810V-OGY R G THE MEASUREMENT OF INDUCTION SHOCKS A MANUAL FOR THE QUANTITATIVE USE OF FARADIC STIMULI BY ERNEST G. MARTIN, PH.D. ASSISTANT PROFESSOR OF PHYSIOLOGY IN THE HARVARD MEDICAL SCHOOL FIRST EDITION FIRST THOUSAND NEW YORK JOHN WILEY & SONS LONDON: CHAPMAN & HALL, LIMITED 1912 BIOLOGY LIBRARY G COPYRIGHT. 1912, BY ERNEST G. MARTIN Stanbopc F. H. GILSON COMPANY BOSTON, U.S.A. QT3-4I BIOLOGY LIBRARY PREFATORY NOTE THE method of measuring induction shocks described in the following pages was developed in a series of papers published between 1908 and 1911 in the American Jour- nal of Physiology. Extended use of the method by myself and coworkers has shown it to have great value in many physiological and psychological researches. In order to make the method more readily available for investigators, and with the hope that thereby quantita- tive studies may be more generally made, the scattered material of the original papers has been assembled into the form herein presented. Since the work aims to serve rather as a manual than as an exposition of prin- ciples, only so much theoretical matter is included as is necessary to make intelligible the procedures adopted. E. G. M. BOSTON, April, 1912. iii 798044 CONTENTS CHAPTER I. PAGE THE CHARACTERISTICS OF INDUCED CURRENTS i Introductory i Historical 2 Structure of the Inductorium 3 Principle of the Inductorium 4 The Form of Make and Break Induced Currents 8 CHAPTER II. FACTORS WHICH AFFECT THE STRENGTHS OF FARADIC STIMULI 12 Sources of Variation 13 Methods Previously Proposed 14 Pfluger 14 Meyer-Fick 15 Kronecker 16 v. Fleischl 18 Wertheim-Salomonson 18 Edelmann 20 Hoorweg-Giltay 21 CHAPTER III. A SUMMARY OF PROCEDURE 23 Instruments Required for the Calibration 23 Ammeter and Shunt 24 Stimulating Electrodes 27 Procedure 28 v vi CONTENTS CHAPTER IV. PAGE THE PHYSICAL PRINCIPLES UNDERLYING THE MEASUREMENT OF BREAK SHOCKS 32 The Course of Break Induced Currents 32 CHAPTER V. THE DETERMINATIONS OF MUTUAL INDUCTION BETWEEN PRIMARY AND SECONDARY COILS 38 CHAPTER VI. EFFECTS PRODUCED BY AN IRON CORE IN THE PRIMARY COIL .... 43 CHAPTER VII. COMPARISON OF ONE COIL WITH ANOTHER — THE VALUE OF £ ... 50 CHAPTER VIII. THE PREPARATION OF A CALIBRATION SCALE FOR BREAK SHOCKS . . 55 CHAPTER IX. THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 60 The Knife-blade Key 63 The Operating Device 65 The Short-circuiting Device 67 CHAPTER X. THE INFLUENCE OF SECONDARY RESISTANCE AND OF CATHODE SURFACE 71 The Relation of Tissue Resistance to Secondary Resistance as a Whole 71 Determination of Tissue Resistance 72 Effect upon the Stimulus of Varying the Secondary Resistance 73 Current Density, an Important Factor 76 CONTENTS VU CHAPTER X — Continued. PAGE The Dependence of Factor A upon Inductorium Construction 78 Conditions in which the Specific Stimulus need not be De- termined 80 A Standard of Inductorium Construction Necessary 88 CHAPTER XI. THE MEASUREMENT OF MAKE SHOCKS 94 Comparison of the General Formulae for Break and Make Stimuli 99 CHAPTER XII. ERRORS TO BE AVOIDED 107 INDUCTION SHOCKS -a' •". » 1 1* ' „ " > CHAPTER I THE CHARACTERISTICS OF INDUCED CURRENTS Introductory. The inductorium has become one of the most familiar and most useful instruments in the physiological laboratory. There are few physiological researches which do not involve artificial stimulation of tissues; and for the production of stimuli induction shocks are in most cases the first choice. They are easier to use and they subject the stimulated tissue to less permanent modification than do other forms of artificial stimulus. Induction shocks are, however, very variable in intensity; and as commonly used there is no means of knowing or of stating their physiological effectiveness in other than the most general terms. An induction shock is weak, medium, or strong. More closely than that the user does not attempt to describe it. This lack of knowledge as to the strengths of the stimuli employed is often a serious handicap in the pros- ecution of individual researches, particularly such as call for the use of stimuli of varying strengths. It also 2 INDUCTION SHOCKS operates to make uncertain the attempts of investigators to duplicate the experiments of others. No one will question the desirability of being able to measure f aradic stiniuli, both for the sake of controlling the stimuli used iii pne's own experiments, and also in orrier 'tjiart ^these/'.s.tiniuli may be so described as to enable other workers to duplicate them as occasion arises. The purpose of this work is to outline a system for calibrating the apparatus used in generating induction shocks, so that the value of the shocks may be expressed in terms of stimulation units; these units to be appli- cable to any properly constructed induction apparatus, and to be based upon determinations which can be made in any ordinarily equipped physiological laboratory. The system proposed is not a new departure, but is an extension and amplification of previous systems. Historical. The phenomenon of electromagnetic in- duction was discovered by Faraday in 1831, and its physical characteristics were very thoroughly worked out by him and by Henry about the same time. The first suggestion for the physiological use of induction shocks appears to have been made by Sturgeon* hi 1837, and from that time to the present their use in this connection has continued. Various forms of induction apparatus have been de- * Annales de Sturgeon: 1837, p. 477. THE CHARACTERISTICS OF INDUCED CURRENTS 3 vised, but for physiological purposes only one has come into common use; this form, designed by E. du Bois- Reymond * in 1848, is illustrated in Figs, i and 2. Such modifications of this design as have arisen since its introduction have to do only with details, and not at all with the underlying principle of the apparatus. Structure of the Inductorium. The induction coil, as adapted by du Bois-Reymond to physiological use, con- FIG. i. The induction coil as used for physiological purposes (du Bois-Reymond pattern): A, the primary coil; B, the secondary coil; Pr, binding posts to which are attached the wires from the battery — they connect with the ends of coil A; P", binding posts connecting with ends of coil B, through which the induction current is led off; S, the slide, with scale, in which coil B is moved to alter its distance from A. sists, in essence, of two coils of carefully insulated copper wire. One of these, the primary coil, is made up of two or three layers of rather coarse wire wound upon a hollow core of nonconducting material. Usually the outside diameter of this coil is about 2.5 to 4 cm., and its length between 8 and 14 cm. The number of turns * du Bois-Reymond: Unters. iiber tierische Electrizitat, 1848, Bd. 1, S. 4471 also, Bd. II, i, S. 393. 4 INDUCTION SHOCKS of wire does not ordinarily exceed 600. The coil is mounted horizontally by one end upon a suitable sup- port. The ends of the wire are brought to two binding posts, situated at some convenient place on the support. The other coil, the secondary, consists of numerous turns of very fine insulated wire, wound upon a hollow spool whose inside diameter is such that the secondary coil can be brought over the primary. The number of turns of wire is usually between 5000 and 10,000. The length of the secondary coil is about equal to that of the primary. The ends of the wire are brought to binding posts mounted upon the spool. A slide, 30 or 40 cm. long, projects from the support of the primary. The secondary is mounted upon this slide with its axis coincident with the axis of the primary. A scale, grad- uated in millimeters, is mounted on the slide. A pointer on the secondary coil is so placed that it indicates zero on the scale when the secondary covers the primary completely. A device for making and breaking the primary circuit automatically is usually included as part of the apparatus; and a bundle of soft iron wire, so constructed as to slide into the hollow core of the pri- mary coil, is likewise provided. Principle of the Inductorium. Whenever a steady current is flowing through the primary coil there exists about it a magnetic "field of force." This field may be THE CHARACTERISTICS OF INDUCED CURRENTS 5 pictured as consisting of " lines of force " each of which passes lengthwise through the primary coil, and, ex- tending a greater or less distance from it into space at either end, curves outward and back so that the two ends meet, making each " line of force " a closed ellipse. The lines of force are very numerous near the primary coil, but become less and less frequent as the distance from the coil increases. The number of lines of force present and the distance from the coil at which they can be detected depend upon the intensity of the current flowing through the coil. If another coil of wire, the secondary, be placed within the field of force about the primary in such position that lines of force pass lengthwise through it, any alteration in the number of lines of force compre- hended within the secondary generates within it a cur- rent which is the induced current. This current, which depends upon changes within the field of force, ceases to be generated whenever the field of force becomes steady, and outlasts the change in the field only the brief frac- tion of a second required for the current to die away. The direction of the induced current depends upon the direction of the current through the primary coil, and also upon whether the change in the field is an increase or a decrease in the number of lines of force. The intensity of the currents induced in any secondary coil depends upon the number of lines of force moving through it, 6 INDUCTION SHOCKS and also upon the rate of their movement; the more rapid the change in the field, the higher the intensity. The method used in physiology for bringing about alterations of the field within the secondary coil is to make and break the current through the primary. FIG. 2. Schema of induction apparatus (Lombard), h repre- sents the galvanic battery connected by wires to the primary coil A. On the course of one of these wires is a key, k, to make and break the current. B shows the principle of the secondary coil and the connec- tion of its two ends with the nerve of a nerve-muscle preparation. When the battery current is closed or made in A, a brief current of high intensity is induced in B. This is known as the making or closing shock. When the battery current is broken in A, a second brief induc- tion current is aroused in B. This is known as the breaking or opening shock. When the primary current is made there is a sudden in- crease in the lines of force cutting the secondary coil; when the primary current is broken these lines of force suddenly disappear. The currents induced by the make and the break of the primary circuit are obviously of THE CHARACTERISTICS OF INDUCED CURRENTS 7 very short duration, since the time required to establish the field of force on the one hand, and for its disappear- ance on the other, is measured in thousandths of a second, and, as we have seen, only during these periods do induced currents flow. The current induced in the secondary by the make of the primary circuit is usually spoken of in physiology as the make shock; that indj*ced by the break of the primary is the break shock. A feature of induction shocks which commends them particularly to the physiologist is the ease with which their intensity may be varied. For securing this varia- tion advantage is taken of the dependence of the induced current upon the number of lines of force which cut the secondary coil. There are two ways of varying this number : One is by changing the intensity of the primary current; the other, by shifting the position of the sec- ondary coil with reference to the primary. This latter method is the one used in the du Bois-Reymond induc- torium, and it is a very satisfactory method, since by means of it the strength of the stimulus can be varied several hundredfold, from the maximum for the appa- ratus to a value negligibly small, by simple shifting of the secondary from one end of its slide to the other. Many inductoria are so constructed that the secondary coil can be rotated about an axis midway of its length. In this way the intensity of the induced current can be cut down to zero, since when the secondary is at right 8 INDUCTION SHOCKS angles to the primary no lines of force pass lengthwise through it. For quantitative purposes, however, it is better to have a rather long slide and to keep the sec- ondary coil always with its axis coincident with that of the primary. The Form of Make and Break Induced Currents. When a circuit is closed through the primary coil of an inductorium there is a growth of the current within this coil from zero to its full value. Coincidently with this growth of current there is being established a field of force about the coil, and if there is a secondary coil within this field a current is being induced therein. This induced current also begins at zero and increases in intensity during the establishment of the field of force about the primary. As soon as the field is fully established, so that movement of the lines of force ceases, there is no further induction and the current within the secondary dies away. We may represent the successive changes in intensity of the induced current by a curve such as that shown in Fig. 3 in which the height of the curve at any point represents the intensity of the induced current at that instant. The rise of the make induced current from zero to the maximum, although rapid, is by no means instantaneous, there being a well marked delay in the establishment of the -current through the primary coil after the circuit is closed. This delay is due to the phenomenon of indue- THE CHARACTERISTICS OF INDUCED CURRENTS 9 tance within the primary coil. This phenomenon may be explained as follows : When the current sweeps through any turn of wire of the primary coil it tends to establish a field of force about that turn; but as the lines of force composing this field cut through adjacent turns of wire of the primary they induce currents therein. Since en- ergy is expended in this inductance the currents thus induced cannot be in the same direction as the inducing current; inasmuch as if they were, there would be a A B FIG. 3. Curve illustrating the growth and decline of a make induced current. AB represents the time required for the primary current to become fully established. gain of energy — a thing impossible ; they oppose the in- ducing current and allow it to reach its full value only after it has yielded the energy necessary for the induc- tance. In Fig. 3 the line AB represents the time occu- pied by the primary current in establishing itself against the inductance, and therefore the time during which the induced current increases. Any condition which diminishes the inductance within the primary coil, thereby allowing the primary current to establish itself more quickly, will not only make the 10 INDUCTION SHOCKS ascending limb of the curve of Fig. 3 steeper, but will also carry it higher; that is, the current induced in the secondary will not only reach its maximum intensity more quickly, but that maximum will be greater; this result being due to the fact that the intensity is greater the more rapid is the alteration in the field of force cutting the coil. While a current is flowing steadily through the pri- mary coil no induction is manifest; but when the current is broken there is produced in the secondary coil a break induced current. The agency generating this cur- rent is the sudden withdrawal of the field of force from the secondary coil. With the breaking of the primary circuit it would seem at first thought that the lines of force should dis- appear instantly and that there should be an instan- taneous leap of the break induced current from zero to maximum. As a matter of fact the growth of the break current, although very rapid, is not instantaneous, for the reason that with the breaking of the primary circuit the energy absorbed from the current at its make by the inductance within the coil is released and manifests itself as the " extra current," jumping across the points of broken contact as a spark and prolonging slightly the decay of the primary current. The chief difference between Fig. 10, p. 33, which rep- resents the course of a break induced current, and Fig. 3, THE CHARACTERISTICS OF INDUCED CURRENTS II representing a make current, lies in the greater steep- ness of the ascending limb of the curve of the break cur- rent, due to the shorter period occupied by the spark in passing. Here again any condition that hastens the passage of the spark brings about increased intensity of induced current by accelerating the disappearance of the field of force. Since under most conditions the delay in establishing the primary current, -due to inductance, is greater than the delay in its disappearance, from sparking at the con- tacts, make shocks are usually less intense physiologi- cally than are break shocks. CHAPTER II FACTORS WHICH AFFECT THE STRENGTHS OF FARADIC STIMULI ANY scheme for measuring induction shocks, if it is to be wholly satisfactory, must take into account all the sources of possible variation present in the mechan- isms by which the shocks are generated and applied to tissues. The numerous methods which have been worked out hitherto have been uniformly based upon sound physical principles, and give accurate results so far as they go; they leave something to be desired, how- ever, in that none of them deals with all the conditions of variation which are actually present whenever tis- sues are stimulated, and their usefulness is limited by just that much. The justification for the present work lies in its attempt to take into account all the sources of variation which exist. These are to be divided into those whose influence upon the strength of stimuli is in accordance with mathematical laws, determinable by the experimenter, and those which are not apparently so determinable. The former are made the basis for the system of measuring stimuli herein described; the latter are studied with a view to showing how their effects may be minimized. 12 STRENGTHS OF FARADIC STIMULI 13 Sources of Variation. The induction apparatus, as used in the physiological laboratory, consists of two cir- cuits: the primary, or inducing circuit, which includes the primary coil of the inductorium, a source of current, and a device for making and breaking the circuit, to- gether with the necessary connecting wires; and the secondary circuit, including the secondary coil, wires leading thence to suitable stimulating electrodes, and the tissue to be stimulated. In Fig. 2, p. 6, these cir- cuits are illustrated diagrammatically. In any given primary circuit variations may arise either in the amount of current yielded by whatever source of current is used; or in the key, whereby the circuit is made and broken. In any given secondary circuit variations may arise in the position of the sec- ondary coil with respect to the primary, this being, as we have seen, the usual method of bringing about varia- tions in stimulating strength; in the electrical resistance of the tissue which is being stimulated; and in the con- tacts between the stimulating electrodes and the tissue to which they are applied. Also different inductoria usually present structural differences, such as different dimensions and different numbers of turns of wire in primary and secondary coils, which themselves bring about wide differences in the strengths of stimuli gen- erated by the different inductoria. The presence or absence of an iron core within the primary coil is also 14 INDUCTION SHOCKS a source of great modification of stimuli. Finally, as we have seen, there is a difference in physiological effect between make shocks and break shocks. Of the sources of variation just described the following are subject to laws which are determinable, and are to be included, therefore, in our quantitative scheme: The construction of the inductorium, the position of the sec- ondary coil with respect to the primary, the presence or absence of an iron core in the primary, the intensity and voltage of the primary current, the use of make or break shocks, the electrical resistance of the stimulated tissue and the mode of contact of the stimulating electrodes with the tissue. The variable which is not determinable is the effect on the stimulus of the manner of making or breaking the primary circuit. This must be, so far as possible, made uniform. Methods Previously Proposed. The first attempt to measure induction shocks is said to have been made by Rosenthal in 1 85 7 .* Two years later Pfliiger made quan- titative comparisons between shocks, varying their in- tensities by varying the primary current, leaving all other factors constant. His method gives accurate rela- tive results, but seems not to have commended itself to physiologists, probably because it calls for a rather com- * See Garten: Handbuch der physiol. Methodik, 1908, Bd. II, Abt. 3, S. 393. STRENGTHS OF FARADIC STIMULI 15 plex mechanism for varying and at the same time measuring the primary current. The earliest method of measuring induction shocks which received wide recognition was worked out under the direction of Fick by his student, Meyer, in 1869.* This method concerned itself altogether with the effect upon the intensity of break shocks of shifting the posi- tion of the secondary coil relative to the primary, and amounts, therefore, to a calibration of the slide upon which the secondary coil moves. By such calibration the relative intensities of the shocks given by the in- ductorium at the various secondary positions are accu- rately indicated, so long as all the other variable factors remain unchanged. A similar calibration is an essential feature of any scheme for the quantitative use of the inductorium, and indeed the only criticism of the Fick method of measuring stimuli is for its incompleteness. The Fick calibration was accomplished by including in the secondary circuit a galvanometer and determining the current induced in the secondary coil at its various positions by the deflection produced when a given cur- rent was made or broken through the primary. This method, although simple in theory, was in fact rather difficult to put into practice with the electrical measuring apparatus available in Fick's time; and accordingly * Meyer: Unters. phys. Labor, d. Zuricher Hochschule, Wien, 1869, 8.36. 16 INDUCTION SHOCKS Kronecker,* in 1871, introduced a modification of the method whereby its application was simplified. He used two inductoria, connected their secondary coils in series with a galvanometer and connected both primary coils with a single source of current in such fashion that the two secondaries gave induced currents opposite in direc- tion when the primary circuit was broken. Thus the galvanometer deflection was used merely as an indicator that one induced current was stronger than the other, rather than as a measure of the strength of the induced current itself. With both secondaries at zero the primary current was broken and the amount and direction of deflection noted. The coil giving a stronger shock was then moved outward till no deflection occurred. Then the weaker coil was moved outward till a deflection equal to the first one was obtained. This procedure was repeated till the whole length of the slide had been traversed, the number of times the stronger secondary was moved be- ing noted. If this number is multiplied by the original galvanometer deflection we have a value which ex- presses how many times greater the galvanometer de- flection would be with the secondary at zero than at the end of the slide. To calibrate the slide on the basis of 1000 units, as Kronecker does, the total deflection noted * Kronecker: Arbeiten aus der physiologischen Anstalt zu Leipzig, 1871, S. 186. STRENGTHS OF FARADIC STIMULI 17 above is divided by 1000 and the quotient gives the gal- vanometer deflection per unit. If now the weaker coil is set at zero and the stronger at a point such that the galvanometer deflection is that called for per unit, it is possible, by repeating the original procedure, to divide the scale into 1000 parts, each of which represents a given galvanometer deflection, and therefore an equal decrement in stimulating value. This method has the advantage that after one inductorium is calibrated it is extremely easy to calibrate others to correspond with it, by connecting the calibrated and uncalibrated coils in the manner described above and finding the corre- sponding points on the two slides. Kronecker, by sub- stituting a telephone for the galvanometer, made the taking of readings even more simple. The method has the disadvantage that it is purely arbitrary, depending at the outset on a chance difference of stimulating strength occurring in two inductoria; for this reason the calibration can only be duplicated through access to a coil already calibrated. An ob- server, unable for any reason to obtain a Kronecker coil, might, it is true, prepare a calibration of his own by repeating Kronecker's original procedure, but he could not know whether his units represented the same stimu- lating values as the corresponding Kronecker units, and so could not express satisfactorily the strengths of stimuli used by him. 1 8 INDUCTION SHOCKS v. Fleischl,* in 1875, proposed a method of calibrating the inductorium in which for the galvanometer deflec- tion was substituted the threshold contraction of a nerve-muscle preparation. In this calibration the de- creases in stimulating value which result from moving the secondary coil outward were compensated by in- creasing the current through the primary coil, the in- creases required being taken as the measure of the change in stimulating intensity resulting from the move- ment of the secondary. This method has the advantage of being available in situations where no galvanometer can be obtained. Its greatest importance lies, however, in confirming the assumption of Fick and of Kronecker that the physiological intensities of break induced cur- rents are proportional to the galvanometer deflections they produce. Wertheim-Salomonsonf has recently described a method for obtaining a physiological calibration in which variations in the primary current are avoided. He places the nerve of the nerve-muscle preparation to be used as an indicator in one branch of a divided sec- ondary circuit, and in the other branch places a re- sistance equal to that of the nerve. (See Fig. 4.) The resistance of the divided circuit is then one-half that of * v. Fleischl: Sitzb. d. k. Akad. d. Wissensch. Wien, 1875, Bd. Ixxii, Abth. III. Also Ges. Abh., 1893, S. 475. t Wertheim-Salomonson: Zeitschr. f. Elektrother. I., 1899, S. 97. STRENGTHS OF FARADIC STIMULI 19 the nerve alone. By placing in the circuit beyond the shunt another resistance equal to one-half that of the nerve the total resistance of the secondary circuit is made equal to what it would be if the shunt and the added resistance were both removed. Since, however, the nerve is in a divided circuit, both branches of which have equal resistance, it receives only one-half the cur- rent generated in the secondary coil. That secondary position at which the nerve receives threshold stimula- tion when in the divided circuit is determined, and then 'Nerve, of Res. W / ~w~^ FIG. 4. Diagram showing method of inserting resistances in the Wertheim-Salomonson method of calibration. After Gasten. the shunt and the additional resistance are cut out. Now the nerve receives the whole current from the sec- ondary instead of half of it, and if the secondary posi- tion is found at which the threshold stimulus is again imparted we know that this second current has just half the stimulating value of the first. We have thus a method for comparing stimuli, which admits of exten- sion sufficient for the complete calibration of a coil. It has, however, the shortcoming, already noted for Kronecker's method, of giving values applicable only 20 INDUCTION SHOCKS to the single coil on which it is worked out. One very important feature of a wholly satisfactory calibration must be its general applicability, so that any properly constructed inductorium can be calibrated in any labo- ratory to give results comparable with those obtained from other calibrated instruments. Moreover, it is not to be forgotten that no method of calibration thus far described takes into account the effects of strength of primary current, of tissue resistance, or the method of applying the stimulating electrodes, all of which are important, and at the same time de- terminable, and therefore to be included in a complete calibration scheme; nor do any of them consider the strength of make shocks, all being available only for breaks. A device which is superior in certain respects to any thus far described for measuring stimuli is the "fara- dimeter " of Edelmann. In this apparatus a galvanom- eter in the secondary circuit registers the voltage of the induced current. The galvanometer readings give cor- rect indications of the values of stimuli only when a current of definite, fixed amperage is broken in the primary circuit. It is necessary, therefore, to have a source of currents specially selected to give this amper- age, and by means of an ammeter in the primary cir- cuit to insure that it is maintained. The Edelmann method is an advance over others in that it takes STRENGTHS OF FARADIC STIMULI 21 account of the factor of primary current strength and provides for its regulation. It does not, however, take account of the influence upon the strength of stimulus of variations in tissue resistance, since the quantity measured by the galvanometer, namely the voltage, is independent of the resistance. Nor does it consider the effect of the method of application of the stimulating electrodes. But so long as these two factors remain constant the Edelmann faradimeter gives accurate re- sults for break shocks, and expresses them in terms such that the stimuli used by one worker can, save for the factors above mentioned, be duplicated by others. The importance of taking secondary resistance into account was brought out by Hoorweg* in 1893. He demonstrated the effect of variations in resistance in modifying stimulation strengths, and emphasized the necessity of working out some method by which to ascertain this effect. At his suggestion Giltay f de- signed an electrodynamometer by which the variations in strength of stimulus due to varying secondary re- sistances can be read directly. This apparatus fulfils admirably the purpose for which it was designed. It is, however, of little practical use in physiology, since its readings, to be comparable, must be made with the * Hoorweg: Die medicinische Elektrotechnik und ihre physikalischen Grundlagen, Leipzig, 1893. t Giltay: Annalen der Physik und Chemie, 1893, Bd. 50, S. 756. 22 INDUCTION SHOCKS same inductorium or with inductoria of precisely similar construction, and the position of the secondary coil with respect to the primary must not be altered. In view of the fact that moving the secondary coil is the usual method among physiologists for varying the strength of stimulus, this instrument clearly does not altogether meet the requirements of physiological work. It has, moreover, the somewhat serious shortcoming of taking no account of the method of applying the stimulating electrodes, so that, even were all the other conditions met, the electrodynamometer would still fail to give wholly complete measurements. Our examination of the various systems hitherto pro- posed for measuring induction shocks bears out the statement made at the outset that none of them meets fully the requirements of quantitative work. We are justified therefore in submitting a system which, although not new, being an extension of the Fick-Kronecker method, attempts to deal with all the factors concerned in the production of faradic stimuli, so that henceforth the values of stimuli may be expressed in such terms that they can be duplicated or modified quantitatively at will. CHAPTER III A SUMMARY OF PROCEDURE FOR the convenience of users of the method herein presented it has been thought worth while to describe briefly at the outset the various pieces of apparatus used and to summarize the various procedures involved in making the necessary calibrations and in using the calibrated apparatus. Instruments Required for the Calibration. The in- ductorium to be calibrated should be of " standard " construction (see p. 88), that is, it should have a sec- ondary coil approximately 13 cm. long and having about 10,000 turns of wire. The number of turns and the mean cross section of the secondary coil must be accu- rately known (p. 55). The slide upon which the sec- ondary moves should be not less than 30 cm. long. It should be accurately graduated in millimeters, and a pointer fixed to the secondary coil in such position as to stand at zero when the secondary is pushed completely over the primary. To increase the stimulating effec- tiveness of the instrument the primary coil should have a core made of a bundle of soft iron wires. In addition to this inductorium there is needed a con- 23 INDUCTION SHOCKS slant source of current sufficient in amount to yield at least i ampere through the resistance of the primary coil. Where a charging current is available, probably a good storage battery will be found most convenient as a source of current. Several Daniell cells in series, how- ever, answer every pur- pose. A good ammeter for measuring the inten- sity of the primary current is required, as is also a variable resistance for ad- justing its amount. Since it is often necessary in the course of the work to use currents ranging from o.oooi ampere to i ampere the ammeter must be able to cover this range. No instrument is, of course, able to measure FIG. 5. Diagram showing ammeter the small currents with shunt made from a Porter metal- suffident accuracy and contact rocking key. at the same time to give direct readings for the larger ones. To give the ammeter the desired range, therefore, recourse must be had to a system of shunts. I have found it convenient to use a milammeter having a scale capacity of 10 mil am- A SUMMARY OF PROCEDURE 25 peres and reading directly to o.i mil ampere, and to provide it with two shunts, one adjusted to carry nine- tenths of the total current, the other to carry ninety- nine one-hundredths of the current. For these shunts I use an ordinary Porter metal-contact rocking key connected as shown in the diagram, Fig. 5. For the TV shunt, German silver wire is used between one pair of end contacts; for the •£$$ shunt, copper wire is used between the other pair of end contacts. To cali- brate the shunts, resistance is introduced into the am- meter circuit until exactly o.oi ampere is flowing; then the shunts are adjusted until the ammeter reading is exactly o.ooi ampere, when the & shunt is in circuit, and o.ooo i ampere when the 1% shunt is in. The shunts must be recalibrated at frequent intervals, but this is not a difficult task. As a means of adjusting the amount of primary cur- rent flowing I have found a dial resistance box most satisfactory, although any available variable resistance can be used. The total resistance should not be less than 11,000 or 12,000 ohms, since with a source of cur- rent yielding 2 volts that amount of resistance is often necessary to cut the current down to the point where threshold stimuli are produced. For making and breaking the primary circuit some form of automatic key is required. A satisfactory one is described in Chapter IX. Experience shows that trust- 26 INDUCTION SHOCKS worthy results cannot be obtained with a key which fails to give uniform breaks. Uniform makes are very desirable, but for many sorts of work, including the routine of making the calibration, make shocks need not be employed. All the apparatus thus far described is required for the quantitative use of the induction coil as well as for its calibration. Additional instruments needed for mak- ing the calibration are a good ballistic galvanometer and a standard induction apparatus. A satisfactory form of ballistic galvanometer is the d'Arsonval wall instru- ment with moving coil and reflected scale, read with a telescope. The standard induction apparatus can be made in any machine shop. It consists of a primary coil, at least 75 cm. long and composed of a single layer of heavy insulated wire, carefully wound, and a sec- ondary coil, not over 15 cm. long, of about 2000 turns of fine wire, placed exactly at the center of the primary coil. The cross section and number of turns per centi- meter of the primary coil must be known, and the total number of turns of the secondary. Additional apparatus required in the use of the in- ductorium, but not in the calibration, is, first, a device for determining tissue resistance, and, second, suitable stimulating electrodes. I have found the Kohlrausch method of measuring resistance perfectly satisfactory (see p. 72). This method requires an ordinary meter A SUMMARY OF PROCEDURE 27 bridge, a small inductorium to give an alternating cur- rent, a telephone receiver for an indicator and a resist- ance box. By suitable wiring, illustrated in Fig. 15, p. 73, a single resistance box can be used both for vary- ing the primary current and as the known resistance in the Kohlrausch determinations. The stimulating electrodes must be selected with special reference to uniformity of contact. Accurate quantitative results cannot be gotten under conditions of contact variation. For the direct stimulation of muscles I have found platinum needle electrodes most satisfactory. A piece of platinum wire 2.5 to 3 cm. long, and 0.5 mm. in diameter, pointed somewhat at the end with a file, is soldered to a suitable length of very fine copper wire (diameter 0.2 mm.). The platinum needle is thrust directly into or through the muscle tissue; the copper wire, carried to the secondary ter- minal, affords the very flexible connection necessary for avoiding interference with the free movement of the muscle. For stimulating nerves the glass-inclosed electrodes described by Sherrington * are as reliable as any I know of. They answer well either for the stimulation of nerves deeply imbedded within the body, or for stimulating the nerve of the ordinary nerve-muscle preparation. In the use of this form of electrode care must be taken that the * Sherrington: Jour, of Physiol., 1909, xxxviii, p. 382. 28 INDUCTION SHOCKS interior of the glass tube is clear of liquid. The elec- trode is shown in Fig. 6; contact is made by rotating slightly the stopper carrying the two platinum wires. For the determination of " specific " stimulation val- ues (see p. 76), a rather large known resistance, ten thousand to twenty thousand ohms, must be arranged to be included in the secondary circuit as required. FIG. 6. Shielded electrodes (Sherrington). The arrangement of apparatus for making the cali- bration is illustrated diagrammatically in Fig. 7. The procedure is by the following steps, for each of which a page reference is given. 1. Determination of the formula for core magnetiza- tion (p. 43). 2. Determination of the mutual induction for a series of selected secondary positions from 12 cm. outward (p. 38). A SUMMARY OF PROCEDURE FIG. 7. Arrangement of apparatus for calibrating the inducto- rium. A, ammeter; B, battery; C, standard coil; G, galvanometer; 7, inductorium to be calibrated; K, make and break key; P, apparatus for physiological calibration;. R, resistance box; 5 and Si, switches. 3. Determination of the inductance of the secondary coil (p. 50). 4. Determination of — for the secondary positions jL whose mutual inductions have been established (p. 53). 5. Physiological corroboration of this calibration by the v. Fleischl method (p. 56), accompanied by physi- ological determination of the " calibration numbers " for the inner secondary positions (p. 58). 6. Construction of a curve to establish calibration numbers for intermediate secondary positions (p. 56). 7. Determination of the constant C in the formula for make shocks (pp. 94 and 104). INDUCTION SHOCKS FIG. 8. Arrangement of apparatus for the use of the quantitative method, i, battery; 2, resistance box in primary circuit; 3, slide wire resistance for fine adjustment; 4, ammeter; 5, ammeter shunt; 6, make and break key with automatic short-circuiting device for make or break shocks; 7, inductorium; 8, resistance box in secondary circuit; 9, wires leading to stimulating electrodes. FIG. 9. View of apparatus in actual use. Significance of numbers is the same as in Fig. 8. A SUMMARY OF PROCEDURE 31 The arrangement of apparatus for the use of the quantitative method is indicated diagrammatically in Fig. 8. The diagram is self-explanatory. As an addi- tional guide, a photograph of a set of apparatus in actual use is reproduced in Fig. 9. In the final chapter of the book various precautions are described which much ex- perience with the method has suggested. CHAPTER IV THE PHYSICAL PRINCIPLES UNDERLYING THE MEASURE- MENT OF BREAK SHOCKS HELMHOLTZ* appears to have been the first to study in detail break induction shocks. He established the principles which are still accepted as to their formation and course. His work was chiefly from the physical standpoint, although he gave attention also to the physi- ological aspect of the problem. More recently Fleming f has given a clear and concise discussion of break incluc- tion shocks, his presentation agreeing in every essential particular with the earlier one of Helmholtz. The fol- lowing statement is, in the main, condensed from Flem- ing's discussion. The Course of Break Induced Currents. The current induced in a secondary coil by the breaking of the primary current may be represented graphically by such a curve as is given in Fig. 10, beginning at zero, increas- ing rapidly to a maximum, and then falling more slowly away to zero. If the break of the primary were abso- * Helmholtz: Poggendorf's Annalen der Physik und Chemie, 1851, Ixxxiii, S. 536. Also, Ges. Abh., S. 459. t Fleming: The Alternate Current Transformer, London, 1892, i, pp. 184 et seq. 32 THE MEASUREMENT OF BREAK SHOCKS 33 lutely instantaneous, the initial rise would be instan- taneous likewise and the secondary current would begin with its maximum value. Since, however, there is al- ways, even under most favorable conditions, a certain amount of sparking at the contacts, there is never an instantaneous break, and the initial rise is constantly present. Helmholtz * . ..__. demonstrated, with the FlG I0 Curve mustrating the course aid of. an ingenious ap- of a break induced current — after paratus, that the phys- Fleming' iological effect of a break induced current is chiefly exerted by that part embraced within the ascending limb of the curve. By breaking the secondary current at various points in its course he found that the physiolog- ical effect was virtually as great when the current was broken at the moment of reaching its maximum intensity as when it was allowed to run its entire course. Recent investigations carried out by means of short galvanic currents have shown, it is true, that the stimulating effectiveness of a shock is to some extent dependent as well upon the descending portion of the curve,t so that * Helmholtz: Loc. cit., S. 537. t Gildemeister: Pfliiger's Archiv filr die gesammte Physiologic, cxxxi, 1910, S. 199. 34 INDUCTION SHOCKS Helmholtz' conclusion is not wholly valid. But at this stage of the discussion we may neglect the effect of the descending portion of the curve, and proceed as though the ascending limb were the sole determining factor. Since the chief physiological effect is exerted during the growth of the current this effect will be greater the higher the curve rises; in other words, the strength of stimulus tends to be proportional to the maximum in- tensity of the induced current. In the diagram, Fig. 10, the maximum intensity is represented by the ordinate CB, drawn from the base line to the summit of the curve, and with the factors determining the value of this ordi- nate we are at present concerned. Helmholtz showed that the induced current reaches its maximum intensity at the instant the spark ceases to pass. The abscissa AB, therefore, represents the time occupied by the spark. In a properly constructed ap- paratus AB will be constant. Helmholtz showed also that the value of the ordinate CB is approximately equal to — > in which M is the mutual induction be- JM tween primary and secondary, / the intensity of the cur- rent through the primary, and L the inductance of the secondary. If the break were instantaneous, making AB zero, CB would equal the expression given above; it falls below that value more and more as AB increases, but so long as AB is constant the relation between the THE MEASUREMENT OF BREAK SHOCKS 35 true value of CB and the value — — -> which it approxi- JLi mates, does not vary. We may use the expression — — -> therefore, as a physi- Lt cal basis for the measurement of break shocks, although we must note that the expression will not serve fully, since the factor of secondary resistance is not included in it, nor is there any factor for the influence of the manner of applying the stimulating electrodes. More- over, the expression is proportional to the strength of the stimulus only so long as the circuit is broken uni- formly. The expression serves in our quantitative scheme, therefore, only as a starting point. Its use even so far is justifiable only if physiological tests confirm the applicability of the physical relationships. That they do so completely will be shown in due course. Our next step is a consideration of the individual MI factors in the expression — and a discussion of the Li means whereby they are to be determined. Of the three factors which make up the expression, one, /, the intensity of the primary current, is an easily measured electrical quantity, and is best determined directly by means of an ammeter in the primary circuit. The other two, M and L, are functions of the construc- tion of the inductorium, either by itself or as modified 36 INDUCTION SHOCKS by the relative positions of the primary and secondary coils. M, the mutual induction between the primary and secondary coils, varies with changes in the position of the secondary relative to the primary, but is fixed for each position. It can therefore be determined once for each position of the secondary coil, and the values thus obtained used in all future calculations. Since mutual induction is the factor which varies with shifts in the position of the secondary coil relative to the primary, most of the calibrations hitherto pro- posed amount in effect to determinations of the relative mutual inductions for the various secondary positions. That the stimulating power should theoretically be pro- portional to the mutual induction so long as the other factors remain constant is obvious from inspection of the expression — — • That the proportion really does exist j^i is proved by the experimental verification of the Fick, Kronecker, and Edelmann calibrations, as well as by the experiments carried out in the development of the pres- ent method.* L, the inductance of the secondary coil, is a function of the construction of the coil and is therefore constant for any given inductorium except as it is modified by extraneous influences. When the inductorium is used * Martin: Amer. Jour, of Physiol., 1908, xxii, p. 123. THE MEASUREMENT OF BREAK SHOCKS 37 with an iron core in the primary, this acts to modify the value of L whenever the secondary coil is directly over the iron core. The methods by which M and L are determined in practice are outlined in succeeding chapters. CHAPTER V THE DETERMINATIONS OF MUTUAL INDUCTION BETWEEN PRIMARY AND SECONDARY COILS IN determining the mutual induction for the various secondary positions advantage is taken of the fact that this factor appears in the expression for the integral effect of the induced current. This integral effect is represented in the diagram (Fig. 10), by the entire area A BCD', its expression is -=-» in which M and / have JK. the same meanings as hitherto, and R equals the resist- ance in the secondary circuit. The integral effect can be measured by means of the ballistic galvanometer. For this purpose the secondary of the induction coil under examination is connected in series with a good ballistic galvanometer and with the secondary of a standard induction coil, the latter apparatus being so constructed that the mutual induction between its pri- mary and secondary coils can be computed from the con- struction of the apparatus and the current through the primary. The special features of its construction are found in the primary, which is a solenoid of one-layer thickness, very evenly wound, and several times longer PRIMARY AND SECONDARY COILS 39 than the secondary. The lines of force through the secondary, placed at the middle of the primary, are then practically straight. The arrangement of the apparatus is shown diagrammatically in Fig. 7. The secondary of the inductorium whose values of M are desired is set successively at points i or 2 cm. apart. At each point the galvanometer deflection caused by breaking a primary current of known inten- sity is determined. Since each galvanometer deflec- tion represents a certain integral effect, no matter how produced, and since the integral effect affords means of computing M, a determination of the intensity of cur- rent which has to be broken in the primary of the standard coil to produce these same deflections provides all the data required for calculating the values sought. The formula used for computing M is developed in the following manner: The expression for the integral effect MI is, as stated above, — — • Let this represent the gal- R vanometer deflection caused by breaking a current of intensity / in the primary of the coil whose values of M M'S are desired. Let the expression — — represent the same R galvanometer deflection caused by breaking a current of intensity S through the primary of the standard coil. Equating these, we have-^ - = - — • The method of R R 40 INDUCTION SHOCKS connecting the secondaries is, as stated previously, pur- posely such that the value of R is constant throughout. It therefore disappears from the equation and we have MI = M'S. The value of M ' is computed from the construction of the standard coil according to the formula M' = 4 irnNASj in which n equals the number of turns in the primary coil per centimeter of length, N the total number of turns in the secondary coil, A the area of the cross section of the primary, and S the current through the primary in electromagnetic units. Since this current is measured in amperes, it is necessary in practice to call S the intensity of the primary current in amperes and divide the expression by 10 to reduce to electro- magnetic units. The formula for M' then becomes 4 irnNAS 4 irnNA . — The value — - is corstant for any given 10 10 standard coil, and once determined is substituted for M' in the equation MI = M'S. To illustrate the process of determining mutual in- ductions by this method, suppose the standard coil has the following dimensions: Number of turns in primary per centimeter. . . 5.4 Total number of turns in secondary 1865 Area of cross section of primary 6 sq. cm. The value of - - is 75,870, and the equation for 10 mutual induction is M = — '— Now suppose that PRIMARY AND SECONDARY COILS 41 with the secondary coil at 12 cm. from the zero position the breaking of a primary current of o.i ampere gives a deflection on the galvanometer scale of 5, and that to secure the same deflection with the standard coil a cur- rent of 6.8 amperes must be broken through its primary. Substituting these values in the equation we obtain for M 5,150,000. By repeating this procedure the values of M for every secondary position can be obtained. If —— is a true expression for the physiological effect i-j of break shocks, evidently with L constant the product M I must also be constant so long as it represents a uni- form stimulus, no matter how the value of M may be varied by shifting the secondary coil. Experiment shows that MI does remain constant for a constant stimulus over the entire field of the inductorium, except that, when an iron core is present, it varies in the part of the field directly over the iron core. This is the region in which, as stated in a former paragraph, the value of L is affected by the presence of such a core.* If a constant stimulus gives a constant value of M7, however the secondary coil may be shifted, it follows that if / is made constant, — in other words, if a fixed cur- rent is broken through the primary coil, — the strengths of stimulus at different secondary positions must vary * For experimental evidence, see Martin: Amer. Jour, of PhysioL, 1908, xxii, p. 124. 42 INDUCTION SHOCKS directly as the values of M for those positions. By de- termining these values, then, we provide ourselves with a calibration which reveals accurately the effect on stim- ulating strength of shifting the secondary coil. Such a calibration, as previously stated, is a necessary basis in any scheme for the quantitative use of induction shocks. CHAPTER VI EFFECTS PRODUCED BY AN IRON CORE IN THE PRIMARY COIL INASMUCH as the almost universal practice in physio- logical work is to use inductoria with iron cores, a brief discussion of the effects of such cores on stimulation strengths seems desirable at this point. Thus the method becomes at once applicable to inductoria with iron cores as well as to those not provided with them. The principal effect of the iron core is that which has led to its use, namely a great increase in the number of lines of force surrounding the primary coil, with a cor- responding increase in the intensity of the stimuli gen- erated. Another effect is that noted in a previous paragraph (p. 36), of altering the effectiveness of the stimuli gen- erated when the secondary coil is directly over the pri- mary, so that in these positions M I is not constant for a constant stimulus. The method of correcting the cali- bration for this effect of the iron core is given in Chap. VIII, p. 58. The iron core has also an effect upon stimulation strength due to its magnetization by the primary current, an effect which appears, however, only when primary currents of considerable intensity are used. Allowance 43 44 INDUCTION SHOCKS for this effect in computing the values of MI must be made, whenever / is large, by introducing a correc- tion factor. This factor can be obtained without diffi- culty by the use of the ballistic galvanometer, since the deflections of that instrument are affected by core mag- netization. Inspection of the formula MI = M'S (p. 40) shows that so long as M and M ' remain constant, /, the current through the primary of the coil under examina- tion, must vary directly as S, the current through the primary of the standard coil. This relationship is found by experiment to hold in ordinary induction coils for values of / up to o.i ampere, but above that point the value of S is always larger than the equation calls for. In other words, when core magnetization is present the primary current produces a greater deflection than it does in the absence of this effect. The variation due to the magnetization of the core is not very difficult to correct, because, as repeated experiment has shown, the ratio between the actual values of / and those computed from the values of S depend upon an easily determined factor which is constant for any given iron core. To determine this factor some position of the second- ary coil must be selected at which primary currents up to i ampere give galvanometer deflections not greater than the entire scale. With the secondary in this posi- tion primary currents of increasing intensity, beginning at about o.oi ampere, are broken, and the deflections EFFECTS OF IRON CORE IN THE PRIMARY COIL 45 produced by each carefully noted. Then with the stand- ard inductorium the values of S giving these same de- flections are determined. Although at first the ratio of S to / remains constant, as the values of / begin to exceed o.i ampere the ratio steadily increases. It is evident, therefore, that large currents are producing relatively greater deflections than small ones. By mul- tiplying the different values of S by the ratio of S to /, which was constant, we obtain a series of computed values of 7 representing the currents which would be required to produce the observed galvanometer deflections if no iron core were present. These are, of course, the values of I which are to be employed in computing the strengths of stimuli according to the expression — — • LI Table I, column 3, gives the values of / computed from a series of observed values of / and S in actual experiments. TABLE I Value of 7 ob- served in am- peres. Value of 5 ob- served. Value of / com- puted in am- peres. Ratio computed value of / to its observed value. Decimal part of ratio divided by observed value of /. 0.01 0.005 O.OI .O 0.05 0.025 0.05 .O .... O. IO 0.05 O.IO .O .... O.2O 0.1044 0.2088 •044 .22 0.30 0.1597 0.3194 .065 .217 0.40 0.2180 0.4360 .OQO .225 0.50 0.2782 0.5564 •113 .226 O.6O 0.3396 0.6792 I.I32 .22 46 INDUCTION SHOCKS y To derive the equation for obtaining / computed when I observed is known we determine in a series of experi- ments the ratios of / computed to 7 observed (see column 4 of the table). If now the decimal part of each ratio is divided by its corresponding value of 7 observed, a con- stant is obtained which represents the number by which 7 observed must be multiplied to obtain this decimal part of the ratio. This constant is shown in column 5. After the constant is found it is used for computing 7 according to the formula Tr = 7o X (i + KI0). In this formula 7C is the computed value of 7, 7o is its observed value, and K is the constant, — in the case cited in the table equaling .22. The method of correcting for the magnetization of the iron core is given in detail since, in spite of the abun- dant theoretical justification for the omission of the iron core, especially where quantitative estimations are sought, for the practical purposes of the physiologist the inductorium as commonly used, with the iron core present, is usually to be preferred. The intensity of stimulus, other factors being equal, is at least five times greater with the iron core than without it in inductoria of the usual type. This increased efficiency makes it possible to obtain with primary currents of moderate intensity as strong stimuli as the physiologist ordinarily requires. The use of moderate primary currents is of great importance in quantitative estimations of indue- EFFECTS OF IRON CORE IN THE PRIMARY COIL 47 tion shocks, since thereby is avoided that heavy sparking at the contacts which always accompanies the break of a current of high intensity, and which affects the intensity of the stimulus in a manner that cannot be foretold. When the secondary coil of an inductorium is moved from the zero position until nearly clear of the primary coil, it enters a " critical region" where small changes in position are accompanied by great changes in the in- tensity of the stimuli given by the instrument. The impression seems to prevail among physiologists that inductoria having iron cores show so much greater vari- ations of intensity in this " critical region" than do those without iron cores as to make the omission of the iron core a distinct advantage in many experiments. As a matter of fact, however, Kronecker inductoria, such as are used in most physiological laboratories, show for given changes in secondary position in the " critical region" greater variations in stimulation intensity with cores removed than with cores present. This is appar- ent when the Kronecker graduations of such coils are compared with the calibrations made for them by the method of the present work (see p. 55). In the prep- aration of the Kronecker graduations the iron cores were withdrawn from the instruments. For the cali- brations made in connection with this work the iron cores were in place. INDUCTION SHOCKS TABLE II Effect of the Iron Core on the Rate of Change of Stimulation Intensity in the " Critical Region " of the Inductorium Iron core absent. Iron core present. Position of sec- ondary in cen- timeters. Kronecker graduation. Percentage de- crease per centi- meter. Author's cali- bration. Percentage de- crease per centi- meter. 8 6190 6240 9 5150 17.0 5340 14.4 10 4I50 19.4 4500 15-7 ii 3250 21.7 3600 20 12 2375 27.0 2640 26.7 13 1570 33-9 1920 27-3 14 IOOO 36.3 1270 33-8 15 625 37-5 860 32.1- 16 435 30-4 600 30.3 17 310 28.7 455 24.2 18 230 25-7 35° 23.1 iQ 178 22.7 280 20.0 Table II gives a comparison of the calibrations in the " critical region" of one inductorium made without and with the iron core. The primary coil of this instrument was 14 cm. long. The table shows clearly that the rate of decrease of stimulation intensity from point to point is greater when the iron core is absent than when it is present. Table III is the record of experimental verification of the same fact. Stimulation intensities were compared in these experiments according to the v. Fleischl method (p. 56), namely by comparing the primary currents required to produce stimuli of equal value with the secondary coil at different positions. EFFECTS OF IRON CORE IN THE PRIMARY COIL 49 According to this method increases in the primary current represent corresponding decreases in the stimulating efficiency of the inductorium. TABLE III Experimental Proof that Stimulation Intensity shows Greater Variation in the " Critical Region " when the Iron Core is Absent than when it is Present. Break Shocks Iron core absent. Iron core present. Date of experiment. Position of secondary Primary current, Per- centage increase Primary current. Per- centage increase in centi- amperes. in cur- amperes. in cur- rent. rent. Dec. 21, 1906 . . 8.0 O OIQ1? 0.00187 12. 0 w • wx VO 0.0505 159 0.00463 148 16.0 0.260 415 O.O22 375 Dec. 24, 1906 8.0 o 00^76 o . 0008 12.0 \S . W*M^ 1 \J 0.01523 164 O.OOI97 146 16.0 0.091 432 0.00934 374 Apr. i«;, 1007. . 8.2 O OI7 0.0036 11.28 w / 0-035 107 0.0063 75 12.45 0-0535 50 O.OO92 46 14.0 0.107 TOO 0.016 74 16.2 0.2485 132 0.034 112 CHAPTER VII COMPARISON OF ONE COIL WITH ANOTHER — THE VALUE OF L WE have seen (p. 41) that in any given inductorium, after allowing for certain exceptions due to the iron core, if one is present, the strengths of stimuli produced by a given primary current with the secondary coil at various positions are directly proportional to the mutual induc- tions for those positions. When, however, the attempt is made to compare the stimuli generated by one in- ductorium with those produced by another, it is at once apparent that the relation between stimulating value and mutual induction holds only for stimuli pro- duced by the same instrument. This, indeed, was rec- ognized by Helmholtz, who pointed out the necessity of including in the expression for stimulating value the factor L, whereby to take account of the influence of inductorium construction. This factor, according to Helmholtz, is dependent on the inductance of the sec- ondary coil, and is to be derived, therefore, from the expression for inductance. The common formula for AW2 the inductance of a coil is L = — — > in which L is the 50 COMPARISON OF ONE COIL WITH ANOTHER 51 inductance of the coil, A its mean cross section, W the number of turns of wire composing it, and / its length. When, in the course of developing this method of measuring stimuli, the attempt was made to apply the above expression for L in the formula -— > the curious ob- it servation resulted that it applied perfectly with some inductoria and not with others. That is to say, when equal stimuli were generated by means of different in- ductoria, equal values of — — were given by some, but LJ not by all, of the instruments compared. Upon analyz- ing the reason for the difference the following fact came out clearly; equal values of — — were given by those in- j_j ductoria whose secondary coils had the same number of turns of wire per centimeter of length, regardless of the total number of turns of wire; unequal values were given by those inductoria whose secondaries had different numbers of turns per centimeter of length. If we look now at the AW2 expression for L given above, i.e., L = — — > and sepa- rate within it the factor of turns per unit of length, the W expression reads L = AW X — • The experimental re- sults showed as stated above that in all the inductoria 52 INDUCTION SHOCKS W having the same value of — > namely the same number of turns per centimeter, the expression L = AW might AW2 be substituted for the expression L = — — and equal values of — - — for equal stimuli would be given. The j^ next step was to see whether those inductoria which for- merly gave non-concordant results would give concordant ones if for the value of L the expression AW, namely the product of the cross section of the secondary by the num- ber of turns in it, were used. It was found that when this was done all the inductoria examined gave for equal stim- uli corresponding values of — - ' regardless of the dimen- Li sions of the coils, but subject to a certain restriction as to secondary resistance to be discussed later (p. 78). In order to bring this point out clearly some of the ex- periments upon which it is based are cited below (Table V). The inductoria used are described in Table IV. In this table only those inductoria are considered whose secondaries have different numbers of turns per centi- meter, since only by them can be determined which of the two expressions for L is correct. In all the experi- ments, comparisons were made between the various in- ductoria and a single one known as coil B. This is a large inductorium with a Kronecker calibration whose COMPARISON OF ONE COIL WITH ANOTHER 53 secondary has 800 turns per centimeter; it was selected as a basis of comparison merely for convenience. In Table IV, columns 5 and 6, are given, for the differ- ent inductoria examined, the values of L — AW and AW2 L = — — To simplify the comparisons between the AW2 various coils the values of — - — as given in Table IV were all divided by 800, the number of turns per centi- meter in the secondary of coil B, thus making the value of L for coil B the same by either formula. These values are set down in column 7 of the table. To bring the final results into convenient denominations these figures and also those in column 5 were divided by 100. It is understood, of course, that these divisions, made purely for convenience, in no wise modify the relations between the coils. In Table V are set down the experimental results of the comparisons between the various inductoria. Since details would only confuse, they are omitted. The fig- ures presented in the table show clearly that the proper AW2 expression for L is AW rather than— — • 54 INDUCTION SHOCKS TABLE IV Description of inductoria used in establishing expression for L Coil. Length of sec- ondary coil. Turns in secondary coil. Cross sec- tion of sec- ondary coil. Cross sec- tion X turns in secon- dary coil. Cross section X turns in sec.2 length Column 6 divided by 800. cm. sq. cm. B 13 10,35° I7.6 182,000 145,000,000 182,000 C 7-4 4,830 22 105,000 69,500,000 87,000 F 13-5 3,000 15-4 46,000 10,250,000 12,800 H 9-3 6,000 16.6 100,000 64,300,000 8o,OOO N 9-3 8,000 17.8 142,000 I22,5OO,OOO 153,000 TABLE V Demonstrating that the expression for L should be A W rather AW2 than MI — coil B. Coil. MI AW' MI AW MI L coil B. Coil. MI AW' MI AW* JXSoo iXSoo 8 C 7-7 4-5 7-5 H 7-5 9-4 12.6 13 7.6 7 7.2 9 xi. 4 ix. 7 6.9 5-3 5-3 6.6 28.2 F 28 100 2-57 N 2.43 2.25 17 16.4 57 30.5 28.6 26.5 2.6 H 2.8 3-5 64 60 56 30.5 30.9 38.6 10.2 10.4 9-7 64 61.1 76.4 7-5 7 6-5 CHAPTER VIII THE PREPARATION OF A CALIBRATION SCALE FOR BREAK SHOCKS IN previous chapters the methods of obtaining the individual factors making up the expression for break stimulation strength have been discussed in detail. To show how these methods are put into practice in pre- paring an inductorium for quantitative use is next in order. The first step is the determination of the mutual inductions by the method hitherto described, for a series of positions, preferably not more than 2 cm. apart, along the scale. If the instrument to be cali- brated is without the iron core these measurements should be taken from the zero position outward; if an iron core is present there is no advantage gained by determinations of mutual induction for secondary posi- tions in the region where the secondary coil overlaps the primary. Having determined these values, each is divided by L, the product of the cross section by the number of turns of the secondary coil. The mean cross section must be determined with great care, a rather difficult procedure in completed inductoria, and one which ought to be carried out in connection with their manufacture. 55 56 INDUCTION SHOCKS In order that the final stimulation units may be of convenient size the value of L which has been adopted in this scheme is not the direct product of the cross section by the number of turns of the secondary, but is that product divided by 100. Having determined this value, the mutual inductions previously established are divided by it. The resulting figures are the " calibra- tion numbers" for the particular secondary positions to which they apply. To determine the numbers for in- termediate positions those determined as above are plot- ted on a rather large scale on coordinate paper and a smooth curve is drawn connecting them. Since the mutual induction necessarily diminishes, not by fits and starts, but smoothly, as the secondary is moved out- ward, such a curve, if carefully made, will indicate the calibration numbers for intermediate positions with a high degree of accuracy. To prove the accuracy of the calibration the method of v. Fleischl is employed (p. 18) in which the minimal contraction of a frog's gastrocnemius is used as the index of a constant stimulus. In detail this procedure as carried out by myself was as follows : The freshly isolated gas- trocnemius was suspended by its attached femur in a moist chamber, and its lower end connected by a small copper wire to a muscle lever whose effective weight was about 10 gm. ; the muscle was not afterloaded. The lever had a magnification of about ten, and its point pressed CALIBRATION SCALE FOR BREAK SHOCKS 57 lightly upon a smoked drum. The minimal contraction could be detected without difficulty, since the whole appa- ratus was made rigid enough for the slightest movement of the muscle to show itself at the end of the lever. Connection between the muscle and the terminals of the secondary coil was by means of two platinum needles soldered to fine copper wires leading from the secondary terminals. These needles were thrust directly through the muscle tissue, — one about 5 mm. below its origin, the other the same distance above the distal tendon, both in the same vertical plane. By this method of connecting the muscle, variations in the secondary re- sistance aside from those in the tissue itself were avoided. At least half an hour was allowed to elapse after the muscle was hung in position before stimulation was begun; in order that summation might not enter, the shortest interval allowed between successive stimuli was ten seconds; to avoid fatigue the strength of stimulus used was always kept as near minimal as possible. The results of repeated experiments show that under these conditions a high degree of constancy is usually main- tained during the interval, about three hours, required for a single experiment. That each experiment be com- plete in itself is, of course, necessary, since no means has suggested itself for obtaining a response which shall remain constant through a period of successive days. To have conditions uniform the electrode nearer to the 58 INDUCTION SHOCKS origin of the muscle was in most cases made the cathode. With the minimal contraction of the muscle as the index, the primary current necessary to arouse it, measured in amperes, is determined with the secondary coil in various positions. To allow for variations in irritability of the tissue the experiment should be repeated a number of times. If the calibration is carefully made in the be- ginning it will be found that in each individual experi- ment the product -— X /, — primary current times cali- Lt bration number, — is virtually constant, showing that the calibration is correct. Should the inductorium being calibrated have an iron core, there still remains the establishment of calibra- tion numbers for the region where the secondary coil overlaps the primary. These, however, can easily be determined by extending the experiments, just de- scribed for proving the calibration, to cover this part of the field. The value of — - X / is established in any .L/ M given experiment from the part of the field where — is Li known, that is, where the calibration has already been worked out. Since this is constant so long as the stim- ulus is unchanged a determination of the primary current, M 7, for this stimulus, in the region where — is unknown, CALIBRATION SCALE FOR BREAK SHOCKS 59 yields at once data for computing — r • By averaging several experiments this part of the field can be cali- brated with sufficient accuracy. It must be stated, however, that in the innermost part of the field, including about half of the length of the primary coil from zero outward, the calibration num- bers determined by the v. Fleischl method will be found to differ somewhat according as the tissue used as an indicator has high or low resistance, high resistances showing larger calibration numbers than low ones. For this reason it is desirable to avoid using this region in work which requires a high degree of accuracy, unless a calibration has been previously worked out for the resistance actually to be employed. Experience shows that occasions when it is necessary to use the first 5 or 6 centimeters of the scale are of rare occurrence in most kinds of experimental work. CHAPTER IX THE MAKE AND BREAK OF THE PRIMARY CIRCUIT FROM the beginning of the use of induction shocks for stimulating living tissues investigators have recognized that the physiological intensities of these shocks are markedly affected by the manner of making or breaking the primary circuit. Helmholtz * called attention to this fact in his study of induced currents, and in the dis- cussion of the variable factors to be considered in the attempt to measure induction shocks (p. 14), I pointed out that the manipulation of the primary key is a vari- able whose influence cannot be mathematically deter- mined, and which, therefore, must be made as uniform as possible. Before entering upon a discussion of means whereby the manipulation of the primary make and break key can be made uniform, it is desirable to point out briefly the manner in which variations in the break and make of the primary circuit modify stimulating intensities. In the account of the theoretical basis for the break M shock formula, Z = -— / (p. 34), the statement was Lt * Helmholtz: Poggendorf's Annalen der Physik und Chemie, 1851, Ixxxiii, p. 538. 60 THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 6l made that this expression applies exactly only when the break is instantaneous, although it holds relatively so long as the time occupied by the break does not vary. Since this in turn depends on the duration of the spark, our present inquiry resolves itself, so far as break shocks are concerned, into a study of the conditions governing contact sparking. The duration of the spark at a broken primary con- tact depends in part upon the intensity of the primary current, in part upon the amount of volatilization occur- ring at the contact, and in part upon the speed with which the points are separated. This last factor ex- plains why keys operated by hand cannot be depended upon to give uniform results, and why some form of automatic key is required, since only thus can a uniform speed of separation be secured. Moreover, ordinary mercury keys cannot be depended on even when oper- ated automatically, because of the tendency of mercury when not absolutely clean to cling in drops and thus vary the speed with which the contact points actually separate. In practically all keys there is some volatil- ization; platinum contacts giving the least, ordinary mercury contacts the most. It is impracticable to use always primary currents of a single intensity; but, in primary currents not exceeding i ampere, the variation is too slight to be of practical importance. The making of a primary circuit is not attended with 62 INDUCTION SHOCKS sparking, so that the sources of error for makes are not the same as for breaks. As a circuit is made the re- sistance falls from infinity to the resistance of the closed circuit itself. It is during the change from the first of these resistances to the second that the secondary cur- rent is induced. The more nearly instantaneous the change, the greater is the physiological intensity of the induced current. In hand-operated metal-contact keys there can be no assurance that the contact points will be pressed together with the same firmness twice in succes- sion, so that to secure uniformity of contact automatic keys are required for make shocks as well as for breaks. A further and more serious defect in metal-contact keys for make shocks is their liability to rebound slightly, or to slip sidewise, jthus giving not a single clean-cut make, but a succession of make, break, and make. So con- stantly has this defect shown itself in my experiments, even with carefully constructed automatic metal-contact keys, that I have found it necessary to use mercury con- tacts altogether in studying make shocks. The considerations stated above lead to the following conclusions: That hand-operated keys are not to be de- pended on for uniform makes and breaks ; that for break shocks platinum contacts are to be preferred to mercury because of their less volatilization, while for make shocks, on account of the rebound or side-slip of metal contacts, mercury affords the only trustworthy contact. THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 63 ^ M , / \ 8 / It is, of course, wholly undesirable to equip the pri- mary circuit with two keys, — one of mercury to be used for making the circuit, and another of platinum for breaking it. I shall describe, therefore, an automatic make and break key with mercury contacts which has been proved by several years' experience to give uniform breaks and makes.* The key consists of a block of vulcanite 30 mm. long, 20 mm. wide, and 25 mm. deep, having cut in it two vertical chambers (see Fig. FlG TI Diagram illustrating II), one (a) rectangular, 20 the principle of the vulcanite mm. long, 8 mm. wide, and 20 mm. deep; the other (b) cylindrical, 6 mm. in diameter and 20 mm. deep. A hole, c (Fig. n), 3 mm. in diameter, is bored through from one of these cavities to the other at a depth of about 16 mm. Each of the chambers is in electrical communication with a binding post, and when filled with mercury they are in electrical communication with each other through the connecting- hole, c. * Martin: Am. Jour, of PhysioL, 1910, xxvi, p. 181. knife-blade key. The front of the block is broken away to show the relations of the parts within the chamber, a. a and b, mercury chambers; c, open- ing between a and b; d, vul- canite knife blade supported upon axis, o, which rotates within collar, e. 64 INDUCTION SHOCKS A strip of vulcanite, d (Fig. n), 18 mm. long, 8 mm. wide, and i mm. thick, flat on one side and on the other tapered toward the edges, is supported at the top of the block by a horizontal rod working freely in a collar, e (Fig. n), in such fashion as to press closely against the inner surface of the cavity, a, and when rotated about its axis of support to cover or uncover the open- ing, c. When the vulcanite strip is brought over the opening, it cuts the mercury connection between cavi- ties a and b, and therefore breaks any electric circuit which may include them. This method of breaking a circuit has many points in its favor. The break cannot be delayed through the tendency of mercury drops to cling together, for the severance of the mercury column is not the withdrawal of one mass of mercury from another, but is the forcible interposition of a nonconductor in the path.* Moreover, the vulcanite strip cuts off not only the liquid mercury, but if it fits tightly, as it should, cuts off as well any mercury vapor that may be formed. Thus the effect of volatilization of mercury is minimized. Since the point where the break occurs is beneath a con- siderable depth of mercury, air does not have access to it, and oxidation does not occur. I have found, as a matter of fact, that the same mercury may be used in one of these keys for months without any appreciable varia- tion in the effectiveness of the break. * A device employing the same principle was described by Lombard in 1902: Am. Jour, of Physiol., 1902, viii, p. xx. THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 65 When the vulcanite strip is so rotated as to uncover the hole, c, the mercury in the two cavities reunites and thus makes the circuit. The reunion of the separated mer- cury masses should take place as smoothly as possible. To bring this about, the vulcanite knife blade is tapered at the edges so that it may plough through the mercury with as little disturbance as possible. FIG. 12. Diagram of the operating device for the knife-blade key; vertical view. /, triangle of brass bearing slits, g, g', and wings, w, w', rotating about axis, 0; /, /', actuating springs; &, &', levers for bringing tension upon springs, and at the same time operating release, i; m, m', stops for limiting motion of knife blade. The Operating Device. To secure uniformity of ac- tion the vulcanite blade must be operated automati- cally, hand operation being liable to wide variations in the speed with which the contact is made or broken. The method adopted in this instrument is illustrated by the diagrams (Figs. 12 and 13). The axis of rotation of the blade, o (Figs, n and 12), after passing through the 66 INDUCTION SHOCKS supporting collar, e (Fig. n), is fastened into a trian- gular sheet of brass, / (Fig. 12), from whose apex pro- ject horizontally two brass arms, w and w'\ these are bent at right angles at their outer ends, as shown in Fig. 13. From the tip of each of these arms a coiled spring, / and I' (Fig. 12), extends down to the end of a lever, k and k'. Each spring consists of twenty-seven turns of spring brass wire, 0.6 mm. in diameter. The length of the spring is about 16 mm., and the outside di- ameter of the coil 5 to 6 FIG. 13. Diagram of the operating mm The depression of device for the knife-blade key; horizontal view. Significance of either lever puts the spring letters the same as in Figs. 1 1 and connecting with it under 12. s, cavity in base for holding short-circuiting device. tension and tends to draw downward the correspond- ing arm, rotating the vulcanite blade with it. To pre- vent movement of the blade until the spring has been put under a certain degree of tension, two slits, g and g', are cut into the lower edge of the triangle, /. A re- leasing device, i, is pressed upward against the lower THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 67 edge of / by a stout spring, in such fashion that when either slit is engaged/ is prevented from moving. Each of the levers, k and k' bears at its tip an arm, r, r' (Fig. 13), which presses upon the releasing device, and when the lever is depressed to a certain point disengages it, allowing the blade to rotate. The amount of motion of the blade is limited by setting two posts, m and m', Sit such positions that the lower apices of / strike them when sufficient movement has occurred. After experimenting with various operating devices the one described above has been adopted as combining the greatest number of desirable features with the fewest defects. The two levers, k and k1 ', which are depressed alternately for making and breaking the circuit, are so placed as to lie naturally under the first and second fingers of either the right or the left hand. The springs, / and lf, need not be stiff, hence little pressure need be exerted upon the levers, and there is correspondingly little fatigue from continuous operation of the key. The springs are brought under tension only during the use of the instrument; when it is not in use, they hang free. Thus their stiffness does not vary with the lapse of time, as would be the case were one or the other under constant tension. The Short-circuiting Device. A desideratum in any key which is to be used for stimulating tissues with single induction shocks is a device for short-circuiting auto- 68 INDUCTION SHOCKS matically either the make shocks or the break shocks at the will of the operator. The instrument under con- sideration lends itself so readily to the incorporation of such a device that I shall include a brief descrip- tion of one, believing that the value of the key is enough enhanced thereby to justify its inclusion. The entire mechanism, shown in ground plan in Fig. 13, is mounted upon a slab of vulcanite, which in turn rests upon a base of soapstone, slate, or other suitable material. The vulcanite is cut a- (Eh (0) FIG. 14. Diagram of the short- circuiting device. /, brass bar, rotating horizontally about axis, way between and under- u and bearing mercury cup, o, neath the leye k and which is in electrical communi- cation with post, p. z, z' ', platinum k , as indicated at s (Fig. pins mounted upon levers, k, k', and in electrical communication with post, p'. 13). A brass rod, t (Fig. 14), is mounted upon an axis, u, in such fashion that it can be rotated horizontally about this axis within the confines of the space, s. At the end of the rod is a mercury cup, o. Two binding posts, p and pf, stand THE MAKE AND BREAK OF THE PRIMARY CIRCUIT 69 at one margin of the base. From p a wire leads through the body of the vulcanite block to the rod, /, to which it is soldered near the axis of rotation of the rod. From p' two wires are carried through the block, one to the axis of rotation of the lever, k, to which it is soldered, the other to the axis of k', where it is soldered likewise. Thus both levers are in electrical connection with the post, p', and the rod, t, in similar connection with the post, p. Soldered to the levers, k and k', at the points, z and z', are pins of platinum projecting downward. These pins are so placed that the mercury cup, 0, can be brought directly below one or the other of them according as t is rotated. Their length is so adjusted that the pin dips into the mercury when the lever is depressed enough to release the mechanism, but is clear of the mercury at all other times. If the binding posts, p and p1 ', are connected in parallel into the secondary circuit of the inductorium and the rod, /, is rotated so as to bring the mercury cup below the lever which is pressed when the primary circuit is made (the left-hand one in this instrument) the make shocks are all short-circuited. Bringing the mercury cup be- low the other lever short-circuits all the break shocks. When the rod is placed in an intermediate position, neither makes nor breaks are affected. To prevent all possibility of accidental diversion of the secondary cur- rent into the hand of the operator, vulcanite shields are 70 INDUCTION SHOCKS placed on the levers at the points where the ringers press upon them, and upon the handle by which the rod, £, is rotated. In addition to its applicability for both make and break shocks this key has the advantage of preserving uniformity of action for a long time with little attention. In this respect it is superior even to platinum contact keys, which, as is well known, suffer from oxidation after prolonged use. There is no doubt, however, that well made automatic platinum-contact keys, properly looked after, give break shocks of sufficient uniformity for the general purposes of the physiologist. CHAPTER X THE INFLUENCE OF SECONDARY RESISTANCE AND OF CATHODE SURFACE IN the preceding chapters the scheme for measuring break shocks has been developed to the point where it becomes necessary to turn from the induction apparatus to the tissue to be stimulated and to inquire how varia- tions in the tissue may modify stimulation strengths. Two possible modifying factors have been indicated (p. 14), as due to variations in the tissue; they are sec- ondary resistance, and the manner of applying the elec- trodes. The Relation of Tissue Resistance to Secondary Re- sistance as a Whole. The secondary circuit usually has a comparatively high resistance. Most indue toria used in physiological laboratories have secondary coils with resistances mounting into hundreds of ohms, and the resistances of the tissues undergoing stimulation are usually high likewise. In numerous determinations of the resistance of stimulated tissues I have met with only one or two under 1000 ohms and have found many ex- ceeding 50,000 ohms. Since the stimuli imparted by faradic currents as 71 72 INDUCTION SHOCKS well as by those of galvanic origin arise from the cath- ode,* and since the resistance of the physiological cathodes must be small in comparison with that of the whole mass of tissue traversed by the current, we are justified in considering tissue resistance as external to the actual seat of stimulation, and need make no dis- tinction between this and the other resistances that may be included in the secondary circuit. The Method of Experimentation. In studying the influence of secondary resistance experimentally the usual procedure has been to introduce known, non- inductive, resistances into the secondary circuit and to observe the effect of their introduction upon the stimu- lating value of the shocks sent through the circuit. As a check upon this method some experiments were per- formed in which different amounts of tissue were in- cluded between the stimulating electrodes, and thus the resistance of the tissue itself was varied. This latter method is of course less certain than the former, since the inclusion of more or less tissue in the circuit may mean a variation in the number and irritability of the physio- logical cathodes involved. Tissue resistances were determined by means of an ordinary Wheatstone bridge according to the Kohl- rausch method, with an alternating current to avoid * Chauveau: Journal de la physiologic, 1859, ii, pp. 490, 553. See also Biedermann: Elektrophysiologie, Jena, 1895, ii, p. 622. THE INFLUENCE OF SECONDARY RESISTANCE 73 polarization, and a telephone in place of the galvanom- eter. Figure 15 is a diagram of the apparatus required. The average of three readings was always taken. This procedure, in the hands of one experienced in its use, gives results accurate within 4 or 5 per cent, a degree of accuracy sufficient for the purposes of this inquiry. FIG. 15. Diagram of apparatus for measuring tissue resistance. A, Wheatstone bridge; B, telephone; C, small induction coil; D, battery for same; E, key for same; T, wires leading to tissue; R, resistance box con- nected with switch, S, in such fashion as to be available for use as known resistance of Wheatstone bridge, or as part of primary circuit, P. . Break shocks were used for determining the threshold of contraction. The expression for the value of the stimulus is Z, determined from the formula, Z = — 7. it The Effect upon the Stimulus of Varying the Sec- ondary Resistance. The effect upon the value of Z of varying the secondary resistance is shown in two repre- sentative experiments cited in Table VI. As appears 74 INDUCTION SHOCKS TABLE VI The Influence of Secondary Resistance upon the Stimulating Values of Induced Currents Experiment of Dec. 15, 1909. Resistance of Secondary Coil = 1400 ohms; of Tissue = 1700 ohms. Tissue = Frog's Gastrocnemius, Uncurarized. Resistance in secondary circuit 3100 6100 10,100 15,100 18,100 Value of Z 4.96 6.81 9.45 12.45 I4-1 Experiment of March i, 1910. Resistance of Secondary Coil = 1400 ohms; of Tissue = 16,600. Tissue = Frog's Sartorius, Uncura- rized. Resistance in secondary circuit . . 18,000 28,000 48,000 68,000 Value of Z 3.97 5.24 6.8 9 from this table, stronger stimuli are required to produce a given physiological effect when the secondary resist- ance is high than when it is low. That there is a defi- nite mathematical relationship between the effective- ness of the stimulus and the secondary resistance is shown by plotting these values as a curve. Such a curve for the first experiment of Table VI is given in Fig. 16. It is virtually a straight line having the gen- eral equation A (I) in which Z is the intensity of the shock required at re- sistance R to produce the desired effect, and ft and A THE INFLUENCE OF SECONDARY RESISTANCE 75 are constants. This formula has been found to hold in all of the several hundred experiments, in which it has been applied. The value of the constant /3 in any 12 10 4000 8000 16000 20000 FIG. 16. Showing that the curve of increasing stimulus against increasing resistance is a straight line. Abscissae represent values of Z; ordinates represent resistances in ohms. given experiment can be determined geometrically by producing the curve to where it cuts the ordinate for zero resistance. According to Fig. 16, the value of /3 76 INDUCTION SHOCKS for the experiment of Table VI from which that curve is derived is 3. Since this represents the value of Z, whose effect at zero resistance would equal that of the various other values of Z at their respective resistances, it affords a measure of the irritability of the physiological cathode where the stimulus actually arose, on the as- sumption that the resistance of the cathode is negligibly small. We have, therefore, in 0 an expression for the value of any stimulus as it affects the seat of actual stimulation, namely, the physiological cathode, irre- spective of the resistance of the secondary circuit. By a slight transposition of equation (i) the equation for /3 becomes: ZA . . '-R + A' (2) and if the value of Z for any secondary resistance is known, the actual or " specific" stimulus can be calcu- lated from equation (2), provided only the value of the other constant, A, is known. For measuring stimuli with reference to the resistance through which they are applied there must be added to the determinations previously required, therefore, not only the secondary resistance, but a constant A. Current Density an Important Factor. That the stim- ulating effectiveness of electric currents varies with their density has long been recognized,* although practical * Biedermann: Loc. cit., i, p. 185. THE INFLUENCE OF SECONDARY RESISTANCE 77 application of the fact has hitherto been reserved for galvanic stimulation. The expression for 0 shows that current density is a factor to be taken into account in measuring faradic stimuli as well. ZA The factor A in the expression /3 = — is the pro- R -f~ A. vision by which allowance is made for the influence of current density. The stimulating effectiveness of dense currents is greater than of diffuse ones. In order that the expression for /3 agree with this fact the value of A must increase as the density of the stimulating current increases. Experimental evidence showing that A is actually larger for dense currents than for diffuse cur- rents is contained in an experiment cited on p. 109, Chap. XII. I do not know of any reliable method of determining the value of the constant, A, other than that used in this work, namely to establish experimentally two or more values of Z for different secondary resistances, and from these values compute the value of A. This can be done by means of the equation ZRRf — ZR>R ( A = —j ^— ' (3) ^w — £R in which Z# and ZK are the stimuli required, with re- sistances R and Rf respectively, to produce the minimal contractions used as the index. 78 INDUCTION SHOCKS The Dependence of Factor A upon Inductorium Con- struction. In discussing the method of comparing one inductorium with another by the introduction of the factor L in the expression Z = — — > it was stated (p. 52) LI that this comparison is subject to a certain restriction as to secondary resistance. This restriction rests upon an observation of Gildemeister,* according to which, if two dissimilar inductoria are compared quantitatively by the method outlined here, in which the expression for the M value of a stimulus is Z = — X /, it will be found that Li although equal stimuli may yield corresponding values of Z from the two inductoria, with certain secondary resistances, when other secondary resistances are used equal stimuli will not give corresponding values of Z. In earlier paragraphs of this chapter it was pointed out that the true or specific value of a stimulus is not afforded by the expression Z, but by the expression 0, which depends not only upon Z but upon the secondary resistance and a constant A as well. The determination of A, as previously shown, is according to the formula ZRR'-ZR>R ~ 7 7~ £R' — £R in which ZR and ZR> are stimuli which, with resistances * Gildemeister: Archiv fur die ges. Physiologic, 1910, Bd. 131, S. 604. THE INFLUENCE OF SECONDARY RESISTANCE 79 R and Rf respectively, have equal physiological effect. Since dissimilar inductoria fail to give corresponding values of Z at all secondary resistances, the value of A determined by this formula from one inductorium will not necessarily agree with its value as obtained from another. The value of A, therefore, does not depend solely upon the surface of the physiological cathodes, but in part also upon the construction of the inducto- rium. This variation in the values of A determined from dis- similar inductoria, which might lead one to question the validity o£ the equation in which A is employed, i.e., ZA |8 = — — — > serves in fact to confirm strongly the valid- j\. -p A ity of that equation and the use of the expression 0 to signify the specific value of the stimulus. This con- firmation rests upon the repeated observation that when equal stimuli are generated by dissimilar inductoria the values of 0 are equal even though the observed values of Z and the computed values of A may be quite divergent. An experiment illustrating this point is summarized in Table VII. Details of the construction of the induc- toria used are given in Table VIII. The experiment shows that dissimilar inductoria give for equal break stimuli perfectly concordant values if all the factors which make up the final expression for stimulation strength are taken into account. 8o INDUCTION SHOCKS TABLE VII Demonstrating that Equal Stimuli give Equal Values of /3 in the Equation /9 = ~ . » when the Stimuli are generated by Dissimilar Inductoria Inductorium. H. N. B. First sec resistance 8 850 ohms o ooo ohms o 800 ohms First Z o 76 o 604 o 588 Second sec. resistance Second Z 25,500 ohms i. 60 25,600 ohms i 18 26,400 ohms i 06 Calculated A 6,200 8,400 10,800 Calculated /8 o. 31 O.2Q2 0.308 The differences in secondary resistance in corresponding columns are due to the different resistances of the secondary coils, it being necessary to include these resistances as part of the secondary circuit. TABLE VIII Details of Construction of the Inductoria used in this Study Coil. Length of secondary. Turns in sec- ondary. Resistance of second- ary. Remarks. A cm. 12.5 IO,OOO 850 ( Kronecker ( graduation B 13-0 10,350 1400 ( Kronecker \ graduation G 13.0 10,260 770 ( Kronecker ( graduation E 6-5 5,OOO 300 Porter inductorium H 9-3 6,OOO 450 N 9-3 8,000 600 Conditions in which the Specific Stimulus need not ZA be determined. While we have in the formula /? R + A THE INFLUENCE OF SECONDARY RESISTANCE 8l a means of expressing the specific value of any break in- duction shock, no matter how the factors concerned in its production may vary, we must recognize that in the ordinary practice of the physiologist the attempt to make use of this formula presents very considerable difficulties. These difficulties, moreover, are chiefly in connection with the inclusion of the factors R and A, and we may well inquire how great errors are likely to arise in comparing faradic stimuli if these two factors are completely disregarded. We must realize at the outset of this part of our in- quiry that if comparisons are attempted between stimuli used under conditions of widely varying secondary re- sistance and divergent cathode surface, disregard of these two factors is sure to lead to erroneous conclu- sions; but probably in a majority of physiological experiments the stimuli to be compared are produced under conditions which tend to be closely similar. With regard to such cases as these we may properly inquire whether the factors under consideration need be taken into account. Successive Stimulation of the Same Tissue. Prob- ably the experiments in which accurate comparisons of stimuli are most needed are those in which a given tissue is to be stimulated successively. But in experi- ments of this class neither the tissue resistance nor the electrode surfaces undergo noteworthy variation during 82 INDUCTION SHOCKS the course of the experiment and so do not enter as modifying factors. Stimulation of Corresponding Tissues in Different Animals. Next in importance are cases- in which it is desired to impart comparable stimuli to corresponding tissues through a series of experiments. Cases of this sort arise frequently in the course of physiological re- search, and I have therefore given them special consid- eration. While this subject was before me there was being car- ried on in the laboratory at Harvard an investigation which involved, among other things, determining in a series of cats the threshold stimulus for producing ex- tension of the wrist, when the stimulus was applied to the deep branch of the radial nerve below the elbow; and reflex flexion of the hind leg through stimulation of the tibial. Here was presented a typical example of the class of experiments described in the paragraph heading, and I therefore utilized it in the study of my problem. In several cases the threshold stimulus was determined when the tissue only was in the secondary circuit, and immediately afterward, the threshold when an additional resistance of 10,000 ohms had been introduced. I was thus able in these cases to compute the value of the con- stant A , and from it to obtain the solution of the equa- ZA tion for ''specific" irritability, /3 = ~^~~~r' In the ex- THE INFLUENCE OF SECONDARY RESISTANCE 83 periments of this series, ten in all, the secondary re- sistances ranged from 2800 ohms to 6000 ohms, averag- ing 3900 ohms. The values of A ranged from 4300 to 14,000, averaging 7800. The statistics for this series are given in Table IX. TABLE IX Illustrating the Tendency of ft and Z to vary similarly in Direc- tion and Extent. Z represents the Stimulus producing Just Perceptible Wrist Extension in Cat. Stimulus applied to Deep Branch of Radial Nerve Date, 1910. Secondary resistance. Value of A. Value ofZ. Value of/3. Ratio ft z' Aug. 8 6000 7"?OO 2 77 I "?4 <;6 Tulv 28. . 44QO tJOOO •2 , IQ i 7 C2 Aug. "\. . 4800 8000 3.84 2 -4 62 AUJ? 3 •24.00 7800 432 30 7O Auer. Q 3000 0800 r ij2 4 22 77 Aug. 2 4600 yow OOOO 6 O< 4 08 68 Aug. 17. . 2800 4600 2S.4 15.8 .62 As Above except that Stimulus was applied to Tibial Nerve, and Reflex Flexion of Hind Leg was Movement Evoked July 18. . 3000 4,300 4 08 2 4 . ^O T 1 TulV 22 4OOO 14 ooo 6 6 SI 77 4 *y lulv 20. 3OOO 7,000 24 7 17 3 7O Average 6 the product Li — X / was nearly constant; as the secondary coil was Li moved out into the parts of the field where the values of —are small, the product — X / became progressively Li L* larger the farther out the secondary coil was pushed, and M consequently the smaller were the values of — Nu- LI merous repetitions of the experiment gave precisely sim- ilar results. These experiments indicated quite clearly the exist- ence of a comparatively simple relationship between make and break stimuli, and also suggested a method * For experimental data see Martin: Loc. tit., p. 272, 96 INDUCTION SHOCKS for expressing the relationship mathematically in the simplest possible fashion, namely through the introduc- tion of a single factor into the break shock formula, which when introduced would cause it to give equal values for Z for equal make stimuli. Study of the data showed that the factor to be introduced must be M relatively larger the smaller the value of — , and must jL* M tend to diminish — • A constant number has this effect j^t if it is subtracted from — -• The formula modified in is accordance with this idea becomes In practically every experiment of a large series some number could be selected to be substituted for K in formula (i) with a fairly constant value of Z resulting. For each experiment the value of K had to be deter- mined empirically, and it varied widely in different ex- periments. In all the experiments the values of K were negligibly small in comparison with the values of — for it secondary positions of 1 2 cm. or less. The discovery of the above formula is a decided step toward the ultimate solution of the problem of measur- * To distinguish between break stimuli and make stimuli the former are represented by Zb, the latter by Zm. THE MEASUREMENT OF MAKE SHOCKS 97 ing make shocks, but it is not a complete solution, since it offers no means of determining in advance what the value of K will be under any given set of conditions. The next step was to study a large series of experiments with reference to the conditions upon which the values of K depend. It became apparent at an early stage of the investi- gation that make shocks, unlike breaks, are modified in intensity by changes in the voltage of the primary cur- rent. This observation suggested the grouping of all the experiments according to the primary voltage used in performing them. After this had been done the values of K for the different experiments of any group still differed widely, but now wherever the value of K was large the value of Z was also large and vice versa. This suggested at once a possible dependence of the value of K upon that of Z. To test this possibility the experiments of each group were plotted, values of K against values of Z. The resulting curve in each case is a straight line, having the simple equation K = aZ. (2) Fig. 1 8 gives the curve for coil B obtained by plotting the experiments at 2 volts. The value of a given by this curve is 18. Substituting in equation (i) the value of K given in equation (2), we have M (3) 98 INDUCTION SHOCKS This solved for simplified gives M L Zm and FIG. 18. Curve obtained when the values of Z given by the application of the formula Z = fj- - K\ I to the experi- ments performed with a primary voltage of 2 are plotted against the values of K used in these ex- periments. Abscissae represent values of K; ordinates represent values of Z. The equation for this curve is K = 18 Z. (4) an equation which enables us to determine the value of make stimuli at any given primary voltage, for which the value of a is known. There remains now for the completion of the make shock formula only the establishment of a definite relationship between the values of a at various primary voltages and the voltages themselves. To determine whether such a relationship exists another curve was plotted, prim- ary voltages against values of a previously determined. This curve is represented in Fig. 19. It has the THE MEASUREMENT OF MAKE SHOCKS simple equation = a-C, 99 (S) in which C represents a constant. Substitut- ing in equation (4) the value of a given by 20 equation (5), we have (6) which is the general equation for make in- duction shocks. The value of C is fixed FIG. 19. Curve obtained by plotting for each inductorium. against the different primary voltages used in these experiments the values of a obtained from curves plotted as in Fig. i. The equation for this curve is E X a = 36. Abscissas represent values of a; ordinates represent primary voltages. For the one with which this equation was developed, coil B, its value is 36. Comparison of the General Formulae for Break and Make Stimuli. If the general equation for break shocks be written in the same form as the one for make shocks and the two placed side by side, the simple mathematical relationship existing between make and break stimuli becomes apparent. Written thus, the break shock 100 INDUCTION SHOCKS formula is M z.-f. . / Comparing this with the make shock formula, M L the difference between them is seen to be wholly in the denominator, and to consist of the addition of a simple expression to the denominator of the break shock for- mula to give the one for make shocks. Inasmuch as in- creasing the denominator of a fraction diminishes the value of the fraction, the formulae express the well- known fact that make shocks are weaker than break shocks produced under equivalent conditions. In the formulae as here presented the numerators ex- press the influence upon the value of Z of the position of the secondary coil with respect to the primary. The denominators express the influence upon Z of the in- tensity of the primary current, and for make stimuli the influence of its voltage also. Since the numerator is M the same in both formulae, i.e., — ' it follows that how- THE MEASUREMENT OF MAKE SHOCKS IOI ever the break stimulus Z& may compare with the make M stimulus Zm, changing the value of — by moving the 44 secondary coil does not affect the relationship between them. To illustrate, if we suppose the ibtfefcli ^stimulus to be twice as intense as the make stimulus v/Jien tfrq secondary coil is at zero, the break will cbntinufe to be twice as intense as the make wherever the secondary coil is placed, provided, of course, that all other condi- tions remain constant. Since the difference between the two formulae is wholly in their denominators, we may expect careful analysis of these to yield a full understanding of the conditions upon which depend the relationships between make and break stimuli. The denominator of the make shock formula will always be larger than that of the break formula, but the amount of difference between the two will vary greatly according to the relative values of- £ and - • This can best be shown by a concrete case. Let hi us first compare the values of Z6 and Zm in a hypotheti- cal experiment with coil B in which a primary current of 0.0005 ampere at 20 volts is employed. The expression for Zb is M L 2000 102 INDUCTION SHOCKS For Zm the expression is M M L L__ ^ 2000 + |f ~~ 2001.8 The difference between the stimulating intensities of the two sects of shocks is in this case less than one-tenth of one per cent. Compare now the values of Z& and Zm when a primary current of 0.4 ampere at 2 volts is used. The expression for Zb is M_ L_ 2-5' and for Zm is M M L L 2.5+526- 20.5 In this case the break shock is more than eight times as intense as the make. The above illustrations present in concrete form the effects upon the relation between break and make stim- uli of variations in intensity and voltage of the primary current. These effects may be stated in general thus: The higher the voltage of the primary current and the less its intensity, the more nearly will make shocks equal break shocks: conversely, the lower the voltage of the primary current and the greater its intensity, the more will break shocks exceed make shocks. THE MEASUREMENT OF MAKE SHOCKS 103 The make shock formula shows that make stimuli do not vary directly with the intensity of the primary current as break stimuli do. Although make shocks increase absolutely with every increase in primary inten- sity, other conditions remaining uniform, the increase is relatively slight when primary intensities of consid- erable magnitude are compared. For example, if with coil B a 2 volt primary current be increased from 0.5 ampere to i .o ampere, the make stimuli will be increased only 5 per cent, while break shocks under the same cir- cumstances would be doubled. This peculiarity of relation of make shocks to primary currents of high intensity shows itself very strikingly in many experiments in which minimal muscular contrac- tions are used as indicators of stimulation strength. In the outer parts of the field of the inductorium, where the values of — are small, primary currents of high intensity .L* must be employed to give shocks sufficient to elicit visible response. I have often found when studying make shocks, especially with primary currents of low voltage, that as the secondary coil was pushed out to a point where primary currents of o.i or 0.2 ampere failed to elicit response, no increase of primary intensity up to the limits of my apparatus would raise the stimulus to the threshold. This frequent failure of relatively enor- mous primary currents to give detectable make stimuli 104 INDUCTION SHOCKS was wholly inexplicable until the development of the make shock formula made its meaning clear. Although the make shock formula presents the appearance of some complexity, as a matter of fact it is a comparatively easy task to derive the value of C, which is the only new constant the equation re- quires, and with the constant once established the use of the formula is perfectly simple. To determine how laborious is the task of determining the value of C, an inductorium was taken which had been previously cali- brated for break shocks, and seven experiments were found to yield sufficient data to establish conclusively the value of the constant. The experimental procedure is that described on p. 95. The interpretation of the results so as to establish the constant depends upon recognition of the fact that in such experiments as these the value of Zm for the inner positions of the secondary coil, where threshold stimu- lation is obtained with very small primary currents, is practically independent of the value of the constant; whereas the value of Zm for secondary positions far out on the scale, where heavy primary currents must be THE MEASUREMENT OF MAKE SHOCKS 105 used, can be correctly determined only if the constant is accurately known. By transposition of the equation M L we obtain the formula for the constant M £-i_i. w E'Zm I (7) By taking advantage of the fact above noted, that the value of Zm for the inner secondary positions is inde- pendent of C, we can obtain Zm for any given experiment M by taking the product of — X / for these positions. Li Since the value of ZTO is assumed to be constant through- out the experiment we can apply this value to the solu- tion of equation (7), using the data obtained at the outer M i secondary positions to give — and - • From four experi- JLt L ments at 2 and 4 volts were obtained by this method the following values of C: 8.16, 8.0, 6.8, 9.0, 8.0, 9.8, 8.0, 5.2, 8.0. The average of these is 7.9. The nearest round number, 8, was taken as a sufficiently close approximation to the constant, and was applied to three other experi- 106 INDUCTION SHOCKS ments at primary voltage ranging from 2 to 12. When so applied, constant values of Zm were obtained,* thus proving the correctness of the determination. * For data see Martin: Amer. Jour, of Physiology, 1909, xxiv, pp. 279 and 280. CHAPTER XII ERRORS TO BE AVOIDED INCIDENTAL results of the several years of study spent in developing the quantitative method here presented have been to emphasize the importance of certain pre- cautions, and also to reveal the errors committed by some users of induction shocks in their efforts to make quantitative comparisons by indirect methods. Probably the most urgent general precaution calling for discussion is that of maintaining good electrical con- tacts throughout. In a mechanism so complicated as that shown in Fig. 8 loose contacts which may easily escape observation are likely to render quantitative ob- servations completely valueless. The user of the appa- ratus must keep continually in mind the importance of maintaining tight contacts, and by frequent inspection must assure himself that they are so. The sliding con- tacts provided for the secondary coils in some forms of inductoria are very untrustworthy and should not be used if fixed ones are available. In applying stimulating electrodes one must have in mind that the induced current stimulates at the cathode, and must know which electrode this is. A simple 107 108 INDUCTION SHOCKS means of distinguishing the poles of the secondary cir- cuit is to apply them to a sheet of filter paper moistened with a mixture of starch paste and potassium iodide solution. If a strong primary current is made and broken rapidly, and the secondary makes or breaks are short-circuited each time, a blue deposit presently ap- pears at the anode, indicating the accumulation there of iodin ions which react with the starch. It should be remembered that make shocks and break shocks are opposite in direction, so that the pole which is revealed as the anode for break shocks is the cathode for makes. The development of a mathematical expression for the influence of secondary resistance on stimulating value has shown the fallacy of a method sometimes employed for varying stimulating strengths quantitatively by in- cluding known resistances in the secondary circuit and assuming that the strength of stimulus is reduced in exact proportion with the increase of resistance. As the equation (p. 76) shows, the strength of stimulus not only does not vary in exact proportion with the resist- ance, but the relationship actually existing is not apt to be the same in two successive experiments, owing to the interrelation between secondary resistance and cathode surface. This same interrelation explains the error of another procedure which has sometimes been employed for the purpose of overcoming inequalities in stimulation ERRORS TO BE AVOIDED ICQ strength due to differences in secondary resistance, namely the introduction of a very high additional re- sistance into the secondary circuit, thereby making fluc- tuations in tissue resistance relatively negligible. That this device is perfectly adequate in experiments in which a single tissue of varying resistance is under examination is of course obvious; there being under such circum- stances no variation in cathode surface. But in ex- periments in which different tissues are being compared the introduction of high additional resistance into the secondary circuit is more apt to be misleading than otherwise because of the cumulative effect of variations in cathode surface. The point can best be illustrated by a concrete example: Experiment of March 7, 1910. — Frog's gastrocnemius muscle stim- ulated directly. In the first test the cathode was in contact with the surface of the muscle, but did not penetrate it. When the tissue only was in the secondary circuit, the total secondary resistance was 17,000 ohms. A minimal contraction was secured with a value of Z equal to 6.6. When 70,000 ohms' additional secondary resistance was intro- duced, the value of Z was 16.8. By calculation the value of A was found'to be 28,000, and that of the specific stimulus /3 to be 4.1-* In the second test the cathode was thrust directly through the muscle tissue; the secondary resistance was 5400 ohms; the value of Z was 6.1. When 70,000 ohms' additional resistance was introduced, the value of Z was 40.5. The calculated value of A was 7000, and of 0 3-45- In this case the values of Z as determined with the tissue only in the secondary circuit represent much more nearly the true relationships between the stimuli than do the values as determined with a large additional re- sistance in the circuit. In reality the stimulus applied in the first test * For the equations used in this calculation see p. 77. 110 INDUCTION SHOCKS was stronger than in the second, whereas, if reliance were placed upon the results given when the high additional resistance was in circuit, it would appear that the second stimulus was more than twice as strong as the first. The subjoined tabulation will serve to emphasize the error: First Z (tissue only) 6 6 Z (70,000 g ohms added) 16 8 41 Second 6 i do <\ 3 d Ratio of ist to 2d... i. 08 0.41 I.I In determining specific stimulation values by means ZA of the expression /3 = -=— - — > particularly when the J\. ~\~ A. tissues stimulated have high resistances, errors in de- termining the value of A may easily vitiate the results. It will usually be found desirable to determine values of Z for at least three secondary resistances in addition to the tissue resistance itself. If the values of Z thus obtained are plotted against their respective resistances the curve which they yield reveals at once whether errors have been made in the determinations. The curve should be a straight line, cutting the ordinate for zero resistance at some point above the base line. Minor errors may be allowed for by drawing the curve to make them balance one another. This precaution is unnec- essary when tissues of low resistance are studied, since with them small errors in determining A are less sig- nificant. These are among the less obvious sources of error in ERRORS TO BE AVOIDED III quantitative work, and are therefore discussed here. The more apparent ones need not be mentioned, since they are sure to suggest themselves to any user of the method here presented. In the use of this quantitative method, as in most procedures involving numerous factors, a technique, which seems at the outset highly complicated, becomes with practice easy to carry out. Its inclusion as part of the experimental routine of the working physiologist is therefore justified. To facilitate such inclusion is the purpose of this manual. INDEX Ammeter, use of, 24. shunt for, 24. du Bois Reymond inductorium, 3. Break induced currents, 7. Break shocks, course of, 32. equation for, 35, 60. Calibration of inductorium, apparatus required for, 23. for break shocks, 55. in region of iron core, 58. Cathode, method of determining, 107. Circuit, primary, make and break of, 60. variables concerned in, 13. variations in break of, 60. variations in make of, 61. secondary, variables concerned in, 13. Coil, secondary, effect of position of on strength of shock, 7, 13, 15. Core, iron, correction for magnetization of, 46. effects of on stimulation strengths, 43. in critical region, 47. magnetization of, 43. Current density, importance of, 76. extra, 10. induced, 5. direction and intensity of, 5. method of varying, 7. sources of variation in, 13. primary, adjustment of, 25. measurement of, 24. voltage, relation of to make stimuli, 97. "3 114 INDEX Density of current, importance of, 76. Edelmann method of measuring induction shocks, 20. Electrodynamometer of Hoorweg-Giltay, 21. Electrode contacts, effect of on strength of shocks, 13, 76. Electrodes, needle, 27. Sherrington, 27. Extra current, 10. Faradimeter of Edelmann, 20. Fick-Meyer method of measuring induction shocks, 15. v. Fleischl method of measuring induction shocks, 18. application of, to calibration, 56. Force, lines of, 5. Galvanometer, ballistic, 26. Hoorweg-Giltay method of measuring induction shocks, 21. Induced current, direction and intensity of, 5. form of, 8. break, course of, 32. make and break, 7. measurement of, historical, 14. method of varying, 7. sources of variation in, 13. Inductance, 8. of secondary coil, 34. determination of, 50. equation for, 53. Induction, discovery of, 2. mutual, 34. determination of, 38. relation of to calibration, 36. Induction coil, standard, for use in calibration, 26. structure of, 3. Induction shocks, apparatus for quantitative use of, 30. break, course of, 32. INDEX 115 Induction shocks, break, equation for, 35. comparison of make and break, 102. make, measurement of, 94. equation for, 99. measurement of historical, 14. Edelmann method, 20. v. Fleischl method, 18. Hoorweg-Giltay method, 21. Kronecker method, 16. Meyer-Fick method, 15. Pfluger method, 14. Wertheim-Salomonson method, 18. sources of variation in, 13. stimulate at cathode, 72, 107. Inductorium, du Bois Reymond type, 3. principle of, 4. calibration of, apparatus required, 23. procedure, 28. for break shocks, 55. for make shocks, 94. in region of iron core, 58. "standard," 23, 88. Berlin standard, 88. shortcomings of, 92. structure of, 3. effect of on strength of shock, 13. relation to determination of specific stim- ulus, 78. Iron core, effect of on strength of shock, 13, 43. in critical region, 47. magnetization of, 43. correction for, 46. Key, automatic, necessity for, 61. knife-blade, construction of, 63. advantages of, 64, 67, 70. operating device for, 65. Il6 INDEX Key, knife-blade, short-circuiting device for, 67. make and break, essentials of, 62. Kronecker method of measuring induction shocks, 16. Magnetization of core, correction for, 46. Make induced currents, 7. shocks, equation for, 99. measurement of, 94. constant, determination of, 104. Meyer-Fick method of measuring induction shocks, 15. Pfluger method of measuring induction shocks, 14. Primary circuit, make and break of, 60. variables concerned in, 13. variations in break of, 60. in make of, 61. current, adjustment of, 25. measurement of, 24. relation of to strength of shock, 13. voltage, relation of to make stimuli, 97. Resistance of tissue, apparatus for measuring, 26. determination of, 72. effect of on strength of shock, 13, 73. relation of to secondary resistance, 71. Secondary circuit, variables concerned in, 13. Shocks, induction, sources of variation in, 13. comparison of make and break, 102. break, course of, 32. equation for, 35, 60. make, form of, 8. equation for, 99. determination of constant for, 104. Short-circuiting device for knife-blade key, 67. Shunt for ammeter, 24. Specific stimuli, precautions necessary in obtaining, no. Stimuli, faradic, historical, 14. INDEX 117 Stimulus, actual, equation for, 76. precautions necessary in obtaining, no. when not essential, 80. Tissue resistance, apparatus for measuring, 26. determination of, 72. effect of, on strength of stimulus, 13, 73. importance of, 21. relation of to entire resistance, 71. Voltage of primary current, relation of to make stimuli, 97. Wertheim-Salomonson method of measuring induction shocks. T.'>. SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF JOHN WILEY & SONS NEW YORK LONDON: CHAPMAN & HALL, LIMITED ARRANGED UNDER SUBJECTS Descriptive circulars sent on application. Books marked with an asterisk (*) ar« sold at net prices only. All books are bound in cloth unless otherwise stated. AGRICULTURE— HORTICULTURE— FORESTRY. Armsby 's Principles of Animal Nutrition ' 8vo, $4 00 * Bowman's Forest Physiography 8vo, 5 00 Budd and Hansen's American Horticultural Manual: Part I. Propagation, Culture, and Improvement 12mo,t 1 50 Part II. 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