The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 26 of 35

When the air space was at its greatest distance from the plane the sparking distance attained a maximum value of from 2 to 3 millimetres. The sparks were shown to be due to the fundamental vibration by slightly varying the secondary so as to throw it out of unison with the primary when the sparking distance was diminished, which would not have been the case if the sparks had been due to overtones. Moreover, the sparks disappeared when the secondary was cut at its points of intersection with the horizontal plane through the primary, though these would be nodal points for the first overtone.

When the air space was kept at its greatest possible distance from the horizontal plane through the primary, and turned about a vertical axis, the sparking distance attained two maxima at the points for which <£ = 0, and almost dis- appeared at the points for which <£ = 90°.

The lower half of Fig. 158 shows the different positions of minimum sparking. A A' is the primary conductor, and the lines in n represent the projections of the secondary circuit on the horizontal plane. The arrows perpendicular to these give the direction of the resultant lines of force. As this did not anywhere vanish in passing from the sphere A to the sphere A', it could not change its sign.

The diagram brings out the two following points : —

1. The distribution of the resultant E.M.F. in the vicinity of the rectilinear vibration is very similar to that of the electro-

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443

static E.M.F. due to the action of its two extremities. It should be specially noted that near the centre of the primary the direction is that of the electrostaiic E.M.F., showing tha"t it is more powerful than the electro-dynamic, as required by theory.

2. The lines of force deviate more rapidly from the line A A' than the electrostatic lines, though thia is not so evident on the reduced scale of the diagram as in the author's original drawings on a much larger scale.

It is due to the components of the electrostatic E.M.F. parallel to A A' being weakened by the E.M.F. of induction, while the parpendicular components remained unaffected.

FIG. 158.

Experiments with the Secondary Circuit in a Horizontal Plane. The results obtained when the plane of the secondary was horizontal can best be explained by reference to the upper half of the diagram in Fig 158.

In the position I., with the centre of the circle in the line A A' produced, the sparks disappeared when the air space occupied either of the positions bl or b, while two equal maxima of the sparking distance were obtained at % and a'1} the length of the spark in these positions being 2-5 millimetres. Both these results are in accordance with theory.

In the position II. the circle is cut by the electro-magnetic lines of force, and therefore a does not vanish. It will, how-

444 DYNAMICAL THEORY OF INDUCTION.

ever, be small, and we should expect that the expression a + /? sin 0 would have two unequal maxima, /3 + a and (3 -a, both for 0 = 90°, and having the line joining them perpendicular to the resultant E.M.F., and between these two maxima we should expect two points of no sparking near to the smaller maximum. This was confirmed by the observations.

The maximum sparking distances were 3-5 millimetres at #2 and 2 millimetres at a'2. Now, with the air space at o2, the sphere A being positive, the resultant E.M.F. in the oppo- site portion of the circle will repel positive electricity from A, and therefore tend to make it flow round the circle clockwise. Between the two spheres the electrostatic E.M.F. acts from A towards A', and the opposite E.M.F. of induction in the neigh- bourhood of the primary acts from A' to A, parallel to the former, and, acting more strongly on the nearer than on the further portion of the secondary, tends to cause a current in same direction as that due to the former, namely, in a clock- wise direction. Thus the resultant E.M.F. is the sum of the two as required by theory, and in the same way it is easily seen that when the air space is at a'a the resultant E.M.F. is equal tc their difference.

As the position III. is gradually approached the maximum disappears, and the single maximum sparking distance as was found to be four millimetres in length, having opposite to it a point of disappearance «'3. In this case clearly a = /?, and the sparking distance is given by the expression a(l + sin 0). The line a3 a'& is again perpendicular to the resultant E.M.F.

As the circle approaches further towards the centre of A A'f a will become greater than (3, and the expression a + ft sin 0 will not vanish for any value of 6, but will have a maximum a + /3 and a minimum a -(3; and in the experiments it was found that the sparks never entirely disappeared, but varied between a maximum and a minimum, as indicated by theory.

In the position IV. a maximum sparking distance of 5-5 millimetres was observed at «4, and a minimum of 1-5 milli- metre at o'4.

In the position V. there was a maximum sparking distance of 6 millimetres at a5, and a minimum of 2-5 millimetres at a't. In these experiments the air space should be screened off from the primary in the latter positions as well as in the earlier

DYNAMICAL THEORY OF INDUCTION. 445

ones, in which it is unavoidable, as otherwise the results would not be comparable.

In passing from the position III. to the position V. the line a a' rapidly turned from its position of parallelism to the primary circuit into a position perpendicular to it. In the latter positions the sparking was essentially due to the induc- tive action, and therefore Hertz was justified in his previous experiments in assuming the effect in these positions to be due to induction.

Even in these positions, however, the sparking is not totally independent of electrostatic action, except when the air space is half-way between the maximum and minimum positions, and therefore & sin 6 = 0.

Other Positions of the Secondary Circuit. — Hertz made numerous observations with the secondary circuit in other positions, but in no case were any phenomena observed which were not completely in accordance with theory. As an

example of these consider the following experiment :

The secondary was first placed in the horizontal plane in the position V. (Fig. 158), and the air space was in the position a. relatively to the primary. The circle was then turned about a horizontal axis through its centre and parallel to the primary, so as to raise the air space above the horizontal plane. During this rotation 9 remained equal to 90deg., and the value of /8 remained nearly constant, but a varied approximately in the same ratio as cos W, "& being the angle between the plane of the circle and the horizontal, for a is proportional to the number of magnetic lines of force passing through the circle. Let a0 be the value of a in the initial position, then in the other postions its value would be o<, cos "?, and therefore the sparking dis- tance should be given by the expression an cos ^F + /3, in which a0 was known to be greater than (3. This was confirmed by observation, for it was found that as the air space increased its height above the horizontal plane the sparking distance diminished from 6 millimetres down to 2 millimetres, its value when the air space was at its greatest distance above the hori- zontal plane. During the rotation through the next quadrant the sparking distance diminished almost to zero, and then increased to the smaller maximum of 2-5 millimetres, which it attained when the circle had turned through ISOdeg., and was

446 DYNAMICAL THEORY OF INDUCTION.

therefore again horizontal. Similar results were obtained in the opposite order as the circle was rotated from 108deg. to 360deg. When the circle was kept with the air space at its maximum height above the horizontal plane, and then raised or lowered bodily without rotation, the sparking distance was found to diminish in the former case and to increase in the latter — results completely in accordance with theory.

Forces at Greater Distances. — Experiments with the secondary at greater distances from the primary are of great importance, as the distribution of E.M.F. in the field of an open circuit is very different according to different theories of electro-dynamic action, and the results may, therefore, serve to eliminate some of them as untenable. In making these experiments, how- ever, an unexpected difficulty was encountered, as it was found that at distances of from 1 to 1'5 metre from the primary, the maximum and minimum, except in certain positions, became indistinctly defined ; but when the distance was increased to upwards of two metres, though the sparks were then very small, the maximum and minimum were found to be very sharply marked when the sparks were observed in the dark. The positions of maximum and minimum were found to occur with the circle in planes at right angles to each other. At considerable distances the sparking diminished very slowly as the distance was increased. Hertz was not able to determine an upper limit to the distance at which sensible effects took place, but, in a room 14 metres by 12, sparks were distinctly observed when the primary was placed in one corner of the room, wherever the secondary was placed. When, however, the primary was slightly displaced no effects could be observed, even when the secondary was brought considerably nearer. The interposition of solid screens between the two circuits greatly diminished the effect.

Hertz mapped out the distribution of force throughout the room by means of chalk lines on the floor, putting stars at the points where the direction of the E.M.F. became indeter- minate. A portion of the diagram obtained in this manner is shown on a reduced scale in Fig. 159, with respect to which the following points are noteworthy : —

1. At distances beyond three metres the E.M.F. is every- where parallel to the primary oscillation. Within this region,

DYNAMICAL THEORY OF INDUCTION. 447

therefore, the electrostatic E.M.F. is negligible in comparison with the E.M.F. of induction. Now all the theories of the mutual action of current elements agree in giving an E.M.F. of induction inversely proportional to the distance ; while the electrostatic E.M.F., being due to the differential action of the two extremities of the primary, is approximately inversely proportional to the cube of the distance. Some of these theories, however, are not in accordance with the experi- mental result that the effect diminishes much more rapidly in the direction of the primary oscillation than in a direc- tion at right angles to it, induced sparks being observed at a distance exceeding 12 metres in the latter direction, while they disappeared at a distance of about four metres in the former direction.

FIG. 159.

2. That, as already proved, for distances less than one metre the distribution of E.M.F. is practically that of the electrostatic E.M.F.

3. There are two straight lines at all points of which the direction of the E.M.F. is determinate, namely, the line in which the primary oscillation takes place, and the perpendicular to the primary through its middle point. Along the latter the E.M.F. does not vanish at any point : the sparking diminishes gradually as the distance is increased. This, again, 1? incon- sistent with some of the theories of mutual action of current elements, according to which it should vanish at a certain definite distance. A very important result of the investigation is the demonstration of the existence of regions within which

448 DYNAMICAL THEORY OF INDUCTION.

the direction of the E.M.F. becomes indeterminate. These regions form two rings encircling the primary circuit. Since the E.M.F. within them acts very nearly equally in every direction, it must assume different directions in succession, for, of course, it cannot act in different directions simultaneously.

The observations, therefore, lead to the conclusion that within these regions the magnitude of the E.M.F. remains very nearly constant, while its direction varies through all the points of the compass at each oscillation. Hertz stated that he was unable to explain this result, as also the existence of overtones, by means of the simplified theory in which the higher terms of the expansion of F are neglected, and he considers that no theory of simple action at a distance is capable of explaining it. If, however, the electrostatic E.M.F. and the E.M.F. of induction are propagated through space with unequal velocities, it admits of very simple explana- tion. For within these annular regions the two E.M.F.s are at right angles and of the same order of magnitude ; they will, therefore, in consequence of the distance traversed, differ in phase, and the direction of the resultant will turn through all the points of the compass at each oscillation.

This phenomenon appeared to him to be the first indication which had been observed of a finite rate of propagation through space of electrical actions, for, if there is a difference in the rate of propagation of the electrostatic and electro-dynamic E.M.F., one at least of them must be definite.

At the end of the Paper in which the preceding experiments are described, Hertz describes some observations which he made' on the conditions at the primary sparking point which affect the production of sparks in the secondary circuit. He found that illuminating the primary spark diminished its power of exciting rapid oscillations, the sparks in the secondary being observed to cease when a piece of magnesium wire was burnt or an arc lamp lighted near the primary point. The observed effect on the primary sparks is that they are no longer accompanied by a sharp crackling sound as before. The effect of a second discharge is especially note- worthy, and it was found that the secondary sparks could be made to disappear by bringing an insulated conductor close to the opposed surfaces of the spheres forming the terminals

DNYAM1CAL THEORY OF INDUCTION. 449

at the primary air space, even when no visible sparking took place between the latter and the insulated conductor. The secondary sparking could also be stopped by placing a fine point close to the primary air space, or by touching one of the opposed surfaces of the terminals with a piece of sealing- wax, glass, or mica. Hertz states that further experiments led him to conclude that, even in these cases, the effect is due to light too feeble to be perceived by the eye, arising from a side discharge. He points out that these effects afford another example of the effects of light on electric discharges, which have been observed by E. Wiedemann, H. Hebert, and W. Hallwachs.

Hertz's next Paper in order of publication in Wiedemann's Annalen is "On Some Induction Phenomena Arising from Electrical Actions in Dielectrics " (Vol. XXXIV., p. 273), and contains an account of some researches which were under- taken with a view of obtaining direct experimental confirma- tion of the assumption involved in the most suggestive theory of electrical actions, viz., that of Faraday and Maxwell, that the well-known electrostatic phenomena observed in dielectrics are accompanied by corresponding electro-dynamic actions. The method of observation consisted in placing a secondary conductor adjusted to unison, as regards electrical oscillations, with the primary, as near as possible to the former, and in such a relative position that the sparks in the primary pro- duced no sparking in the secondary. As the equilibrium could be disturbed and sparking induced in the secondary by the approach of conductors, it formed a kind of induction balance ; but the point of special interest in connection with it was that a similar effect was produced when the conductors were replaced by insulators, provided the latter were of com- paratively large size. The observed rapidity of the oscillations induced in the dielectrics showed that the quantities of elec- tricity in motion under the influence of dielectric polarisation were of the same order of magnitude as in the case of metallic conductors.

The apparatus employed is shown diagrammatically in Fig. 160, and was supported on a light wooden framework, not shown in the illustration. The primary conductor consisted of two brass plates, A A', with sides 40 centimetres in length,

oo

450

DYNAMICAL THEORY OF INDUCTION.

joined by a copper wire 70 centimetres long and half a centi- metre in diameter, containing an air space of three-quarters of a centimetre, with terminals formed of polished brass spheres. When placed in connection with a powerful induction coil, oscillations are set up, the period of which, determined by the dimensions of the primary, can be determined to within a hundred-millionth of a second. The secondary conductor con- sisted of a circle, 35 centimetres in radius, of copper wire two millimetres in diameter, containing an air space, the length of which could be varied by means of a screw from a few

FIG. 160.

hundredths of a millimetre up to several millimetres. The dimensions stated were such as to bring the two conductors into unison, and secondary sparks up to six or seven milli- metres in length could be obtained.

The circle was movable about an axis through its centre perpendicular to its plane, to enable the position of the air space to be varied. The axis was fixed in the position m n in the plane of A and A', and half-way between them. The centre of the circle was at a distance of 12 centimetres from the nearest points of A and A'.

DYNAMICAL THEORY OF INDUCTION. 451

When / was in either of the positions a or a' lying in the plane of A A' no sparking occurred in the secondary, while maximum sparking took place at b and V 90deg. from the former positions. The E.M.F. giving rise to the secondary sparks is, as in previous experiments, partly electrostatic and partly electro-magnetic, and the former being the greater will determine the sign of the resultant E.M.F. The oscillations must, for the reason previously explained, be considered as produced in the part of the secondary most remote from the air space. Assuming the E.M.F. and the amplitude of the resulting oscillation to be positive when/ is in the position b', they will both be negative when /is at b.

When the circle was slightly lowered in its own plane the sparking distance was increased at b' and diminished at b, and the null points lay at a certain distance below a and a'. The electrostatic E.M.F. is scarcely affected by such a displacement, but the integral of the E.M.F. of induction taken round the circle is no longer zero, and therefore gives rise to an oscil- lation which will be of positive sign whatever be the position of /, for the direction of the resultant E.M.E\ of induction is opposite to that of the electrostatic E.M.F. in the upper half of the circle, and coincides with it in the lower half, where the electrostatic E.M.F. has been assumed to be positive. Since the new oscillation so produced is in the same phase as the previously existing one, their amplitudes must be added io give the resultant amplitude, which explains the pheno- mena.

Effects of tJie Approach of Conductors. — In making these observations it was found necessary to remove all conductors to a considerable distance from the apparatus, in order to obtain a complete disappearance of sparking at the points a and a'. Even the neighbourhood of the observer was sufficient to set up sparking when the air space / was in either of these posi- tions, and the sparks had therefore to be observed from a distance. The conductors used for the experiments were of the form shown at C (Fig. 160), and consisted of thin metal foil. The objects kept in view in selecting the material and dimensions were to obtain a conductor which would give a moderately large effect and having an oscillation period less than that of the primary.

GG 2

452 DYNAMICAL THEORY OF INDUCTION.

When the conductor C was brought near to A A', it was found that the sparking distance decreased at b and increased at b', and the null points were displaced upwards — that is, in the direction of C.

From the results of experiments already described it is evident that the effect of displacing A A' upwards would be the same, qualitatively, as that of a current in the same direction as that in A A' directly above it. The effect pro- duced by the approach of C was the reversa of this, and could be explained by an inductive action, supposing there were a current in C in the opposite direction to that in A A', which is exactly what must occur ; for the electrostatic E.M.F. would give rise to such a current, and since the oscillations in C are more rapid than those of the E.M.F., the current must be in the same phase as the inducing E.M.F. The truth of this explanation was confirmed by the following experiments. The horizontal plates of the conductor C being left in the same position as before, the vertical plate was removed, and succes- sively replaced by wires of increasing length and fineness, in order to lengthen the oscillation period of C. The effect of this was to displace the null points more and more in an upward direction, while at the same time they became less sharply defined, a minimum sparking taking the place of the previous absolute disappearance. The sparking distance at the highest point had previously been much less than at the lowest point, but after the disappearance of the null points it began to increase. At a certain stage the sparking distance at the two positions became equal, and then no definite minimum points could be found, but sparking took place freely at all positions of/. Beyond this stage the sparking distance at the lowest point diminished, and very soon two minimum points made their appearance close to it, not clearly defined at first, but gradually becoming more distinct, and at the same time approaching the points a a' , with which they ultimately coin- cided, when the minimum points again became absolute null points. These results are in agreement with the conclusion drawn from the former observations, for as the oscillation period of C approaches that of A A' the intensity of the current in the former increases, but a difference of phase arises between it and the existing E.M.F. When the two-

DYNAMICAL THEORY OF INDUCTION. 453

are in unison the current in C attains its maximum, and, as in other cases of resonance, the difference of phase gives rise to a slightly clamped oscillation, having a period of about a quarter that of the original one, which makes any inter- ference between the oscillations excited in the circle B by A A' and C respectively impossible. These conditions clearly corre- spond to the stage at which the sparking distances at b and V were equal. When the oscillation period of C becomes decidedly greater than that of A A', the amplitude of the oscillation in the former will again diminish, so that the difference in phase between it and the exciting E.M.F. will approach half of the original period. The current in C will therefore always be in the same direction as that in A A', so that interference between the two oscillations excited in B will again become possible, and the effect of C will then be opposite to its original effect. When the conductor C was made to approach A A' the sparks in B became much smaller, which is explained by the fact that its effect will be to increase the oscillation period of A A', and therefore to throw it out of unison with B.

Effects of the Approach of Dielectrics. — A very rough estimate shows that when a dielectric of large mass is brought near to the apparatus the quantities of electricity set in motion by dielectric polarisation are at least as large as in metallic wires or thin rods. If, therefore, the action of the apparatus were unaffected by the approach of such masses, it would show that, in contradiction to the theories of Faraday and Maxwell, no electro -dynamic actions are called into play by means of dielectric polarisation, or as Maxwell calls it, electric displace- ment. The experiments, however, showed an effect similar to that which would be produced if the dielectric were replaced by a conductor with a very small oscillation period. In the first experiment made, the mass of dielectric consisted of a pile of books, 1-5 metre long, Opo metre broad, and 1 metre high, placed under the plates A A'. Its effect was to displace the null points through about lOdeg. towards the pile. A block of asphalte (D, in Fig. 160), weighing 800 kilogrammes, and measuring 1-4 metre in length, 0-4 metre in breadth, and 0-6 metre in height, was then used in place of the books, the plates being allowed to rest upon it.

454 DYNAMICAL THEORY OF INDUCTION.

The following results were then obtained : —

1. The spark at the highest point of the circle -was now decidedly stronger than that at the lowest point, which was nearer to the asphalte.

2. The null points were displaced through about 23deg. downwards — that is, in the direction of the block — and at the same time were transformed into mere points of mini- mum sparking, a complete disappearance being no longer obtainable.

3. When the plates A A' rested on the asphalte block the oscillation period of the primary was increased, as shown by the fact that the period of B had to be slightly increased in order to obtain the maximum sparking distance.

4. When the apparatus was moved gradually away from the block its action steadily diminished without changing its character.

5. The action of the block could be compensated by bringing the conductor C over the plates A A' while they rested on the block, the null points being brought back to a and a' when C was at a height of 11 centimetres above the plates. When the upper surface of the asphalte was 5 centimetres below the plates, compensation was obtained when C was placed at a height of 17 centimetres above them, showing that the action of the dielectric was of the order of magnitude which had been anticipated.

The asphalte contained about 5 per cent, of aluminium and iron compounds, 40 per cent, of calcium compounds, and 17 per cent, of quartz sand. In order to make sure that the observed effects were not due to the conductivity of some of these substances a number of further experiments were made.

In the first place, the asphalte was replaced by a mass of the same dimensions of the so-called artificial pitch prepared from coal, and effects of a similar kind were observed, but slightly weaker, the greatest displacement of the null points amounting to 19deg. Unfortunately this pitch contains free carbon, the amount of which it is difficult to determine, and this would have some conductivity.

The experiments were then repeated with a conductor, C, of half the linear dimensions of the former one, and smaller blocks

DYNAMICAL THEORY OF INDUCTION. 455

of various substances, on account of the great cost of obtaining large blocks of pure materials. The substances used were asphalte, coal-pitch, paper, wood, sandstone, sulphur, paraffin, and also a fluid dielectric, namely, petroleum. With the smaller apparatus it was not possible to obtain quantitative results of the same accuracy as before, but the effects were of an exactly similar character, and left little room for doubt of the reality of the action of the dielectric.

The results might possibly be supposed to be due to a change in the distribution of the electrostatic E.M.F. in the neighbour- hood of the dielectric, but, in the first place, Hertz stated that he was unable to explain the details of the observations on this hypothesis, and in the second place it is disproved by the following experiment : —

The smaller apparatus was placed with the line r s on the upper near corner of one of the large blocks, in which position the dielectric was bounded by the plane of the plates A A' and the perpendicular plane through r s, both of which are equi- potential surfaces, so that if the action were electrostatic no effect should be produced by the dielectric. It was found, however, to produce the same effect as in other positions. It might also be supposed that the effects were due to a slight conductivity, but this could hardly be the case with such good insulators as sulphur and paraffin. Suppose, moreover, that the conductivity of the dielectric is sufficient to discharge the plate A in the ten-thousanth of a second, but not much more rapidly; then, during one oscillation, the plates would loose only the ten-thousandth part of their charge, and the conduction current in the substance experimented on would not exceed the ten-thousandth part of the primary current in A A', so that the effect would be quite insensible.

It is thus shown in the experiments described above that when variable electrical forces act in the interior of dielec- trics of specific inductive capacity not equal to unity the corresponding electric displacements produce electro-dynamic effects. In a Paper, " On the Velocity of Propagation of Electro- Dynamic Actions," in Wiedeniann's Annalen, Vol. XXXIV., p. 551, Hertz showed that similar actions take place in the air, which proves, as was previously pointed out, that electro- dynamic action must be propagated with a finite velocity.

456

DYNAMICAL THEORY OF INDUCTION.

The method of investigation was to excite electrical oscilla- tions in a rectilinear conductor in the same manner as in former experiments, and then to produce effects in a secondary conductor by exciting electrical oscillations in it by means of those in the rectilinear conductor, and at the same time by the primary conductor acting through the intervening space. This distance was gradually increased, when it was found that the phase of the vibrations at a distance from the primary lagged behind those in its immediate neighbourhood, showing that the action is propagated with a finite velocity which was found to be greater than the velocity of propagation of electrical waves in wires in the ratio of about 45 to 28, so that the former is of the same order as the velocity of light. Hertz was unable to obtain any evidence with respect to the velocity of propagation of electrostatic actions.

FIG. 161.

The primary conductor A A' (Fig. 161) consisted of a pair of square brass plates with sides 40 centimetres in length, con- nected by a copper wire 60 centimetres in length, at the middle point of which was an air space, across which sparks were made to pass by means of powerful discharges from the induc- tion coil J. The conductor was fixed at a height of 1*5 metre above the base -plate of the coil, with its plates vertical, and the connecting wire horizontal. A straight line, rs, drawn horizontally through the air space of the primary, and perpen- dicular to the direction of the primary oscillation, will be called " the base-line ; " and a point in this, situated at a distance of 45 centimetres from the air space, will be referred to as " the null point."

D YNA MICAL THEOE Y OF IND UC TWN. 457

The experiments were made in a large lecture-room, with nothing near the base-line for a distance of 12 metres from the primary conductor. The room was darkened during the •experiments.

The secondary conductor consisted either of a circular wire, •C, of 35 centimetres radius, or of a square of wire, B, with sides 60 centimetres long. The primary and secondary air spaces were both capable of adjustment by means of micro- meter screws. Both the secondary conductors were in unison with the primary, the (half) vibration period of each being one hundred- millionth of a second, as calculated from the capacity and coefficient of self-induction. It is doubtful whether the ordinary theory of electrical oscillations would lead to accurate results under the conditions of these experiments, but as it gives correct numerical results in the case of Leyden jar dis- charges, it may be expected to be correct as far as the order of the results is concerned. When the centre of the secondary lies in the base-line, and its plane coincides with the vertical plane through the base-line, no sparks are observed in the secondary, the E.M.F. being everywhere perpendicular to the direction of the secondary. This will be referred to as " the first principal position" of the secondary. When the plane of the secondary is vertical and perpendicular to the base-line, the centre still lying in the base-line, the secondary will be said to be in its " second principal position." Sparking then occurs in the secondary when its air space is either above or below the horizontal plane through the base-line, but not when it is in this plane. As the distance from the primary was increased, the sparking distance was observed to decrease, rapidly at first, but ultimately very slowly. Sparks were observed throughout the whole distance of 12 metres available for the experiments. The sparking in this position is due essentially to the E.M.F. produced in the portion of the secondary remote from the air space. The total E.M.F. is partly electrostatic and partly electro-dynamic, and the experiments show beyond the possi- bility of doubt that the former is greater, and therefore deter- mines the direction of the total E.M.F. close to the primary, while at greater distances it is the electro-dynamic E.M.F. which is the greater.

The plane of the secondary was then turned into the hori-

458 DYNAMICAL THEORY OF INDUCTION.