The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 30 of 36

neighbourhood of the closed end — that is, at the point a, "which corresponds to the spark-gap A of our previous experiments — there were now no sparks observable in the resonator. But on moving away firom this position towards p sparks appeared, became very brilliant at a distance of 15 metre firom a, then decreased again in intensity, then almost entirely vanished at 8 metres distance firom a, and increased again until the end of the tube was reached. We thus find our theory borne out by flBMst. That we obtain a node at the closed end is clear, for at the metallic contact between the central wire and the surface of the tube the electric force between the two must necessarily vanish. It is dififerent when we cut the central conductor at this point just near the end, and insert a gap of several centimetres length. In this case the wave will be reflected in a phase opposite to that of the previous case, and we should expect a ventral segment at a. As a matter of fact we find brilliant sparks in the resonator in tliis case; they rapidly decrease in strength if we move from a towards P, almost entirely vanish at a distance of 15 metre, and become brilliant again at a distance of 8 metres; moreover they give a second well-marked node at 45 metres distance — that is, 05 metre from the open end. The nodes and loops which we have described are situated at fixed distances from the closed end, and alter only with this distance ; they are, however, quite independent of the occurrences outside the tube, for example, of the nodes and Ipops formed there. The phenomena occur in exactly the same way if we allow the wave to travel through the apparatus in the direction from the open to the closed end ; their interest is, however, smaller, since the mode of transmission of the wave deviates from that usually conceived less in this case than in the one which has just been under our consideration. If both ends of the tube are left open with the central wire undivided, and stationary waves with nodes and loops are now set up in the whole system, there is always found for every node outside the tube a corresponding node in the interior, which proves that the propagation takes place inside and outside with, at .any rate approximately, the same velocity.

'< On looking over the experiments which we have described, and the interpretation put upon them, as well as the explana-

t>YKAMtCAL TMBOnt Of It^DVCtlOlt. 4M

tions of the physicists referred to in the introduction, a difference will be noticed between the views here put forward and the usaal theory. According to the latter, conductors are represented as those bodies which alone take part in the pro- pagation of electric disturbances ; non-conductors are the bodies which oppose this propagation. According to the modem view, on the contrary, all transmission of electrical disturbances is brought about by non-conductors: conductors oppose a great resistance to any rapid changes in this transmission. One might almost be inclined to maintain that conductors and non-conductors should, on this theory, have their names interchanged. However, such a paradox only arises because one does not specify the kind of conduction or non-conduction considered. Undoubtedly metals are non-conductors of elec- tric force, and just for this reason they compel it, under certain circumstances, to remain concentrated instead of becoming dissipated, and thus they become conductors of the apparent source of these forces, electricity, to which the usual termi- nology has reference."

§16. Experimental Determination of Electromagnetic Wave Velocity. — Space does not permit us to make further mention of the important and valuable work which has been carried out in recent years in confirming and extending this work of Hertz. We refer the reader specially, however, on this subject, to Dr. Lodgers monograph on this subject.*

We shall conclude this chapter by presenting an abstract of an interesting research by Messrs. Trowbridge and Duane on the "Velocity of Electric Waves "t because it furnishes a proof, having a high degree of accuracy, that the velocity of an electromagnetic wave is identical with the velocity of light.

Broadly speaking, the method employed consisted in establishing stationary waves in a conducting circuit and determining the period of oscillation by photographing the oscillating spark in a spark gap, and at the same time measuring the wave-length of the stationary waves induced in

• " The Work of Hertz and some of his Suoceesors." By Dr. 0. J. Lodge, published by " The Electrician ** Printing and Publishing Co., London, t PhiL Mag,, August, 1895 | also The BUotrioian, VoL XXXV., p. 712i

kk2

500

DYNAMICAL TIIMOMY OP IKDUCTlON.

a secondary circait turned to resonance with the primary. In the following paragraphs the description of their experiments is taken from the Paper by Messrs. Trowbridge and Doane. They say : —

''The first point in the coarse of the investigation worth detailed description is the production of electric waves along parallel wires in such a manner that they are actually visible to the eye. The arrangement of the apparatus to accomplish this was as follows : —

"A primary condenser, AB (Fig. 165), was held with its plates in vertical planes by means of suitable wooden supports (not represented in the figure), and was joined in a circait, BG, consisting of two wires about 75cm. long, placed 4cm. apart. In reality this circait B G should be represented as perpendicular to the plane of the paper (which is taken as the horizontal plane passing through the centre of the apparatus).

.E

J

1 1

=S°

F

H Fio. 165.

L

The plates of the condenser A B were sheets of tinfoil 101 X dOcm., glued to hard rubber sheets, and the dielectric between them consisted of other similar sheets of hard rubber sufficient in number and thickness to make the distance between the condenser plates 4-2cm. Outside the primary condenser plates, and separated from them by hard rubber plates (total thickness 0-6cm.), were two secondary plates, E and F, each 40cm. square. To these plates was attached the secondary circuit EGJHF, the form of which is represented in the figure. This latter circuit consisted of copper wire, diameter O'lScm., and its total length from E to F was 4,200cm. A spark-gap with spherical terminals 2- 5cm. in diameter was placed at C in the primary circuit, and another spark-gap with pointed terminals was sometimes inserted at J in the secondary circuit, although this latter spark-gap had no effect upon the phenomena to be

DYNAMICAL THEORY OF INDUCTION. 601

described. The primary condenser was charged by means of a large Bohmkorff coil excited by five storage cells with a total voltage of 10 volts. The current from these cells was made and broken by an automatic interrupter. Every time the primary condenser was charged a spark passed at G, causing an oscillatory discharge. A convenient method of forming a mental picture of the oscillation excited in the secondary circuit is the conception of Faraday tubes elaborated by J. J. Thomson in his 'Becent Researches in Electricity and Magnetism.' The oscillations of the primary acted inductively upon the secondary and sent out groups of Faraday tubes which travelled along the secondary circuit, with their ends on the wires, and lying chiefly in the space between them. At the end J they reversed their direction and travelled back along the circuit. The period of oscillation of the primary circuit was altered, until by trial it was found that groups of returning tubes met groups of advancing tubes between the points G and H. As the two sets of moving tubes were oppositely directed they annulled each other and produced a node. Thus a system of stationary waves is set up with a node at J, another node at G H, and a ventral segment at K L. The method of dis- covering when the circuits were in tune and of investigating the shape of the waves will be described later. The point to be noticed here is that the vibrations were sufficiently powerful to cause a luminous discharge on the surface of the wvtQ where the accumulation of tubes was a maximum, i,e., at £L, while at the nodal points J and GH the wire was entirely dark. Still further, the wave formation could be made apparent to the sense of hearing as well as that of sight ; for, placing the ear within a few centimetres of the wire and walking beside it, a distinct crackling sound could be heard at the points £ and L, whereas no such sound could be heard at G, J and H. By placing bits of glass tubing on the wire the sound was much intensified at the points K and L, and the phenomena made more striking. It might be supposed that by decreasing the capacity of the primary condenser, and therefore the period of its oscillation, the secondary circuit could be broken up into a new set of shorter stationary waves, with nodes at J and at points somewhere near K, L, G and H, and ventral segments between them. This was tried with

602 DYNAMICAL THEORY OF INDUCTION.

perfect suooesSy except that it was not possible to cause the light at £ and L to actually disappear. There was decidedly less light at these points, however, than on either side of them. The light, of course, is simply that which always appears around wires carrying very high-potential currents, the in- teresting point being that it appears in some places on the circuit and not in others. The experiment showing how the circuit breaks up in several different ways would form a most beautiful lecture experiment.

< As a means of ascertaining when the circuits were in resonance, and of investigating the form of the wave in the secondary circuit, a bolometer similar to that designed by Paalzow and Bubens was used.

''The bolometer as an instrument for measuring electrio waves is so well known, that it is not necessary to state here more than its fundamental principles. It consists essentially of a well-balanced Wheatstone bridge, to one of the arms of which are metallically connected two small conductors. These conductors are brought near the circuit to be tested, and the oscillating charges induced in them and sent through the arm of the Wheatstone bridge develop enough heat to throw the bridge out of balance. By moving the conductors along the circuit different deflections are produced according to the magnitude of the charges on the wire in their neighbourhood, and thus an excellent estimate of the wave formation can be obtained. In the present case the conductors that were brought near the secondary circuit consisted of two pieces of wire insulated with rubber, bent into circles of about 2cm. radius, and fastened to a bit of pine-wood by means of a heavy coating of paraffin. The two wires of the secondary circuit passed tbrough holes in this bit of wood in such a manner as to pass through the centres of the two circles. In the early part of the investigation the bolometer and galvanoscope were placed at a sufficient distance from the oscillating circuits to prevent any direct action of one on the other, and the leads running from the circular conductors to the bolometer consisted of long fine wires. Later, when longer circuits and longer waves were experimented with, great inconvenience

• " Anwendung de« Bolometriachen Princips auf Klectriacbe Measungeo,'* WieO. 4nn., XXXVU., p. 629,

DYNAMICAL THEORY Of INVVCTION. 603

was experienced from the long leads, since their relative position had considerable effect upon the galvanoscope deflec- tions. In order to obviate this difficulty, short leads of lieavily insulated wire were used, and the bolometer was placed on wheels and moved along from place to place. A bolometric study of the circuit just described showed the character of the oscillation to be that mentioned — namely, nodes at the points J and GH, and a ventral segment at KL. A careful run was made from one end of the circuit to the other, which furnished data from which a very regular curve was drawn.

" The insertion of a small spark-gap (1mm. to 8mm.) at the point in the secondary circuit marked J (Fig. 165, p. 500) had no appreciable effect upon the position of the nodal point O H, or of the point of maximum accumulation E L. The form of the wave was slightly altered for a metre on each side of J, and the bolometer showed a slight accumulation in the immediate neighbourhood of the spark-gap. This was probably due to the charging of the spark terminals to a sufficiently high potential to break through the dielectric. The feict that the insertion of a spark-gap into a secondary circuit in the manner described has no effect upon the length of the waves set up in that circuit was tested for a number of different cases (in none of which, however, was the length of the waves greater than in the present case), and found to be true in each one of them.

'' In order to determine the time of vibration, we used a concave rotating mirror, and the images of the oscillating sparks were thrown on a sensitive plate. If the mirror rotated about a horizontal axis the photographs showed bright horizontal lines, perpendicular to which at their extremities extended two series of dots. The distance between successive dots was the distance on the plate through which the image of the spark-gap moved during the time of a complete oscillation. Hence, by determining the speed of the mirror, and measuring the distances from the mirror to the plate, the time of oscillation could be calculated. To measure the sparks we used a sharp pointer, moved at the end of a micrometer screw under a magnifying glass of bw power. The instrument was originally intended

604 DYNAMICAL THEORY OF INDUCTION.

for microscopic measurements, and was very accoratelj con- structed. The rotating mirror was driven by an electric motor by means of a current from a storage battery of extremely constant voltage. To give great steadiness a heavy flywheel was attached to the axis of the mirror. The speed of the mirror was determined to within about one part in 500 by means of an electric chronograph. This apparatus, requiring great technical skill, was made for us by the mechanician of the laboratory. The mirror consisted of a thick piece of glass with a concave surface accurately ground for this research and silvered by ourselves.

'* There are many advantages in photographing the secon- dary spark rather than the primary. In the first place, to properly photograph a spark it is necessary to use pointed terminals ; but experiment has shown that the waves excited in a secondary circuit depend to a large extent upon the character of the primary spark, and that the most active sparks are those between metallic spheres with polished sur- faces. It is true that waves can be produced by sparks between points, but the oscillations are not so powerful or weU marked. In the second place, from the results obtained by Bjerknes, one would expect the oscillations in the secondary circuit to be much less damped than those in the primary. This expectation has been fully realised. Photographs show from ten to twelve times as many oscillations in the secondary as in the primary. The longest secondary spark we counted indicated 60 complete oscillations. In the third, and by no means the least important case, the question how dose the resonance is does not affect the accuracy of the results. By photographing the sparks in the secondary the period of oscillation is determined, not of a circuit that is altered until by trial it is found to' have as nearly as po3sible the same period of vibration as the circuit on which the length of the wave is measured, but that of the circuit along which the wave itself is actually travelling ; and hence the con- clusions in regard to the effect of damping reached by Bjerknes in his admirable Paper on ' Electric Besonance '* do not affect the accuracy of the results.

♦ " Ueber electrische Rcsonanz/' Wied. Ann.^ LV., p. 121 (1895).

DYNAMICAL THEORY OF INDUCTION.

606

«< The great difficulty to be overcome is the production of secondary oscillations that will produce sparks sufficiently bright to photograph. It is comparatively an easy task to photograph the primary spark, but in order to photograph the secondary the dimensions of the circuit must be chosen with great care.

" With a view to increasing the light of the spark, together with the length of the waves, it seemed desirable to lengthen the period of oscillation by enlarging the condensers rather than by increasing the self-induction of the primary circuit. A castor-oil condenser, therefore, was designed and con- structed on the following plan : — Eight plates (25cm. by 20cm.) were cut out of sheet zinc, and were held in vertical planes side by side 2cm. apart by a suitable hard-rubber

,0.

B

E

Q

K

M

-.. J ,_

4

f

«—

h — 1

——J

F

H

M

Fio. 166.

frame. The plates were entirely immersed in castor-oil con- tained in a glass jar. They were connected together in the manner shown in Fig. 166. The plates marked a, c and 6 were fastened to the conductor A B, and formed one armature of the condenser. Those marked d^ f and h were joined to C D, and formed the other armature. The two ends of the secondary circuit E, G, J, H, F were fastened to the plates h and g. The plane of the secondary circuit was 50cm., and that of the primary dcm. above the upper edge of the con- denser plate. The total length of the secondary circuit from one condenser plate through E, G, J, H, F to the other plate was 6,886cm. The circuit consisted of copper wire (diameter 0*21 5cm.) supported at each end by suitable wooden frames, and also once in the middle by hard-rubber hooks, fastened by long pieces of twine to a wooden crossbar above. The

506 DYNAMICAL THEORY OF INDUCTION.

distances from F to E and from E to L were 80cm., and a spark-gap with pointed tin terminals was inserted at J. The primary circuit consisted of copper wire (diameter 0'd4cm.). The distances between the two parts A 6 and C D were 45cm. The portion B D contained a spark-gap with platinum-faced spherical terminals, and was made so as to slide back and forth, to and horn the condenser. The motion of this movable piece varied the self-induction, and therefore the period of oscillation of the primary circuit. By this means the circuits were brought into resonance. With certain arrangements of the condensers the resonance was very sharp, and the position of the movable portion could be determined to within 0*25cm. In the arrangement which was finally adopted the resonance was not so sharp. Even in this case the distance of the sliding part from plate a could not have been in error by more than 2cm. The length 65cm. was finally chosen for .its value.

'' The automatic current interrupter that worked so beauti- fully in connection with the Hertz vibrator would not operate well when used to excite the circuits just described. After trying many devices, we finally adopted an ordinary reed interrupter with a comparatively large hammer -and -anvil arrangement, which gave little trouble.

<< At first it was found impossible to produce anything but a complex vibration in the secondary circuit when the spark- gap was open. Some slight evidence of resonance was obtained, but nothing of a decided character. When, how- ever, the spark-gap was closed, very good resonance ensued, and a wave the length of which could be measured to withia 0*4 per cent, was excited. Some photographs were taken of the spark in the secondary circuit, and they showed immediately the character of the complex wave formation. The secondary circuit could and did oscillate in three difiierent ways, and the ratios of the periods were those of the notes in an open organ pipe, namely 1:2:3. Usually the lowest or fiindamental oscillation together with one of the overtones was present ; but several sparks were noticed that furnished unmistakable evidence of the simultaneous existence of all three. We have observed in a circuit 10,000cm. long the same peculiarities of oscillation, excited by a primary circuit that, judging from its dimensions, could not have been in

DYNAMICAL THEORY OF INDUCTION.

607

resonanoe with the secondary. It was evident that the osoil- Jation havmg a node between the points marked E and F (Fig. 166) is that whose period is one-third of the fundamental.

'< A number of measurements of this period have been made, and from these values the velocity of the waves has been calculated. The results appear in the table below. As an average of five measurements of the wave length, none of which differed from the mean by more than 20om., the value 5,888cm. was chosen. The distance from the mirror to the photographic plate in each case except the last was 800- 1cm. Each of the first five values in the second column of the table is an average of 80 measurements of distances ranging in the neighbourhood of 1cm.

' The last line in the table contains the results of measure- ments on photographs of the primary spark instead of the secondary. In this case the distance from the mirror to the photographic plate was 3115cm.

'' These results were published as a preliminary record in the American Journal of Science for April, 1895. Since then the authors succeeded in producing much better waves and much more regular sparks, and discovered a phenomenon which renders a measurement on a photograph over a space where the dots are obliterated a questionable proceeding. The new data have given a value for the velocity more in accord with theory.

Number of revolu-

tioDB of mirror

per second.

Distance between two

successive points on plate.

Centimetres.

Velocity of waves. Centimetres.

71-2

70-85 ^ 70-7 71-3 70-8

0-05608 005600 0-05532 005637 0-05611

2-819 xlO»» 2-810x10" 2*835x1010 2-808 X low 2-808 X low

69-2

Average

005340

2-816 X low 2-988 X low

<' Since the waves in the secondary were not well formed when the spark-gap was inserted, it seemed desirable to try to find an arrangement that would produce simultaneously a good wave and a photographable spark. A number of con-

606 JDYNAMICAL THEORY OF INDUCTION.

densers with plates of different sizes and shapes and different substances for the dielectric were tried, and tbe apparatos to be described was finally adopted. The difficulties to be over- come were these. Too strong a reaction between the primary and secondary condensers could not be employed, because the increase in the damping of the primary duo to the large amount of energy drawn off by the secondary made good resonance impossible. The amount of energy in the primary at full charge must be much greater than that in the secondary. On the other hand, the capacity of the primary condenser must not be too great ; for the self-induction of the primary circuit would have to be proportionately small, and this, too, means an increase in the damping. The secondary con- denser, too, must have a capacity of less than a certain magnitude in order that the node may fall on the circuit and not in the condenser plate. These points seem to indicate that small condensers are preferable to large ones; but a

1

I A

or

E

"^ a

,1

ll

Fio.

-d "

F

1

I

) ' C

decrease in the size of the plates means a decrease in the light of the secondary sparks, and the sparks are at best barely photographable. Practically, therefore, our choice was much limited, and the particular arrangement to give the best results had to be selected by experiment after a long series of trials. The arrangement and dimensions of the apparatus finally adopted were as follows : —

"Two metallic plates, a and b (Fig. 167), 30 x 80cm., placed in vertical planes, formed the primary condenser. The dielec- tric between them consisted of the best French plate glass obtainable (E « 8 + probably) and was 2cm. thick. Outside the plates a and 6, and separated from them by a hard-rubber dielectric (K-2 + about) l'8cm. thick, were the secondary plates, 26 x 26cm. The primary and secondary circuits were

DYNAMICAL TBEOttT OF INDVCTION. 609

joined to the condenser plates as indicated in the figure. The primary circuit lay in the horizontal plane passing through the centres of condenser plates, and consisted of copper wires 0*d4cm. in diameter. In order to control the period of oscillation of the primary circuit, the portion B D containing a spark-gap with spherical terminals was made, as before, so as to slide along parallel to itself. The distance between the straight portions A B and C D was 40cm., and the lengths of AB and CD finally chosen for best resonance were 85cm. Most of the secondary circuit lay in a horizontal plane 16cm. above that of the primary. The lengths GE and H F, however, were bent down and fastened to the middle points G and H of the secondary plates. The circuit consisted of copper wire (diameter 0'215cm.), and its total length from G through J to H was 5,860cm. At J was a spark-gap with pointed terminals. With this apparatus we succeeded in producing a very regular wave formation, as indicated by the bolometer, even when there was a spark-gap at J. So many curves have been plotted and pubhshed to illustrate the characteristics of electrical waves that it does not seem worth while to add to the number here. It will be sufficient to state that the ratio of the maximum and minimum deflections in the bolometer was about 15 : 1, and that there was a node at J and another about 40cm. to the right of £ and F.

''Upon photographing the secondary spark some curious phenomena were observed. In the first place, the dots usually appeared in pairs. There would be two black dots followed by a space where two or three dots either appeared faintly or were absent altogether; after that two black dots would reappear, followed again by a faint space, and so on for six or seven repetitions. All this, of course, occurred in a single spark.

'* The explanation that first presents itself is that the two black dots are the result of the first two oscillations in the primary circuit, which, owing to the damping, are much more powerful than the others. If this were the true reason, the first of the pair of dots always ought to be blacker than the second, and every third dot ought to be the first of a pair. This is not the case, however. On the other hand, the phenomena cannot be explained as the result of a complex vibrationy for the bolometer readings, taken only a few

610 DYNAMICAL TBEOMY OF INDUCTION.

minutes before the photographic plates were exposed, and with exactly the same arrangement of apparatus, indicated extremely regular waves. A clue to the mystery was furnished by several sparks in which the dots made by one spark terminal had the characteristics just described, whereas those made by the other were quite regular. Following out this hint, wti found that the particular substances used for the secondary spark terminals had a large effect upon the charac- teiistics of the photographs. We tried spark terminals made of a number of different metals — tin, aluminium, magnesium, fuse-metal, &c. — and finally adopted cadmium as productive of the best sparks. In the case of cadmium the characteristics described are much less marked, and we have succeeded even in producing a few sparks in which no difference in blackness could be detected between one dot and the next. The photo- graphs from cadmium terminals, too, are far more distinct and far more easily measured than those from terminals of any other metal that we tried.

<'An interesting question arose here as to whether the distance between two successive dots would depend upon the period of oscillation of the primary circuit if the secondary were unaltered. To test this point the circuits were brought into resonance, and a photograph taken. The self-induction of the primary circuit was increased by about 20 per cent, of its value, and a second photograph taken. In the first case the distances between successive dots were all within 2 or 8 per cent, of the average obtained by measuring over several dots and dividing by the number of intervening spaces; whereas in the second case the measurements of some of the single spaces were from 8 to 12 per cent, greater than before, the average from long measurements being the same. This indicates that the vibrations of the secondary circuit are not necessarily perfectly regular, and at a distance apart fixed by the character of the circuit, but are to be looked upon as a series of pulses started travelling along the circuit and keeping at a distance from each other that is determined by the exciter. Owing to the fact that the damping of the primary is much greater than that of the secondary, the seventh and eighth pulses started are too weak to obliterate the first and second, which have travelled the length of the

DYKAmCAL TBEOBT OF IKDITCTION. 511

cirotdt and back. We should expect from this that the bolometer throws, which measure the average length of the wave, would not indicate a shifting of the node when the circuits are thrown slightly out of resonance, but that the minimum throws would be greater than when the circuits are exactly in resonance. This, as is well known, is what happens. '*The improved sparks which the new arrangement of apparatus and the use of cadmium as material for the spark terminals have enabled us to produce, have brought to light another interesting fact, namely, that even when the best resonance is obtained and the most regular wave formation is excited, the distances between the first three or four dots are slightly greater than the distances between three or four dots taken farther down the spark. The explanation we offer for this is the following, and it applies as a criticism to all cases in which waves are excited in a circuit by a neighbouring circuit possessing a much larger damping factor: The fact that the secondary waves last longer than the primary oscillations means that the last times that the waves travel over the circuit they do so under different end conditions from the first few times. The capacity of the secondary plates is slightly less after the primary spark has stopped than it was before, and therefore the length of the wires equivalent to the secondary plates is slightly less, and it takes a shorter time for the waves to travel along the circuit and back. Hence the observed decrease in the distance between the spark points and a certain mixing up of the dots, which occurs after the sixth or seventh oscillation (see Fig. 166). The sixth dot in the figure, apparently following its predecessor after about half an interval, is not a usual characteristic. In the vast majority of sparks the first few dots are far more powerful than those that follow them, and only occasionally do sparks occur that indicate more than five or six good complete oscillations. Hence these first few oscillations have the preponderating influence in fixing the length of the waves as indicated by the bolometer. In examining the sparks, therefore, we measured from the first oscillation as far down the spark as we could without passing over a space where dots were obliterated; and hence in every case we knew the number of dots between the points from which measurements

612 DYNAMICAL TBEOHY OP iKDUCTlOlf.

were taken, and did not have to assume that good oecillations had occurred without affecting the plate.

** The following table, containing the results of our meaeure- ments with the improved apparatus, explains itself. The distance from the mirror to the photographic plate was 302om« in each case : —

Number of revolutions of

Distance be- tween successive points on plate.

Centimetre.

Time of oscillation.

Length of wave.

Velocity of wave.

mirror per sec.

Seconds.

Ceniim.

Centim. per sec.

70-8

005028

1-871 X 10'

5,670

3 030xl0>*

737

005247

1-876x10^

5,670

3022xl0>»

75-2

0-05536

1-940x107

5,670

2-923 xlO«»

69-5

005002

1-897x10'

5,690

3-00OxlO»»

68 9

004900

1-874 X 10'

5,690

3 036xl0»»

690

0-04974

1-899 X 10'

5,690

2-996 xlO»»

71-2

0-05076

1-878x107

5,660

3 014xl0«»

Average Value of Velocity 3-003 x 10"

** With the exception of three preliminary trials, which gave values differing from the mean by 10 per cent, or by 12 per cent., these are the only determinations we have made. In some cases the waves in the circuit were just as good with the spark-gap as without it. In others there was a decided wave formation when sparks occurred, but the node was not quite 80 well marked. For this reason, and since it did not appear to make any difference in their length, the waves usually were measured without the spark-gap. As the sparks were quite regular, the difference in the bolometer readings must have been due to Faraday tubes that were reflected from the spark-gap without forming a spark and reversing themselves. The variation in the number of revolutions of the mirror per second is due to the fact that different cells were used to drive the motor on different occasions."

As an example of the data taken to ascertain the position of the node the authors give the following table. The top line contains the distances of the bolometer terminals from a pair of arbitrary fixed points on the circuit : —

"Distances from fixed points 20cm. 40cm. 60cm.

r4-3

4-5

(4-5

Bolometer deflections .

4-0 4-1 4-0

4-3 4-4 4-2

Average deflections 4*43

4-03

4-3"

LYNAMIOAL THEORY OF INDUCTION. ftl3