Or (2) if you know what the electromotive force of the current is in _volts_ and the resistance of the circuit is in _ohms_ then you can find what the current flowing in the circuit is in _amperes_, thus:

Volts E ----- = Amperes, or --- = I Ohms R

That is, by dividing the resistance of the circuit in ohms, by the electromotive force of the current you will get the amperes flowing in the circuit.

Finally (3) if you know what the resistance of the circuit is in _ohms_ and the current is in _amperes_ then you can find what the electromotive force is in _volts_ since:

Ohms x Amperes = Volts, or R x I = E

That is, if you multiply the resistance of the circuit in ohms by the current in amperes the result will give you the electromotive force in volts.

From this you will see that if you know the value of any two of the constants you can find the value of the unknown constant by a simple arithmetical process. This relation between these three constants is known as _Ohm's Law_ and as they are very important you should memorize them.

What the Watt and Kilowatt Are.--Just as _horsepower_ or _H.P._, is the unit of work that steam has done or can do, so the _watt_ is the unit of work that an electric current has done or can do. To find the _watts_ a current develops you need only to multiply the _amperes_ by the _volts_. There are _746 watts_ to _1 horsepower, and 1,000 watts are equal to 1 kilowatt_.

Electromagnetic Induction.--To show that a current of electricity sets up a magnetic field around it you have only to hold a compa.s.s over a wire whose ends are connected with a battery when the needle will swing at right angles to the length of the wire. By winding an insulated wire into a coil and connecting the ends of the latter with a battery you will find, if you test it with a compa.s.s, that the coil is magnetic.

This is due to the fact that the energy of an electric current flowing in the wire is partly changed into magnetic lines of force which rotate at right angles about it as shown at A in Fig. 32. The magnetic field produced by the current flowing in the coil is precisely the same as that set up by a permanent steel magnet.

Conversely, when a magnetic line of force is set up a part of its energy goes to make up electric currents which whirl about in a like manner, as shown at B.

[Ill.u.s.tration: (A) and (B) Fig. 32.--How an Electric Current is Changed into Magnetic Lines of Force and These into an Electric Current.]

[Ill.u.s.tration: (C) and (D) Fig. 32.--How an Electric Current Sets up a Magnetic Field.]

Self-induction or Inductance.--When a current is made to flow in a coil of wire the magnetic lines of force produced are concentrated, as at C, just as a lens concentrates rays of light, and this forms an intense _magnetic field_, as it is called. Now if a bar of soft iron is brought close to one end of the coil of wire, or, better still, if it is pushed into the coil, it will be magnetized by _electromagnetic induction,_ see D, and it will remain a magnet until the current is cut off.

Mutual Induction.--When two loops of wire, or better, two coils of wire, are placed close together the electromagnetic induction between them is reactive, that is, when a current is made to flow through one of the coils closed magnetic lines of force are set up and when these cut the other loop or turns of wire of the other coil, they in turn produce electric currents in it.

It is the mutual induction that takes place between two coils of wire which makes it possible to transform _low voltage currents_ from a battery or a 110 volt source of current into high pressure currents, or _high potential currents_, as they are called, by means of a spark coil or a transformer, as well as to _step up_ and _step down_ the potential of the high frequency currents that are set up in sending and receiving oscillation transformers. Soft iron cores are not used in oscillation inductance coils and oscillation transformers for the reason that the frequency of the current is so high the iron would not have time to magnetize and demagnetize and so would not help along the mutual induction to any appreciable extent.

High-Frequency Currents.--High frequency currents, or electric oscillations as they are called, are currents of electricity that surge to and fro in a circuit a million times, more or less, per second. Currents of such high frequencies will _oscillate_, that is, surge to and fro, in an _open circuit_, such as an aerial wire system, as well as in a _closed circuit_.

Now there is only one method by which currents of high frequency, or _radio-frequency_, as they are termed, can be set up by spark transmitters, and this is by discharging a charged condenser through a circuit having a small resistance. To charge a condenser a spark coil or a transformer is used and the ends of the secondary coil, which delivers the high potential alternating current, are connected with the condenser. To discharge the condenser automatically a _spark,_ or an _arc,_ or the _flow of electrons_ in a vacuum tube, is employed.

Constants of an Oscillation Circuit.--An oscillation circuit, as pointed out before, is one in which high frequency currents surge or oscillate. Now the number of times a high frequency current will surge forth and back in a circuit depends upon three factors of the latter and these are called the constants of the circuit, namely: (1) its _capacitance,_ (2) its _inductance_ and (3) its _resistance._

What Capacitance Is.--The word _capacitance_ means the _electrostatic capacity_ of a condenser or a circuit. The capacitance of a condenser or a circuit is the quant.i.ty of electricity which will raise its pressure, or potential, to a given amount. The capacitance of a condenser or a circuit depends on its size and form and the voltage of the current that is charging it.

The capacitance of a condenser or a circuit is directly proportional to the quant.i.ty of electricity that will keep the charge at a given potential. The _farad,_ whose symbol is _M,_ is the unit of capacitance and a condenser or a circuit to have a capacitance of one farad must be of such size that one _coulomb,_ which is the unit of electrical quant.i.ty, will raise its charge to a potential of one volt.

Since the farad is far too large for practical purposes a millionth of a farad, or _microfarad_, whose symbol is _mfd._, is used.

What Inductance Is.--Under the sub-caption of _Self-induction_ and _Inductance_ in the beginning of this chapter it was shown that it was the inductance of a coil that makes a current flowing through it produce a strong magnetic field, and here, as one of the constants of an oscillation circuit, it makes a high-frequency current act as though it possessed _inertia_.

Inertia is that property of a material body that requires time and energy to set in motion, or stop. Inductance is that property of an oscillation circuit that makes an electric current take time to start and time to stop. Because of the inductance, when a current flows through a circuit it causes the electric energy to be absorbed and changes a large part of it into magnetic lines of force. Where high frequency currents surge in a circuit the inductance of it becomes a powerful factor. The practical unit of inductance is the _henry_ and it is represented by the symbol _L_.

What Resistance Is.--The resistance of a circuit to high-frequency currents is different from that for low voltage direct or alternating currents, as the former do not sink into the conductor to nearly so great an extent; in fact, they stick practically to the surface of it, and hence their flow is opposed to a very much greater extent. The resistance of a circuit to high frequency currents is generally found in the spark gap, arc gap, or the s.p.a.ce between the electrodes of a vacuum tube. The unit of resistance is, as stated, the _ohm_, and its symbol is _R_.

The Effect of Capacitance, Inductance and Resistance on Electric Oscillations.--If an oscillation circuit in which high frequency currents surge has a large resistance, it will so oppose the flow of the currents that they will be damped out and reach zero gradually, as shown at A in Fig. 33. But if the resistance of the circuit is small, and in wireless circuits it is usually so small as to be negligible, the currents will oscillate, until their energy is damped out by radiation and other losses, as shown at B.

[Ill.u.s.tration: Fig. 33.--The Effect of Resistance on the Discharge of an Electric Current.]

As the capacitance and the inductance of the circuit, which may be made of any value, that is amount, you wish, determines the _time period_, that is, the length of time for a current to make one complete oscillation, it must be clear that by varying the values of the condenser and the inductance coil you can make the high frequency current oscillate as fast or as slow as you wish within certain limits. Where the electric oscillations that are set up are very fast, the waves sent out by the aerial will be short, and, conversely, where the oscillations are slow the waves emitted will be long.

CHAPTER VI

HOW THE TRANSMITTING AND RECEIVING SETS WORK

The easiest way to get a clear conception of how a wireless transmitter sends out electric waves and how a wireless receptor receives them is to take each one separately and follow: (1) in the case of the transmitter, the transformation of the low voltage direct, or alternating current into high potential alternating currents; then find out how these charge the condenser, how this is discharged by the spark gap and sets up high-frequency currents in the oscillation circuits; then (2) in the case of the receptor, to follow the high frequency currents that are set up in the aerial wire and learn how they are transformed into oscillations of lower potential when they have a larger current strength, how these are converted into intermittent direct currents by the detector and which then flow into and operate the telephone receiver.

How Transmitting Set No. 1 Works. The Battery and Spark Coil Circuit.--When you press down on the k.n.o.b of the key the silver points of it make contact and this closes the circuit; the low voltage direct current from the battery now flows through the primary coil of the spark coil and this magnetizes the soft iron core. The instant it becomes magnetic it pulls the spring of the vibrator over to it and this breaks the circuit; when this takes place the current stops flowing through the primary coil; this causes the core to lose its magnetism when the vibrator spring flies back and again makes contact with the adjusting screw; then the cycle of operations is repeated.

A condenser is connected across the contact points of the vibrator since this gives a much higher voltage at the ends of the secondary coil than where the coil is used without it; this is because: (1) the self-induction of the primary coil makes the pressure of the current rise and when the contact points close the circuit again it discharges through the primary coil, and (2) when the break takes place the current flows into the condenser instead of arcing across the contact points.

Changing the Primary Spark Coil Current Into Secondary Currents.--Now every time the vibrator contact points close the primary circuit the electric current in the primary coil is changed into closed magnetic lines of force and as these cut through the secondary coil they set up in it a _momentary current_ in one direction. Then the instant the vibrator points break apart the primary circuit is opened and the closed magnetic lines of force contract and as they do so they cut the turns of wire in the secondary coil in the opposite direction and this sets up another momentary current in the secondary coil in the other direction. The result is that the low voltage direct current of the battery is changed into alternating currents whose frequency is precisely that of the spring vibrator, but while the frequency of the currents is low their potential, or voltage, is enormously increased.

What Ratio of Transformation Means.--To make a spark coil step up the low voltage direct current into high potential alternating current the primary coil is wound with a couple of layers of thick insulated copper wire and the secondary is wound with a thousand, more or less, number of turns with very fine insulated copper wire. If the primary and secondary coils were wound with the same number of turns of wire then the pressure, or voltage, of the secondary coil at its terminals would be the same as that of the current which flowed through the primary coil. Under these conditions the _ratio of transformation_, as it is called, would be unity.

The ratio of transformation is directly proportional to the number of turns of wire on the primary and secondary coils and, since this is the case, if you wind 10 turns of wire on the primary coil and 1,000 turns of wire on the secondary coil then you will get 100 times as high a pressure, or voltage, at the terminals of the secondary as that which you caused to flow through the primary coil, but, naturally, the current strength, or amperage, will be proportionately decreased.

The Secondary Spark Coil Circuit.--This includes the secondary coil and the spark gap which are connected together. When the alternating, but high potential, currents which are developed by the secondary coil, reach the b.a.l.l.s, or _electrodes_, of the spark gap the latter are alternately charged positively and negatively.

Now take a given instant when one electrode is charged positively and the other one is charged negatively, then when they are charged to a high enough potential the electric strain breaks down the air gap between them and the two charges rush together as described in the chapter before this one in connection with the discharge of a condenser. When the charges rush together they form a current which burns out the air in the gap and this gives rise to the spark, and as the heated gap between the two electrodes is a very good conductor the electric current surges forth and back with high frequency, perhaps a dozen times, before the air replaces that which has burned out. It is the inrushing air to fill the vacuum of the gap that makes the crackling noise which accompanies the discharge of the electric spark.

In this way then electric oscillations of the order of a million, more or less, are produced and if an aerial and a ground wire are connected to the spark b.a.l.l.s, or electrodes, the oscillations will surge up and down it and the energy of these in turn, are changed into electric waves which travel out into s.p.a.ce. An open circuit transmitter of this kind will send out waves that are four times as long as the aerial itself, but as the waves it sends out are strongly damped the Government will not permit it to be used.

The Closed Oscillation Circuit.--By using a closed oscillation circuit the transmitter can be tuned to send out waves of a given length and while the waves are not so strongly damped more current can be sent into the aerial wire system. The closed oscillation circuit consists of: (1) a _spark gap_, (2) a _condenser_ and (3) an _oscillation transformer_. The high potential alternating current delivered by the secondary coil not only charges the spark gap electrodes which necessarily have a very small capacitance, but it charges the condenser which has a large capacitance and the value of which can be changed at will.

Now when the condenser is fully charged it discharges through the spark gap and then the electric oscillations set up surge to and fro through the closed circuit. As a closed circuit is a very poor radiator of energy, that is, the electric oscillations are not freely converted into electric waves by it, they surge up to, and through the aerial wire; now as the aerial wire is a good radiator nearly all of the energy of the electric oscillations which surge through it are converted into electric waves.

How Transmitting Set No. 2 Works. With Alternating Current. The operation of a transmitting set that uses an alternating current transformer, or _power transformer,_ as it is sometimes called, is even more simple than one using a spark coil. The transformer needs no vibrator when used with alternating current. The current from a generator flows through the primary coil of the transformer and the alternations of the usual lighting current is 60 cycles per second.

This current sets up an alternating magnetic field in the core of the transformer and as these magnetic lines of force expand and contract they set up alternating currents of the same frequency but of much higher voltage at the terminals of the secondary coil according to the ratio of the primary and secondary turns of wire as explained under the sub-caption of _Ratio of Transformation_.

With Direct Current.--When a 110 volt direct current is used to energize the power transformer an _electrolytic_ interruptor is needed to make and break the primary circuit, just as a vibrator is needed for the same purpose with a spark coil. When the electrodes are connected in series with the primary coil of a transformer and a source of direct current having a potential of 40 to 110 volts, bubbles of gas are formed on the end of the platinum, or alloy anode, which prevent the current from flowing until the bubbles break and then the current flows again, in this way the current is rapidly made and broken and the break is very sharp.

Where this type of interrupter is employed the condenser that is usually shunted around the break is not necessary as the interrupter itself has a certain inherent capacitance, due to electrolytic action, and which is called its _electrolytic capacitance_, and this is large enough to balance the self-induction of the circuit since the greater the number of breaks per minute the smaller the capacitance required.

The Rotary Spark Gap.--In this type of spark gap the two fixed electrodes are connected with the terminals of the secondary coil of the power transformer and also with the condenser and primary of the oscillation transformer. Now whenever any pair of electrodes on the rotating disk are in a line with the pair of fixed electrodes a spark will take place, hence the pitch of the note depends on the speed of the motor driving the disk. This kind of a rotary spark-gap is called _non-synchronous_ and it is generally used where a 60 cycle alternating current is available but it will work with other higher frequencies.

The Quenched Spark Gap.--If you strike a piano string a single quick blow it will continue to vibrate according to its natural period. This is very much the way in which a quenched spark gap sets up oscillations in a coupled closed and open circuit. The oscillations set up in the primary circuit by a quenched spark make only three or four sharp swings and in so doing transfer all of their energy over to the secondary circuit, where it will oscillate some fifty times or more before it is damped out, because the high frequency currents are not forced, but simply oscillate to the natural frequency of the circuit. For this reason the radiated waves approach somewhat the condition of continuous waves, and so sharper tuning is possible.

The Oscillation Transformer.--In this set the condenser in the closed circuit is charged and discharged and sets up oscillations that surge through the closed circuit as in _Set No. 1_. In this set, however, an oscillation transformer is used and as the primary coil of it is included in the closed circuit the oscillations set up in it produce strong oscillating magnetic lines of force. The magnetic field thus produced sets up in turn electric oscillations in the secondary coil of the oscillation transformer and these surge through the aerial wire system where their energy is radiated in the form of electric waves.

The great advantage of using an oscillation transformer instead of a simple inductance coil is that the capacitance of the closed circuit can be very much larger than that of the aerial wire system. This permits more energy to be stored up by the condenser and this is impressed on the aerial when it is radiated as electric waves.

How Receiving Set No. I Works.--When the electric waves from a distant sending station impinge on the wire of a receiving aerial their energy is changed into electric oscillations that are of exactly the same frequency (a.s.suming the receptor is tuned to the transmitter) but whose current strength (amperage) and potential (voltage) are very small. These electric waves surge through the closed circuit but when they reach the crystal detector the contact of the metal point on the crystal permits more current to flow through it in one direction than it will allow to pa.s.s in the other direction. For this reason a crystal detector is sometimes called a _rectifier_, which it really is.