and hence, if the value of the current resulting is known, we have the capacity of the aerial or conductor expressed in microfarads, given by the formula
A series of experiments made on this plan have revealed the fact that if a number of vertical insulated wires are hung up in the air and rather near together, the electrical capacity of the whole of the wires in parallel is not nearly equal to the sum of their individual capacities. If a number of parallel insulated wires are separated by a distance equal to about 3 per cent. of their length, the capacity of the whole lot together varies roughly as the square root of their number. Thus, if we call the capacity of one vertical wire in free space unity, then the capacity of four wires placed rather near together will only be about twice that of one wire, and that of twenty-five wires will only be about five times one wire.
This approximate rule has been confirmed by experiments made with long wires one hundred or two hundred feet in length in the open air. Hence it points to the fact that the ordinary plan of endeavouring to obtain a large capacity by putting several wires in parallel and not very far apart is very uneconomical in material. The diagrams in Fig. 8 show the various methods which have been employed by Mr. Marconi and others in the construction of such multiple wire aerials. If, for instance, we put four insulated stranded 7/22 wires each 100 feet long, about six feet apart, all being held in a vertical position, the capacity of the four together is not much more than twice that of a single wire. In the same manner, if we arrange 150 similar wires, each 100 feet long, in the form of a conical aerial, the wires being distributed at the top round a circle 100 feet in diameter, the whole group will not have much more than twelve times the capacity of one single wire, although it weighs 150 times as much.
The author has designed an aerial in which the wires, all of equal length, are arranged sufficiently far apart not to reduce each other's capacity.
As a rough guide in practice, it may be borne in mind that a wire about one tenth of an inch in diameter and one hundred feet long, held vertical and insulated, with its bottom end about six feet from the ground, has a capacity of 0·0002 of a microfarad, if no other earthed vertical conductors are very near it. The moral of all this is that the amount of electric energy which can be stored up in a simple Marconi aerial is very limited, and is not much more than one-tenth of a joule or one-fourteenth of a foot-pound, per hundred feet of 7/22 wire. The astonishing thing is that with so little storage of energy it should be possible to transmit intelligence to a distance of a hundred miles without connecting wires.
One consequence, however, of the small amount of energy which can be accumulated in a simple Marconi aerial is that this energy is almost entirely radiated in one oscillation or wave. Hence, strictly speaking, a simple aerial of this type does not create a train of waves in the ether, but probably at most a single impulse or two.
We shall later on consider some consequences which follow from this fact. Meanwhile, it may be explained that there are methods by which not only a much larger amount of energy can be accumulated in connection with an aerial, but more sustained oscillations created than by the original Marconi method. One of these methods originated with Professor Braun, of Strasburg, and a modification was first described by Mr. Marconi in a lecture before the Society of Arts of London.[7] In this method the charge in the aerial is not created by the direct application to it of the secondary electromotive force of an induction coil, but by means of an induced electromotive force created in the aerial by an oscillation transformer. The method due to Professor Braun is as follows: A condenser or Leyden jar has one terminal, say, its inside, connected to one spark ball of an induction coil. The other spark ball is connected to the outside of the Leyden jar or condenser through the primary coil of a transformer of a particular kind, called an oscillation transformer (see Fig. 9). The spark balls are brought within a few millimetres of each other. When the coil is set in operation, the jar is charged and discharged through the spark gap, and electrical oscillations are set up in the circuit consisting of the dielectric of the jar, the primary coil of the oscillation transformer and the spark gap. The secondary circuit of this oscillation transformer is connected in between the earth and the insulated aerial wire; hence, when the oscillations take place in the primary circuit, they induce other oscillations in the aerial circuit. But the arrangement is not very effective unless, as is shown by Mr. Marconi, the two circuits of the oscillation transformer are tuned together.
We shall return presently to the consideration of this form of transmitter; meanwhile we may notice that by means of such an arrangement it is possible to create in the aerial a far greater charging electromotive force than would be the case if the aerial were connected directly to one terminal of the secondary circuit of the induction coil, the other terminal being to earth, and the two terminals connected as usual by spark balls. By the inductive arrangement it is possible to create in an aerial electromotive forces which are equivalent to a spark of a foot in length, and when the length of the aerial is also properly proportioned the potential along it will increase all the way up, until at the top or insulated end of the aerial it may reach an amount capable of giving sparks several feet in length. From the remarks already made on the analogy between the closed organ-pipe and the Marconi aerial wire, it will be seen that the wave which is radiated from the aerial must have a wave length four times that of the aerial if the aerial is vibrating in its fundamental manner. It is also possible to create electrical oscillations in a vertical wire which are the harmonics of the fundamental.
All musicians are aware that in the case of an organ-pipe if the pipe is blown gently it sounds a note which is called the fundamental of the pipe. The celebrated mathematician, Daniel Bernouilli, discovered that an organ-pipe can be made to yield a succession of musical notes by properly varying the pressure of the current of air blown into it. If the pipe is an open pipe, and if we call the frequency of the primary note obtained when the pipe is gently blown, unity, then when we blow more strongly the pipe yields notes which are the harmonics of the fundamental one; that is to say, notes which have frequencies represented by the numbers 2, 3, 4, 5, &c. If, however, the pipe is closed at the top, then over-blowing the pipe makes it yield the odd harmonics or the tones which are related to the primary tone in the ratio of 3, 5, 7, &c., to unity. Accordingly, if a stopped pipe gives as its fundamental the note C, its first overtone will be the fifth above the octave or G'.
As already remarked, the aerial wire or radiator as used in Marconi telegraphy may be looked upon as a kind of ether organ-pipe or siren tube, and its electrical phenomena are in every respect similar to the acoustic phenomena of the ordinary closed organ-pipe. When the aerial is sounding its fundamental ether note, the conditions which pertain are that there is a current flowing into the aerial at the lower end, but at that point the variation in potential is very small, whereas at the upper end there is no current, but the variations of potential are very large. Accordingly, we say that at the upper end of the aerial there is an antinode of potential and a node of current, and at the bottom an antinode of current and a node of potential. By altering the frequency of the electrical impulses we can create in the aerial an arrangement of nodes of current or potential corresponding to the overtones of a closed organ-pipe. But whatever may be the arrangement the conditions must always hold that there is a node of current at the upper end and an antidote of current at the lower end. In other words, there are large variations of current at the place where the aerial terminates on the spark-gap and no current at the upper end. The first harmonic is formed where there is a node of potential at one-third of the length of the aerial from the top. In this case we have a node of potential not only at the lower end of the wire, but at two-thirds of the way up. In the same way we can create in the closed organ-pipe, by properly overblowing the pipe, a region about two-thirds of the way up the pipe, where the pressure changes in the air are practically no greater than they are at the mouthpiece. We can make evident visually in a beautiful manner the existence of similar stationary electrical waves in an aerial by means of an ingenious arrangement devised by Dr. Georg Seibt, of Berlin. It consists of a very long silk-covered copper wire, A (see Fig. 10), wound in a close spiral of single layer round a wooden rod six feet long and about two inches in diameter. This rod is insulated, and at the lower end the wire is connected to a Leyden jar circuit, consisting of a Leyden jar or jars and an inductance coil, L, the inductance of which can be varied. Oscillations are set up in this jar circuit by means of an induction-coil discharge, and the lower end of the long spiral wire is attached to one point on the jar circuit. In this manner we can communicate to the bottom end of the long spiral wire a series of electric impulses, the time period of which depends upon the capacity of the jar and the inductance of the discharge circuit. We can, moreover, vary this frequency over wide limits. Parallel to the long spiral wire is suspended another copper wire, E (see Fig. 10), and between this wire and the silk-covered copper wire discharges take place due to the potential difference between each part of the wire and this long aerial wire. If we arrange matters so that the impulses communicated to the bottom end of the long spiral wire correspond to its fundamental note or periodic time, then in a darkened room we shall see a luminous glow or discharge between the vertical wire and the spiral wire, which increases in intensity all the way up to the top of the spiral wire. The luminosity of this brush discharge at any point is evidence of the potential of the spiral wire at that point, and its distribution clearly demonstrates that the difference of potential between the spiral wire and the aerial increases all the way up from the bottom to the top of the spiral wire. In the next place, by making a little adjustment and by varying the inductance of the jar circuit, we can increase the frequency of the impulses which are falling upon the spiral wire; and then it will be noticed that the distribution of the brush discharge or luminosity is altered, and that there is a maximum now at about one-third of the height of the spiral wire, and a dark place at about two-thirds of the height, and another bright place at the top, thus showing that we have a node of potential at about two-thirds the way up the wire (see Fig. 11), and we have therefore set up in the spiral wire electrical oscillations corresponding to the first overtone. It is possible to show in the same way the existence of the second harmonic in the coil, but the luminosity then becomes too faint to be seen at a distance.
An interesting form of aerial devised by Professor Slaby, of Berlin, depends for its action entirely on the fact that the electrical oscillations set up in it which radiate are harmonics of the fundamental tone.
A closed vertical loop, A1A2 (see Fig. 12), is formed by erecting two parallel insulated wires vertically a few feet apart and joining them together at the top. At the bottom these wires are connected, with the secondary terminals of an induction coil, a condenser, C, or Leyden jar, being bridged across the terminals and a pair of spark balls, S, inserted in one side of the loop. It will readily be seen that on setting the coil in action, oscillations will take place in these vertical wires, but that if the oscillations are simply the fundamental note of the system, then at any moment corresponding to a current going up one side of the loop of wire there must be a current coming down the other. Accordingly, an arrangement of this kind, forming what is called a closed circuit, will not radiate or radiates but very feebly. Professor Slaby found, however, that it might be converted into a powerful radiator if we give the two sides of the loop unequal capacity or inductance and at the same time earth one of the lower ends of the loop, as shown in Fig. 13. By this means it is possible to set up in the loop electrical overtones or harmonics of the fundamental oscillation, and if we cause the system to vibrate so as to produce its first odd harmonic, there is a potential node at the lower end of both vertical sides of the loop, a potential node on both vertical sides at two-thirds of the way up, and a potential antinode at the summit of the loop; then, under these circumstances, the closed loop of wire is in the same electrical condition as if two simple Marconi aerials, both emitting their first odd harmonic oscillation, were placed side by side and joined together at the top.
It is a little difficult without the employment of mathematical analysis to explain precisely the manner in which earthing one side of the loop or making the loop unsymmetrical as regards inductance has the effect of creating overtones in it. The following rough illustration may, however, be of some assistance. Imagine a long spiral metallic spring supported horizontally by threads. Let this represent a conductor, and let any movement to or fro of a part of the spring represent a current in that conductor. Suppose we take hold of the spring at one end, we can move it bodily to and fro as a whole. In this case, every part of the spring is moving one way or the other in the same manner at the same time. This corresponds with the case in which the discharge of the condenser through the uniform loop conductor is a flow of electricity, all in one direction one way or the other. The current is in the same direction in all parts of the loop at the same time, and, therefore, if the current is going up one side of the loop it is at the same time coming down the other side. Hence the two sides of the loop are always in exact opposition as regards the effect of the current in them on the external space, and the loop does not radiate. Returning again to the case of the spring. Supposing that we add a weight to one end of the spring by attaching to it a metal ball, and then move the other end to and fro with certain periodic motion, it will be found quite easy to set up in the spring a pulsatory motion resembling the movement of the air in an open organ-pipe. Under these circumstances both ends of the spring will be moving inwards or outwards at the same time, and the central portions of the spring, although being pressed and expanded slightly, are moving to and fro very little. This corresponds in the case of the looped aerial with a current flowing up or down both sides at the same time; in other words, when this mode of electrical oscillation is established in the loop, its electrical condition is just that of two simple Marconi aerials joined together at the top and vibrating in their fundamental manner. Accordingly, if one side of the double loop is earthed, we then have an arrangement which radiates waves. Professor Slaby found that by giving one side of the loop less inductance than the other, and at the same time earthing the side having greater inductance at the bottom, he was able to make an arrangement which radiated, not in virtue of the normal oscillations of the condenser, but in virtue of the harmonic oscillations set up in the conductor itself. The mathematical theory of this radiator has been very fully developed by Dr. Georg Seibt.
It will be seen, therefore, that there are several ways in which we may start into existence oscillations in an aerial. First, the aerial may be insulated, and we may charge it to a high potential and allow this charge suddenly to rush out. Although this process gives rise to a disturbance in the ether, as already explained, it is analogous to a pop or explosion in the air, rather than to a sustained musical note. The exact acoustic analogue would be obtained if we imagine a long pipe pumped full of air and then suddenly opened at one end. The air would rush out, and, communicating a blow to the outer air, would create an atmospheric disturbance appreciated as a noise or small explosion. This is what happens when we cut the string and let the cork fly out from a bottle of champagne. At the same time, the inertia of the air rushing out of the tube would cause it to overshoot the mark, and a short time after opening the valve the tube, so far from containing compressed air, would contain air slightly rarefied near its mouth, and this rarefication would travel back up the tube in the form of wave motion, and, being reflected as condensation at the closed end, travel down again; and so after being reflected once or twice at the open or closed end, become damped out very rapidly in virtue of both air friction and the radiation of the energy. In the case, however, of the ordinary organ-pipe, we do not depend merely upon a store of compressed air put into the pipe, but we have a store of energy to draw upon in the form of the large amount of compressed air contained in a wind chest, which is being continually supplied by the bellows. This store of compressed air is fed into the organ-pipe, with the result that we obtain a continuous radiation of sound waves. The first case, in which the only store of energy is the compressed air originally contained in the pipe, illustrates the operation of the simple Marconi aerial. The second case, in which there is a larger store of energy to draw upon, the organ-pipe being connected to a wind chest, illustrates the Marconi-Braun method, in which an aerial is employed to radiate a store of electric energy contained in a condenser, gradually liberated by the aerial in the form of a series of electrical oscillations and waves. In this arrangement the condenser corresponds to the wind chest, and it is continually kept full of electrical energy by means of the induction coil or transformer, which answers to the bellows of the organ. From the condenser, electrical energy is discharged each time the spark discharge passes at a spark gap in the form of electrical oscillations set up in the primary circuit of an oscillation transformer. The secondary circuit of this transformer is connected in between the earth and the aerial, and therefore may be considered as part of it, and, accordingly, the energy which is radiated from the aerial is not simply that which is stored up in it in virtue of its own small capacity, but that which is stored up in the much larger capacity represented by the primary condenser or, as it may be called, the electrical wind chest. By the second arrangement we have therefore the means of radiating more or less continuous trains of electric waves, corresponding with each spark discharge. To create powerful oscillations in the aerial, one condition of success is that there shall be an identity in time-period between the circuit of the aerial and that of the primary condenser. The aerial is an open circuit which has capacity with respect to the earth, and it has also inductance, partly due to the wire of the aerial and partly due to the secondary circuit of the oscillation transformer in series with it. The primary circuit or spark circuit has capacity—viz., the capacity of the energy-storing condenser—and it has also inductance—viz., the inductance of the primary circuit of the oscillation transformer. We shall consider at a later stage more particularly the details of syntonising arrangements, but meanwhile it may be said that one condition for setting up powerful waves by means of the above arrangement is that the electrical time-period of both the two circuits mentioned shall be the same. This involves adjusting the inductance and capacity so that the product of conductance and capacity for each of these two circuits is numerically the same. Instead of employing an oscillation transformer between the condenser circuit and the aerial, the aerial may be connected directly to some point on the condenser circuit at which the potential oscillations are large, and we have then another arrangement devised by Professor Braun (see Fig. 14). In this case, in order to accumulate large potential oscillations at the top of the aerial, it is, as we have seen, necessary that the length of the aerial shall be one quarter the length of the wave. If, therefore, the electrical oscillations in the condenser circuit are at the rate of N per second, in other words, have a frequency N, the wave-length correponding to this frequency is given by the expression,
The number 3×1010 is the value in centimetres per second of the velocity of the electromagnetic wave, and is identical with that of light. The corresponding resonant length of the aerial is therefore one-fourth of this wave-length, or 3 \times 10^{10}/4N. Generally speaking, however, it will be found that with any length of aerial which is practicable, say, 200 feet or 6,000 cms., this proportion necessitates rather a high frequency in the primary oscillation circuit. In the case considered—viz., for an aerial 200 feet in height—the oscillations in the primary circuit must have a frequency of one and a quarter million. This high frequency can only be obtained either by greatly reducing the inductance of the primary discharge circuit, or reducing the capacity. If we reduce the capacity, we thereby greatly reduce the storage of energy, and it is not practicable to reduce the inductance below a certain amount.
Summing up, it may be said that there are three, and, as far as the writer is aware, at present only three, modes of exciting the electrical oscillations in an aerial wire. First, the aerial may itself be used as an electrical reservoir and charged to a high potential and suddenly discharged to the earth. This is the original Marconi method. The second method, due to Braun, consist of attaching the aerial to some point on an oscillation circuit consisting of a condenser, an inductance coil and a spark gap, in series with one another, and charging and discharging the condenser across the spark gap so as to create alterations of potential at some point on the oscillation circuit. The length of the aerial must then be so proportioned as above described that it is resonant to this frequency. Thirdly, we may employ the arrangement involving an oscillation transformer, in which the oscillations in the primary condenser circuit are made to induce others in the aerial circuit, the time-period of the two circuits being the same. This method may be called the Braun-Marconi method. Professor Slaby has combined together in a certain way the original Marconi simple aerial with the resonant quarter-wave-length wire of Braun. He constructs what he calls a multiplicator, which is really a wire wound into a loose spiral connected at one point to an oscillation circuit consisting of a condenser inductance, the length of this wire being proportioned so that there is a great resonance or multiplication of tension or potential at its free end. This free end is then attached to the lower end of an ordinary Marconi aerial, and serves to charge it with a higher potential than could be obtained by the use of the induction coil directly attached to it.
We have next to consider the appliances for creating the necessary charging electromotive force, and for storing and releasing this charge at pleasure, so as to generate the required electrical oscillations in the aerial.
It is essential that this generator should be able to create not only large potential difference, but also a certain minimum electric current. Accordingly, we are limited at the present moment to one of two appliances—viz., the induction coil or the alternating current transformer.
It will not be necessary to enter into an explanation of the action of the induction coil. The coil generally employed for wireless telegraphy is technically known as a ten-inch coil—i.e., a coil which is capable of giving a ten-inch spark between pointed conductors in air at ordinary pressure. The construction of a large coil of this description is a matter requiring great technical skill, and is not to be attempted without considerable previous experience in the manufacture of smaller coils. The secondary circuit of a ten-inch coil is formed of double silk-covered copper wire; generally speaking, the gauge called No. 36, or else No. 34 S.W.G. is used, and a length of ten to seventeen miles of wire is employed on the secondary circuit, according to the gauge of wire selected. For the precautions necessary in constructing the secondary coil, practical manuals must be consulted.[8]
Very great care is required in the insulation of the secondary circuit of an induction coil to be used in Hertzian wave telegraphy, because the secondary circuit is then subjected to impulsive electromotive forces lasting for a short time, having a much higher electromotive force than that which the coil itself normally produces.
The primary circuit of a ten-inch coil generally consists of a length of 300 or 400 feet of thick insulated copper wire. In such a coil the secondary circuit would require about ten miles of No. 34 H.C. copper wire, making 50,000 turns round the core. It would have a resistance at ordinary temperatures of 6,600 ohms, and an inductance of 460 henrys. The primary circuit, if formed of 360 turns of No. 12 H.C. copper wire, would have a resistance of 0·36 of an ohm, and an inductance of 0·02 of a henry.
An important matter in connection with an induction coil to be used for wireless telegraphy is the resistance of the secondary circuit. The purpose for which we employ the coil is to charge a condenser of some kind. If a constant electromotive force (V) is applied to the terminals of a condenser having a capacity C, then the difference of potential (v) of the terminals of the condenser at any time that the contact is made is given by the expression:
In the above equation, the letter e stands for the number 2·71828, the base of the Napierian logarithms, and R is the resistance in series with the condenser, of which the capacity is C, to which the electromotive force is applied. This equation can easily be deduced from first principles,[9] and it shows that the potential difference v of the terminals of the condenser does not instantly attain a value equal to the impressed electromotive force V, but rises up gradually. Thus, for instance, suppose that a condenser of one microfarad is being charged through a resistance of one megohm by an impressed voltage of 100 volts, the equation shows that at the end of the first second after contact, the terminal potential difference of the condenser will be only 63 volts, at the end of the second second, 86 volts, and so on.
Since e-10 is an exceedingly small number, it follows that in 10 seconds the condenser would be practically charged with a voltage equal to 100 volts. The product CR in the above equation is called the time-constant of the condenser, and we may say that the condenser is practically charged after an interval of time equal to ten times the time-constant, counting from the moment of first contact between the condenser and the source of constant voltage. The time-constant is to be reckoned as the product of the capacity (C) in microfarads, by the resistance of the charging circuit (R) in megohms. To take another illustration. Supposing we are charging a condenser having a capacity of one-hundreth of a microfarad, through a resistance of ten thousand ohms. Since ten thousand ohms is equal to one-hundredth of a megohm, the time-constant would be equal to one-ten-thousandth of a second, and ten times this time-constant would be equal to a thousandth of a second. Hence, in order to charge the above capacity through the above resistance, it is necessary that the contact between the source of voltage and the condenser should be maintained for at least one-thousandth part of a second.
In discussing the methods of interrupting the circuit, we shall return to this matter, but, meanwhile, it may be said that in order to secure a small time-constant for the charging circuit, it is desirable that the secondary circuit of the induction coil should have as low a resistance as possible. This, of course, involves winding the secondary circuit with a rather thick wire. If, however, we employ a wire larger in size than No. 34, or at the most No. 32, the bulk and the cost of the induction coil began to rise very rapidly. Hence, as in all other departments of electrical construction, the details of the design are more or less a matter of compromise. Generally speaking, however, it may be said that the larger the capacity which is to be charged, the lower should be the resistance of the secondary circuit of the induction coil.
In the practical construction of induction coils for wireless telegraphy, manufacturers have departed from the stock designs. We are all familiar with the appearance of the instrument maker's induction coil; its polished mahogany base, its lacquered brass fittings, and its secondary bobbin constructed of and covered with ebonite. But such a coil, although it may look very pretty on the lecture table, is yet very unsuited to positions in which it may be used in connection with Hertzian wave telegraphy.
Three important adjuncts of the induction coil are the primary condenser, the interrupter and the primary key. The interrupter is the arrangement for intermitting the primary current. We have in some way or other to rapidly interrupt the primary current, and the torrent of sparks that then appears between the secondary terminals of the coil is due to the electromotive force set up in the secondary circuit at each break or interruption of the primary circuit. We may divide interrupters into five classes.
We have first the well-known hammer interrupter which Continental writers generally attribute to Neef or Wagner.[10] In this interrupter, the magnetisation of the iron core of the coil is caused to attract a soft-iron block fixed at the top of a brass spring, and by so doing to interrupt the primary circuit between two platinum contacts. Mr. Apps, of London, added an arrangement for pressing back the spring against the back contact, and the form of hammer that is now generally employed is therefore called an Apps break.
As the ten-inch coil takes a primary current of ten amperes at sixteen volts when in operation, it requires very substantial platinum contacts to withstand the interruption of this current continuously without damage. The small platinum contacts that are generally put on these coils by instrument makers are very soon worn out in practical wireless telegraph work. If a hammer break is used at all, it is essential to make the contacts of very stout pieces of platinum, and from time to time, as they get burnt away or roughened, they must be smoothed up with a fine file. It does not require much skill to keep the hammer contacts in good order and prevent them from sticking together and becoming damaged by the break spark.
By regulating the pressure of the spring against the back contact, by means of an adjusting screw, the rate at which the break vibrates can be regulated, but as a rule it is not possible, with a hammer break, to obtain more than about 800 interruptions per minute, or, say, twelve a second. The hammer break is usually operated by the magnetism of the iron core of the coil, but for some reasons it is better to separate the break from the coil altogether, and to work it by an independent electromagnet, which, however, may be excited by a current from the same battery supplying the induction coil. For coils up to the ten-inch size the hammer break can be used when very rapid interruptions are not required. It is not in general practicable to work coils larger than the ten-inch size with a platinum contact hammer break, as such a butt contact becomes overheated and sticks if more than ten amperes is passed through it. In the case of larger coils, we have to employ some form of interrupter in which mercury or a conducting liquid forms one of the contact surfaces.
The next class of interrupter is the vibrating or hand-worked mercury break, in which a platinum or steel pin is made to vibrate in and out of mercury. This movement may be effected by the attraction of an iron armature by an electromagnet, or by the varying magnetism of the core of the coil, or it may be effected more slowly by hand.
The mercury surface must be covered with water, alcohol, paraffin or creosote oil to prevent oxidation and to extinguish the break spark. The interruption of the primary current obtained by the mercury break is more sudden than that obtained by the platinum contact in air, in consequence of the more rapid extinction of the spark; hence the sparks obtained from coils fitted with mercury interrupters are generally from twenty to thirty per cent. longer than those obtained from the same coil under the same conditions, with platinum contact interrupters. The mercury breaks will not, however, work well unless cleaned at regular intervals by emptying off the oil and rinsing well with clean water, and hence they require rather more attention than platinum interrupters. It is not generally possible to obtain so many interruptions per minute with the simple vibrating mercury interrupter as with the ordinary hammer interrupter. The mercury interrupter has, however, the advantage that the contact time during which the circuit is kept closed may be made longer than is the case with the hammer break. Also, if fresh water is allowed to flow continuously over the mercury surface, it can be kept clean, and the break will then operate for considerable periods of time without attention. The mercury interrupter may be worked by a separate electromagnet or by the magnetism of the core of the induction coil.
The third class of interrupter may be called the motor interrupter, of which a large number have been invented in recent years. In this interrupter some form of a continuously-rotating electromotor is employed to make and break a mercury or other liquid contact. In one simple form the motor shaft carries an eccentric, which simply dips a platinum point into mercury, or else a platinum horseshoe into two mercury surfaces, making in this manner an interruption of the primary circuit at one or two places. As a small motor can easily be run at twelve hundred revolutions per minute, or twenty per second, it is possible to secure easily in this manner a uniform rate of interruption of the primary current at the rate of about twenty per second. If, however, much higher speeds are employed, then the time of contact becomes abbreviated, and the ability of the coil to charge a capacity is diminished.
Professor J. Trowbridge has described an effective form of motor break for large coils, in which the interruption is caused by withdrawing a stout platinum wire from a dilute solution of sulphuric acid, and by this means he increased the spark given by a coil provided with hammer break and condenser from fifteen inches to thirty inches when using the liquid break and no condenser.[11]
A good form of motor-interrupter, due to Dr. Mackenzie Davidson, consists of a slate disc bearing pin contacts fixed on the prolonged steel axle of a motor placed in an inclined position; the disc and the lower part of the axle lie in a vessel filled one-third with mercury and two-thirds with paraffin oil. The circuit is made and broken by the revolution of the disc causing the pins to enter and leave the mercury. The speed of the motor can be regulated by a small resistance, and can be adapted to the electromotive force used in the primary circuit. When the motor is running slowly the interrupter can be used with a low electromotive force, that is to say, something between twelve and twenty volts, but with a higher speed a large electromotive force can be used without danger of overheating the primary coil, and with an electromotive force of about fifty volts, the interruptions may be so rapid that an unbroken arc of flame, resembling an alternating-current arc, springs between the secondary terminals of the coil.
Mr. Tesla has devised numerous forms of rotating mercury break. In one, a star-shaped metal disc revolves in a box so that its points dip into mercury covered with oil, and make and break contact. In another form, a jet of mercury plays against a similar shaped rotating wheel. For details, the reader must consult the fuller descriptions in The Electrical World of New York, Vol. XXXII., p. 111, 1898; also Vol. XXXIII., p. 247; or Science Abstracts, Vol. II., pp. 46 and 47, 1898.
The fourth class of interrupter is called a turbine interrupter. In this appliance, a jet of mercury is forced out of a small aperture by means of a centrifugal pump, and is made to squirt against a metal plate, and interrupted intermittently by a toothed wheel made of insulating material rotated by the motor which drives the pump. The current supplying the coil passes through or along this jet of mercury, and is therefore rendered intermittent when the wheel revolves. In the case of this interrupter, the duration of the contacts, as well as the number of interruptions per second, is under control, and for this reason better results are probably obtained with it than with any other form of break.
A description of a turbine mercury break devised by M. Max Levy was given in the Elektrotechnische Zeitschrift, Vol. XX., p. 717, October 12, 1899 (see also Science Abstracts, Vol. III., p. 63, abstract No. 165) as follows:—
A toothed wheel made of insulating material carries from 6 to 24 teeth, and can be made to rotate from 300 to 1,000 times per minute, the interruptions being thus regulated between 5 and 400 per second. By raising or lowering the position of the jet of mercury and that of the plate against which it strikes, the duration of the contact can be varied, so that it is possible to regulate this period without disturbing the number of interruptions per second.
The sparks obtained from a coil worked with a turbine interrupter have more quantity than the sparks obtained with any other interrupter under similar conditions, and the coil can be worked with a far higher voltage than is possible when using the hammer break. In this manner, the appearance of the secondary sparks can be varied from the thin snappy sparks given by the hammer break to the thick flame-like arc sparks given by the electrolytic break. This break can be adapted for any voltage from twelve to two hundred and fifty volts, and the primary circuit cannot be closed before the interrupter is acting. The mercury in the break is generally covered with alcohol or paraffin oil to reduce oxidation, and the appliance is nearly noiseless when in operation. The mercury has to be cleaned at intervals, if the interrupter is much used. If alcohol is used to cover the mercury, the cleaning is very simple; the break requires only to be rinsed under a water tap. When paraffin oil is used, the cleaning is generally effected with the help of a few ounces of sulphuric acid in a very few minutes. It is best, however, to clean the mercury continuously by allowing the water to flow over it.
The motor driving the centrifugal pump and the fan can be wound for any voltage, and it is best to have it so arranged that this motor works on the same battery which supplies the primary circuit of the coil, the two circuits working parallel together. A rheostat can be added to the motor circuit to regulate the speed.
The turbine break driven by an independent motor, which is kept always running, has another advantage over the hammer break in practical wireless telegraphy, viz., that a useful secondary spark can be secured with a shorter time of closure of the primary circuit, since there is no inertia to overcome as in the case of the hammer break. This latter form has only continued in use because of its simplicity and ease of management by ordinary operators.
The mercury turbine interrupter has been extensively adopted both in the German and British navies in connection with induction coils used for wireless telegraphy.
Lastly we have the electrolytic interrupters, the first of which was introduced by Dr. Wehnelt, of Charlottenburg, in the year 1899, and modified by subsequent inventors. In its original form, a glass vessel filled with dilute sulphuric acid (one of acid to five or else ten parts of water) contains two electrodes of very different sizes; one is a large lead electrode formed of a piece of sheet lead laid round the interior of the vessel, and the other is a short piece of platinum wire projecting from the end of a glass or porcelain tube. The smaller of these electrodes is made the positive, and the large one the negative. If this electrolytic cell is connected in series with the primary circuit of the induction coil (the condenser being cut out) and supplied with an electromotive force from forty to eighty volts, an electrolytic action takes place which interrupts the current periodically.[12] An enormous number of interruptions can, by suitable adjustment, be produced per second, and the appearance of a discharge from the secondary terminals of the coil, while using the Wehnelt break, more resembles an alternate-current arc than the usual disruptive spark.
At the time when the Wehnelt break was first introduced, great interest was excited in it, and the technical journals in 1899 were full of discussions as to the theory of its operation.[13] The general facts concerning the Wehnelt break are that the electrolyte must be dilute sulphuric acid in the proportion of one of acid to five or ten of water. The large lead plate must be the cathode or negative pole, and the anode or positive pole must be a platinum wire, about a millimetre in diameter, and projecting one or two millimetres from the pointed end of a porcelain, glass or other acid-proof insulating tube. The aperture through which the platinum wire works must be so tight that acid cannot enter, yet it is desirable that the platinum wire should be capable of being projected more or less from the aperture by means of an adjusting screw. The glass vessel which contains these two electrodes should be of considerable size, holding, say, a quart of fluid, and it is better to include this vessel in a larger one in which water can be placed to cool the electrolyte, as the latter gets very warm when the break is used continuously. If such an electrolytic cell has a continuous electromotive force applied to it tending to force a current through the electrolyte from the platinum wire to the lead plate, we can distinguish three stages in its operation, which are determined by the electromotive force and the inductance in the circuit. First, if the electromotive force is below sixteen or twenty volts, then ordinary and silent electrolysis of the liquid proceeds, bubbles of oxygen being liberated from the platinum wire and hydrogen set free against the lead plate. If the electromotive force is raised above twenty-five volts, then if there is no inductance in the circuit, the continuous flow of current proceeds, but if the circuit of the electrolyte possesses a certain minimum inductance, the character of the current flow changes, and it becomes intermittent, and the cell acts as an interrupter, the current being interrupted from 100 to 2,000 times per second, according to the electromotive force and the inductance of the circuit. Under these conditions, the cell produces a rattling noise and a luminous glow appears round the tip of the platinum wire. Thus, in a particular case, with an inductance of 0·004 millihenry in the circuit of a Wehnelt break, no interruption of the circuit took place, but with one millihenry of inductance in the circuit, and with an electromotive force of 48 volts, the current became intermittent at the rate of 930 per second, and by increasing the voltage to 120 volts, the intermittency rose to 1,850 a second.
The Wehnelt break acts best as an interrupter with an electromotive force from 40 to 80 volts. At higher voltages a third stage sets in: the luminous glow round the platinum wire disappears, and it becomes surrounded with a layer of vapour, as observed by MM. Violle and Chassagny; the interruptions of current cease, and the platinum wire becomes red hot. If there is no inductance in the circuit, the interrupter stage never sets in at all, but the first stage passes directly into the third stage. In the first stage bubbles of oxygen rise steadily from the platinum wire, and in the interrupted stage they rise at longer intervals, but regularly. The cell will not, however, act as a break at all unless some inductance exists in the circuit.
In applying the Wehnelt break to an induction coil, the condenser is discarded and also the ordinary hammer break, and the Wehnelt break is placed in circuit with the primary coil. In some cases, the inductance of the primary coil alone is sufficient to start the break in operation, but with voltages above 50 or 60, it is generally necessary to supplement the inductance of the primary coil by another inductive coil. The best form of Wehnelt break for operating induction coils is the one with multiple anodes (see Dr. Marchant, The Electrician, Vol. XLII., p. 841, 1899), and when it has to be used for long periods, the cathode may advantageously be formed of a spiral of lead pipe, through which cold water is made to circulate.
Another form of electrolytic break was introduced by Mr. Caldwell. In this, a vessel containing dilute sulphuric acid is divided into two parts. In the partition is a small hole, and in the two compartments are electrodes of sheet lead. The small hole causes an intermittency in the current which converts the arrangement into a break. Mr. Campbell Swinton modified the above arrangement by making the partition to consist of a sort of porcelain test-tube with a hole in the bottom. This hole can be more or less plugged up by a glass rod drawn out to a point, and this is used to more or less close the hole. This porcelain vessel contains dilute acid and stands in a larger vessel of acid, and lead electrodes are placed in both compartments. The current and intermittency can be regulated by more or less closing the aperture between the two regions.
When the Wehnelt break is applied to an ordinary ten-inch induction coil, and the inductance of the primary circuit and the electromotive force varied until the break interrupts the current regularly and with the frequency of some hundred a second, the character of the secondary discharge is entirely different from its appearance with the ordinary hammer break. The thin blue lightning-like sparks are then replaced by a thicker mobile flaming discharge, which resembles an alternating-current arc, and, when carefully examined or photographed, is found to consist of a number of separate discharges superimposed upon one another in slightly different positions.
Many theories have been adopted as to the action of the break, but time will not permit us to examine these. Professor S. P. Thompson and Dr. Marchant have suggested a theory of resonance.[14] One difficulty in explaining the action of the break is created by the fact that it will not work if the platinum wire is made a cathode.
Although the Wehnelt break has some advantages in connection with the use of the induction coil for Röntgen ray work, its utility as far as regards Hertzian wave telegraphy is not by any means so marked. It has already been explained that, in order to charge a condenser of a given capacity at a constant voltage, the electromotive force must be applied for a certain minimum time, which is determined by the value of the capacity and the resistance of the secondary circuit of the induction coil. If the coil is a ten-inch coil and has a secondary resistance of, say, 6,000 ohms, and if the capacity to be charged has a value, say, of one-thirtieth of a microfarad, then the time-constant of the circuit is 1/5,000 of a second. Therefore, the contact with the condenser must be maintained for at least 1/500 of a second, during the time that the secondary electromotive force of the coil is at its maximum, so that the condenser may become charged to a voltage which the coil is then capable of producing.
In the induction coil, the electromotive force generated in the secondary coil at the "break" of the primary current is higher than that at the "make," and this electromotive force, other things being equal, depends upon the rate at which the magnetism of the iron core dies away, and its duration is shorter in proportion as the whole time occupied in the disappearance of the magnetism is less. The Wehnelt break does not increase the actual secondary electromotive force, nor apparently its duration, but it greatly increases the number of times per second this electromotive force makes it appearance. Hence this break increases the current, but not the electromotive force in the secondary coil. It, therefore, does not assist us in the direction required—viz., in prolonging the duration of the secondary electromotive force to enable larger capacities to be charged.
The important point in connection with the working of a coil used for charging a condenser is not the length of spark which the coil can give alone, but the length of spark which can be obtained between small balls attached to the secondary terminals, when these terminals are also connected to the two surfaces of the condenser. Thus, a coil may give a ten-inch spark if worked alone, but on a capacity of one-thirtieth of a microfarad it may not be able to give more than a five-millimetre spark. Hence, in describing the value of a coil for wireless telegraph purposes, it is not the least use to state the length of spark which the coil will give between the pointed conductors in air, but we must know the spark length which it will give between brass balls, say, 1 centimetre in diameter, connected to the secondary terminals, when these terminals are also short-circuited by a stated capacity, the spark not exceeding that length at which it becomes non-oscillatory.
A good way of describing the value of an induction coil for wireless telegraph purposes is to state the length of oscillatory spark which can be produced between balls one centimetre in diameter connected to the secondary terminals, when these balls are short-circuited by a condenser having a capacity, say, of one-hundredth of a microfarad, and also one-tenth of a microfarad.
If a hammer or motor interrupter is employed with the coil, then a primary condenser must be connected across the points between which the primary circuit is broken. This condenser generally consists of sheets of tinfoil alternated with sheets of paraffin paper, and for a ten-inch coil may have a capacity of about 0·4 or 0·5 of a microfarad.[15]
Lord Rayleigh discovered that if the interruption of the primary circuit is sufficiently sudden and complete, as when the primary circuit is severed by a bullet from a gun, the primary condenser can be removed and yet the sparks obtained from the secondary circuit are actually longer than those obtained with the condenser and the ordinary break.[16]
In the use, however, of the coil for Hertzian wave telegraphy, with all interrupters except the Wehnelt break a condenser of suitable capacity must be joined across the break points.
Turning in the next place to the primary key, or signalling interrupter, it is necessary to be able to control the torrent of sparks between the secondary terminals of the coil, and to cut them up into long and short periods in accordance with the letters of the Morse alphabet. This is done by means of the primary key. The primary key generally consists of an ordinary massive single contact key with heavy platinum contacts. As the current to be interrupted amounts to about ten amperes and is flowing in a highly inductive circuit, the spark at break is considerable. If the attempt is made to extinguish this spark by making the contacts move rapidly away from one another through a long distance, in other words, by using a key with a wide movement, then the speed at which the signals can be set is greatly diminished. The speed of sending greatly depends upon the time taken to move the key up and down between sending two dots, and hence a short range key sends quicker than a long range key. If it is desired to use a short range key, then some method must be employed to extinguish the spark at the contacts. This is done in one of three ways: Either by using a high resistance coil to short-circuit these contacts, or by a condenser, or by a magnetic blow-out, as in the case of an electric tramcar circuit controller. Of these, the magnetic blow-out is probably the best.
Mr. Marconi has designed a signalling key which performs the function not only of interrupting the primary circuit, but at the same time breaks connection between the receiving appliance and the aerial.
The author has designed for signalling purposes a multiple contact key which interrupts the circuit simultaneously in ten or twelve different places. The particular point about this break is the means which are taken to make the twelve interruptions absolutely simultaneous. If these interruptions are not simultaneous, the spark always takes place at the contact which is broken first, but if the circuit is interrupted in a dozen places quite simultaneously, then the spark is cut up into a dozen different portions, and the spark at each contact is very much diminished. By this break, voltages up to two thousand volts may be quite easily dealt with.
Various forms of break have been devised in which the circuit is broken under oil or insulating fluids, but, generally speaking, these devices are not very portable, and a dry contact between platinum surfaces with appropriate means for cutting up the spark and blowing it out so that the mechanical movement of the switch may be small is the best thing to use.
The signalling key is really a very important part of the transmitting arrangement, because whatever may be the improvements in receiving instruments, it is not possible to receive faster than we can send. A great many statements have appeared in the daily papers as to the possibility of receiving hundreds of words a minute by Hertzian wave telegraphy, but the fact remains that whatever may be the sensibility of the receiving appliance, the rate at which telegraphy of any kind can be conducted is essentially dependent upon the rate at which the signals can be sent, and this in turn is largely dependent upon the mechanical movement which the key has to make to interrupt the primary circuit, and so interrupt the secondary discharge.
In order to make the separation of the contact points of the switch as small as possible, and yet prevent an arc being established, various blow-out devices have been employed. The simplest arrangement for this purpose is a powerful permanent magnet so placed that its inter-polar field embraces the contact points and is at right angles to them.
As already explained, the applicability of the induction coil in wireless telegraphy is limited by the fact of the high resistance of the secondary circuit and the small current that can be supplied from it. Data are yet wanting to show what is the precise efficiency of the induction coil, as used in Hertzian wave telegraphy, but there are reasons for believing that it does not exceed 50 or 60 per cent.
Where large condensers have to be charged—in other words, where we have to deal with larger powers—we are obliged to discard the induction coil and to employ the alternating-current transformer. But this introduces us to a new class of difficulties. If an alternating-current transformer wound for a secondary voltage, say, of 20,000 or 30,000 volts, has its primary circuit connected to an alternator, then if the secondary terminals, to which are connected two spark balls, are gradually brought within striking distance of one another, the moment we do this an alternating-current arc starts between these balls. If the transformer is a small one, there is no difficulty in extinguishing this arc by withdrawing the secondary terminals, but if the transformer is a large one, say, of ten or twenty kilowatts, dangerous effects are apt to ensue when such an experiment is tried. The short circuiting of the secondary circuit almost entirely annuls the inductance of the primary circuit. There is, therefore, a rush of current into the transformer, and if it is connected to an alternator of low armature resistance the fuses are generally blown and other damage done.
Let us supppse, then, that the secondary terminals of the transformer are also connected to a condenser. On bringing together the spark balls connected with the secondary terminals we may have one or more oscillatory discharges, but the process will not be continuous, because the moment that the alternating-current arc starts between the spark balls it reduces their difference of potential to a comparatively low value, and hence the charge taken by the condenser is very small, and, moreover, the circuit is not interrupted periodically so as to re-start a train of oscillations.
When, therefore, we desire to employ an alternating-current transformer as a source of electromotive force, although it may have the advantage that the resistance of the secondary circuit of the transformer is generally small compared with that of the secondary circuit of an induction coil, yet, nevertheless, we are confronted with two practical difficulties: (1) How to control the primary current flowing into the transformer, and (2) how to destroy the alternating-current arc between the spark balls and reduce the discharge entirely to the disruptive or oscillatory discharge of the condenser.
The control over the current can be obtained, in accordance with a plan suggested by the author, by inserting in the primary circuit of the transformer two variable choking coils. The form in which it is preferred to construct these is that of a cylindrical bobbin standing upon a laminated cross-piece of iron. These bobbins can have let down into them an E-shaped piece of laminated iron, so as to complete the magnetic circuit, and thus raise the inductance of the bobbin. By placing two of these variable choking coils in series with the primary circuit, the current is under perfect control. We can fix a minimum value below which the current shall not fall, by adjusting the position of the cores of these two choking coils, and we can then cause that current to be increased up to a certain limit which it cannot exceed, by short-circuiting one of these choking coils by an appropriate switch. Several ways have been suggested for extinguishing the alternating current arc which forms between the spark balls connected to the secondary terminals when these are brought within a certain distance of one another. One of these is due to Mr. Tesla. He places a strong electromagnet so that its lines of magnetic flux pass transversely between the spark balls. When the discharge takes place the electric arc is blown out, but if the balls are short-circuited by a condenser the oscillatory discharge of the condenser still takes place across the spark gap. Professor Elihu Thomson achieves the same result by employing a blast of air thrown on the spark gap. This has the effect of destroying the alternating-current arc, but still leaves the oscillating discharge of the condenser. The action is somewhat tedious to explain in words, but it can easily be understood that the blast of air, by continually breaking down the alternating-current arc which tends to form, allows the condenser connected to the spark balls to become charged with the potential of the secondary circuit of the transformer, and that this condenser then discharges across the spark gap, producing an oscillatory discharge in the usual manner. The author has found that, without the use of any air blast or electromagnet, simple adjustment of the double choking coil in the primary circuit of the transformer, as above described, is sufficient to bring about the desired result, when the capacity of the condenser is adjusted to be in resonance.
Another method, which has been adopted by M. d'Arsonval, is to cause the spark to pass between two balls placed at the extremities of metal rods, which are in rapid rotation like the spokes of a wheel. In this case, the draught of air produced by the passage of the spark balls blows out the arc and performs the same function as the blast of air in Professor Elihu Thomson's method. When these adjustments are properly made, it is possible, by means of a condenser and an alternating-current transformer supplied with current from an alternator, to create a rapidly intermittent oscillatory discharge, the sparks of which succeed one another so quickly that it appears almost continuous. When using a large transformer and condenser, the noise and brilliancy of these sparks are almost unbearable, and the eyes may be injured by looking at this spark for more than a moment. In the construction of transformers intended to be used in this manner, very special precautions have to be taken in the insulation of the primary and secondary circuits, and the insulation of these from the core.
It may be remarked in passing that experimenting with large high-tension transformers coupled to condensers of large capacity is exceedingly dangerous work, and the greatest precautions are necessary to avoid accident. In the light, however, of sufficient experience there is no difficulty in employing high-tension transformers in the above-described manner, and in obtaining electromotive forces of upwards of a hundred thousand volts supplied through transformers capable of yielding any required amount of current.
On occasions where continuous current alone is available, a motor generator has to be employed converting the continuous current into an alternating current. This is best achieved by the employment of a small alternator directly coupled to a continuous-current motor; or by providing the shaft of a continuous-current motor with two rings connected to two opposite portions of its armature, so that when continuous current is supplied to the brushes pressing against the commutator, an alternating current can be drawn off from two other brushes touching the above-mentioned insulated rings.
The next element of importance in the transmitting arrangement is the spark gap. In the case of those transmitters employing an ordinary induction coil, the secondary spark, or the discharge of any condenser connected to the secondary terminals can be taken between the brass balls about half an inch or one inch in diameter, with which the terminals of the secondary coil are usually furnished; and it is generally the custom to allow this spark discharge to take place in air at ordinary pressure. In the very early days of his work Mr. Marconi adopted the discharger devised by Professor Rhigi, in which the spark takes place between two brass balls placed in vaseline or other highly insulating oil.[17] But whatever advantage may accrue from using oil as the dielectric in which the spark discharge takes place, when carrying out simple laboratory experiments on Hertzian waves, there is no advantage in the case of wireless telegraphy. The Rhigi discharger was, therefore, soon discarded. If discharges having large quantity are passed through oil, it is rapidly decomposed or charred, and ceases to retain the special insulating and self-restoring character which is necessary in the medium in which an oscillating spark is formed. The conditions when the discharges of large condensers are passed between spark balls are entirely different from those when the quantity of the spark, or to put it in more exact language, the current passing, is very small. In the case of Hertzian experiments it is necessary, as shown by Hertz, to maintain a high state of polish on the spark balls when they are employed for the production of short waves of small energy, but when we are dealing with large quantities of energy at each discharge, those methods which succeed for laboratory experiments are perfectly impracticable. The conditions necessary to be fulfilled by a discharger for use in Hertzian wave telegraphy are that the surfaces shall maintain a constant condition and not be fused or eaten away by the spark, and, next, that the medium in which the discharge takes place shall not be decomposed by the passage of the spark, but shall maintain the property of giving way suddenly when a certain critical pressure is reached, and passing instantly from a condition in which it is a very perfect insulator to one in which it is a very good conductor; and, thirdly, that on the cessation of the discharge, the medium shall immediately restore itself to its original condition.
When using the ordinary ten-inch induction coil, and when the capacity charged by it does not exceed a small fraction of a microfarad, it is quite sufficient to employ brass or steel balls separated by a certain distance in air, at the ordinary pressure, as the arrangement of the discharger. When, however, we come to deal with the discharges of very large condensers, at high electromotive forces, then it is necessary to have special arrangements to prevent the destruction of the surfaces between which the spark passes, or their continual alteration, and many devices have been invented for this purpose. The author has devised an arrangement which fulfils the above conditions very perfectly for use in large power stations, but the details of this cannot be made public at the present time.
We have to consider in connection with this part of the subject the dielectric strength of air under different pressures and for different thicknesses. It was shown by Lord Kelvin, in 1860, that the dielectric strength of very thin layers of air is greater than that of thick layers.[18] The electric force, reckoned in volts per centimetre, required to pierce a thickness of air from two to ten millimetres in thickness, at atmospheric pressure, may be taken at 30,000 volts per centimetre. The same force in electrostatic units is represented by the number 100, since a gradient of 300 volts per centimetre corresponds to a force of one electrostatic unit. It appears also that for air and other gases there is a certain minimum voltage (approximately 400 volts) below which no discharge takes place, however near the conducting surfaces may be approximated. In this particular practical application, however, we are only concerned with spark lengths which are measured in millimetres or centimetres, lying, say, between one or two millimetres and five or six centimetres. Over this range of spark length we shall not generally be wrong in reckoning the voltage required to produce a spark between metal balls in air at the ordinary pressure to be given by the rule: