater, be- cause the impressed electromotive force gen- erated by the induction coil of a good trans- mitter is much greater than the voltage with Which I started in the above calculation. To State, in a concise form, this very im- portant improvement in cables constructed according to my invention I introduce now the following definition:-Consider the cur- rent in the conductor of any section of the cable. That current consists of two distinct parts. One part is due to the charging of the terminal condensers of that section, and the other is due to the charging of the surface of the conductor itself. The first current I call the longitudinal displacement component, and the second current I call the lateral dis- placement component of the current in that Section. The above mentioned very impor- tant improvement consists, therefore, in di- minishing the ratio between the lateral and the longitudinal displacement components of a rapidly varying current. The wasting of a current due to the lateral displacement com- ponents in the various parts of a cable acts evidently like an impedence, therefore it is to be understood that the word “impedence” herein includes the impedence due not only to Ohmic resistance, self-induction, &c., but also the impedence resulting from the lateral displacement currents. Referring now more particularly to Fig. 2, for the purpose of giving the divided cable an uninterrupted metallic circuit so that in Case of a break the fault may be located by Ordinary methods, there is connected with each condenser in shunt a coil, as m 'm', 'm m', Of many turns, surrounding a closed or sub- Stantially closed magnetic circuit, such as an iron ring, r. These coils, in consequence of their large self-induction and also in conse- Quence of the electro-magnetic property which I have before mentioned, and will now de- Scribe more fully, will not allow an appreciable part of the main current to pass from one sec- tion of the cable to the next as long as the frequency of that main current is anywhere above fifty periods per second. In fact, these Coils act, with regard to these frequencies, like electro-magnetic valves. It has long been known that when a condenser is connected in shunt with a coil and an electromotive force is used having a periodicity somewhere about that of the periodicity of the circuit composed of the condenser and coil, then considerable current will pass through the coil even if the self-induction of the coil is Very large; but this relation holds true, as I have experimentally discovered, only when the iron core of the coil is exceedingly well laminated and does not form a closed mag- netic circuit. But if the magnetic circuit is closed, then this relation is far from the truth. The mean value of the current that will pass then from one section of the cable to the next through any one of the auxiliary coils is equal to the mean value of the difference of poten- tial in the conductor which is shunted by that coil divided by the impedence which the Self- induction and the ohmic resistance offer to this difference of potential. Making, there- fore, this impedence large, the leakage cur- rent can be reduced to any limit, especially for frequencies-above fifty periods per Sec- ond. In other words, the auxiliary coils act somewhat like electro-magnetic valves. effect is that, so long as the condensers re- main in order, only an inappreciable part of the main current will pass through the aux- iliary coils, and hence the coils will not exer- cise any material influence upon the results before noted; but if a condenser should, from any cause, become inoperative, then this will be at once shown by the increase in the im- pedence of the line,—but as the line remains continuous, it is possible to locate the fault by determining the capacity of the cable, or by other suitable means which might not be applicable if the sections of the line had no metallic connection between them. Or, if the cable should be broken, in which case it would The . 76 75 8o 90 ! { 95 I OO Io 5 I IO II 5 I 2 O I 25 I 3o - 6 519,346 become inoperative, the fault may be located #. ordinary methods applicable to metallic 1I] eS. If the sections of the cable, instead of being 5 equal and similar, as above described, were made unequal and dissimilar, then substan- tially the same results would be obtained. I should simply deal with the mean perio- dicity of the line, and establish it with ref- 1o erence to Some previously selected periodic- ity, which in the case of telephonic trans- mission through sub-marine cables, I should make preferably higher than that of the high- est strong note of the voice. For telephonic I5 transmission over land lines we should make the previously selected periodicity consider- ably lower than the lowest note of the voice. While I have described my aforesaid in- vention in the foregoing specification more 20 particularly as applied to, and embodied in apparatus for telegraphic or telephonic pur- poses it is to be distinctly understood that, I do not limit it in any wise to such specific ap- plication; but on the contrary my invention 25 includes broadly any and all applications of my method and apparatus aforesaid to, the transmission of electrical currents, whether for lighting, power, heating or any other pur- pose wherein the same may be applied to pro- 30 duce beneficial results. I claim— 1. The method of overcoming the imped- ence which a circuit divided into sections of- fers to variable currents which consists in 35 tuning the various sections of the circuit to ~ give a selected periodicity to the circuit by interposing a capacity or capacities large in comparison with the distributed capacity of the sections. º 2. The method of overcoming the imped- ence which a circuit divided into sections disposed in inductive relation and in series offers to variable currents which consists in tuning the various sections of the circuit to 45 give a selected periodicity to the circuit by interposing a capacity or capacities large in comparison with the distributed capacity of the Sections. ...” 3. The art of transmitting articulate sounds 5o telephonically by causing undulations simi- lar in form to the vibrations in the air ac- companying Said Sounds to pass by electro- static induction from one member to the rest of a series of conductors tuned to a periodic- 55 ity which is considerably outside of the perio- dicity of said electrical undulations. 4. The art of transmitting articulate seunds telephonically by causing undulations simi- lar in form to the vibrations in the air ac- 60 companying Said Sounds to pass by electro- static induction from one member to the next of a series of conductors tuned to a periodic- ity considerably higher than that of the notes in the average human Voice. 5. A circuit for variable currents divided 4O 65 into sections having the various sections tuned to a selected periodicity by the inter- position of a capacity or capacities large in comparison with, the distributed capacity of the sections. 6. A circuit divided into sections disposed in inductive relation and in series having the various sections tuned to a selected pe. riodicity by the interposition of a capacity or capacities large in comparison with the dis’ tributed capacity of the sections. T 7. An electric circuit for variable currents divided into sections in inductive relation and in series and tuned to give a selected-pe- riodicity by the interposition between the sections of substantially equal capacities which are large in comparison with the dis- tributed capacity of the sections. 8. An electric circuit for variable currents divided into sections by means of condensers interposed between said sections, a coil in shunt with each condenser and a closed or substantially closed magnetic circuit Sur- rounded by said coil, the line being tuned to a selected periodicity by having the inter- posed condensers of a capacity which is large in comparison with the distributed capacity of the sections. 9. The combination of electric transmitting and receiving instruments and a circuit join- ing them divided into sections and having the various sections tuned to -a selected pe- riodicity by the interposition of a capacity or -capacities large in comparison with the dis- tributed capacity of the sections. 10. The combination of telephonic trans- mitting and receiving instruments and a cir- cuit joining them divided into sections and having the various sections tuned to a selected periodicity by the interposition of a capacity or capacities large in comparison with the dis- tributed capacity of the sections. - 11. In eombination with an electrical con- ductor tuned to a periodicity of higher pitch than a given Sound, a telephone transmitter having a diaphragm tuned to a lower pitch than said sound: whereby the tendency of the telephone diaphragm to strengthen the lower harmonics of Said sound is counterbalanced or substantially counterbalanced by the tend- ency of the conductor to strengthen the up- per harmonics So that said sound becomes transmitted substantially without distortion. 12. An electric conductor composed of sec- tions placed in Series, the said sections being tuned by the predetermined proportioning of the electro-magnetic constants so that the total periodicity of the conductor shall ap- proximately equal a certain predetermined periodicity, substantially as described. MICHAEL IDWORSKY PUPIN. Witnesses: H. R. MoLLER, M. BOSCH. 7o 75 3o 85 90 95 I OO IC 5 II 5 I 2 O (No Model.) M. I. PUPIN. APPARATUS FOR TELEGRAPHIC OR TELEPHONIC TRANSMISSION, No. 519,346, Patented May 8, 1894. SI, sſ N §§ Niſs s_cºs nº *s ** geºg S|S N|S ^ Ü R & –CTP-\ – Q##9 N || * , || N. § & ||\ § \ll \) R R \S < Bis º Go S|S § s 2-, s , As-lºs 's S SO= \ S § sº § ZZzzezzzzzz- //zzesses:- s i V&a. A 7%evo Ży A%v/.4%22222(...) nº- SS */...//w/ UNITED STATES PATENT OFFICE. IO 15 2O 25 3o 35 4O 45 5o MICHAEL I. PUPIN, OF NEW YORK, N. Y. TRANSFORMER FOR TELEGRAPHIC, TELEPHONIC, OR OTHER ELECTRICAL SYSTEMS, / SPECIFICATION forming part of Letters Patent No. 519,347, dated May 8, 1894. Application filed February 10, 1894, Serial No. 499,716. (No model.) To alſº whom it may concern. Be it known that I, MICHAEL I. PUPIN, of the city, county, and State of New York, have invented a new and useful Improvement in Transformers for Telegraphic, Telephonic, or other Electrical Systems, of which the fol- lowing is a specification. My invention relates first to the construc- tion of the transformer, and second, to the combination of such a transformer with a line conductor having in circuit telephone or tele- graph instruments, or both. When the sec- ondary coil of an induction transformer con- sists of a large number of turns of wire, it then possesses defects which materially im- pair its efficiency. First, its electrostatic ca- pacity checks the separated electrifications in their exit from the coil. Second, the nor- mally large self induction gives the Second- ary coil too large a time constant and renders it very inefficient when acted upon by elec- tromotive forces of high frequencies. This evil is especially serious in case of induction transformers which are used in connection with telephone transmitters, because the self induction of the secondary coils of such trans- formers tends to weaken the upper harmonics and so to distort the voice. If, however, the secondary coil of such a transformer be di- vided into a number of preferably equal parts or sections, and these placed in Series and in inductive relation by disposing condensers between the successive sections, then I have discovered that both the capacity effect of the coil can be reduced to any desirable limit, and the time constant may also be made as small as may be wished. If such a trans- former be combined with a line conductor also divided into sections, arranged in in- ductive relation and in Series, or in other words, provided with condensers between the sections, and if both the line and the trans- former coil be properly tuned then the rapid- ity of transmission may be exceedingly great, the number of messages which may be trans- mitted over such a line is independent of elec- trical conditions, simultaneous telephony and telegraphy is practicable, and a telephonic current will control a recording telegraphic receiver. Referring to the accompanying drawings: Figure 1 is a partial longitudinal section show- *ºm ing the construction of my transformer. Fig. 2 shows said transformer connected with a telephone line. Fig. 3, shows the arrange- ment of the same line for both telegraphic and telephonic purposes. Similar letters and figures of reference in- dicate like parts. In Fig. 1, A is the core of the transformer, preferably of fine iron wire, which is sur- rounded by the primary coil B. Inclosing the primary coil B is a spool C, upon which is wound the secondary coil D. Said secondary coil is divided into a number of preferably equal parts or sections as a a', b b', c c', &c. Between these parts are interposed the equal or nearly equal condensers, 1, 2, 3, 4, so that the Said Sections and the said condensers are connected in Series. The size of the various coils and condensers determines, the time con- stant of the whole secondary coil D. It is not, of course, essential to divide the second- ary coil into equal parts, or to insert equal condensers in order to shorten the time con- stant, for the latter will always be between the Shortest and longest time constant of the Various parts. So also the various sections of the coil can be connected partly in series and partly in parallel, or any like adjustment be made. I will now describe the arrangement of my Said transformer in combination with a tele- phone line. It is to be understood that the line conductor here illustrated is not specifi- cally claimed in this application, because it forms the subject matter of another applica- tion for Letters Patent, Serial No. 493,651, al- ready filed by me December 14, 1893, and now pending. Referring to Fig. 2 in circuit with the primary B. of the transformer is a tele- phone transmitter E of any suitable construc- tion and a source of electricity F. The terminals of the secondary D are con- nected with the line conductor G, which is made up of Sections as gg', between which sec- tions are interposed the condensers h, h’, &c. H is a telephone receiver in circuit. The arrangement of the line for telegraphic or combined telephonic and telegraphic pur- poses is represented in Fig. 3. The line ter- minals at a y are connected to the terminals of the Secondary coil D as in Fig. 2. At I is a telegraphic key. At the distant station is 55 6o 65 8o 85 90 95 I O Q 2 519,347 IO 15 25 3o 35 4O 45 5o 55 Öo 65 arranged a relay connected with the line. This may be of any desired form and operate either to open and close a circuit or to pro- duce variations of current strength therein. Thus there may be an electro-magnet J con- nected to line and Operating the diaphragm of a telephone transmitter K in local circuit with the primary of an induction coil L, the secondary of which coil is in circuit with the metal drum m and the marking point m. Over the drum may be drawn by clockwork o or any other Suitable means a strip of chemi- cally prepared paper p which will be marked wherever the current passes through it as it is carried between the point ºn and drum m. The paper is of course moved along at a uni- form rate of Speed. The impressed electro- motive force in the primary circuit of the transformer at the transmitting end, may be caused by the telephone transmitter E set in operation by the voice or by any Sounding ap- paratus such as an organ reed in front of it or by an alternating current dynamo. The induced current on the secondary is inter- rupted in the usual way to send Morse sig- nals for example by the key I. It is advis- able that the periodicity of the impressed electromotive force be as nearly equal to the periodicity of the circuit as practicable. If the secondary of the transformer is tuned to a high pitch and the line be also tuned to the same high pitch, then any known means for very rapid telegraphy, Such as the Wheat- stone system may be employed, and the num- ber of messages that can be transmitted will be limited only by the mechanism of the trans- mitting and receiving devices, and not by any electrical conditions. When an alternating current generator is employed to feed the pri- mary of such a transformer, then the primary coil also may be divided into a suitable num- ber of parts in the Same Way as the secondary with condensers in like manner interposed. This is especially desirable when the primary has large self-induction. The metallic return shown in Figs. 2 and 3 is not essential, as the line can be grounded in the usual way. Long telephone lines act in consequence of their distributed capacity like lines of low impedence, that is to Say, a comparatively speaking low electromotive force at the trans- mitting end can produce a large current at that end, but a very Small part of this initial large current reaches the receiving end of the line. This effect is Well known and is at- tributed to the attenuating effect of the line. Owing to this attenuating power of the line, it becomes necessary to work with transmit- ters which are capable of Sustaining a large current in the Secondary Core of the trans- former, that is to Say, the number of turns in the secondary coil must be kept low. Driefly stated, long distance telephone lines are worked to-day on the principle of large cur- rent and low voltage. But in a long distance line of very high impedence but no attenu- ating power, it is desirable to work with high electromotive forces and small currents. Hence, the induction transformer of the trans- mitter must have a much larger number of turns in the secondary, than the transformer now in use. But on account of the well known fact that high self induction kills upper har- monics, it is evident that a large number of turns in the secondary cannot be employed un- less somedevice isintroduced which will dimin- ish the tendency of the self induction of the coil to weed out the upper harmonics. This is accomplished by dividing the secondary coil into sections and interposing condensers as hereinbefore described, so that thus I may use very high electromotive force without weakening of the upper harmonics. It will be seen therefore that by this invention I may operate a long distance telephone line on the opposite principle from that now followed; that is instead of using low electromotive forces and large currents, I may employ high electromotive forces and small currents. I claim— 1. A transformer having one of its coils divided into sections, the said sections being connected in series and in electrostatic in- ductive relation and each section being tuned to a certain predetermined periodicity. 2. A transformer having its secondary coil divided into Sections, and condensers con- nected in Series and interposed between said Sections and each Section being tuned to a certain predetermined periodicity. 3. A transformer having its primary coil in circuit with a Source of electricity and a means of varying the electrical condition of said cir- cuit, and its Secondary coil connected to a line Conductor, the Said secondary coil and line conductor being each divided into sections, the Said Sections being placed in series and in electrostatic inductive relation. 4. A transformer having its primary coil in circuit with a Source of electricity and a means of Varying the electrical condition of said cir- cuit and its Secondary coil connected to a line conductor, the said secondary coil and line conductor being each divided into sections the Said Sections being placed in series in elec- trostatic inductive relation and each tuned to a certain predetermined periodicity. 5. A transformer having its primary coil in circuit with a source of electricity and a means of Varying the electrical condition of said cir- cuit and its Secondary coil connected to a line Conductor and condensers, the said Secondary coil and line conductor being each divided into Sections, and connected in series with Said condensers; and the said sections being tuned so that the total periodicity of the sec. ondary coil and line conductor shall equal or Very nearly equal a certain predetermined periodicity. 6. In combination a transformer having its primary coil in circuit with a source of elec- tricity and a telephone transmitter, and a Secondary coil divided into sections disposed in Series and in electrostatic relation: a line 7o 75 8o 85 9 O 95 I OO IoS I ICN I I5 I 2 O I 25 I 30 I O I5 519,347 3 conductor also divided into sections disposed in Series and in electrostatic inductive rela- tion, and a telephone receiver connected with Said line conductor. 7. In combination a transformer having its primary coil in circuit with a source of elec- tricity and a telegraphic transmitter and a Secondary coil divided into sections disposed in series and in electrostatic inductive rela- tion, a line conductor' also divided into sec- tions disposed in series and in electrostatic relation, and a telegraphic receiver connected with said line conductor. 8. In combination, a transformer having its primary coil in electrical circuit with a tele- phone, and its secondary coil divided into Sections disposed in series and in electrostatic inductive relation and a telegraphic trans- mitter and receiver connected with said line conductor. { 9. In combination a transformer having its primary coil in circuit with a source of elec- tricity and a means of producing periodic electrical vibrations, and a secondary coil di- vided into sections disposed in series and in electrostatic inductive relation, a line con- ductor also divided into sections disposed in series and in electrostatic relation and a tele- graphic transmitter and receiver connected with said line conductor. MICHAEL I. PUPIN. Witnesses: * H. R. MOLLER, E. MARTIN. ' A ', 2O 25 (No Model.) M. I. PUPIN, TRANSFORMER FOR TELEGRAPHIC, TELEPHONIC, 0B 0THER BLECTRICAL SYSTEMS, No. 519,347. Zºzz, *} May 8, 1894. |H|H|H|Hºmº #E r |||| i.7 ,'Rºl / C2/ Z 2 3 4. Zºzz | * Z." -Z/ º |||||||ſº ...A 2. 9 H 2 >3 4– ===== IT-TD=#. h, 7. - - Zºzº, /??’zzesses.— 4%zzº z 2–60.24%