Letters of a Radio-Engineer to His Son
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You can see that as we make the grid more and more positive, that is, make it call louder and louder, a condition will be reached where it won't do it any good to call any louder, for it will already be getting all the electrons away from the filament just as fast as they are emitted. Making the grid more positive after that will not increase the plate current any. That's why the characteristic flattens off as you see at high values of grid voltage.

The arrangement which we pictured in Fig. 22 for making changes in the grid voltage is simple but it doesn't let us change the voltage by less than that of a single battery cell. I want to show you a way which will. You'll find it very useful to know and it is easily understood for it is something like the arrangement of Fig. 14 in the preceding letter.

Connect the cells as in Fig. 24 to a fine wire. About the middle of this wire connect the filament. As before use a clip on the end of the wire from the grid. If the grid is connected to a in the figure there is applied to the grid circuit that part of the e. m. f. of the battery which is active in the length of wire between o and a. The point a is nearer the positive plate of the battery than is the point o. So the grid will be positive and the filament negative.

On the other hand, if the clip is connected at b the grid will be negative with respect to the filament. We can, therefore, make the grid positive or negative depending on which side of o we connect the clip. How large the e. m. f. is which will be applied to the grid depends, of course, upon how far away from o the clip is connected.

Suppose you took the clip in your hand and slid it along in contact with the wire, first from o to a and then back again through o to b and so on back and forth. You would be making the grid alternately positive and negative, wouldn't you? That is, you would be applying to the grid an e. m. f. which increases to some positive value and then, decreasing to zero, reverses, and increases just as much, only to decrease to zero, where it started. If you do this over and over again, taking always the same time for one round trip of the clip you will be impressing on the grid circuit an "alternating e. m. f."

What's going to happen in the plate circuit? When there is no e. m. f. applied to the grid circuit, that is when the grid potential (possibilities) is zero, there is a definite current in the plate circuit. That current we can find from our characteristic of Fig. 23 for it is where the curve crosses Zero Volts. As the grid becomes positive the current rises above this value. When the grid is made negative the current falls below this value. The current, I{B}, then is made alternately greater and less than the current when E{C} is zero.

You might spend a little time thinking over this, seeing what happens when an alternating e. m. f. is applied to the grid of an audion, for that is going to be fundamental to our study of radio.

[Footnote 3: A mil-ampere is a thousandth of an ampere just as a millimeter is a thousandth of a meter.]

LETTER 10

CONDENSERS AND COILS

DEAR SON:

In the last letter we learned of an alternating e. m. f. The way of producing it, which I described, is very crude and I want to tell how to make the audion develop an alternating e. m. f. for itself. That is what the audion does in the transmitting set of a radio telephone. But an audion can't do it all alone. It must have associated with it some coils and a condenser. You know what I mean by coils but you have yet to learn about condensers.

A condenser is merely a gap in an otherwise conducting circuit. It's a gap across which electrons cannot pass so that if there is an e. m. f. in the circuit, electrons will be very plentiful on one side of the gap and scarce on the other side. If there are to be many electrons waiting beside the gap there must be room for them. For that reason we usually provide waiting-rooms for the electrons on each side of the gap. Metal plates or sheets of tinfoil serve nicely for this purpose. Look at Fig. 25. You see a battery and a circuit which would be conducting except for the gap at C. On each side of the gap there is a sheet of metal. The metal sheets may be separated by air or mica or paraffined paper. The combination of gap, plates, and whatever is between, provided it is not conducting, is called a condenser.

Let us see what happens when we connect a battery to a condenser as in the figure. The positive terminal of the battery calls electrons from one plate of the condenser while the negative battery-terminal drives electrons away from itself toward the other plate of the condenser. One plate of the condenser, therefore, becomes positive while the other plate becomes negative.

You know that this action of the battery will go on until there are so many electrons in the negative plate of the condenser that they prevent the battery from adding any more electrons to that plate. The same thing happens at the other condenser plate. The positive terminal of the battery calls electrons away from the condenser plate which it is making positive until so many electrons have left that the protons in the atoms of the plate are calling for electrons to stay home just as loudly and effectively as the positive battery-terminal is calling them away.

When both these conditions are reached—and they are both reached at the same time—then the battery has to stop driving electrons around the circuit. The battery has not enough e. m. f. to drive any more electrons. Why? Because the condenser has now just enough e. m. f. with which to oppose the battery.

It would be well to learn at once the right words to use in describing this action. We say that the battery sends a "charging current" around its circuit and "charges the condenser" until it has the same e. m. f. When the battery is first connected to the condenser there is lots of space in the waiting-rooms so there is a great rush or surge of electrons into one plate and away from the other. Just at this first instant the charging current, therefore, is large but it decreases rapidly, for the moment electrons start to pile up on one plate of the condenser and to leave the other, an e. m. f. builds up on the condenser. This e. m. f., of course, opposes that of the battery so that the net e. m. f. acting to move electrons round the circuit is no longer that of the battery, but is the difference between the e. m. f. of the battery and that of the condenser. And so, with each added electron, the e. m. f. of the condenser increases until finally it is just equal to that of the battery and there is no net e. m. f. to act.

What would happen if we should then disconnect the battery? The condenser would be left with its extra electrons in the negative plate and with its positive plate lacking the same number of electrons. That is, the condenser would be left charged and its e. m. f. would be of the same number of volts as the battery.

Now suppose we connect a short wire between the plates of the condenser as in Fig. 26. The electrons rush home from the negative plate to the positive plate. As fast as electrons get home the e. m. f. decreases. When they are all back the e. m. f. has been reduced to zero. Sometimes we say that "the condenser discharges." The "discharge current" starts with a rush the moment the conducting path is offered between the two plates. The e. m. f. of the condenser falls, the discharge current grows smaller, and in a very short time the condenser is completely discharged.

That's what happens when there is a short conducting path for the discharge current. If that were all that could happen I doubt if there would be any radio communication to-day. But if we connect a coil of wire between two plates of a charged condenser, as in Fig. 27, then something of great interest happens. To understand you must know something more about electron streams.

Suppose we should wind a few turns of wire on a cylindrical core, say on a stiff cardboard tube. We shall use insulated wire. Now start from one end of the coil, say a, and follow along the coiled wire for a few turns and then scratch off the insulation and solder onto the coil two wires, b, and c, as shown in Fig. 28. The further end of the coil we shall call d. Now let's arrange a battery and switch so that we can send a current through the part of the coil between a and b. Arrange also a current-measuring instrument so as to show if any current is flowing in the part of the coil between c and d. For this purpose we shall use a kind of current-measuring instrument which I have not yet explained. It is different from the hot-wire type described in Letter 7 for it will show in which direction electrons are streaming through it.

The diagram of Fig. 28 indicates the apparatus of our experiment. When we close the switch, S, the battery starts a stream of electrons from a towards b. Just at that instant the needle, or pointer, of the current instrument moves. The needle moves, and thus shows a current in the coil cd; but it comes right back again, showing that the current is only momentary. Let's say this again in different words. The battery keeps steadily forcing electrons through the circuit ab but the instrument in the circuit cd shows no current in that circuit except just at the instant when current starts to flow in the neighboring circuit ab.

One thing this current-measuring instrument tells us is the direction of the electron stream through itself. It shows that the momentary stream of electrons goes through the coil from d to c, that is in the opposite direction to the stream in the part ab.

Now prepare to do a little close thinking. Read over carefully all I have told you about this experiment. You see that the moment the battery starts a stream of electrons from a towards b, something causes a momentary, that is a temporary, movement of electrons from d to c. We say that starting a stream of electrons from a to b sets up or "induces" a stream of electrons from d to c.

What will happen then if we connect the battery between a and d as in Fig. 29? Electrons will start streaming away from a towards b, that is towards d. But that means there will be a momentary stream from d towards c, that is towards a. Our stream from the battery causes this oppositely directed stream. In the usual words we say it "induces" in the coil an opposing stream of electrons. This opposing stream doesn't last long, as we saw, but while it does last it hinders the stream which the battery is trying to establish.

The stream of electrons which the battery causes will at first meet an opposition so it takes a little time before the battery can get the full-sized stream of electrons flowing steadily. In other words a current in a coil builds up slowly, because while it is building up it induces an effect which opposes somewhat its own building up.

Did you ever see a small boy start off somewhere, perhaps where he shouldn't be going, and find his conscience starting to trouble him at once. For a time he goes a little slowly but in a moment or two his conscience stops opposing him and he goes on steadily at his full pace. When he started he stirred up his conscience and that opposed him. Nobody else was hindering his going. It was all brought about by his own actions. The opposition which he met was "self-induced." He was hindered at first by a self-induced effect of his own conscience. If he was a stream of electrons starting off to travel around the coil we would say that he was opposed by a self-induced e. m. f. And any path in which such an effect will be produced we say has "self-inductance." Usually we shorten this term and speak of "inductance."

There is another way of looking at it. We know habits are hard to form and equally hard to break. It's hard to get electrons going around a coil and the self-inductance of a circuit tells us how hard it is. The harder it is the more self-inductance we say that the coil or circuit has. Of course, we need a unit in which to measure self-inductance. The unit is called the "henry." But that is more self-inductance than we can stand in most radio circuits, so we find it convenient to measure in smaller units called "mil-henries" which are thousandths of a henry.

You ought to know what a henry[4] is, if we are to use the word, but it isn't necessary just now to spend much time on it. The opposition which one's self-induced conscience offers depends upon how rapidly one starts. It's volts which make electrons move and so the conscience which opposes them will be measured in volts. Therefore we say that a coil has one henry of inductance when an electron stream which is increasing one ampere's worth each second stirs up in the coil a conscientious objection of one volt. Don't try to remember this now; you can come back to it later.

There is one more effect of inductance which we must know before we can get very far with our radio. Suppose an electron stream is flowing through a coil because a battery is driving the electrons along. Now let the battery be removed or disconnected. You'd expect the electron stream to stop at once but it doesn't. It keeps on for a moment because the electrons have got the habit.

If you look again at Fig. 28 you will see what I mean. Suppose the switch is closed and a steady stream of electrons is flowing through the coil from a to b. There will be no current in the other part of the coil. Now open the switch. There will be a motion of the needle of the current-measuring instrument, showing a momentary current. The direction of this motion, however, shows that the momentary stream of electrons goes through the coil from c to d.

Do you see what this means? The moment the battery is disconnected there is nothing driving the electrons in the part ab and they slow down. Immediately, and just for an instant, a stream of electrons starts off in the part cd in the same direction as if the battery was driving them along.

Now look again at Fig. 29. If the battery is suddenly disconnected there is a momentary rush of electrons in the same direction as the battery was driving them. Just as the self-inductance of a coil opposes the starting of a stream of electrons, so it opposes the stopping of a stream which is already going.

So far we haven't said much about making an audion produce alternating e. m. f.'s and thus making it useful for radio-telephony. Before radio was possible all these things that I have just told you, and some more too, had to be known. It took hundreds of good scientists years of patient study and experiment to find out those ideas about electricity which have made possible radio-telephony.

Two of these ideas are absolutely necessary for the student of radio-communication. First: A condenser is a gap in a circuit where there are waiting-rooms for the electrons. Second: Electrons form habits. It's hard to get them going through a coil of wire, harder than through a straight wire, but after they are going they don't like to stop. They like it much less if they are going through a coil instead of a straight wire.

In my next letter I'll tell you what happens when we have a coil and a condenser together in a circuit.

[Footnote 4: The "henry" has nothing to do with a well-known automobile. It was named after Joseph Henry, a professor years ago at Princeton University.]

LETTER 11

A "C-W" TRANSMITTER

DEAR SON:

Let's look again at the coils of Fig. 28 which we studied in the last letter. I have reproduced them here so you won't have to turn back. When electrons start from a towards b there is a momentary stream of electrons from d towards c. If the electron stream through ab were started in the opposite direction, that is from b to a the induced stream in the coil cd would be from c towards d.

It all reminds me of two boys with a hedge or fence between them as in Fig. 30. One boy is after the other. Suppose you were being chased; you know what you'd do. If your pursuer started off with a rush towards one end of the hedge you'd "beat it" towards the other. But if he started slowly and cautiously you would start slowly too. You always go in the opposite direction, dodging back and forth along the paths which you are wearing in the grass on opposite sides of the hedge. If he starts to the right and then slows up and starts back, you will start to your right, slow up, and start back. Suppose he starts at the center of the hedge. First he dodges to the right, and then back through the center as far to the left, then back again and so on. You follow his every change.

I am going to make a picture of what you two do. Let's start with the other fellow. He dodges or alternates back and forth. Some persons would say he "oscillates" back and forth in the same path. As he does so he induces you to move. I am on your side of the hedge with a moving-picture camera. My camera catches both of you. Fig. 31 shows the way the film would look if it caught only your heads. The white circle represents the tow-head on my side of the hedge and the black circle, young Brown who lives next door. Of course, the camera only catches you each time the shutter opens but it is easy to draw a complete picture of what takes place as time goes on. See Fig. 32.

Now suppose you are an electron in coil cd of Fig. 33 and "Brownie" is one in coil ab. Your motions are induced by his. What's true of you two is true of all the other electrons. I have separated the coils a little in this sketch so that you can think of a hedge between. I don't know how one electron can affect another on the opposite side of this hedge but it can. And I don't know anything really about the hedge, which is generally called "the ether." The hedge isn't air. The effect would be the same if the coils were in a vacuum. The "ether" is just a name for whatever is left in the space about us when we have taken out everything which we can see or feel—every molecule, every proton and every electron.

Why and how electrons can affect one another when they are widely separated is one of the great mysteries of science. We don't know any more about it than about why there are electrons. Let's accept it as a fundamental fact which we can't as yet explain.

And now we can see how to make an audion produce an alternating current or as we sometimes say "make an audion oscillator." We shall set up an audion with its A-battery as in Fig. 34. Between the grid and the filament we put a coil and a condenser. Notice that they are in parallel, as we say. In the plate-filament circuit we connect the B-battery and a switch, S, and another coil. This coil in the plate circuit of the audion we place close to the other coil so that the two coils are just like the coils ab and cd of which I have been telling you. The moment any current flows in coil ab there will be a current flow in the coil cd. (An induced electron stream.) Of course, as long as the switch in the B-battery is open no current can flow.

The moment the switch S is closed the B-battery makes the plate positive with respect to the filament and there is a sudden surge of electrons round the plate circuit and through the coil from a to b. You know what that does to the coil cd. It induces an electron stream from d towards c. Where do these electrons come from? Why, from the grid and the plate 1 of the condenser. Where do they go? Most of them go to the waiting-room offered by plate 2 of the condenser and some, of course, to the filament. What is the result? The grid becomes positive and the filament negative.

This is the crucial moment in our study. Can you tell me what is going to happen to the stream of electrons in the plate circuit? Remember that just at the instant when we closed the switch the grid was neither positive nor negative. We were at the point of zero volts on the audion characteristic of Fig. 35. When we close the switch the current in the plate circuit starts to jump from zero mil-amperes to the number of mil-amperes which represents the point where Zero Volt St. crosses Audion Characteristic. But this jump in plate current makes the grid positive as we have just seen. So the grid will help the plate call electrons and that will make the current in the plate circuit still larger, that is, result in a larger stream of electrons from a to b.

This increase in current will be matched by an increased effect in the coil cd, for you remember how you and "Brownie" behaved. And that will pull more electrons away from plate 1 of the condenser and send them to the waiting-room of 2. All this makes the grid more positive and so makes it call all the more effectively to help the plate move electrons.

We "started something" that time. It's going on all by itself. The grid is getting more positive, the plate current is getting bigger, and so the grid is getting more positive and the plate current still bigger. Is it ever going to stop? Yes. Look at the audion characteristic. There comes a time when making the grid a little more positive won't have any effect on the plate-circuit current. So the plate current stops increasing.

There is nothing now to keep pulling electrons away from plate 1 and crowding them into waiting-room 2. Why shouldn't the electrons in this waiting-room go home to that of plate 1? There is now no reason and so they start off with a rush.

Of course, some of them came from the grid and as fast as electrons get back to the grid it becomes less and less positive. As the grid becomes less and less positive it becomes less and less helpful to the plate.

If the grid doesn't help, the plate alone can't keep up this stream of electrons. All the plate can do by itself is to maintain the current represented by the intersection of zero volts and the audion characteristic. The result is that the current in the plate circuit, that is, of course, the current in coil _ab_, becomes gradually less. About the time all the electrons, which had left the grid and plate 1 of the condenser, have got home the plate current is back to the value corresponding to _E_{C}_=_0_.

The plate current first increases and then decreases, but it doesn't stop decreasing when it gets back to zero-grid value. And the reason is all due to the habit forming tendencies of electrons in coils. To see how this comes about, let's tell the whole story over again. In other words let's make a review and so get a sort of flying start.

When we close the battery switch, S in Fig. 34, we allow a current to flow in the plate circuit. This current induces a current in the coil cd and charges the condenser which is across it, making plate 1 positive and plate 2 negative. A positive grid helps the plate so that the current in the plate circuit builds up to the greatest possible value as shown by the audion characteristic. That's the end of the increase in current. Now the condenser discharges, sending electrons through the coil cd and making the grid less positive until finally it is at zero potential, that is neither positive nor negative.

While the condenser is discharging the electrons in the coil cd get a habit of flowing from c toward d, that is from plate 2 to plate 1. If it wasn't for this habit the electron stream in cd would stop as soon as the grid had reduced to zero voltage. Because of the habit, however, a lot of electrons that ought to stay on plate 2 get hurried along and land on plate 1. It is a little like the old game of "crack the whip." Some electrons get the habit and can't stop quickly enough so they go tumbling into waiting-room 1 and make it negative.

That means that the condenser not only discharges but starts to get charged in the other direction with plate 1 negative and plate 2 positive. The grid feels the effect of all this, because it gets extra electrons if plate 1 gets them. In fact the voltage effective between grid and filament is always the voltage between the plates of the condenser.

The audion characteristic tells us what is the result. As the grid becomes negative it opposes the plate, shooing electrons back towards the filament and reducing the plate current still further. But you have already seen in my previous letter what happens when we reduce the current in coil ab. There is then induced in coil cd an electron stream from c to d. This induced current is in just the right direction to send more electrons into waiting-room 1 and so to make the grid still more negative. And the more negative the grid gets the smaller becomes the plate current until finally the plate current is reduced to zero. Look at the audion characteristic again and see that making the grid sufficiently negative entirely stops the plate current.

When the plate current stops, the condenser in the grid circuit is charged, with plate 1 negative and 2 positive. It was the plate current which was the main cause of this change for it induced the charging current in coil cd. So, when the plate current becomes zero there is nothing to prevent the condenser from discharging.

Its discharge makes the grid less and less negative until it is zero volts and there we are—back practically where we started. The plate current is increasing and the grid is getting positive, and we're off on another "cycle" as we say. During a cycle the plate current increases to a maximum, decreases to zero, and then increases again to its initial value.

This letter has a longer continuous train of thought than I usually ask you to follow. But before I stop I want to give you some idea of what good this is in radio.

What about the current which flows in coil cd? It's an alternating current, isn't it? First the electrons stream from d towards c, and then back again from c towards d.

Suppose we set up another coil like CD in Fig. 36. It would have an alternating current induced in it. If this coil was connected to an antenna there would be radio waves sent out. The switch S could be used for a key and kept closed longer or shorter intervals depending upon whether dashes or dots were being set. I'll tell you more about this later, but in this diagram are the makings of a "C-W Transmitter," that is a "continuous wave transmitter" for radio-telegraphy.

It would be worth while to go over this letter again using a pencil and tracing in the various circuits the electron streams which I have described.

LETTER 12

INDUCTANCE AND CAPACITY

DEAR SIR:

In the last letter I didn't stop to draw you a picture of the action of the audion oscillator which I described. I am going to do it now and you are to imagine me as using two pencils and drawing simultaneously two curves. One curve shows what happens to the current in the plate circuit. The other shows how the voltage of the grid changes. Both curves start from the instant when the switch is closed; and the two taken together show just what happens in the tube from instant to instant.

Fig. 37 shows the two curves. You will notice how I have drawn them beside and below the audion characteristic. The grid voltage and the plate current are related, as I have told you, and the audion characteristic is just a convenient way of showing the relationship. If we know the current in the plate circuit we can find the voltage of the grid and vice versa.

As time goes on, the plate current grows to its maximum and decreases to zero and then goes on climbing up and down between these two extremes. The grid voltage meanwhile is varying alternately, having its maximum positive value when the plate current is a maximum and its maximum negative value when the plate current is zero. Look at the two curves and see this for yourself.

Now I want to tell you something about how fast these oscillations occur. We start by learning two words. One is "cycle" with which you are already partly familiar and the other is "frequency." Take cycle first. Starting from zero the current increases to a maximum, decreases to zero, and is ready again for the same series of changes. We say the current has passed through "a cycle of values." It doesn't make any difference where we start from. If we follow the current through all its different values until we are back at the same value as we started with and ready to start all over, then we have followed through a cycle of values.

Once you get the idea of a cycle, and the markings on the curves in Fig. 31 will help you to understand, then the other idea is easy. By "frequency" we mean the number of cycles each second. The electric current which we use in lighting our house goes through sixty cycles a second. That means the current reverses its direction 120 times a second.

In radio we use alternating currents which have very high frequencies. In ship sets the frequency is either 500,000 or 1,000,000 cycles per second. Amateur transmitting sets usually have oscillators which run at well over a million cycles per second. The longer range stations use lower frequencies.

You'll find, however, that the newspaper announcements of the various broadcast stations do not tell the frequency but instead tell the "wave length." I am not going to stop now to explain what that means but I am going to give you a simple rule. Divide 300,000,000 by the "wave length" and you'll have the frequency. For example, ships are supposed to use wave lengths of 300 meters or 600 meters. Dividing three hundred million by three hundred gives one million and that is one of the frequencies which I told you were used by ship sets. Dividing by six hundred gives 500,000 or just half the frequency. You can remember that sets transmitting with long waves have low frequencies, but sets with short waves have high frequencies. The frequency and the wave length don't change in the same way. They change in opposite ways or inversely, as we say. The higher the frequency the shorter the wave length.

I'll tell you about wave lengths later. First let's see how to control the frequency of an audion oscillator like that of Fig. 38.

It takes time to get a full-sized stream going through a coil because of the inductance of the coil. That you have learned. And also it takes time for such a current to stop completely. Therefore, if we make the inductance of the coil small, keeping the condenser the same, we shall make the time required for the current to start and stop smaller. That will mean a higher frequency for there will be more oscillations each second. One rule, then, for increasing the frequency of an audion oscillator is to decrease the inductance.

Later in this letter I shall tell you how to increase or decrease the inductance of a coil. Before I do so, however, I want to call your attention to the other way in which we can change the frequency of an audion oscillator.

Let's see how the frequency will depend upon the capacity of the condenser. If a condenser has a large capacity it means that it can accommodate in its waiting-room a large number of electrons before the e. m. f. of the condenser becomes large enough to stop the stream of electrons which is charging the condenser. If the condenser in the grid circuit of Fig. 38 is of large capacity it means that it must receive in its upper waiting-room a large number of electrons before the grid will be negative enough to make the plate current zero. Therefore, the charging current will have to flow a long time to store up the necessary number of electrons.

You will get the same idea, of course, if you think about the electrons in the lower room. The current in the plate circuit will not stop increasing until the voltage of the grid has become positive enough to make the plate current a maximum. It can't do that until enough electrons have left the upper room and been stored away in the lower. Therefore the charging current will have to flow for a long time if the capacity is large. We have, therefore, the other rule for increasing the frequency of an audion oscillator, that is, decrease the capacity.

These rules can be stated the other way around. To decrease the frequency we can either increase the capacity or increase the inductance or do both.

But what would happen if we should decrease the capacity and increase the inductance? Decreasing the capacity would make the frequency higher, but increasing the inductance would make it lower. What would be the net effect? That would depend upon how much we decreased the capacity and how much we increased the inductance. It would be possible to decrease the capacity and then if we increased the inductance just the right amount to have no change in the frequency. No matter how large or how small we make the capacity we can always make the inductance such that there isn't any change in frequency. I'll give you a rule for this, after I have told you some more things about capacities and inductances.

First as to inductances. A short straight wire has a very small inductance, indeed. The longer the wire the larger will be the inductance but unless the length is hundreds of feet there isn't much inductance anyway. A coiled wire is very different.

A coil of wire will have more inductance the more turns there are to it. That isn't the whole story but it's enough for the moment. Let's see why. The reason why a stream of electrons has an opposing conscience when they are started off in a coil of wire is because each electron affects every other electron which can move in a parallel path. Look again at the coils of Figs. 28 and 29 which we discussed in the tenth letter. Those sketches plainly bring out the fact that the electrons in part cd travel in paths which are parallel to those of the electrons in part ab.

If we should turn these coils as in Fig. 39 so that all the paths in cd are at right angles to those in ab there wouldn't be any effect in cd when a current in ab started or stopped. Look at the circuit of the oscillating audion in Fig. 38. If we should turn these coils at right angles to each other we would stop the oscillation. Electrons only influence other electrons which are in parallel paths.

When we want a large inductance we wind the coil so that there are many parallel paths. Then when the battery starts to drive an electron along, this electron affects all its fellows who are in parallel paths and tries to start them off in the opposite direction to that in which it is being driven. The battery, of course, starts to drive all the electrons, not only those nearest its negative terminal but those all along the wire. And every one of these electrons makes up for the fact that the battery is driving it along by urging all its fellows in the opposite direction.

It is not an exceptional state of affairs. Suppose a lot of boys are being driven out of a yard where they had no right to be playing. Suppose also that a boy can resist and lag back twice as much if some other boy urges him to do so. Make it easy and imagine three boys. The first boy lags back not only on his own account but because of the urging of the other boys. That makes him three times as hard to start as if the other boys didn't influence him. The same is true of the second boy and also of the third. The result is the unfortunate property owner has nine times as hard a job getting that gang started as if only one boy were to be dealt with. If there were two boys it would be four times as hard as for one boy. If there were four in the group it would be sixteen times, and if five it would be twenty-five times. The difficulty increases much more rapidly than the number of boys.

Now all we have to do to get the right idea of inductance is to think of each boy as standing for the electrons in one turn of the coil. If there are five turns there will be twenty-five times as much inductance, as for a single turn; and so on. You see that we can change the inductance of a coil very easily by changing the number of turns.

I'll tell you two things more about inductance because they will come in handy. The first is that the inductance will be larger if the turns are large circles. You can see that for yourself because if the circles were very small we would have practically a straight wire.

The other fact is this. If that property owner had been an electrical engineer and the boys had been electrons he would have fixed it so that while half of them said, "Aw, don't go; he can't put you off"; the other half would have said "Come on, let's get out." If he did that he would have a coil without any inductance, that is, he would have only the natural inertia of the electrons to deal with. We would say that he had made a coil with "pure resistance" or else that he had made a "non-inductive resistance."

How would he do it? Easy enough after one learns how, but quite ingenious. Take the wire and fold it at the middle. Start with the middle and wind the coil with the doubled wire. Fig. 40 shows how the coil would look and you can see that part of the way the electrons are going around the coil in one direction and the rest of the way in the opposite direction. It is just as if the boys were paired off, a "goody-goody" and a "tough nut" together. They both shout at once opposite advice and neither has any effect.

I have told you all except one of the ways in which we can affect the inductance of a circuit. You know now all the methods which are important in radio. So let's consider how to make large or small capacities.

First I want to tell you how we measure the capacity of a condenser. We use units called "microfarads." You remember that an ampere means an electron stream at the rate of about six billion billion electrons a second. A millionth of an ampere would, therefore, be a stream at the rate of about six million million electrons a second—quite a sizable little stream for any one who wanted to count them as they went by. If a current of one millionth of an ampere should flow for just one second six million million electrons would pass along by every point in the path or circuit.

That is what would happen if there weren't any waiting-rooms in the circuit. If there was a condenser then that number of electrons would leave one waiting-room and would enter the other. Well, suppose that just as the last electron of this enormous number[5] entered its waiting-room we should know that the voltage of the condenser was just one volt. Then we would say that the condenser had a capacity of one microfarad. If it takes half that number to make the condenser oppose further changes in the contents of its waiting-rooms, with one volt's worth of opposition, that is, one volt of e. m. f., then the condenser has only half a microfarad of capacity. The number of microfarads of capacity (abbreviated mf.) is a measure of how many electrons we can get away from one plate and into the other before the voltage rises to one volt.

What must we do then to make a condenser with large capacity? Either of two things; either make the waiting-rooms large or put them close together.

If we make the plates of a condenser larger, keeping the separation between them the same, it means more space in the waiting-rooms and hence less crowding. You know that the more crowded the electrons become the more they push back against any other electron which some battery is trying to force into their waiting-room, that is the higher the e. m. f. of the condenser.

The other way to get a larger capacity is to bring the plates closer together, that is to shorten the gap. Look at it this way: The closer the plates are together the nearer home the electrons are. Their home is only just across a little gap; they can almost see the electronic games going on around the nuclei they left. They forget the long round-about journey they took to get to this new waiting-room and they crowd over to one side of this room to get just as close as they can to their old homes. That's why it's always easier, and takes less voltage, to get the same number of electrons moved from one plate to the other of a condenser which has only a small space between plates. It takes less voltage and that means that the condenser has a smaller e. m. f. for the same number of electrons. It also means that before the e. m. f. rises to one volt we can get more electrons moved around if the plates are close together. And that means larger capacity.

There is one thing to remember in all this: It doesn't make any difference how thick the plates are. It all depends upon how much surface they have and how close together they are. Most of the electrons in the plate which is being made negative are way over on the side toward their old homes, that is, toward the plate which is being made positive. And most of the homes, that is, atoms which have lost electrons, are on the side of the positive plate which is next to the gap. That's why I said the electrons could almost see their old homes.

All this leads to two very simple rules for building condensers. If you have a condenser with too small a capacity and want one, say, twice as large, you can either use twice as large plates or bring the plates you already have twice as close together; that is, make the gap half as large. Generally, of course, the gap is pretty well fixed. For example, if we make a condenser by using two pieces of metal and separating them by a sheet of mica we don't want the job of splitting the mica. So we increase the size of the plates. We can do that either by using larger plates or other plates and connecting it as in Fig. 41 so that the total waiting-room space for electrons is increased.

If you have got these ideas you can understand how we use both sides of the same plate in some types of condensers. Look at Fig. 42. There are two plates connected together and a third between them. Suppose electrons are pulled from the outside plates and crowded into the middle plate. Some of them go on one side and some on the other, as I have shown. The negative signs indicate electrons and the plus signs their old homes. If we use more plates as in Fig. 43 we have a larger capacity.

What if we have two plates which are not directly opposite one another, like those of Fig. 44? What does the capacity depend upon? Imagine yourself an electron on the negative plate. Look off toward the positive plate and see how big it seems to you. The bigger it looks the more capacity the condenser has. When the plates are right opposite one another the positive plate looms up pretty large. But if they slide apart you don't see so much of it; and if it is off to one side about all you see is the edge. If you can't see lots of atoms which have lost electrons and so would make good homes for you, there is no use of your staying around on that side of the plate; you might just as well be trying to go back home the long way which you originally came.

That's why in a variable plate condenser there is very little capacity when no parts of the plates are opposite each other, and there is the greatest capacity when they are exactly opposite one another.

While we are at it we might just as well clean up this whole business of variable capacities and inductances by considering two ways in which to make a variable inductance. Fig. 45 shows the simplest way but it has some disadvantages which I won't try now to explain. We make a long coil and then take off taps. We can make connections between one end of the coil and any of the taps. The more turns there are included in the part of the coil which we are using the greater is the inductance. If we want to do a real job we can bring each of these taps to a little stud and arrange a sliding or rotating contact with them. Then we have an inductance the value of which we can vary "step-by-step" in a convenient manner.

Another way to make a variable inductance is to make what is called a "variometer." I dislike the name because it doesn't "meter" anything. If properly calibrated it would of course "meter" inductance, but then it should be called an "inducto-meter."

Do you remember the gang of boys that fellow had to drive off his property? What if there had been two different gangs playing there? How much trouble he has depends upon whether there is anything in common between the gangs. Suppose they are playing in different parts of his property and so act just as if the other crowd wasn't also trespassing. He could just add the trouble of starting one gang to the trouble of starting the other.

It would be very different if the gangs have anything in common. Then one would encourage the other much as the various boys of the same gang encourage each other. He would have a lot more trouble. And this extra trouble would be because of the relations between gangs, that is, because of their "mutual inductance."

On the other hand suppose the gangs came from different parts of the town and disliked each other. He wouldn't have nearly the trouble. Each gang would be yelling at the other as they went along: "You'd better beat it. He knows all right, all right, who broke that bush down by the gate. Just wait till he catches you." They'd get out a little easier, each in the hope the other crowd would catch it from the owner. There's a case where their mutual relations, their mutual inductance, makes the job easier.

That's true of coils with inductance. Suppose you wind two inductance coils and connect them in series. If they are at right angles to each other as in Fig. 46a they have no effect on each other. There is no mutual inductance. But if they are parallel and wound the same way like the coils of Fig. 46b they will act like a single coil of greater inductance. If the coils are parallel but wound in opposite directions as in Fig. 46c they will have less inductance because of their mutual inductance. You can check these statements for yourself if you'll refer back to Letter 10 and see what happens in the same way as I told you in discussing Fig. 28.

If the coils are neither parallel nor at right angles there will be some mutual inductance but not as much as if they were parallel. By turning the coils we can get all the variations in mutual relations from the case of Fig. 46b to that of Fig. 46c. That's what we arrange to do in a variable inductance of the variometer type.

There is another way of varying the mutual inductance. We can make one coil slide inside another. If it is way inside, the total inductance which the two coils offer is either larger than the sum of what they can offer separately or less, depending upon whether the windings are in the same direction or opposite. As we pull the coil out the mutual effect becomes less and finally when it is well outside the mutual inductance is very small.

Now we have several methods of varying capacity and inductance and therefore we are ready to vary the frequency of our audion oscillator; that is, "tune" it, as we say. In my next letter I shall show you why we tune.

Now for the rule which I promised. The frequency to which a circuit is tuned depends upon the product of the number of mil-henries in the coil and the number of microfarads in the condenser. Change the coil and the condenser as much as you want but keep this product the same and the frequency will be the same.

[Footnote 5: More accurately the number is 6,286,000,000,000.]

LETTER 13

TUNING

I want to tell you about receiving sets and their tuning. In the last letter I told you what determines the frequency of oscillation of an audion oscillator. It was the condenser and inductance which you studied in connection with Fig. 36. That's what determines the frequency and also what makes the oscillations. All the tube does is to keep them going. Let's see why this is so.

Start first, as in Fig. 47a, with a very simple circuit of a battery and a non-inductive resistance, that is, a wire wound like that of Fig. 40 in the previous letter, so that it has no inductance. The battery must do work forcing electrons through that wire. It has the ability, or the energy as we say.

Now connect a condenser to the battery as in Fig. 47b. The connecting wires are very short; and so practically all the work which the battery does is in storing electrons in the negative plate of the condenser and robbing the positive plate. The battery displaces a certain number of electrons in the waiting-rooms of the condenser. How many, depends upon how hard it can push and pull, that is on its e. m. f., and upon how much capacity the condenser has.

Remove the battery and connect the charged condenser to the resistance as in Fig. 47c. The electrons rush home. They bump and jostle their way along, heating the wire as they go. They have a certain amount of energy or ability to do work because they are away from home and they use it all up, bouncing along on their way. When once they are home they have used up all the surplus energy which the battery gave them.

Try it again, but this time, as in Fig. 47d, connect the charged condenser to a coil which has inductance. The electrons don't get started as fast because of the inductance. But they keep going because the electrons in the wire form the habit. The result is that about the time enough electrons have got into plate 2 (which was positive), to satisfy all its lonely protons, the electrons in the wire are streaming along at a great rate. A lot of them keep going until they land on this plate and so make it negative.

That's the same sort of thing that happens in the case of the inductance and condenser in the oscillating audion circuit except for one important fact. There is nothing to keep electrons going to the 2 plate except this habit. And there are plenty of stay-at-home electrons to stop them as they rush along. They bump and jostle, but some of them are stopped or else diverted so that they go bumping around without getting any nearer plate 2. Of course, they spend all their energy this way, getting every one all stirred up and heating the wire.

Some of the energy which the electrons had when they were on plate 1 is spent, therefore, and there aren't as many electrons getting to plate 2. When they turn around and start back, as you know they do, the same thing happens. The result is that each successive surge of electrons is smaller than the preceding. Their energy is being wasted in heating the wire. The stream of electrons gets smaller and smaller, and the voltage of the condenser gets smaller and smaller, until by-and-by there isn't any stream and the condenser is left uncharged. When that happens, we say the oscillations have "damped out."

That's one way of starting oscillations which damp out—to start with a charged condenser and connect an inductance across it. There is another way which leads us to some important ideas. Look at Fig. 48. There is an inductance and a condenser. Near the coil is another coil which has a battery and a key in circuit with it. The coils are our old friends of Fig. 33 in Letter 10. Suppose we close the switch S. It starts a current through the coil ab which goes on steadily as soon as it really gets going. While it is starting, however, it induces an electron stream in coil cd. There is only a momentary or transient current but it serves to charge the condenser and then events happen just as they did in the case where we charged the condenser with a battery.

Now take away this coil ab with its battery and substitute the oscillator of Fig. 36. What's going to happen? We have two circuits in which oscillations can occur. See Fig. 49. One circuit is associated with an audion and some batteries which keep supplying it with energy so that its oscillations are continuous. The other circuit is near enough to the first to be influenced by what happens in that circuit. We say it is "coupled" to it, because whatever happens in the first circuit induces an effect in the second circuit.

Suppose first that in each circuit the inductance and capacity have such values as to produce oscillations of the same frequency. Then the moment we start the oscillator we have the same effect in both circuits. Let me draw the picture a little differently (Fig. 50) so that you can see this more easily. I have merely made the coil ab in two parts, one of which can affect cd in the oscillator and the other the coil L of the second circuit.

But suppose that the two circuits do not have the same natural frequencies, that is the condenser and inductance in one circuit are so large that it just naturally takes more time for an oscillation in that circuit than in the other. It is like learning to dance. You know about how well you and your partner would get along if you had one frequency of oscillation and she had another. That's what happens in a case like this.

If circuit L-C takes longer for each oscillation than does circuit ab its electron stream is always working at cross purposes with the electron stream in ab which is trying to lead it. Its electrons start off from one condenser plate to the other and before they have much more than got started the stream in ab tries to call them back to go in the other direction. It is practically impossible under these conditions to get a stream of any size going in circuit L-C. It is equally hard if L-C has smaller capacity and inductance than ab so that it naturally oscillates faster.

I'll tell you exactly what it is like. Suppose you and your partner are trying to dance without any piano or other source of music. She has one tune running through her head and she dances to that, except as you drag her around the floor. You are trying to follow another tune. As a couple you have a difficult time going anywhere under these conditions. But it would be all right if you both had the same tune.

If we want the electron stream in coil ab to have a large guiding effect on the stream in coil L-C we must see that both circuits have the same tune, that is the same natural frequency of oscillation.

This can be shown very easily by a simple experiment. Suppose we set up our circuit L-C with an ammeter in it, so as to be able to tell how large an electron stream is oscillating in that circuit. Let us also make the condenser a variable one so that we can change the natural frequency or tune of the circuit. Now let's see what happens to the current as we vary this condenser, changing the capacity and thus changing the tune of the circuit. If we use a variable plate condenser it will have a scale on top graduated in degrees and we can note the reading of the ammeter for each position of the movable plates. If we do, we find one position of these plates, that is one setting, corresponding to one value of capacity in the condenser, where the current in the circuit is a maximum. This is the setting of the condenser for which the circuit has the same tune or natural frequency as the circuit cd. Sometimes we say that the circuits are now in resonance. We also refer to the curve of values of current and condenser positions as a "tuning curve." Such a curve is shown in Fig. 51.

That's all there is to tuning—adjusting the capacity and inductance of a circuit until it has the same natural frequency as some other circuit with which we want it to work. We can either adjust the capacity as we just did, or we can adjust the inductance. In that case we use a variable inductance as in Fig. 52.

If we want to be able to tune to any of a large range of frequencies we usually have to take out or put into the circuit a whole lot of mil-henries at a time. When we do we get these mil-henries of inductance from a coil which we call a "loading coil." That's why your friends add a loading coil when they want to tune for the long wave-length stations, that is, those with a low frequency.

When our circuit L-C of Fig. 49 is tuned to the frequency of the oscillator we get in it a maximum current. There is a maximum stream of electrons, and hence a maximum number of them crowded first into one and then into the other plate of the condenser. And so the condenser is charged to a maximum voltage, first in one direction and then in the other.

Now connect the circuit L-C to the grid of an audion. If the circuit is tuned we'll have the maximum possible voltage applied between grid and filament. In the plate circuit we'll get an increase and then a decrease of current. You know that will happen for I prepared you for this moment by the last page of my ninth letter. I'll tell you more about that current in the plate circuit in a later letter. I am connecting a telephone receiver in the plate circuit, and also a condenser, the latter for a reason to be explained later. The combination appears then as in Fig. 53. That figure shows a C-W transmitter and an audion detector. This is the sort of a detector we would use for radio-telephony, but the transmitter is the sort we would use for radio-telegraphy. We shall make some changes in them later.

Whenever we start the oscillating current in the transmitter we get an effect in the detector circuit, of which I'll tell you more later. For the moment I am interested in showing you how the transmitter and the detector may be separated by miles and still there will be an effect in the detector circuit every time the key in the transmitter circuit is closed.

This is how we do it. At the sending station, that is, wherever we locate the transmitter, we make a condenser using the earth, or ground, as one plate. We do the same thing at the receiving station where the detector circuit is located. To these condensers we connect inductances and these inductances we couple to our transmitter and receiver as shown in Fig. 54. The upper plate of the condenser in each case is a few horizontal wires. The lower plate is the moist earth of the ground and we arrange to get in contact with that in various ways. One of the simplest methods is to connect to the water pipes of the city water-system.

Now we have our radio transmitting-station and a station for receiving its signals. You remember we can make dots and dashes by the key or switch in the oscillator circuit. When we depress the key we start the oscillator going. That sets up oscillations in the circuit with the inductance and the capacity formed by the antenna. If we want a real-sized stream of electrons up and down this antenna lead (the vertical wire), we must tune that circuit. That is why I have shown a variable inductance in the circuit of the transmitting antenna.

What happens when these electrons surge back and forth between the horizontal wires and the ground, I don't know. I do know, however, that if we tune the antenna circuit at the receiving station there will be a small stream of electrons surging back and forth in that circuit.

Usually scientists explain what happens by saying that the transmitting station sends out waves in the ether and that these waves are received by the antenna system at the distant station. Wherever you put up a receiving station you will get the effect. It will be much smaller, however, the farther the two stations are apart.

I am not going to tell you anything about wave motion in the ether because I don't believe we know enough about the ether to try to explain, but I shall tell you what we mean by "wave length."

Somehow energy, the ability to do work, travels out from the sending antenna in all directions. Wherever you put up your receiving station you get more or less of this energy. Of course, energy is being sent out only while the key is depressed and the oscillator going. This energy travels just as fast as light, that is at the enormous speed of 186,000 miles a second. If you use meters instead of miles the speed is 300,000,000 meters a second.

Now, how far will the energy which is sent out from the antenna travel during the time it takes for one oscillation of the current in the antenna? Suppose the current is oscillating one million times a second. Then it takes one-millionth of a second for one oscillation. In that time the energy will have traveled away from the antenna one-millionth part of the distance it will travel in a whole second. That is one-millionth of 300 million meters or 300 meters.

The distance which energy will go in the time taken by one oscillation of the source of that energy is the wave length. In the case just given that distance is 300 meters. The wave length, then, of 300 meters corresponds to a frequency of one million. In fact if we divide 300 million meters by the frequency we get the wave length, and that's the same rule as I gave you in the last letter.

In further letters I'll tell you how the audion works as a detector and how we connect a telephone transmitter to the oscillator to make it send out energy with a speech significance instead of a mere dot and dash significance, or signal significance. We shall have to learn quite a little about the telephone itself and about the human voice.

LETTER 14

WHY AND HOW TO USE A DETECTOR

DEAR SON:

In the last letter we got far enough to sketch, in Fig. 54, a radio transmitting station and a receiving station. We should never, however, use just this combination because the transmitting station is intended to send telegraph signals and the receiving station is best suited to receiving telephonic transmission. But let us see what happens.

When the key in the plate circuit of the audion at the sending station is depressed an alternating current is started. This induces an alternating current in the neighboring antenna circuit. If this antenna circuit, which is formed by a coil and a condenser, is tuned to the frequency of oscillations which are being produced in the audion circuit then there is a maximum current induced in the antenna.

As soon as this starts the antenna starts to send out energy in all directions, or "radiate" energy as we say. How this energy, or ability to do work, gets across space we don't know. However it may be, it does get to the receiving station. It only takes a small fraction of a second before the antenna at the receiving station starts to receive energy, because energy travels at the rate of 186,000 miles a second.

The energy which is received does its work in making the electrons in that antenna oscillate back and forth. If the receiving antenna is tuned to the frequency which the sending station is producing, then the electrons in the receiving antenna oscillate back and forth most widely and there is a maximum current in this circuit.

The oscillations of the electrons in the receiving antenna induce similar oscillations in the tuned circuit which is coupled to it. This circuit also is tuned to the frequency which the distant oscillator is producing and so in it we have the maximum oscillation of the electrons. The condenser in that circuit charges and discharges alternately.

The grid of the receiving audion always has the same voltage as the condenser to which it is connected and so it becomes alternately positive and negative. This state of affairs starts almost as soon as the key at the sending station is depressed and continues as long as it is held down.

Now what happens inside the audion? As the grid becomes more and more positive the current in the plate circuit increases. When the grid no longer grows more positive but rather becomes less and less positive the current in the plate circuit decreases. As the grid becomes of zero voltage and then negative, that is as the grid "reverses its polarity," the plate current continues to decrease. When the grid stops growing more negative and starts to become less so, the plate current stops decreasing and starts to increase.

All this you know, for you have followed through such a cycle of changes before. You know also how we can use the audion characteristic to tell us what sort of changes take place in the plate current when the grid voltage changes. The plate current increases and decreases alternately, becoming greater and less than it would be if the grid were not interfering. These variations in its intensity take place very rapidly, that is with whatever high frequency the sending station operates. What happens to the plate current on the average?

The plate current, you remember, is a stream of electrons from the filament to the plate (on the inside of the tube), and from the plate back through the B-battery to the filament (on the outside of the tube). The grid alternately assists and opposes that stream. When it assists, the electrons in the plate circuit are moved at a faster rate. When the grid becomes negative and opposes the plate the stream of electrons is at a slower rate. The stream is always going in the same direction but it varies in its rate depending upon the changes in grid potential.

When the grid is positive, that is for half a cycle of the alternating grid-voltage, the stream is larger than it would be if the plate current depended only on the B-battery. For the other half of a cycle it is less. The question I am raising is this: Do more electrons move around the plate circuit if there is a signal coming in than when there is no incoming signal? To answer this we must look at the audion characteristic of our particular tube and this characteristic must have been taken with the same B-battery as we use when we try to receive the signals.

There are just three possible answers to this question. The first answer is: "No, there is a smaller number of electrons passing through the plate circuit each second if the grid is being affected by an incoming signal." The second is: "The signal doesn't make any difference in the total number of electrons which move each second from filament to plate." And the third answer is: "Yes, there is a greater total number each second."

Any one of the three answers may be right. It all depends on the characteristic of the tube as we are operating it, and that depends not only upon the type and design of tube but also upon what voltages we are using in our batteries. Suppose the variations in the voltage of the grid are as represented in Fig. 55, and that the characteristic of the tube is as shown in the same figure. Then obviously the first answer is correct. You can see for yourself that when the grid becomes positive the current in the plate circuit can't increase much anyway. For the other half of the cycle, that is, while the grid is negative, the current in the plate is very much decreased. The decrease in one half-cycle is larger than the increase during the other half-cycle, so that on the average the current is less when the signal is coming in. The dotted line shows the average current.

Suppose that we take the same tube and use a B-battery of lower voltage. The characteristic will have the same shape but there will not be as much current unless the grid helps, so that the characteristic will be like that of Fig. 56. This characteristic crosses the axis of zero volts at a smaller number of mil-amperes than does the other because the B-batteries can't pull as hard as they did in the other case.

You can see the result. When the grid becomes positive it helps and increases the plate current. When it becomes negative it opposes and decreases the plate current. But the increase just balances the decrease, so that on the average the current is unchanged, as shown by the dotted line.

On the other hand, if we use a still smaller voltage of B-battery we get a characteristic which shows a still smaller current when the grid is at zero potential. For this case, as shown in Fig. 57, the plate current is larger on the average when there is an incoming signal.

If we want to know whether or not there is any incoming signal we will not use the tube in the second condition, that of Fig. 56, because it won't tell us anything. On the other hand why use the tube under the first conditions where we need a large plate battery? If we can get the same result, that is an indication when the other station is signalling, by using a small battery let's do it that way for batteries cost money. For that reason we shall confine ourselves to the study of what takes place under the conditions of Fig. 57.

We now know that when a signal is being sent by the distant station the current in the plate circuit of our audion at the receiving station is greater, on the average. We are ready to see what effect this has on the telephone receiver. And to do this requires a little study of how the telephone receiver works and why.

I shall not stop now to tell you much about the telephone receiver for it deserves a whole letter all to itself. You know that a magnet attracts iron. Suppose you wind a coil of insulated wire around a bar magnet or put the magnet inside such a coil as in Fig. 58. Send a stream of electrons through the turns of the coil—a steady stream such as comes from the battery shown in the figure. The strength of the magnet is altered. For one direction of the electron stream through the coil the magnet is stronger. For the opposite direction of current the magnet will be weaker.

Fig. 59 shows a simple design of telephone receiver. It is formed by a bar magnet, a coil about it through which a current can flow, and a thin disc of iron. The iron disc, or diaphragm, is held at its edges so that it cannot move as a whole toward the magnet. The center can move, however, and so the diaphragm is bowed out in the form shown in the smaller sketch.

Now connect a battery to the receiver winding and allow a steady stream of electrons to flow. The magnet will be either strengthened or weakened. Suppose the stream of electrons is in the direction to make it stronger—I'll give you the rule later. Then the diaphragm is bowed out still more. If we open the battery circuit and so stop the stream of electrons the diaphragm will fly back to its original position, for it is elastic. The effect is very much that of pushing in the bottom of a tin pan and letting it fly back when you remove your hand.

Next reverse the battery. The magnet does not pull as hard as it would if there were no current. The diaphragm is therefore not bowed out so much.

Suppose that instead of reversing the current by reversing the battery we arrange to send an alternating current through the coil. That will have the same effect. For one direction of current flow, the diaphragm is attracted still more by the magnet but for the other direction it is not attracted as much. The result is that the center of the diaphragm moves back and forth during one complete cycle of the alternating current in the coil.

The diaphragm vibrates back and forth in tune with the alternating current in the receiver winding. As it moves away from the magnet it pushes ahead of it the neighboring molecules of air. These molecules then crowd and push the molecules of air which are just a little further away from the diaphragm. These in turn push against those beyond them and so a push or shove is sent out by the diaphragm from molecule to molecule until perhaps it reaches your ear. When the molecules of air next your ear receive the push they in turn push against your eardrum.

In the meantime what has happened? The current in the telephone receiver has reversed its direction. The diaphragm is now pulled toward the magnet and the adjacent molecules of air have even more room than they had before. So they stop crowding each other and follow the diaphragm in the other direction. The molecules of air just beyond these, on the way toward your ear, need crowd no longer and they also move back. Of course, they go even farther than their old positions for there is now more room on the other side. That same thing happens all along the line until the air molecules next your ear start back and give your eardrum a chance to expand outward. As they move away they make a little vacuum there and the eardrum puffs out.

That goes on over and over again just as often as the alternating current passes through one cycle of values. And you, unless you are thinking particularly of the scientific explanations, say that you "hear a musical note." As a matter of fact if we increase the frequency of the alternating current you will say that the "pitch" of the note has been increased or that you hear a note higher in the musical scale.

If we started with a very low-frequency alternating current, say one of fifteen or twenty cycles per second, you wouldn't say you heard a note at all. You would hear a sort of a rumble. If we should gradually increase the frequency of the alternating current you would find that about sixty or perhaps a hundred cycles a second would give you the impression of a musical note. As the frequency is made still larger you have merely the impression of a higher-pitched note until we get up into the thousands of cycles a second. Then, perhaps about twenty-thousand cycles a second, you find you hear only a little sound like wind or like steam escaping slowly from a jet or through a leak. A few thousand cycles more each second and you don't hear anything at all.

You know that for radio-transmitting stations we use audion oscillators which are producing alternating currents with frequencies of several hundred-thousand cycles per second. It certainly wouldn't do any good to connect a telephone receiver in the antenna circuit at the receiving station as in Fig. 60. We couldn't hear so high pitched a note.

Even if we could, there are several reasons why the telephone receiver wouldn't work at such high frequencies. The first is that the diaphragm can't be moved so fast. It has some inertia, you know, that is, some unwillingness to get started. If you try to start it in one direction and, before you really get it going, change your mind and try to make it go in the other direction, it simply isn't going to go at all. So even if there is an alternating current in the coil around the magnet there will not be any corresponding vibration of the diaphragm if the frequency is very high, certainly not if it is above about 20,000 cycles a second.

The other reason is that there will only be a very feeble current in the coil anyway, no matter what you do, if the frequency is high. You remember that the electrons in a coil are sort of banded together and each has an effect on all the others which can move in parallel paths. The result is that they have a great unwillingness to get started and an equal unwillingness to stop. Their unwillingness is much more than if the wire was long and straight. It is also made very much greater by the presence of the iron core. An alternating e. m. f. of high frequency hardly gets the electrons started at all before it's time to get them going in the opposite direction. There is very little movement to the electrons and hence only a very small current in the coil if the frequency is high.

If you want a rule for it you can remember that the higher the frequency of an alternating e. m. f. the smaller the electron stream which it can set oscillating in a given coil. Of course, we might make the e. m. f. stronger, that is pull and shove the electrons harder, but unless the coil has a very small inductance or unless the frequency is very low we should have to use an e. m. f. of enormous strength to get any appreciable current.

Condensers are just the other way in their action. If there is a condenser in a circuit, where an alternating e. m. f. is active, there is lots of trouble if the frequency is low. If, however, the frequency is high the same-sized current can be maintained by a smaller e. m. f. than if the frequency is low. You see, when the frequency is high the electrons hardly get into the waiting-room of the condenser before it is time for them to turn around and go toward the other room. Unless there is a large current, there are not enough electrons crowded together in the waiting-room to push back very hard on the next one to be sent along by the e. m. f. Because the electrons do not push back very hard a small e. m. f. can drive them back and forth.

Ordinarily we say that a condenser impedes an alternating current less and less the higher is the frequency of the current. And as to inductances, we say that an inductance impedes an alternating current more and more the higher is the frequency.

Now we are ready to study the receiving circuit of Fig. 54. I showed you in Fig. 57 how the current through, the tube will vary as time goes on. It increases and decreases with the frequency of the current in the antenna of the distant transmitting station. We have a picture, or graph, as we say, of how this plate current varies. It will be necessary to study that carefully and to resolve it into its components, that is to separate it into parts, which, added together again will give the whole. To show you what I mean I am going to treat first a very simple case involving money.

Suppose a boy was started by his father with 50 cents of spending money. He spends that and runs 50 cents in debt. The next day his father gives him a dollar. Half of this he has to spend to pay up his yesterday's indebtedness. This he does at once and that leaves him 50 cents ahead. But again he buys something for a dollar and so runs 50 cents in debt. Day after day this cycle is repeated. We can show what happens by the curve of Fig. 61a.

On the other hand, suppose he already had 60 cents which, he was saving for some special purpose. This he doesn't touch, preferring to run into debt each day and to pay up the next, as shown in Fig. 61a. Then we would represent the story of this 60 cents by the graph of Fig. 61b.

Now suppose that instead of going in debt each day he uses part of this 60 cents. Each day after the first his father gives him a dollar, just as before. He starts then with 60 cents as shown in Fig. 61c, increases in wealth to \$1.10, then spends \$1.00, bringing his funds down to 10 cents. Then he receives \$1.00 from his father and the process is repeated cyclically.

If you saw the graph of Fig. 61c you would be able to say that, whatever he actually did, the effect was the same as if he had two pockets, in one of which he kept 60 cents all the time as shown in Fig. 61b. In his other pocket he either had money or he was in debt as shown in Fig. 61a. If you did that you would be resolving the money changes of Fig. 61c into the two components of Figs. 61a and b.

That is what I want you to do with the curve of Fig. 57 which I am reproducing here, redrawn as Fig. 62a. You see it is really the result of adding together the two curves of Figs. 62b and c, which are shown on the following page.

We can think, therefore, of the current in the plate circuit as if it were two currents added together, that is, two electron streams passing through the same wire. One stream is steady and the other alternates.

Now look again at the diagram of our receiving set which I am reproducing as Fig. 63. When the signal is incoming there flow in the plate circuit two streams of electrons, one steady and of a value in mil-amperes corresponding to that of the graph in Fig. 62b, and the other alternating as shown in Fig. 62c.

The steady stream of electrons will have no more difficulty in getting through the coiled wire of the receiver than it would through the same amount of straight wire. On the other hand it cannot pass the gap of the condenser.

The alternating-current component can't get along in the coil because its frequency is so high that the coil impedes the motion of the electrons so much as practically to stop them. On the other hand these electrons can easily run into the waiting-room offered by the condenser and then run out again as soon as it is time.

When the current in the plate circuit is large all the electrons which aren't needed for the steady stream through the telephone receiver run into one plate of the condenser. Of course, at that same instant an equal number leave the other plate and start off toward the B-battery and the filament. An instant later, when the current in the plate circuit is small, electrons start to come out of the plate and to join the stream through the receiver so that this stream is kept steady.

This steady stream of electrons, which is passing through the receiver winding, is larger than it would be if there was no incoming radio signal. The result is a stronger pull on the diaphragm of the receiver. The moment the signal starts this diaphragm is pulled over toward the magnet and it stays pulled over as long as the signal lasts. When the signal ceases it flies back. We would hear then a click when the signal started and another when it stopped.

If we wanted to distinguish dots from dashes this wouldn't be at all satisfactory. So in the next letter I'll show you what sort of changes we can make in the apparatus. To understand what effect these changes will have you need, however, to understand pretty well most of this letter.

LETTER 15