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Lecher Lines: A Translation of the Original Paper by Ernst Lecher

Orignal Lecher Lines schematic

While reading up on Nikola Tesla‘s Hairpin circuit, I constantly came across people saying that Tesla’s circuit was identical to Lecher Lines, invented by the Austrian physicist Ernst Lecher around 1890, which was an apparatus used to measure the wavelength of high frequency electric waves by creating standing waves on two parallel wires, and then measuring the distance between the antinodes. However, apart from a Wikipedia article and some obscure blog posts, there was not a lot of information available on Lecher Lines, how to use them, and the values of the circuit components. That’s why I decided to look up the original Lecher Lines paper, written by its inventor, Ernst Lecher, titled  Eine Studie über electrische Resonanzerscheinungen 1.

Yes, the paper is written in German. Old, technical German to be precise. Despite this major language barrier, I decided that in order to perform a proper analysis of the Hairpin circuit, a thorough understanding of Lecher Lines was required first, and so I set out to translate all 21 pages to English. This took me several weeks of painstaking work, and since I’m not a native German speaker, the translation is far from perfect, but at least it offers the average reader valuable insight into the construction and workings of Lecher Lines, directly from the mouth of its inventor. If a paragraph seems strangely formulated, it’s probably a combination of 1890 German, and me trying to stay as close as possible to the original sentence structure. Now, without further ado, the original paper in English.

A Study of Electrical Resonance Phenomena; by Ernst Lecher.

The following paper contains the description and research of a new method, to observe and measure electric waves within wires with help of the Resonance studied by Hertz. The work lies entirely within the areas of this extensive territory, which appeared barely accessible before the appearance of Hertz. I have always found the observations of Hertz confirmed; in an important point, however, I got a different result: I found the speed of electricity in wires, for which Hertz indicates 200,000 km/s, to be almost exactly the speed of light, as Maxwell and all other theories demand. Why my results differ from those of Hertz, I cannot say. A possible source of error with Hertz, which I first wanted to use as an explanation of this deviation, proved to be too small on closer inspection. But since my method is very simple and straightforward and at the same time immensely easy (even in the form of a lecture) to perform, I hold my value to be not just theoretically, but also experimentally more likely.

The Experiment in its simplest Form

A and A’ are square sheet metal plates with 40cm sides; they are connected by means of a 100 cm long wire segment, which is cut in the middle and at F two brass balls of 3 cm in diameter are added (in Fig. 1, only the cross-section of the square plates is drawn). The two brass balls are at a distance of 0,75 cm from each other and are connected using thin wires to the poles of a very strong inductor, whose coil has a length of 35 cm and a diameter of 18 cm; the inductor is fed by four powerful accumulators [batteries], and in some cases by a dynamo.

Orignal Lecher Lines schematic
Figure 1. Lecher Lines experiment in its simplest form

A Foucault mercury interrupter serves as electric break. Across from the plates A and A’ are two plates B and B’ of identical size at a distance of around 4 cm. From these plates B, B’ run two wires against s and s’ and from there parallel until t and t’. The distance between the parallel wires (s to s’) is 10-50 cm; the length st (s’ t’), on the other hand, should be at least 400 cm. The diameter of these parallel wires is here and for all experiments in this publication 1 mm. For this first experiment we assume the length [of the wire] to be about 600 cm (drawn too short in the figure ), and the distance of the parallel wires from each other 30 cm. At the end of the parallel wires (t and t’) a cord is connected to each, which extends the length of the wires by about 100 cm, and allows for a gentle and comfortable tensioning thereof.

This part of my arrangement is similar to that stated in the beautiful work of Hertz2, and was also used in the experiments of Sarasin and De la Rive3.

Over the wire ends t and t’ I now lay an exhausted glass tube without electrodes g g’, ideally filled with nitrogen and a trace of turpentine vapor; this glass tube starts to light up due to the electrical vibrations in the wires.

Now, while the tube is shining brightly, place a crossbar over the parallel wires, so it will connect them together metallically (the direction of the wire hanger is perpendicular to the wires and through the dotted line x x’ shown in Fig. 1); then the light of the tube disappears for the moment. Now move the crossbar x x’ along the wires, until one arrives at a certain, strangely sharply defined place, where the tube suddenly lights up again 1). The search for these places and the circumstances surrounding their position constitute the main content of this work.

At the above length of the wires of about 600 cm and a mutual distance of about 30 cm, the place at which, as the connecting bracket slides along the parallel wires, the tube suddenly lights up at the end, is approximately 100 cm from s and s ‘, at approximately the area which is designated in Fig. 1 with x and x’.

Why are the tubes only glowing when bridging this spot?

The first idea in answering this question seems to be that at the points x and x’ there are antinodes of the electric oscillations. In any case, the oscillation in the wire piece Bst is such that, at the end t, alternating large potential fluctuations occur; it would correspond in an acoustic analogy to the closed end of a whistle. The electricity – air – pushes towards and away from this end, so that we have what we call the nodal point in an acoustic motion. Since we also have such alternating compressions and rarefactions in plate B, the idea would be most likely that while the electric current oscillates between B and t, somewhere in the middle must be a place, where the potential during the current flow is always zero; this corresponds to the antinode of a pipe, where the air oscillates back and forth without any compression and rarefaction. In the second wire B’n’t ‘, the sign of the potential, as well as that of the movement, is always the opposite. If, therefore, I connect the (electrical) center of the two wires together, then according to this conception, no movement would take place in the crossbar, and the latter would not disturb the electrical phenomenon at this point, so that at the end, near the tube, violent potential vibrations take place, which make the tube glow4.

These explanations, though not obvious, do not fully explain the nature of the experiment. Rather, we are dealing with a resonance phenomenon. If I put the crossbar over XX ‘, then first of all a main oscillation arises, which, starting from B, goes over sxx’s’ to B’. The ear already recognizes the change of the main vibration from the crackling of the spark. This first oscillation induces through induction a second oscillation, which is excited in xx’ and propagates from t’ over x’x to t. That this view is the right one will be clear from many examples of later measurements, but I will give you a few related experiments here.

Lecher Line cross wire
Figure 2. Lecher Line connecting wire with wooden handle

The connecting wire xx’ must have a certain length; say, according to the above dimensions, 42 cm. (Fig. 2 shows the crossbar with its wooden handles in 1/10 of its natural size.) If you take a long wire as a crossbar, then xx’ moves from or to s’ depending on the circumstances. The main vibration has at first the wire length R available plus the bridge, which we want to neglect for the sake of brevity; the resonating wavelengths would have a smaller length r. Now suppose the bridge is of greater length l, so that the former relation R:r in (R + l):(r + l) shifts, hence the displacement of xx’.

On the other hand, the whole phenomenon is much less pronounced in bridging the parallel wires by means of a longer connection than previously. An exhausted tube has the disagreeableness of reacting to the smallest electric forces, and now that the distance xx’, where the induction takes place, is much greater than before, the resonance is much stronger, so that even with a less good match of the two vibrations, there is still energy to excite the light phenomenon. The tube always remains bright. If on the other hand the wire bow is made very small, if one bends the two wires together in the appropriate place xx’ for actual contact, the tube no longer shines. The distance xx ‘, through whose induction the energy for the unclosed circle txx’t’ is delivered, is now too small, and thereby the phenomenon is disturbed, in the opposite sense as before, where the crossbar was too long. The tube always remains dark.

Lecher Lines with crossbar split lengthwise
Figure 3. Lecher Lines with crossbar split lengthwise

Further proof that we are dealing with a resonance movement, may be the following: I make the crossbar so that is consists of two parallel wires that are isolated from each other, put it exactly in the place xx’, where the tube lights up brightly, fix it at this point and split the bracket xx’ in half over its full length by cutting the main wires. Now we have metallically closed the first circuit Bsxx’s’B’, as well as, completely isolated from the former, the secondary conductor txx’t’. After this lengthwise split of xx’ the tube lights up as it used to (Fig. 3).

Now the wires are tensed just like before, a simple wire of suitable length placed across diagonally and pushed back and forth until the tube at the end lights up brightly. If we now want to prove for the sake of thoroughness that the tube responds to even the smallest potential vibrations, then we can move the tube almost up to xx’, without its light changing in any way.

The bar is in its correct position, the tube lies somewhere in the middle of xx’ and tt’, and I now cut away 100 cm from the wire ends. This makes the secondary circuit smaller, the resonance now stops: the tube is dark. If I now slide bar xx’ against ss’, reducing the primary vibration while at the same time lengthening the secondary one, and when I move xx’ back 50 cm, resonance occurs again: the tube lights up anew. This experiment and those to be described hereafter are particularly suitable for lecture purposes.

Again now, the bar positioned in the right place and the tube lights up. If I now lay a tinfoil sheet over the wire ends tt’, the period of oscillation becomes slower by introducing this capacity at the end, the tube stops shining momentarily, and I have to move bar xx’ against tt’, to make it light up brightly again. On the other hand, one can touch the bar, the antinode, or connect a capacity to it, without disturbing the phenomenon; but if I touch the line in another place, the light goes out immediately.

One can already see from this simple experiment, that this method is suitable, to compare capacities (and dielectric constants) with such rapid oscillations, and that one can also check the equivalence of the self-potentials and the capacitances in the known formula for the period of vibration of electric oscillations.

A proof of that, that one is really dealing with electrical oscillations here, can be provided in the same way Hertz has done. If one places the balls of the spark gap so far apart that the oscillations in the spark gap stop — one can also place the balls so far apart that no spark jumps at all — then the tube always stays dark, even though the full tension of the Ruhmkorff [induction coil] is present undiminished at the wire ends.

Description of some important secondary conditions

To describe my method completely, I want to make special mention of certain secondary conditions, which are important to the success of the experiment.

Instead of the initially described tube, one can also place a Geissler tube over the ends t and t’ 5.

However, this was carefully arranged so that the electrodes of the Geissler tubes did not make any metallic connection with the wire ends t and t ‘, but they were rather a few centimeters away from them. There should namely be no electrical current conveyed between the two wires by placing over them the Geissler tube or the glass tube mentioned earlier. Among a large number of Geissler tubes, which vary in content and pressure, you will always find a few suitable ones. I did not even have to touch the exhausted tube I used to the wires; even with 10 cm distance it still lit up, as soon as electrical oscillations in the wires took place. (With direct induction through the primary vibration I could go to 1 m distance.) Thus I could easily convince myself that, by laying the tube directly over it, the antinodes lie in the same place as when the tube does not touch the wires, that we really have an indicator for the electric oscillations, without them being noticeably disturbed by it.

In lecture experiments, however, where the primary concern is bright lights, or with longer wire lengths, where the vibration is already very weak, it is recommended to bend a small ring of wire or a strip of aluminum foil around the Gassiot tubes at the point where the exhausted tube rests on the wires. Yes, even a direct turn on the Geissler tube changes the position of the waves only slightly.

As for the primary capacitor A B and A’ B’, their composition is also subject to some conditions. Their capacitance should be as large as possible, so that the vibrations in the wires are strong. But if one makes the capacitance too great, the whole phenomenon ceases. In later measurements we will have the opportunity to see that the capacitance of the condenser can not exceed a maximum value for certain wire lengths, since that really, as the theory demands, stops the oscillation of the electricity. With an increase of the condensers, the phenomenon becomes more blurry and capricious, the otherwise uniformly lit tube now only lights up once every few seconds, to finally stay completely dark, so that one has not to do with a sudden failure, but with a continuous blurring of the phenomenon.

Furthermore, for the sake of convenience, I have tried to replace the air condenser with a glass condenser of equal capacitance, but smaller size. Here another disturbing inconvenience emerges: the density of the electricity is too great. I have used glass of 22 mm thick and proportionately glued sheets of aluminum foil over it, and embedded the whole in paraffin or shellac, and yet the radiation of the electricity on the edge of the disc was so great that you could see the light through the paraffin.

To prevent the bothersome polishing of the balls, between which the sparks jump, I made these balls eccentric, so that new parts of the ball were always placed in the spark path by turning the balls on their longitudinal axis, without changing the spark distance. The length of the spark has no influence, as long as it doesn’t become too large or too small; in the former case the oscillation stops completely, in the latter case the potential fluctuation becomes too small.

I further found that the position of the antinodes depends on the distance at which the two parallel wires are strung from each other. On the other hand, I could hardly observe an influence of the surrounding objects, the walls, gas arms etc. on the duration of oscillation. Nevertheless, I avoided changing the location of any larger conductors near the wires during the experiment.

It was also shown that in test series which are to be compared with each other, the lead wire from the inductor must always be supplied at the same point of the primary vibration; it is therefore not unimportant whether the supply line ends more near the electrodes, in the middle of the line or on the condenser. The shape of the lead wire is also of influence on the position of the antinodes. In any case, the lead wire vibrates more or less. I do not want to share the measurements here, as some of the conclusions, which I will show experimentally in the course of the paper, support this claim.

After all these conditions had been tried, I proceeded to the following arrangement.

Wavelength in different lengths of wire

Fig. 4 shows the arrangement of the experiment. The primary oscillation takes place between the vertically standing plates A and A’ (squares with 40 cm sides) by means of spark F.

Lecher Lines experimental arrangement to measure wavelengths
Figure 4. Lecher Lines experimental arrangement to measure wavelengths

The distance between A and A’ is 66 cm. At 6 cm distance from plates A and A’ stand the secondary plates B and B’; moreover, it is between plates A and B that a thin piece of paraffin paper was inserted (not drawn in Fig. 4), to make any overflow of electricity impossible. The wire length from the corner of the plate B to s is 10 cm, the current path from A to F 100 cm.

The supply of electricity is done directly next to the [electrode] balls. In the experiments now to be described, the entire arrangement described remained unchanged, while from s and s’ (ss’ = 31 cm) the two wires were led parallel in the horizontal direction and the length of these wires (st and s’t’) could be varied from 300 to 3500 cm. Then the bridge drawn in Fig. 2 (length = 42 cm) is moved and the place where the tube at the end of the wires lights up, noted.

The following table contains some of these observations, and I indeed limit myself to a length of 2000 cm, because the results of the greater distances do not seem to give me anything fundamentally new and appear to be less accurate.

Table showing wire length and antinode distances
Table 1. Table showing wire length and antinode distances

** Länge des Drahtes in cm = Wire length in cm
** Entfernung der Bäuche von ss’ in cm = Distance of antinodes from ss’ in cm

Next to the figures for the antinodes, g means that the phenomenon appears clear, the light of the tubes is bright; gg means very good, s bad, ss very bad.

These numbers seem to be scattered arbitrarily over the wire lengths, especially at further distances. The following experiment gives an explanation for this.

If, while the first bar remains in its place, we move a second identical bar along the wires, we find again places where the tube lights up, but always only in those places where the first attempt with one bar displayed antinodes. If these two bars are in their right place, you can also add on a third, and so on. The numbers which are underlined once, respectively twice, in the above table, indicate that they belong together in this way.

If, for example, we place a bar 22 [cm] on a 1632 [cm] long wire, the tube will light up. We let the bar lie undisturbed and take a second one, and when we move this, the tube lights up at 631 and at 1232, but not at 145, 1151 or in other places. If we now place this second bar (the first remains at 22) on 631 and probe the wire with a third bar, we have to go exactly to 1232, so that the tube lights up again.

Likewise, with the same wire length of 1632, we can, on the other hand, bridge 145 and 1151 simultaneously in a similar fashion.

Thus, at this wire length, of the five nodal points, 22, 631, and 1232, or 145 and 1151 belong together, which if simultaneously bridged, light up together.

These experiments make a self-evident explanation obvious. The electricity in a wire of definite length oscillates in a similar way to the air in a pipe. Let us imagine a long tube filled with air and at the beginning of the tube a device similar to that of a reed pipe. A short distance behind this pipe, the tube is closed by a longitudinally displaceable, rather rigid transverse [cross] membrane. The period of oscillation of the pipe-mouth determines the pitch, but is influenced to a certain extent by the oscillation of the adjacent air column extending to the membrane. If I move the membrane along the tube here, the end of the tube will in certain cases resonate, but not in others, and the phenomenon will appear to be more complex, because by moving the membrane, we not just change the relationship between the two tube parts, but at the same time – to a certain extent – change the period of oscillation of the excitatory reed.

Fig. 5 presents the rows according to the different wire lengths of the table on p. 10. The wire lengths are recorded so that their ends form a straight line. At the length of 348 cm and 451 cm, the antinode a lies in the electrical middle between the wire ends and B B’. At 648 and 870 we have to move this point further; the primary vibration has thus also been increased. Towards the end of the wires are two more indistinct points c and b, the meaning of which only becomes clear for longer lengths, say, for example, 1435.

Visual representation of wire lengths and antinode locations in Lecher Lines
Figure 5. Visual representation of wire lengths and antinode locations in Lecher Lines

Lets first consider the middle antinode a.

If we make the wire longer and longer, we have to move out completely symmetrical with a, as the drawing shows, which means that because the secondary wire length has been increased, we also have to increase the primary in order to achieve resonance. At some point, however, the primary vibration can not be further increased by the attached wire (just as in the above acoustic example, the vibration of the pipe reed is stronger than that of the resonating air mass). We see this for the first time with a wire length of 1435, although the first signs occur much earlier. From the antinode a we do not have, as in the past, half a wavelength to the end, but three halfs, a new antinode has formed between a and the end, as well, of course, on the other side between a and B, and we can therefore now place three bars across. One curve shows the relevant waveform; it cuts the horizontal in three points, the antinodes, those points that can be bridged simultaneously, c, a and b. However, these lengths, 1435 and the neighboring ones, can still swing in such a way that at d and e antinodes develop.6

From these experiments it can also be seen how small the influence of the surrounding objects is. The numbers 0, 591, 1166 for the length 1435 give the wavelengths 591 and 575, the numbers 22, 631, 1232 for the length 1632 give the wavelengths 609 and 601; finally, the numbers 40, 756 and 1469 for the length 1801 give the wavelengths 716 and 713 etcetera, from which it can be seen that the wavelengths on the right and on the left of a, except for a few per cent, are equal to each other, although the first half of the wire moved quite tightly through a doorway, while the second half passed freely through a large hall. Only if there were metallic conductors in the vicinity, which approximately resonated with the oscillations and with it absorbed a considerable part of the energy of the original vibration, only then an influence on the position of the antinodes would be found.

The fact that this is so, results from the whole series of experiments, and this result does not seem unimportant to me. The oscillation of a primary vibration is not unchangeable under all circumstances. In the experiments just described, which, because a large portion of the energy of the primary vibration is used for the secondary oscillation, are particularly suited for this, we obtain all possible wavelengths within certain limits with one and the same primary oscillation.

Capacities at the wire ends

Both wires each had a wire length of 1122 cm; the primary oscillation and the main condensers A B were exactly like before. The end of the wires were connected by a soft, 69,7 cm long wire to a circular capacitor plate ( R = 8,96 cm ).

Condenser plate distance versus antinode location
Table 2. Condenser plate distance versus antinode location

** Entfernung der Condensatorplatten von einander in cm = Distance of the condenser plates from each other in cm
** Entfernung der Schwingungsbäuche von ss’ in cm = Distance of the antinodes from ss’ in cm
** Sehr schwach nichts zu sehen = Very weak, nothing to see

In this table can be seen, that an increase of the capacitance at the end increases the period of oscillation; I have to move back with the bar. Further, it can be seen that this increase, measured absolutely by the shift in centimeters, outputs much less for the shorter oscillation period. The numbers increase from 1020 to 1081 with 61, while the corresponding numbers 561 and 659 differ by 98. This is a consequence of the equivalence of self-potential and capacity. With an increase in capacitance, if the oscillation period is to remain the same, the longer wire must be reduced much more than the shorter one.

It is further shown, that by increasing the capacitance, the oscillation, as indicated at the beginning, might cease altogether, and indeed only the rapid, because only for this is then the capacitance too large in relation to the self-potential. If the failure were a more precise one, one could calculate the enormous resistance of the copper wire to such rapid oscillations.

Finally, I would like to point out that the same nodal point can be achieved both by changing the length of the wire and the capacitance, and thus proving the equivalence of self-potential and capacitance. The above measurements are, due to not sufficiently accurate parallel positioning of the capacitor plates, probably hardly usable for a more accurate calculation.

Likewise, the same antinode can be obtained by pulling apart the capacitor plates and inserting a dielectric. I will refer in a forthcoming paper to a determination of dielectric constants in this way.7

Speed of electricity in wires

I believe that the method I have described allows for an objection free measurement of the rate of propagation of an electric wave in the wire. For this purpose, the capacitor plates at the end of the wires were brought to a distance of 0.990 cm. Since the plates, although they were mounted especially for this experiment by the mechanic, were not exactly parallel, they were first screwed together by means of a micrometer screw until their contact was shown by the conduction of an electric auxiliary current, and then, with a very flat wedge, the non-superimposed points were measured from the side. The above number is already the mean of these measurements.) The two straight wires had, as before, a length of 1122 cm; from their ends went, as before, each a loosely stretched wire of 69.7 cm length to the center of the two condenser plates O O’. The glass tube g g’ lies over this condenser O O’.

The two long wires were now bridged in two places, d and c, at the same time, and d and c carefully chosen so that the tube at the end lit up as nicely as possible. d is located 121.5 cm from the beginning of ss’, c 1061.1 cm (The average of 20 experiments).

We have now sharply defined two oscillations: half a vibration goes back and forth between the two capacitor plates over c c ‘, while the corresponding whole oscillation fills the closed current path of the distance dcc’d ‘ (Fig. 6). Thus, half the wavelength of the whole oscillation is equal to cd + cross bridge = 982 cm, because the crossbar = 42.0 cm.

Lecher Lines with condenser added to the end
Figure 6. Lecher Lines with condenser added to the end

The period of oscillation, however, can be calculated from the second oscillation according to the formula \pi\sqrt{PC}/v, where P is the self-potential, C the capacity, and v the speed of light respective to the conversion number of the electromagnetic in the electrostatic measuring system, since I express P and C in these two measures. For the self potential P we use the simple Neumann formula 2L(ln (4L/d)-0,75) and results in P = 5248 cm, if we insert here for the length L of the current path:

2 x (distance of antinode c from the end + condenser feed wire) + cross bridge, that is 303,2 cm, and for the diameter of the wired d = 0,1 cm.

The capacity is calculated to be 20 cm according to the simple formula R^2/4\delta; would I use Kirchhoff’s formula, it would be about 22 (R = 8,96 cm und /delta = 0,990 cm). Since the current path is relatively short and does not actually end in the middle of the circular plates, I believe that the condenser is not fully exploited, so that you could cut out a circular hole from the center of the plate without changing the effect significantly. Perhaps one could see through such an experiment, the extent to which the capacitor plates fulfill their theoretical task of forming the ends of the current fluctuation. I therefore believe that the number 20 is still too high, nevertheless I want to use this number for lack of the right one. But also the number 22, which according to the measurements of Klemencic 8 might still be approximately correct at the applied distance, would not significantly alter the final result.

Thus we obtain:

\pi\sqrt{PC} =\pi\sqrt{5248,20} = 1017

This is the distance that light travels during the time of one oscillation. The corresponding wavelength, 982 cm, we found above.

Both these numbers, 1017 and 982, are the same. It follows from this that the electric oscillation propagates not only in the air at the speed of light, as shown so beautifully and convincingly by Hertz, but also in the wire 9. On the other hand, this theoretically very probable equality also allows us to draw conclusions about the certain approximate correctness of the oscillation formula used above for electric oscillations and the formula for self-potential, the probability of which is already assured by the measurements of Hertz.

My method, which eliminates all disturbances of the oscillation by the spark [Hertz used a spark gap in both transmitter and receiver, thereby disturbing the wave], is so simple and clear that I believe in its correctness, without knowing why Hertz received other values. A suspicion in this regard, which forced itself on me upon running my experiments, turned out to be unfounded, as the next section will show.

Studying a possible source of error with Hertz

Since in all the experiments described so far, the period of oscillation of the primary oscillation was changed to a certain extent by the resonance of the other systems, whereby, however, the energy taken from the primary oscillation was very great, the question is not without interest in how far such a source of error occurs in the Hertzian experiments.

Lecher Lines with extra wire added to the end
Figure 7. Lecher Lines with extra wire added to the end

For this purpose, the two wires (length 1124cm), as before, are connected with the main system. At the end of each of the wires t and t’ I hang a vertical floating metal plate (square with 40 cm sides). The plate at t stands at 5 cm distance from a second one of equal size. (Fig 7. The primary excitation apparatus that still connects to ss’ is omitted. Again, the parallel wires are drawn too short.) From the center of the latter plate, a different long wire y-y’ continues horizontally, but perpendicular to the main wires. In this wire y-y’, exactly those waves are now generated which Hertz observed. The glass tube g g’ lies before the condenser plates. If I bridge a or c, then by shifting the antinodes a and c (a, c and d have the meaning from Fig. 5), I can easily study the influence of the wire y y ‘. The length of this wire is varied from 0 – 1060 cm. Is this wire 0, then d lies at 83, a at 487, and c at 919 cm. The table gives the displacement of nodes a and c from their original position in centimeters.

Extra wire length versus displacement of antinodes
Table 3. Extra wire length versus displacement of antinodes

** Verschiebung in cm des Bauches = Shift of the antinodes in cm
** Länge des Nebendrahtes y-y’ = Length of the extra wire
** ohne Bauch = No antinode

Fig. 8 shows, in a clearer way than the table can, the trend. In the same [figure], the horizontal represents the wire length y-y’, the vertical the shift of the antinodes c or a, and when positive, a shift towards t t ‘, and when negative, towards the starting point of the parallel wires.

Visual represenation of extra wire length versus antinode displacement
Figure 8. Visual represenation of extra wire length versus antinode displacement

If I make the wire yy’ longer and longer, c moves more towards the end, the light phenomenon becomes weaker and finally stops completely, when yy’ is 400 cm long. If the extra wire becomes longer, the tube starts to glow again at 600 cm; the antinode is now further away from the end, moves slowly against the original position and then rises again. Exactly the same happens with the antinode a; however, the changes are greater, and the disappearance and recurrence occur at greater lengths of the extra wire.

First let’s take a closer look at antinode c. It moves when I make the extra wire about 200 cm towards the end, that is, I have to increase the main vibration to achieve resonance; thus, the period of oscillation has been increased by the attachment of this wire, and the more so, the longer the wire is. When, however, the extra wire yy’ is approximately equal to 1/4th wavelength, then this second wire no longer seems in unison and increases to vibrate with the main vibration; it seems rather to produce a vibration in the wire which interferes with the main oscillation, hence the absence of the antinodes. If the wire becomes even longer, then this, in and of itself, produces a faster secondary vibration, as indicated by the recession of the antinodes, accelerating to the main vibration, but less and less, the longer the wire becomes. Is y-y’ (see Fig. 8) around 830 cm long, then the influence of the wire has completely disappeared, in order to delay the main vibration at an even greater length, where the secondary vibration is slowing down again. As a measure of the period of oscillation, we can take the wavelength from d to c. Is y y’ equal to zero, then d lies at 83 cm. It is thus:

c – d + crossbar = 919 – 83 + 42 = 878

equal to half the wavelength, while the length of the secondary wire y y’ had to be 830 in order to obtain a match of the new and old antinode. The difference between 878 and 830 is probably due in large part to the condenser at y.

Exactly the same goes for antinode a. As far as the measurements are concerned, we also have a delay first; when about ¼ wavelength, which is larger here than previously, takes place in y y’, suspension and ultimately acceleration of the main vibration occurs.

It is thus proved that in the Hertzian arrangement the main vibration can possibly be disturbed. However, it can easily be calculated from our experiments that this disturbance is comparatively small. The greatest disturbance of antinode c is 30 cm at y-y’ = 340 cm. Point d then lies at 88 cm; the half wavelength is again easy to find, like above:

c – d + crossbar = (919 + 30) – 88 + 42 = 903

The half wavelength changes from 878 to 903, which gives the maximum of the possible source of error.

Likewise, in the vicinity of the parallel conducting wires, I have set up resonators of the same and different periods of vibration at very small distances, and here, too, in the worst case, the changes in the original mode were only a few per cent.

Physikal. Inst. der Univ. Wien. April 1890.

Closing remarks

I sincerely hope that reading this article by Ernst Lecher has given you some food for thought. If you wish to receive a PDF version of both my English translation and the original German paper in your inbox, then fill in your name and email in the form below.


  1. Lecher, E. (1890). Eine Studie über electrische Resonanzerscheinungen. Retrieved from:
  2. Hertz, Wied. Ann. 34.p. 551. 1888
  3. Sarasinu.De la Rive, Arch. des sciences phys. et natur. GenBve. 28. p. 113. 1890
  4. Instead of a glass tube, it would also be possible to use a spark in a very analogous manner, which is obtained between t and t’ by connecting a spark micrometer; however, the measurements seem more accurate, if equalization of the potentials by the conductive spark is avoided. A similar arrangement in some respects has been mentioned by J.J. Thomson. Proc. of Roy. SOC.of Lond. 46. p. 11. 1889.
  5. The usage of Geissler tubes in Hertz’s experiments was first mentioned by Dragoumis (Nat. 39. p. 548. 1889). I have likewise shown most of Hertz’s experiments in a similar way, as described by Dragoumis, with the aid of Geissler tubes in the general assembly of the chemisch-physikalischen Gesellschaft on 12 December 1889 in Vienna, where I, however, so as not to be disturbed by dissipating the electricity, I availed myself for the most part of tubes which had no electrodes. That tubes like this can be lit up through electric induction, is a well known fact, discovered only recently by Hrn. James Moser (Wien. Ber. 99. p. 5. 1890). This light arises, as Worthington (Phil. Mag. (5) 19. p. 218. 1885) already speculated, probably not from current, but it rather corresponds to the oscillation of induction in the tube.
    Only in one case did Geissler’s tubes fail me on replication of Hertz’s experiments. In the well-known experiment with the parabolic concave mirror, I wanted to make the little spark behind the second mirror visible to a larger group of spectators, and first tried various electrodes, and obtained the best results if I let the spark jump between a mercury head and a copper tip. Even better is the spark between a mercury head and zinc, but unfortunately it is only too easily for a strong amalgamation and breaking off of the tip to occur. When I removed the air around the little spark, which passed between mercury and copper, by pumping it out, the spark did not diminish its brightness or shape, so that it could not even be decided with the naked eye whether the discharge was taking place in a vacuum or under normal atmospheric pressure.
    I may also mention that, especially at close distances, some of the sparks produced by Hertz in his experiments in secondary conductors, cause explosive gas to explode, by which means it is equally possible to make the presence of sparks noticeable to a larger auditorium.
  6. I do not consider the similar method, which took place after the first publication of this essay, the seemingly simultaneous work of E. Waitz, to be objection free. For example, two adjacent layers of the bridge, ignoring the other wire lengths, would yield 22 cm at the top and the like. Also, the location of the spark as an indicator is not chosen by luck. Waitz uses the term vibrational nodes differently than I did above according to the example of Hertz.
  7. Vorgelegt in der Sitzung der Wieuer Acad. aui 16. Mei 1890. Ann. d. Phys.u.Chem. N.F.XLI.
  8. Klemencic, Wien. Ber. 86. p. 1190. 1882.
  9. The same result was also obtained by J.J. Thomson (lc); but it seems to me that his whole arrangement is not free of objection and that the margin of error (2 feet by 10 meters) is too great for his measurement to be used at all for the settlement of the above question.