The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 25 of 36

frcme to reach the knobs, and therefore the phenomenon can- not be due simply to single waves in the direction c a and d b respectively, but must be due to repeated reflection of the waves until a condition of stationary vibration is attained, and the addition of the conductor to one of the knobs must diminish or prevent the reflection of the waves from that ter- minal. It must be assumed, then, that definite oscillations are set up in the micrometer circuit just as an elastic bar is thrown into definite vibrations by blows, from a hammer. If this assumption is correct, the condition for the disappearance of-the sparks at M will be that the vibration periods of the two branches e 1 and e 2 shall be equal: These periods are deter- mined by the products of the coefficients of self-induction of these conductors into the capacities of their terminals, and are practically independent of their resistances.

In confirmation of this it is found that if, when the point of contact is at e and the sparks have been made to reappear by connecting a conductor with one of the knobs, this con- ductor is replaced by one of greater capacity, the sparking is greatly increased. If a conductor of equal capacity is con- nected with the other micrometer knob, the sparks disappear again ; the effect of the first conductor can also be counter- acted by shifting the point of contact towards it, thereby diminishing the self-induction in that branch. The conclusions were further confirmed by the results obtained when coils of copper wire were inserted into one or other and then into both of the branches of the micrometer circuit.

Hertz supposed that as the self-induction of iron wires is, for slow alternations, from eight to ten times that of copper wires, therefore a short iron wire would balance a long copper one ; but this was not found to be the case, and. he concludes that, owing to the great rapidity of the alternations, the magnetidm of the iron is unable to follow them, and therefore has no effect^ on the self-induction.* ^

• Id a note in Wiedemann's AnnaUn, Vol. XXXL, p. 543, Dr. Hertz* stated that since the publication of his Paper in the same volume he had^ found that Yon Bezold had published a Paper, in 1870 (PoggendorflTs.^ AnnaUrif Vol. CXL., p. 541), in which he had arrived by a different method, of experimenting at similar results and conclusions as those given by him under the head of Preliminary Experiments.

424

DYNAMICAL THEORY OF INDUCTIOJf.

Indtiction Phenomena in Open Circtdts. — In order to test more fully his conclusion that the sparks obtained in the last experiments described were due to self-induction, Hertz placed a rectangle of copper wire with sides 10 and 20 centi- metres in length respectivQly, broken by a short air space, with one of its sides parallel and close to various portions of the secondary circuit of the coil and of the micrometer circuit, with solid dielectrics interposed to obviate the possibility of sparking across, and he found that sparking in this rectangle invariably accompanied the discharges of the induction coil, the longest sparks being obtained when a side of the rectangle was close to the discharger.

IH

X — _UX — 4

OCUDO

-oc

DO

J z

TiQ. 153.

i

A copper wire, igh (Fig. 158), was next attached to the discharger, and a side of the micrometer circuit, which was supported on an insulating stand, was placed parallel to a portion of this wire, as shown in the diagram* The sparks at M were then found to be extremely feeble until a conductor, Cy was attached to the free end, /t, of the copper wire, when they increased to one or two millimetres in length. That the action of G was not an electrostatic one was shown by its pro- ducing no effect when attached at g instead of at h. When

DYNAMICAL THEORY OF INDUCTION. 425

the knobs of the discharger B were so far separated that no sparking took place there, the sparks at M were also found to disappear, showing that these were due to the sudden dis* charges and not to the charging current. The sparks at the discharger which produced the most effect at the micrometer were of the same character as those described under the head of Preliminary Experiments* Sparks were also found to occur between the micrometer circuit and insulated conductors in its Ticinity. The sparks became much shorter when conductors of large capacity were attached to the micrometer knobs, or when these were touched by the hand, showing that the -quantity of electricity in motion was too small to charge these conductors to a similarly high potentiaL Joining the micrometer knobs by a wet thread did not perceptibly diminish the strength of the sparks. The effects in the micrometer circuit were not of sufficient strength to produce any sensation when it was touched or the circuit completed through the body.

In order to obtain further confirmation of the oscillatory nature of the current in the circuit kihg (Fig. 158), the con- ductor C was again attached to A, and the micrometer knobs drawn apart until sparks only passed singly. A second con- ductor, C\ as nearly as possible similar to G, was. then attached to k, when a stream of sparks was immediately observed, and it continued when the knobs were drawn still further apart. This effect could not be ascribed to a direct action of the portion of circuit i k, for in this case the action of the portion of circuit g h would be weakened, and it must therefore have consisted in 0' acting on the discharging current of 0 — a result which would be quite incomprehensible unless the current ing h were of an oscillatory character.

Since an oscillatory motion between C and 0' is essential for the production of powerful inductive effects, it will not be sufficient for the spark to occur in an exceedingly short time, but the resistance must at the same time not exceed certain limits. The inductive effects will therefore be excessively small if the induction coil included in the circuit G 0' is replaced by an electrical machine alternately charging and discharging itself, or if too small an induction coil is used, or, again, if the air space between the discharger knobs is too great, as in all 4bese cases the motion ceases to be oscillatory.

426

DYNAMICAL THEORY OF INDUCTION.

r Tha reason that the discharge of a powerful indaction coil .gives rise to oscillatory motion is that, firstly, it charges the •terminals C and C to a high potential ; secondly, it produces cfl' sadden spark in the intervening circuit ; and thirdly, as soon •:as the discharge begins the resistance of the air space is so .'much reduced as to allow of oscillatory motion being set up. •:If the terminal conductors are of a very large capacity — ^for -example, if the terminals are in connection with a battery — the .current of discharge may indefinitely reduce the resistance of •:tjia aiir space, but when the terminal conductors are of small Lcapacity this must be done by a separate discharge, and there- .lore» uud^r the conditions of Hertz's experiments, an induction ccoilwfts' absolutely essential for the production of the oscilla- jtioiis.

r?

^^

-^ c y>

Fio. 154.

As the induced sparks in the experiment last described were several milhttiBtres in length. Hertz modified it by using the arrangement shown in Fig. 154, and greatly increasing the distance between the micrometer circuit and the secondary circuit of the induction coil. The terminal conductors G and C were three metres apart, and the wire between them was of copper, 2 millimetres in diameter, with the discharger B at its centre.

The micrometer circuit consisted, as in the preceding experi- ments, of a rectangle 80 centimetres broad by 120 centimetres long. With the nearest side cf the micrometer circuit at a

DYNAMICAL TBEORY OF INDUCTION. 427

dietancd of half a millimetre from C B C, sparks two milli« 9ietrea in length were obtained at M, and though the length of the sparks decreased rapidly as the distance of the micrometer circuit was increased, a continuous stream of sparks was still obtained at a distance of one and a-half metres. The intervene tion of the obsei^ver's body between the micrometer circuit and the wire C B C produced no visible effect on the stream of sparks at M. That the effect was really due to the rectilinear conductor C B CT was proved by the fact that when one or other, or bothy halves of this conductor were removed, the sparks at M ceased. The same effect was produced by drawing the knobs of the discharger B apart until sparks ceased to pass, showing that the effect was not due to the electrostatic potential differ^ eoce of G and C, as this would be increased by siaparating thd discharger knobs beyond sparking distance. : The closed micrometer circuit was then replaced by a straight Qppper wire, slightly shorter than the distance C C, placed parallel to G B C and at a distance of 60 centimetres from its This wire terminated in knobs, 10 centimetres in diameter, att^hed to insulating supports, and the spark micrometer 4iyivded it into two equal parts. Under these circumstances i^»airks were obtained at the micrometer as before. , With the rectilinear open micrometer circuit sparks were still observed at the micrometer when the discharger knobs of the secondary coil circuit were sefparated beyond sparking distance. This was, of course, due simply to electrostatic Induction, and shows that the oscillatory current in G G' was saperposed upon the ordinary discharges. The electrostatic action could be got rid of by joining the micrometer knobs by means of a damp thread. The conductivity of this thread was therefore sufficient to afford a passage to the comparatively slow alternations of the coil discharge, but was not sufficient to provide a passage for the immeasurably more rapid alternations of the oscillatory current. Gonsiderable sparking took place at the micrometer when its distance from G B G' was 1*2 metre, and faint sparks were distinguishable up to 8 metres. At thes^ distances it was not necessary to use the damp thread to get ^d of the electrostatic action, as, owing to its diminishing more rapidly with increase of distance than the effect of the current induction, it was no longer able to produce sparks in the micro-

423 D 7NA MICAL THEOB Y OF IND UCTION.

meter, as was proved by separating the discharger knobs beyond sparking distance, when sparks could no longer be perceived ai the micrometer.

Resonance PJienomena, — In order to determine whether the oscillations were of the nature of a regular vibration, Hertz availed himself of the principle of resonance. According to this principle, an oscillatory current of definite period would, Other conditions being the same, exert a much greater inductive effect upon one of equal period than upon one differing even slightly from it.*

If, then, two circuits are taken having as nearly as possible equal vibration periods, the effect of one upon the other will be diminished by altering either the capacity or the ooefiScient of self-induction of one of them, as a change in either of them would alter the period of vibration of the circuit. : This was carried out by means of an arrangement very simi- lar to that of Fig. 164. The conductor C C was replaced by a straight copper wire 26 metres in length and 5 millimetres in diameter, divided into two equal parts as before by a discharger. The discharger knobs were attached directly to the secondary terminals of the induction coil. Two hollow zinc spheres, 80 centimetres in. diameter, were made. to slide on the wire, one on each side of the discharger, and since, electrically speaking, these formed the terminals of the conductor, its length could be varied by altering their position. The micrometer circuit was chosen of such dimensions as to have, if the author's hypothesis were correct, a slightly shorter vibration period than that of G C It was formed of a square, with sides 75 centi- metres in length, of copper wire 2 millimetres in diameter, and it was placed with its nearest side parallel to G B 0' and at a distance of 80 centimetres from it. The sparking distance at the micrometer was then found to be 09 millimetre. When the terminals of the micrometer circuit was placed in contact with two metal spheres 8 centimetres in diameter, supported on insulating stands, the sparking distance could be increased up to 2*5 millimetres. When these were replaced by much larger spheres the sparking distance was diminished to a small fraction of a millimetre. Similar results were obtained on connecting the micrometer terminals with the plates of a • ♦ Jike Obcrbwk, Wiedemann's Annalen, VoL XXVI., p. 216, 1835.

DYNAMICAL THEORY OF INDUCTION.

42»

Eohlrftusch condenser. When the plates were far apart the increase of capacity increased the sparking distance, but when the plates were brought close together the sparking distances again fell to a very small value.

The simplest method of adjusting the capacity of the micro- meter circuit is to suspend to its ends two parallel wires the distance and lengths of which are capable of variation. By this means the author succeeded in increasing the sparking distance up to three millimetres, after which it diminished when the wires were either lengthened or shortened. The decrease of the sparking distance on increasing the capacity was naturally to be expected ; but it would be difficult to understand, except on the principle of resonance, why a decrease of the capacity should have the same effect.

._^!)-

.__/s

' V

Fid. 155. — Curve showiDg relation between length of aide of rectangle (taken as abscissa) and maximum sparking distance (taken as ordinate), the sides consisting of straight wires of varying lengths*

The experiments were then varied by diminishing the capa- city of the circuit C B C so as to shorten its period of oscil- lation, and the results confirmed those previously obtained ; and a series of experiments in which the lengths and capacities of the circuits were varied in different ways showed conclu- sively that the maximum effect does not depend on the con- ditions of either one of the two circuits, but on the existence of the proper relation between them.

When the two circuits were brought very close together, and the discharger knobs separated by an interval of 7 millimetreSi sparks were obtained at the micrometer, which were also

4de

DYNAMICAL THEORY OF INDUCTION.

7 millimetpes in length, when the two circuits had been care- fully adjusted to have the same period. The induced E.M.F*fl must in this case have attained nearly as high a value as the inducing ones.

To show the effect of varying the coefficient of self-induction, a series of rectangles, abed (Fig. 154), were taken, having a constant breadth, a h, but a length, a c, continually increasing from 10 centimetres up to 250 centimetres : it was found that the maximum effect was obtained with a length of 1-8 metre. The quantitative results of these experiments are shown in Fig. 155, in which the abscisssB of the curve are the double lengths of the rectangles, and the ordinates represent the cor. responding maximum sparking distances. The sparking dis- tances could not be determined with great exactness, bul the

/

'^

\

^

^

\

\

^

/I

fl

to

fiO

EiG. 156. — Curve showiDg relation between length of aide of rectangle '(taken as abscissa) and maximum sparking distance (taken as ordinate), the sides consisting of spirals gradually drawn out.

errors were not sufficient to mask the general nature of the result.

In a second series of experiments the sides a c and h d were formed of loose coils of wire which were gradually pulled out, and the result is shown in Fig. 156. It will be seen that the maximum sparking distance was attained for a somewhat greater length of side, which is explained by the fact that in the latter experiments the self-induction only was increased by increase of length, while in the former series the capacity was increased as well. Varying the resistance of the micrometer

DYNAMICAL THEORY OF INDUCTION. 431

circuit by using copper and German silver wires of vaarious <liameters was found to have no effect on the period of oscilla- tion, and extremely little on the sparking distance.

When the wire cd was surrounded by an iron tube, or whpn it was replaced by an iron wire, no perceptible effect was obtained, confirming the conclusion previously arrived at that the magnetism of the iron is unable to follow such rapid oscillations, and therefore exerts no appreciable effect.

It is only proper, however, to interpolate at this point the remark that other observers do not endorse entirely this statement of Hertz. We may especially draw attention to the work of Prof. J. Trowbridge and of Mr. C. E. St, John* on the propagation of electrical oscillations on iron wires. The experimental results obtained by these investi- gators may be summed up as follows : —

1. The magnetic permeability of iron wires exercises an important influence upon the decay of electrical oscillations of high frequency. The influence is so great that the oscilla- tions may be reduced to half an oscillation on a circuit of suitable self-induction and capacity for producing them.

2. Currents of high frequency such as are produced in Leyden jar discharges therefore magnetise iron.

3. The self-induction of iron circuits is sensibly greater than that of similar copper circuits under rapid electrical oscillations 116 x 10® reversals per second.

4. This increase in self-induction produces a shortening pf the wave-length.

5. The permeability of annealed iron under the above rate of alternation is about 885.

For full information as to the methods of obtaining these results we must refer the reader to the original Papers.

Nodes, — The vibrations in the micrometer circuit which have been considered are the simplest ones possible, but not the only ones. While the potential at the ends alternates between two fixed limits, that at the central portion of the circuit retains, a constant mean value. The electrical vibration, therefore, has

• See PhiL J/o^., December, 1891, Mr. J. Trowbridge on " Damping df Klectrical O^icillatlons on Iron Wires ; " and PJiil. Afay., November, 1894^; ^. C. E. St. John on " Wave- Lengths of Electricity on Iron Wires. '

432 DYNAMICAL THEORY OF INDUCTION.

a node at the centre, and this will be the only nodal point. It? existence may be proved by placing a small insulated sphere close to varioas portions of the micrometer circuit while sparks are passing at the discharger of the coil, when it will be found that if the sphere is placed close to the centre of the circuit the sparking will be very slight, increasing as the sphere is moved further away. The sparking cannot, however, be entirely got rid of, and there is a better way of determining the existence and position of the node. After adjusting the two circuits to unison, and drawing the micrometer terminals so far apart that sparks can only be made to pass by means of resonant action, let different parts of the circuit be touched by a conductor of some capacity, when it will be found that the sparks disappear, owing to interference with the resonant action, except when the point of contact is at the centre of the circuit. Hertz then endeavoured to produce a vibration with two nodes, and for this purpose he modified the appai-atus previously used by adding to the micrometer circuit a second rectangle, efg A, exactly similar to the first (as shown in Fig. 167), and joining the points of the circuit near the terminals by wires 1 8 and 2 4, as shown in the diagram.

The whole system then formed a closed metallic circuit, the fundamental vibration of which would have two nodes. Since the period of this vibration would necessarily agree closely with that of each half of the circuit, and, therefore, with that of the circuit GC, it was to be expected that the vibration would have a pair of loops at the junctions 1 8 and 2 4, and a pair of nodes at the middle points oicd and g h. The vibra- tions were determined by measuring the sparking distance between the micrometer terminals 1 and 2. It was found that, contrary to what was expected, the addition of the second rectangle diminished this sparking distance from about three millimetres to about one millimetre. The existence of resonant action between the circuit C C and the micrometer circuit was, however, fully demonstrated, for any alteration in the circuit efg A, whether it consisted in increasing or in decreasing its length, diminished the sparking distance. It was also found that much weaker sparking took place between edov gh and an insulated sphere than between a e or bf and the same sphere, showing that the nodes were in cd and g h.

DYNAMICAL THEORY OF INDUCTION.

433

as expected. Further, when the sphere was made to touch edoT ghit had no efifect on the sparking distance of 1 and 2; but when the point of contact was at any other portion of the circuit the sparking distance was diminished, showing that these nodes did really belong to the vibration, the resonant action of which increased this sparking distance.

The wire joining the points 2 and 4 was then removed. As the strength of the induced oscillatory current should be zero at these points, the removal ought not to disturb the vibrations, and this was shown experimentally to be the case, the resonant effects and the position of the nodes remaining unchanged. The vibration with two nodal points was, of

Fia. 157.

course, not the fundamental vibration of the circuit, which consisted of a vibration with a node between a and e, and for which the highest values of the potential were at the points 2 and 4.

When these spheres forming the terminals at these points were brought close together shght sparking was found to take place between them, which was attributed to the excitatioOi though only to a small extent, of the fundamental vibration* This explanation was confirmed in the following manner :-« The aparkis between 1 and 2 were broken off, leaving only the

FF

434 DYNAMICAL THEORY OF INDUCTION.

eparks between 2 and 4, which measured the intensity of the fundamental vibration. The period of vibration of the circuit G C was then increased by drawing it out to its full lengtb, and thereby increasing its capacity, when it was observed that the sparking gradually increased to a maximum, and then began to diminish again. The maximum value must evidently occur when the period of vibration of the circuit C 0' is the same as that of the fundamental vibration of the micrometer circuit, and it was shown that when the sparking distance between 2 and 4 had its maximum value the sparks corre- sponded to a vibration with only one nodal point, for the sparks ceased when the previously existing nodes were touched by a conductor, and the only point where contact could take place without effect on the sparking was between a and e. These results show that it is possible to excite at will in the same conductor either the fundamental vibration or its first overtone, to use the language of acoustics.

Hertz appeared to consider it very doubtful whether it was possible to get higher overtones of electrical vibration, the difficulty of obtaining such lying not only in the method of observation, but also in the nature of the oscillations them- selves. The intensity of these is found to vary considerably during a series of discharges from the coil even when all the circumstances are maintained as constant as possible, and the comparative feebleness of the resonant efifeets shows that there must be a considerable amount of damping. There are, more- over, many secondary phenomena which seem to indicate that irregular vibrations are superposed upon the regular ones, as would be expected in complex systems of conductors. If, therefore, we wish to compare electrical oscillations from a mathematical point of view with those of acoustics, we must seek our analogy in the high notes intermixed with irregular Tibrations, obtained, say, by striking a wooden rod with a hammer rather than in the comparatively slow h^rmonio vibration of tuning forks or strings ; and in the case of vibra- tions of the former class we have to be contented even in the study of a^coustics with little more than indications of such phenomena as resonance and nodal points.

Referring to the conditions to be fulfilled in order to obtain the best results, Hertz noted a fact of very considerable intoest

DYNAMICAL THEORY OF INDUCTION. 435

€Lnd novelty, namely, that the spark from the discharger should always be visible from the micrometer, as, when this was not the case, though the phenomena observed were of the same character, the sparking distance was invariably diminished. This effect of the light from the spark of an induction coil in increasing the sparking distance in a secondary circuit has been fully described by Dr. Lodge in Jiis book on the work of Hertz, and he has pointed out that the same efifect is produced by light from burning magnesium wire or other sources rich in the ultra-violet rays.

Theory of the Experiments.— The theories of electrical oscilla- tions which have been developed by Lord Eelvin, von Hehnholtz, and Kirchoff have been shown* to hold good for the open circuit osoillations of induction apparatus, as well as for the oscillatory Leyden jar discharge ; and it is of interest to inquire whether the observed results are of the same order as those indicated by theory.

Hertz considers, in the first place, the vibration period. Let T be the period of a single or half vibration proper to the -cond actor exciting the micrometer circuit ; L its coefficient of self-induction in absolute electromagnetic measure, expressed, therefore, in centimetres ; G the capacity of one of its terminals in electrostatic measure, and therefore also expressed in centi- metres; and V the velocity of light in centimetre-seconds; then, if the resistance of the conductor is small,

V

In the case of the resonance experiments, the capacity 0 was {approximately the radius of the sphere forming the terminal, -80 thpjt 0 = 7-6 centimetres.t The coefficient of self-induction

• Lorentz, WiedemanD's Annalerif Vol. VIL, p. 161, 1879.

t In Hertz's origiDiU. Paper the capacity of the spherical terminal ball was taken as 15 units. M. Poincar^ first drew attention to the fact that the capacity 0 in the above formula denotes the amount of electricity which exists at one end of an oscillating conductor when the difference of potential between the two ends is equal to unity. Hence, if the spheres are far apart, the difference of potential between each of them and sur- rounding space is +). Therefore the charge on the sphere is formed by dividing its capacity, i.c., its radius in oentimetres, by 2. Hence, C in the

Above formula is — =7'5.

FF 2

436 DYNAMICAL THEORY OF INDUCTION.

was that of a wire of length Zal50 centimetres and diameter d^l/2 centimetre.

According to Neumann's formula,

which gives in the case considered

L = 2 ^ Aog i? - 0-75) = 1,902 centimetres.

As, however, it is not quite certain that Neumann's formula is applicable to an open circuit, it is better to use von Helm> holtz's more general formula, containing an undetermined constant k, according to which

L.2z(log^-0-75+lz*).

Putting k — 1, this reduces to Neumann's formula; for k^O* it reduces to that of Maxwell, and for /c = - 1 to Weber's. The greatest difference in the values of L obtained by giving these different values to k would not exceed a sixth of its mean value, and therefore, for the purposes of the present approxi- mation, it is enough to assume that k is not a large positive or negative number; for if the number 1,902 does not give* the correct value of the coefficient for the wire 150 centimetres in length, it will give the value corresponding to a conductor not differing greatly from it in length.

Taking L = 1,902 centimetres, we have ir>/CL=»581 centi- metres, which represents the distance traversed by light during the oscillation, or, according to Maxwell's theory, the length, of an electromagnetic ether wave. The value of T is then found to be 1*26 hundred-millionths of a second, which is of the same order as the observed results. 1

The ratio of damping is then considered. In order that 1

oscillations may be possible, the resistance of the open curcuit 1

must be less than 2 v Jli/C. For the exciting circuit used this '

gives 676 ohms as the upper limit of resistance. If the actual I

resistance, r, is sensibly below this limit, the ratio of damping |

rT

will be 0^. The amplitude will therefore be reduced in thfr ratio 1:2-71 in

2L^2t' /L^676^216

I

DYNAMICAL THEORY OF INDUCTION. 437

^>scilIations. We have, unfortunately, no means of deter- mining the resistance of the air space traversed by the spark, but as the resistance of a strong electric arc is never less than a few ohms we shall be justified in assuming this as the minimum limit. From this it would follow that the number of oscillations due to a single impulse must be reckoned iu tens, and not in hundreds or thousands, which is in accordance with the character of the experimental results, and agrees with aresults observed in the case of the oscillatory Leyden jar -discharge. In the case of closed metallic circuits, on the other hand, theory indicates that the number of oscillations before equilibrium is attained must be reckoned by thousands. Hertz compares, lastly, the order of the inductive actions of these oscillations according to theory with that of the effects actually observed. To do this it must be noted that the maximum E.M.F. induced by the oscillation in its own circuit :is approximately equal to the maximum potential difference at its extremities ; for if there were no damping these quanti- ties would be identical, since at any moment the potential difference at the extremities and the E.M.F. of induction would be in equilibrium. In the experiments under con- sideration the potential difference at the extremities was such as to give a spark 7 to 8 millimetres in length, which must therefore represent the maximum inductive action excited in its own circuit by the oscillation. Again, at any instant the induced E.M.F. in the micrometer circuit must be to that in the exciting conductor in the same ratio as that of the coefficient of mutual induction M of the two circuits to the coefficient of self-induction L of the exciting circuit. The value of M for the case considered is easily calculated from the ordinary formulae, and it is found to lie between one-ninth and one-twelth of L. This would only give sparks of from J to f millimetre in length, so that according to theory visible sparks ought in any case to be obtained ; but, on the other hand, sparks several millimetres in length, as were obtained in the experiments previously described, can only be explained »on the assumption that the successive inductive actions pro- dace an accumulative effect; so that theory indicates the necessity of the existence of the resoc observed.

438 DYNAMICAL THEORY OF INDUCTION.

Hertz was at first inclined to 8uppo3e that as the micro- meter circuit was only broken by the extremely short air space- limited by the maximum sparking distance under the condi- tions of the experiment, it might therefore be treated as a closed circuit, and only the total induction considered. The ordinary methods of electro-dynamics give the means of com- pletely determining the total inductive effect of a current element on a closed circuit, and would, therefore, in tliis case have sufficed for the investigation of the phenomena observed. He found, however, that the treatment of the micrometer circuit as a closed circuit led to incorrect results, so that it, as well as the primary, had to be treated as an open circuity and therefore a knowledge of the total induction was insuffi- cient, and it became necessary to consider the value both of the E.M.F. of induction and of the electrostatic E.M.F. daeta the charged extremities of the exciting circuit at each point of the micrometer circuit.

The investigations to which these considerations led are described by Hertz in a Paper, ** On the Action of a Rectilinear Electrical Oscillation upon a Circuit in its Vicinity," published in Wiedemann's Annaim, Vol. XXXIV., p. 155, 1888.

In what follows the exciting circuit will be spoken of as the primary and the micrometer circuit as the secondary. Hertz points out that the reason that electrostatic effect cannot be neglected is to be found in the extreme rapidity with which the electrostatic forces change their sign. If the electrostatio alternations in the primary were comparatively slow they might attain a very high intensity without giving rise to a spark in the secondary, since the electrostatio distribution on the secondary would vary so as to remain in equilibrium with the external E.M.F. This, however, is impossible, because the variations in direction follow each other too rapidly for the distribution to follow them.

In the present investigations the primary circuit consisted of a straight copper wire 5 millimetres in diameter, carrying nt its extremities hollow zmc spheres 80 centimetres in diameter.. The ceatres of the spheres were one metre apart, and at the middle of the wire was an air space f centimetre in length. The wire was placed in a horizontal position, and the observa- tions were all made at points near to the horizontal plan»

DYNAMICAL THEORY OF INDUCTION, 439

through it, which, however, did not of coarse affect their generality, as the same effects would necessarily be produced in any plane through the horizontal wire. The secondary circuit consisted of a circle of 85 centimetres radius, of copper wire 2 millimetres in diameter, the circle being broken by an air space capable of variation by means of a micrometer screw.*