,transcriber's ,note3 ,an underscore character is used around text to signify italics in the original text1 as illustrated4 ,it also is used to signify a subscript1 used frequently in technical descriptions4 ,for example ,e,c would have been originally typeset as a capital ,e followed by a smaller ,c subscript1 and both would have been in an italic typeface4 ,illustration3 ,pl4 ,i4--,one of the ,lines of ,towers at ,radio ,central 7,courtesy of ,radio ,corporation of ,america74 ,,letters ,,of ,a ,,radio-,,engineer ,,to ,,his ,,son ,,by ,,john ,,mills ,engineering ,department1 ,western ,electric ,company1 ,inc41 ,author of ,radio-,communication1 ,the ,realities of ,modern ,science1 and ,within the ,atom ,,new ,,york ,,harcourt1 ,,brace ,,and ,,company ,,copyright1 #aibb1 ,,by ,,harcourt1 ,,brace ,,and ,,company1 ,,inc4 ,,printed ,,in ,,the ,u4 ,s4 ,a4 ,,by ,,the ,,quinn ,,boden ,,company ,,rahway1 ,n4 ,j4 ,,to ,j4 ,m41 ,jr4 ,,contents #a ,electricity and ,matter #c #b ,why a ,copper ,wire ,will ,conduct ,electricity #i #c ,how a ,battery ,works #af #d ,the ,batteries in ,your ,radio ,set #bg #e ,getting ,electrons from a ,heated ,wire #cd #f ,the ,audion #dj #g ,how to ,measure an ,electron ,stream #dh #h ,electron-,moving-,forces #eg #i ,the ,audion-,characteristic #ff #aj ,condensers and ,coils #gg #aa ,a ,c-,w ,transmitter #hf #ab ,inductance and ,capacity #if #ac ,tuning #aab #ad ,why and ,how to ,use a ,detector #abd #ae ,radio-,telephony #adj #af ,the ,human ,voice #aeb #ag ,grid ,batteries and ,grid ,condensers for ,detectors #afe #ah ,amplifiers and the ,regenerative ,circuit #agf #ai ,the ,audion ,amplifier and ,its ,connections #ahg #bj ,telephone ,receivers and ,other ,electromagnetic ,devices #aii #ba ,your ,receiving ,set and ,how to ,experiment #baa #bb ,high-,powered ,radio-,telephone ,transmitters #bcj #bc ,amplification at ,intermediate ,frequencies #bdb #bd ,by ,wire and by ,radio #bea ,index #bfc ,,list ,,of ,,plates ,i ,one of the ,lines of ,towers at ,radio ,central ,frontispiece ,,ii ,bird's-,eye ,view of ,radio ,central #aj ,,iii ,dry ,battery for ,use in ,audion ,circuits1 and also ,storage ,battery #bg ,,iv ,radiotron #db ,v ,variometer and ,variable ,condenser of the ,general ,radio ,company4 ,voltmeter and ,ammeter of the ,weston ,instrument ,company #ia ,,vi ,low-,power ,transmitting ,tube1 ,u ,v #bjb #ajf ,,vii ,photographs of ,vibrating ,strings #aee ,,viii ,to ,illustrate the ,mechanism for the ,production of the ,human ,voice #agj ,,ix ,western ,electric ,loud ,speaking ,receiver4 ,crystal ,detector ,set of the ,general ,electric ,co4 ,audibility ,meter of ,general ,radio ,co4 #bjc ,x ,audio-,frequency ,transformer and ,banked-,wound ,coil #bah ,,xi ,broadcasting ,equipment1 ,developed by the ,american ,telephone and ,telegraph ,company and the ,western ,electric ,company #bce ,,xii ,broadcasting ,station of the ,american ,telephone and ,telegraph ,company on the ,roof of the ,walker-,lispenard ,bldg4 in ,new ,york ,city where the ,long-distance ,telephone ,lines ,terminate #bej ,,letters ,,of ,a ,,radio-,,engineer ,,to ,,his ,,son ,,letter #a ,,electricity ,,and ,,matter ,,my ,,dear ,,son3 ,you are interested in radio-telephony and want me to explain it to you4 ,i'll do so in the shortest and easiest way which ,i can devise4 ,the explanation will be the simplest which ,i can give and still make it possible for you to build and operate your own set and to understand the operation of the large commercial sets to which you will listen4 ,i'll write you a series of letters which will contain only what is important in the radio of to-day and those ideas which seem necessary if you are to follow the rapid advances which radio is making4 ,some of the letters you will find to require a second reading and study4 ,in the case of a few you might postpone a second reading until you have finished those which interest you most4 ,i'll mark the letters to omit in this way4 ,all the letters will be written just as ,i would talk to you1 for ,i shall draw little sketches as ,i go along4 ,one of them will tell you how to experiment for yourself4 ,this will be the most interesting of all4 ,you can find plenty of books to tell you how radio sets operate and what to do1 but very few except some for advanced students tell you how to experiment for yourself4 ,not to waste time in your own experiments1 however1 you will need to be quite familiar with the ideas of the other letters4 ,what is a radio set8 ,copper wires1 tinfoil1 glass plates1 sheets of mica1 metal1 and wood4 ,where does it get its ability to work--that is1 where does the energy come from which runs the set8 ,from batteries or from dynamos4 ,that much you know already1 but what is the real reason that we can use copper wires1 metal plates1 audions1 crystals1 and batteries to send messages and to receive them8 ,the reason is that all these things are made of little specks1 too tiny ever to see1 which we might call specks of electricity4 ,there are only two kinds of specks and we had better give them their right names at once to save time4 ,one kind of speck is called electron and the other kind proton4 ,how do they differ8 ,they probably differ in size but we don't yet know so very much about their sizes4 ,they differ in laziness a great deal4 ,one is about #ahde times as lazy as the other4 ,that is1 it has eighteen hundred and forty-five times as much inertia as the other4 ,it is harder to get it started but it is just as much harder to get it to stop after it is once started or to change its direction and go a different direction4 ,the proton has the larger inertia4 ,it is the electron which is the easier to start or stop4 ,how else do they differ8 ,they differ in their actions4 ,protons don't like to associate with other protons but take quite keenly to electrons4 ,and electrons--they go with protons but they won't associate with each other4 ,an electron always likes to be close to a proton4 ,two is company when one is an electron and the other a proton but three is a crowd always4 ,it doesn't make any difference to a proton what electron it is keeping company with provided only it is an electron and not another proton4 ,all electrons are alike as far as we can tell and so are all protons4 ,that means that all the stuff1 or matter1 of our world is made up of two kinds of building blocks1 and all the blocks of each kind are just alike4 ,of course you mustn't think of these blocks as like bricks1 for we don't know their shapes4 ,then there is another reason why you must not think of them as bricks and that is because when you build a house out of bricks each brick must rest on another4 ,between an electron and any other electron or between two protons or between an electron and a proton there is usually a relatively enormous distance4 ,there is enough space so that lots of other electrons or protons could be fitted in between if only they were willing to get that close together4 ,sometimes they do get very close together4 ,i can tell you how if you will imagine four small boys playing tag4 ,suppose ,tom and ,dick don't like to play with each other and run away from each other if they can4 ,now suppose that ,bill and ,sam won't play with each other if they can help it but that either of them will play with ,tom or ,dick whenever there is a chance4 ,now suppose ,tom and ,bill see each other2 they start running toward each other to get up some sort of a game4 ,but ,sam sees ,tom at the same time1 so he starts running to join him even though ,bill is going to be there too4 ,meanwhile ,dick sees ,bill and ,sam running along and since they are his natural playmates he follows them4 ,in a minute they are all together1 and playing a great game2 although some of the boys don't like to play together4 ,whenever there is a group of protons and electrons playing together we have what we call an atom4 ,there are about ninety different games which electrons and protons can play1 that is ninety different kinds of atoms4 ,these games differ in the number of electrons and protons who play and in the way they arrange themselves4 ,larger games can be formed if a number of atoms join together4 ,then there is a molecule4 ,of molecules there are as many kinds as there are different substances in the world4 ,it takes a lot of molecules together to form something big enough to see1 for even the largest molecule1 that of starch1 is much too small to be seen by itself with the best possible microscope4 ,what sort of a molecule is formed will depend upon how many and what kinds of atoms group together to play the larger game4 ,whenever there is a big game it doesn't mean that the little atomic groups which enter into it are all changed around4 ,they keep together like a troop of boy scouts in a grand picnic in which lots of troops are present4 ,at any rate they keep together enough so that we can still call them a group1 that is an atom1 even though they do adapt their game somewhat so as to fit in with other groups--that is with other atoms4 ,what will the kind of atom depend upon8 ,it will depend upon how many electrons and protons are grouped together in it to play their little game4 ,how any atom behaves so far as associating with other groups or atoms will depend upon what sort of a game its own electrons and protons are playing4 ,now the simplest kind of a game that can be played1 and the one with the smallest number of electrons and protons1 is that played by a single proton and a single electron4 ,i don't know just how it is played but ,i should guess that they sort of chase each other around in circles4 ,at any rate ,i do know that the atom called hydrogen is formed by just one proton and one electron4 ,suppose they were magnified until they were as large as the moon and the earth4 ,then they would be just about as far apart but the smaller one would be the proton4 ,that hydrogen atom is responsible for lots of interesting things for it is a great one to join with other atoms4 ,we don't often find it by itself although we can make it change its partners and go from one molecule to another very easily4 ,that is what happens every time you stain anything with acid4 ,a hydrogen atom leaves a molecule of the acid and then it isn't acid any more4 ,what remains isn't a happy group either for it has lost some of its playfellows4 ,the hydrogen goes and joins with the stuff which gets stained4 ,but it doesn't join with the whole molecule2 it picks out part of it to associate with and that leaves the other part to take the place of the hydrogen in the original molecule of acid from which it came4 ,many of the actions which we call chemistry are merely the result of such changes of atoms from one molecule to another4 ,not only does the hydrogen atom like to associate in a larger game with other kinds of atoms but it likes to do so with one of its own kind4 ,when it does we have a molecule of hydrogen gas1 the same gas as is used in balloons4 ,we haven't seemed to get very far yet toward radio but you can see how we shall when ,i tell you that next time ,i shall write of more complicated games such as are played in the atoms of copper which form the wires of radio sets and of how these wires can do what we call carrying an electric current4 ,,letter #b ,,why ,a ,,copper ,,wire ,,will ,,conduct ,,electricity ,,my ,,dear ,,young ,,atomist3 ,you have learned that the simplest group which can be formed by protons and electrons is one proton and one electron chasing each other around in a fast game4 ,this group is called an atom of hydrogen4 ,a molecule of hydrogen is two of these groups together4 ,all the other possible kinds of groups are more complicated4 ,the next simplest is that of the atom of helium4 ,helium is a gas of which small quantities are obtained from certain oil wells and there isn't very much of it to be obtained4 ,it is an inert gas1 as we call it1 because it won't burn or combine with anything else4 ,it doesn't care to enter into the larger games of molecular groups4 ,it is satisfied to be as it is1 so that it isn't much use in chemistry because you can't make anything else out of it4 ,that's the reason why it is so highly recommended for filling balloons or airships1 because it cannot burn or explode4 ,it is not as light as hydrogen but it serves quite well for making balloons buoyant in air4 ,this helium atom is made up of four electrons and four protons4 ,right at the center there is a small closely crowded group which contains all the protons and two of the electrons4 ,the other two electrons play around quite a little way from this inner group4 ,it will make our explanations easier if we learn to call this inner group the nucleus of the atom4 ,it is the center of the atom and the other two electrons play around about it just as the earth and ,mars and the other planets play or revolve about the sun as a center4 ,that is why we shall call these two electrons planetary electrons4 ,there are about ninety different kinds of atoms and they all have names4 ,some of them are more familiar than hydrogen and helium4 ,for example1 there is the iron atom1 the copper atom1 the sulphur atom and so on4 ,some of these atoms you ought to know and so1 before telling you more of how atoms are formed by protons and electrons1 ,i am going to write down the names of some of the atoms which we have in the earth and rocks of our world1 in the water of the oceans1 and in the air above4 ,start first with air4 ,it is a mixture of several kinds of gases4 ,each gas is a different kind of atom4 ,there is just a slight trace of hydrogen and a very small amount of helium and of some other gases which ,i won't bother you with learning4 ,most of the air1 however1 is nitrogen1 about #gh percent in fact and almost all the rest is oxygen4 ,about #bj4h percent is oxygen so that all the gases other than these two make up only about #a4b percent of the atmosphere in which we live4 ,illustration3 ,pl4 ,,ii4--,bird's-eye ,view of ,radio ,central 7,courtesy of ,radio ,corporation of ,america74 ,the earth and rocks also contain a great deal of oxygen2 about #dg4c percent of the atoms which form earth and rocks are oxygen atoms4 ,about half of the rest of the atoms are of a kind called silicon4 ,sand is made up of atoms of silicon and oxygen and you know how much sand there is4 ,about #bg4g percent of the earth and its rocks is silicon4 ,the next most important kind of atom in the earth is aluminum and after that iron and then calcium4 ,here is the way they run in percentages3 ,aluminum #g4h percent2 iron #d4e percent2 calcium #c4e percent2 sodium #b4d percent2 potassium #b4d percent2 magnesium #b4b percent4 ,besides these which are most important there is about #j4b percent of hydrogen and the same amount of carbon4 ,then there is a little phosphorus1 a little sulphur1 a little fluorine1 and small amounts of all of the rest of the different kinds of atoms4 ,sea water is mostly oxygen and hydrogen1 about #he4h percent of oxygen and #aj4g percent of hydrogen4 ,that is what you would expect for water is made up of molecules which in turn are formed by two atoms of hydrogen and one atom of oxygen4 ,the oxygen atom is about sixteen times as heavy as the hydrogen atom4 ,however1 for every oxygen atom there are two hydrogen atoms so that for every pound of hydrogen in water there are about eight pounds of oxygen4 ,that is why there is about eight times as high a percentage of oxygen in sea water as there is of hydrogen4 ,most of sea water1 therefore1 is just water1 that is1 pure water4 ,but it contains some other substances as well and the best known of these is salt4 ,salt is a substance the molecules of which contain atoms of sodium and of chlorine4 ,that is why sea water is about #a4a percent sodium and about #b4a percent chlorine4 ,there are some other kinds of atoms in sea water1 as you would expect1 for it gets all the substances which the waters of the earth dissolve and carry down to it but they are unimportant in amounts4 ,now we know something about the names of the important kinds of atoms and can take up again the question of how they are formed by protons and electrons4 ,no matter what kind of atom we are dealing with we always have a nucleus or center and some electrons playing around that nucleus like tiny planets4 ,the only differences between one kind of atom and any other kind are differences in the nucleus and differences in the number and arrangement of the planetary electrons which are playing about the nucleus4 ,no matter what kind of atom we are considering there is always in it just as many electrons as protons4 ,for example1 the iron atom is formed by a nucleus and twenty-six electrons playing around it4 ,the copper atom has twenty-nine electrons as tiny planets to its nucleus4 ,what does that mean about its nucleus8 ,that there are twenty-nine more protons in the nucleus than there are electrons4 ,silver has even more planetary electrons1 for it has #dg4 ,radium has #hh and the heaviest atom of all1 that of uranium1 has #ib4 ,we might use numbers for the different kinds of atoms instead of names if we wanted to do so4 ,we could describe any kind of atom by telling how many planetary electrons there were in it4 ,for example1 hydrogen would be number #a1 helium number #b1 lithium of which you perhaps never heard1 would be number #c1 and so on4 ,oxygen is #h1 sodium is #aa1 chlorine is #ag1 iron #bf1 and copper #bi4 ,for each kind of atom there is a number4 ,let's call that number its atomic number4 ,now let's see what the atomic number tells us4 ,take copper1 for example1 which is number #bi4 ,in each atom of copper there are #bi electrons playing around the nucleus4 ,the nucleus itself is a little inner group of electrons and protons1 but there are more protons than electrons in it2 twenty-nine more in fact4 ,in an atom there is always an extra proton in the nucleus for each planetary electron4 ,that makes the total number of protons and electrons the same4 ,about the nucleus of a copper atom there are playing #bi electrons just as if the nucleus was a teacher responsible for #bi children who were out in the play yard4 ,there is one very funny thing about it all1 however1 and that is that we must think of the scholars as if they were all just alike so that the teacher couldn't tell one from the other4 ,electrons are all alike1 you remember4 ,all the teacher or nucleus cares for is that there shall be just the right number playing around her4 ,you could bring a boy in from some other play ground and the teacher couldn't tell that he was a stranger but she would know that something was the matter for there would be one too many in her group4 ,she is responsible for just #bi scholars1 and the nucleus of the copper atom is responsible for just #bi electrons4 ,it doesn't make any difference where these electrons come from provided there are always just #bi playing around the nucleus4 ,if there are more or less than #bi something peculiar will happen4 ,we shall see later what might happen1 but first let's think of an enormous lot of atoms such as there would be in a copper wire4 ,a small copper wire will have in it billions of copper atoms1 each with its planetary electrons playing their invisible game about their own nucleus4 ,there is quite a little distance in any atom between the nucleus and any of the electrons for which it is responsible4 ,there is usually a greater distance still between one atomic group and any other4 ,on the whole the electrons hold pretty close to their own circles about their own nuclei4 ,there is always some tendency to run away and play in some other group4 ,with #bi electrons it's no wonder if sometimes one goes wandering off and finally gets into the game about some other nucleus4 ,of course1 an electron from some other atom may come wandering along and take the place just left vacant1 so that nucleus is satisfied4 ,we don't know all we might about how the electrons wander around from atom to atom inside a copper wire but we do know that there are always a lot of them moving about in the spaces between the atoms4 ,some of them are going one way and some another4 ,it's these wandering electrons which are affected when a battery is connected to a copper wire4 ,every single electron which is away from its home group1 and wandering around1 is sent scampering along toward the end of the wire which is connected to the positive plate or terminal of the battery and away from the negative plate4 ,that's what the battery does to them for being away from home2 it drives them along the wire4 ,there's a regular stream or procession of them from the negative end of the wire toward the positive4 ,when we have a stream of electrons like this we say we have a current of electricity4 ,we'll need to learn more later about a current of electricity but one of the first things we ought to know is how a battery is made and why it affects these wandering electrons in the copper wire4 ,that's what ,i shall tell you in my next letter4#a ,footnote #a3 ,the reader who wishes the shortest path to the construction and operation of a radio set should omit the next two letters4 ,,letter #c ,,how ,a ,,battery ,,works 7,this letter may be omitted on the first reading47 ,,my ,,dear ,,boy3 ,when ,i was a boy we used to make our own batteries for our experiments4 ,that was before storage batteries became as widely used as they are to-day when everybody has one in the starting system of his automobile4 ,that was also before the day of the small dry battery such as we use in pocket flash lights4 ,the batteries which we made were like those which they used on telegraph systems1 and were sometimes called gravity batteries4 ,of course1 we tried several kinds and ,i believe ,i got quite a little acid around the house at one time or another4 ,i'll tell you about only one kind but ,i shall use the words electron1 proton1 nucleus1 atom1 and molecule1 about some of which nothing was known when ,i was a boy4 ,we used a straight-sided glass jar which would hold about a gallon4 ,on the bottom we set a star shaped arrangement made of sheets of copper with a long wire soldered to it so as to reach up out of the jar4 ,then we poured in a solution of copper sulphate until the jar was about half full4 ,this solution was made by dissolving in water crystals of blue vitriol which we bought at the drug store4 ,blue vitriol1 or copper sulphate as the chemists would call it1 is a substance which forms glassy blue crystals4 ,its molecules are formed of copper atoms1 sulphur atoms1 and oxygen atoms4 ,in each molecule of it there is one atom of copper1 one of sulphur and four of oxygen4 ,when it dissolves in water the molecules of the blue vitriol go wandering out into the spaces between the water molecules4 ,but that isn't all that happens or the most important thing for one who is interested in making a battery4 ,each molecule is formed by six atoms1 that is by six little groups of electrons playing about six little nuclei4 ,about each nucleus there is going on a game but some of the electrons are playing in the game about their own nucleus and at the same time taking some part in the game which is going on around one of the other nuclei4 ,that's why the groups or atoms stay together as a molecule4 ,when the molecules wander out into the spaces between the water molecules something happens to this complicated game4 ,it will be easiest to see what sort of thing happens if we talk about a molecule of ordinary table salt1 for that has only two atoms in it4 ,one atom is sodium and one is chlorine4 ,the sodium molecule has eleven electrons playing around its nucleus4 ,fairly close to the nucleus there are two electrons4 ,then farther away there are eight more and these are having a perfect game4 ,then still farther away from the nucleus there is a single lonely electron4 ,the atom of chlorine has seventeen electrons which play about its nucleus4 ,close to the nucleus there are two4 ,a little farther away there are eight just as there are in the sodium atom4 ,then still farther away there are seven4 ,i am going to draw a picture 7,fig4 #a7 to show what ,i mean1 but you must remember that these electrons are not all in the same plane as if they lay on a sheet of paper1 but are scattered all around just as they would be if they were specks on a ball4 ,illustration3 ,fig4 #a ,you see that the sodium atom has one lonely electron which hasn't any play fellows and that the chlorine atom has seven in its outside circle4 ,it appears that eight would make a much better game4 ,suppose that extra electron in the sodium atom goes over and plays with those in the chlorine atom so as to make eight in the outside group as ,i have shown ,fig4 #b4 ,that will be all right as long as it doesn't get out of sight of its own nucleus because you remember that the sodium nucleus is responsible for eleven electrons4 ,the lonely electron of the sodium atom needn't be lonely any more if it can persuade its nucleus to stay so close to the chlorine atom that it can play in the outer circle of the chlorine atom4 ,illustration3 ,fig4 #b ,the outer circle of the chlorine atom will then have a better game1 for it will have just the eight that makes a perfect game4 ,this can happen if the chlorine atom will stay close enough to the sodium atom so that the outermost electron of the sodium atom can play in the chlorine circle4 ,you see everything will be satisfactory if an electron can be shared by the two atoms4 ,that can happen only if the two atoms stay together2 that is1 if they form a molecule4 ,that's why there are molecules and that's what ,i meant when ,i spoke of the molecule as a big game played by the electrons of two or more atoms4 ,this molecule which is formed by a sodium atom and a chlorine atom is called a molecule of sodium chloride by chemists and a molecule of salt by most every one who eats it4 ,something strange happens when it dissolves4 ,it wanders around between the water molecules and for some reason or other--we don't know exactly why--it decides to split up again into sodium and chlorine but it can't quite do it4 ,the electron which joined the game about the chlorine nucleus won't leave it4 ,the result is that the nucleus of the sodium atom gets away but it leaves this one electron behind4 ,what gets away isn't a sodium atom for it has one too few electrons2 and what remains behind isn't a chlorine atom for it has one too many electrons4 ,we call these new groups ions from a ,greek word which means to go for they do go1 wandering off into the spaces between the water molecules4 ,fig4 #c gives you an idea of what happens4 ,you remember that in an atom there are always just as many protons as electrons4 ,in this sodium ion which is formed when the nucleus of the sodium atom breaks away but leaves behind one planetary electron1 there is then one more proton than there are electrons4 ,because it has an extra proton1 which hasn't any electron to associate with1 we call it a plus ion or a positive ion4 ,similarly we call the chlorine ion1 which has one less proton than it has electrons1 a minus or negative ion4 ,illustration3 ,fig4 #c ,now1 despite the fact that these ions broke away from each other they aren't really satisfied4 ,any time that the sodium ion can find an electron to take the place of the one it lost it will welcome it4 ,that is1 the sodium ion will want to go toward places where there are extra electrons4 ,in the same way the chlorine ion will go toward places where electrons are wanted as if it could satisfy its guilty conscience by giving up the electron which it stole from the sodium atom1 or at least by giving away some other electron1 for they are all alike anyway4 ,sometimes a positive sodium ion and a negative chlorine ion meet in their wanderings in the solution and both get satisfied by forming a molecule again4 ,even so they don't stay together long before they split apart and start wandering again4 ,that's what goes on over and over again1 millions of times1 when you dissolve a little salt in a glass of water4 ,now we can see what happens when copper sulphate dissolves4 ,the copper atom has twenty-nine electrons about its nucleus and all except two of these are nicely grouped for playing their games about the nucleus4 ,two of the electrons are rather out of the game1 and are unsatisfied4 ,they play with the electrons of the part of the molecule which is called sulphate1 that is1 the part formed by the sulphur atom and the four oxygen atoms4 ,these five atoms of the sulphate part stay together very well and so we treat them as a group4 ,the sulphate group and the copper atom stay together as long as they are not in solution but when they are1 they act very much like the sodium and chlorine which ,i just described4 ,the molecule splits up into two ions1 one positive and one negative4 ,the positive ion is the copper part except that two of the electrons which really belong to a copper atom got left behind because the sulphate part wouldn't give them up4 ,the rest of the molecule is the negative ion4 ,the copper ion is a copper atom which has lost two electrons4 ,the sulphate ion is a combination of one sulphur atom1 four oxygen atoms and two electrons which it stole from the copper atom4 ,just as the sodium ion is unsatisfied because in it there is one more proton than there are electrons1 so the copper ion is unsatisfied4 ,as a matter of fact it is twice as badly unsatisfied4 ,it has two more protons than it has electrons4 ,we say it has twice the electrical charge of the sodium ion4 ,just like a sodium ion the copper ion will tend to go toward any place where there are extra electrons which it can get to satisfy its own needs4 ,in much the same way the sulphate ion will go toward places where it can give up its two extra electrons4 ,sometimes1 of course1 as ions of these two kinds wander about between the water molecules1 they meet and satisfy each other by forming a molecule of copper sulphate4 ,but if they do they will split apart later on2 that is1 they will dissociate as we should say4 ,now let's go on with the kind of batteries ,i used to make as a boy4 ,you can see that in the solution of copper sulphate at the bottom of the jar there was always present a lot of positive copper ions and of negative sulphate ions4 ,on top of this solution of copper sulphate ,i poured very carefully a weak solution of sulphuric acid4 ,as ,i told you1 an acid always has hydrogen in its molecules4 ,sulphuric acid has molecules formed by two hydrogen atoms and one of the groups which we decided to call sulphate4 ,a better name for this acid would be hydrogen sulphate for that would imply that its molecule is the same as one of copper sulphate1 except that the place of the copper is taken by two atoms of hydrogen4 ,it takes two atoms of hydrogen because the copper atom has two lonely electrons while a hydrogen atom only has one4 ,it takes two electrons to fill up the game which the electrons of the sulphate group are playing4 ,if it can get these from a single atom1 all right2 but if it has to get one from each of two atoms1 it will do it that way4 ,i remember when ,i mixed the sulphuric acid with water that ,i learned to pour the acid into the water and not the other way around4 ,spatterings of sulphuric acid are not good for hands or clothes4 ,with this solution ,i filled the jar almost to the top and then hung over the edge a sort of a crow's foot shape of cast zinc4 ,the zinc reached down into the sulphuric acid solution4 ,there was a binding post on it to which a wire could be connected4 ,this wire and the one which came from the plate of copper at the bottom were the two terminals of the battery4 ,we called the wire from the copper positive and the one from the zinc negative4 ,now we shall see why and how the battery worked4 ,the molecules of sulphuric acid dissociate in solution just as do those of copper sulphate4 ,when sulphuric acid molecules split1 the sulphate part goes away with two electrons which don't belong to it and each of the hydrogen atoms goes away by itself but without its electron4 ,we call each a hydrogen ion but you can see that each is a single proton4 ,in the two solutions are pieces of zinc and copper4 ,zinc is like all the rest of the metals in one way4 ,atoms of metals always have lonely electrons for which there doesn't seem to be room in the game which is going on around their nuclei4 ,copper as we saw has two lonely electrons in each atom4 ,zinc also has two4 ,some metals have one and some two and some even more lonely electrons in each atom4 ,what happens then is this4 ,the sulphate ions wandering around in the weak solution of sulphuric acid come along beside the zinc plate and beckon to its atoms4 ,the sulphate ions had a great deal rather play the game called zinc sulphate than the game called hydrogen sulphate4 ,so the zinc atoms leave their places to join with the sulphate ions4 ,but wait a minute6 ,the sulphate ions have two extra electrons which they kept from the hydrogen atoms4 ,they don't need the two lonely electrons which each zinc atom could bring and so the zinc atom leaves behind it these unnecessary electrons4 ,every time a zinc atom leaves the plate it fails to take all its electrons with it4 ,what leaves the zinc plate1 therefore1 to go into solution is really not a zinc atom but is a zinc ion2 that is1 it is the nucleus of a zinc atom and all except two of the planetary electrons4 ,every time a zinc ion leaves the plate there are left behind two electrons4 ,the plate doesn't want them for all the rest of its atoms have just the same number of protons as of electrons4 ,where are they to go8 ,we shall see in a minute4 ,sometimes the zinc ions which have got into solution meet with sulphate ions and form zinc sulphate molecules4 ,but if they do these molecules split up sooner or later into ions again4 ,in the upper part of the liquid in the jar1 therefore1 there are sulphate ions which are negative and two kinds of positive ions1 namely1 the hydrogen ions and the zinc ions4 ,before the zinc ions began to crowd in there were just enough hydrogen ions to go with the sulphate ions4 ,as it is1 the entrance of the zinc ions has increased the number of positive ions and now there are too many4 ,some of the positive ions1 therefore1 and particularly the hydrogen ions1 because the sulphate prefers to associate with the zinc ions1 can't find enough playfellows and so go down in the jar4 ,down in the bottom of the jar the hydrogen ions find more sulphate ions to play with1 but that leaves the copper ions which used to play with these sulphate ions without any playmates4 ,so the copper ions go still further down and join with the copper atoms of the copper plate4 ,they haven't much right to do so1 for you remember that they haven't their proper number of electrons4 ,each copper ion lacks two electrons of being a copper atom4 ,nevertheless they join the copper plate4 ,the result is a plate of copper which has too few electrons4 ,it needs two electrons for every copper ion which joins it4 ,how about the zinc plate8 ,you remember that it has two electrons more than it needs for every zinc ion which has left it4 ,if only the extra electrons on the negative zinc plate could get around to the positive copper plate4 ,they can if we connect a wire from one plate to the other4 ,then the electrons from the zinc stream into the spaces between the atoms of the wire and push ahead of them the electrons which are wandering around in these spaces4 ,at the other end an equal number of electrons leave the wire to satisfy the positive copper plate4 ,so we have a stream of electrons in the wire1 that is1 a current of electricity and our battery is working4 ,that's the sort of a battery ,i used to play with4 ,if you understand it you can get the general idea of all batteries4 ,let me express it in general terms4 ,at the negative plate of a battery ions go into solution and electrons are left behind4 ,at the other end of the battery positive ions are crowded out of solution and join the plate where they cause a scarcity of electrons2 that is1 make the plate positive4 ,if a wire is connected between the two plates1 electrons will stream through it from the negative plate to the positive2 and this stream is a current of electricity4 ,illustration3 ,pl4 ,,iii4--,dry ,battery for ,use in ,audion ,circuits 7,courtesy of ,national ,carbon ,co41 ,inc474 ,storage ,battery 7,courtesy of the ,electric ,storage ,battery ,co474 ,,letter #d ,,the ,,batteries ,,in ,,your ,,radio ,,set 7,this letter may be omitted on the first reading47 ,,my ,,dear ,,young ,,man3 ,you will need several batteries when you come to set up your radio receiver but you won't use such clumsy affairs as the gravity cell which ,i described in my last letter4 ,some of your batteries will be dry batteries of the size used in pocket flash lights4 ,these are not really dry1 for between the plates they are filled with a moist paste which is then sealed in with wax to keep it from drying out or from spilling4 ,instead of zinc and copper these batteries use zinc and carbon4 ,no glass jar is needed1 for the zinc is formed into a jar shape4 ,in this is placed the paste and in the center of the paste a rod or bar of carbon4 ,the paste doesn't contain sulphuric acid1 but instead has in it a stuff called sal ammoniac2 that is1 ammonium chloride4 ,the battery1 however1 acts very much like the one ,i described in my last letter4 ,ions of zinc leave the zinc and wander into the moist paste4 ,these ions are positive1 just as in the case of the gravity battery4 ,the result is that the electrons which used to associate with a zinc ion to form a zinc atom are left in the zinc plate4 ,that makes the zinc negative for it has more electrons than protons4 ,the zinc ions take the place of the positive ions which are already in the paste4 ,the positive ions which originally belonged with the paste1 therefore1 move along to the carbon rod and there get some electrons4 ,taking electrons away from the carbon leaves it with too many protons2 that is1 leaves it positive4 ,in the little flash light batteries1 therefore1 you will always find that the round carbon rod1 which sticks out of the center1 is positive and the zinc casing is negative4 ,the trouble with the battery like the one ,i used to make is that the zinc plate wastes away4 ,every time a zinc ion leaves it that means that the greater part of an atom is gone4 ,then when the two electrons which were left behind get a chance to start along a copper wire toward the positive plate of the battery there goes the rest of the atom4 ,after a while there is no more zinc plate4 ,it is easy to see what has happened4 ,all the zinc has gone into solution or been eaten away as most people say4 ,dry batteries1 however1 don't stop working because the zinc gets used up1 but because the active stuff in the paste1 the ammonium chloride1 is changed into something else4 ,there's another kind of battery which you will need to use with your radio set2 that is the storage battery4 ,storage batteries can be used over and over again if they are charged between times and will last for a long time if properly cared for4 ,then too1 they can give a large current1 that is1 a big swift-moving stream of electrons4 ,you will need that when you wish to heat the filament of the audion in your receiving set4 ,the ,english call our storage batteries by the name accumulators4 ,i don't like that name at all1 but ,i don't like our name for them nearly as well as ,i do the name reversible batteries4 ,nobody uses this last name because it's too late to change4 ,nevertheless a storage battery is reversible1 for it will work either way at an instant's notice4 ,a storage battery is something like a boy's wagon on a hill side4 ,it will run down hill but it can be pushed up again for another descent4 ,you can use it to send a stream of electrons through a wire from its negative plate to its positive plate4 ,then if you connect these plates to some other battery or to a generator1 7that is1 a dynamo7 you can make a stream of electrons go in the other direction4 ,when you have done so long enough the battery is charged again and ready to discharge4 ,i am not going to tell you very much about the storage battery but you ought to know a little about it if you are to own and run one with your radio set4 ,when it is all charged and ready to work1 the negative plate is a lot of soft spongy lead held in place by a frame of harder lead4 ,the positive plate is a lead frame with small squares which are filled with lead peroxide1 as it is called4 ,this is a substance with molecules formed of one lead atom and two oxygen atoms4 ,why the chemists call it lead peroxide instead of just lead oxide ,i'll tell you some other time1 but not in these letters4 ,between the two plates is a wood separator to keep pieces of lead from falling down between and touching both plates4 ,you know what would happen if a piece of metal touched both plates4 ,there would be a short circuit1 that is1 a sort of a short cut across lots by which some of the electrons from the negative plate could get to the positive plate without going along the wires which we want them to travel4 ,that's why there are separators4 ,the two plates are in a jar of sulphuric acid solution4 ,the sulphuric acid has molecules which split up in solution1 as you remember1 into hydrogen ions and the ions which we called sulphate4 ,in my gravity battery the sulphate ions used to coax the zinc ions away into the solution4 ,in the storage battery on the other hand the sulphate ions can get to most of the lead atoms because the lead is so spongy4 ,when they do1 they form lead sulphate right where the lead atoms are4 ,they don't really need whole lead atoms1 because they have two more electrons than they deserve1 so there are two extra electrons for every molecule of lead sulphate which is formed4 ,that's why the spongy lead plate is negative4 ,the lead sulphate won't dissolve1 so it stays there on the plate as a whitish coating4 ,now see what that means4 ,what are the hydrogen ions going to do8 ,as long as there was sulphuric acid in the water there was plenty of sulphate ions for them to associate with as often as they met2 and they would meet pretty often4 ,but if the sulphate ions get tied up with the lead of the plate there will be too many hydrogen ions left in the solution4 ,now what are the hydrogen ions to do8 ,they are going to get as far away from each other as they can1 for they are nothing but protons2 and protons don't like to associate4 ,they only stayed around in the first place because there was always plenty of sulphate ions with whom they liked to play4 ,when the hydrogen ions try to get away from each other they go to the other plate of the battery1 and there they will get some electrons1 if they have to steal in their turn4 ,i won't try to tell you all that happens at the other plate4 ,the hydrogen ions get the electrons which they need1 but they get something more4 ,they get some of the oxygen away from the plate and so form molecules of water4 ,you remember that water molecules are made of two atoms of hydrogen and one of oxygen4 ,meanwhile1 the lead atoms1 which have lost their oxygen companions1 combine with some of the sulphate ions which are in that neighborhood4 ,during the mix-up electrons are carried away from the plate and that leaves it positive4 ,the result of all this is a little lead sulphate on each plate1 a negative plate where the spongy lead was1 and a positive plate where the lead peroxide was4 ,notice very carefully that ,i said a little lead sulphate on each plate4 ,the sort of thing ,i have been describing doesn't go on very long4 ,if it did the battery would run down inside itself and then when we came to start our automobile we would have to get out and crank4 ,how long does it go on8 ,answer another question first4 ,so far we haven't connected any wire between the two plates of the battery1 and so none of the electrons on the negative plate have any way of getting around to the positive plate where electrons are badly needed4 ,every time a negative sulphate ion combines with the spongy lead of the negative plate there are two more electrons added to that plate4 ,you know how well electrons like each other4 ,do they let the sulphate ions keep giving that plate more electrons8 ,there is the other question2 and the answer is that they do not4 ,every electron that is added to that plate makes it just so much harder for another sulphate ion to get near enough to do business at all4 ,that's why after a few extra electrons have accumulated on the spongy lead plate the actions which ,i was describing come to a stop4 ,do they ever begin again8 ,they do just as soon as there is any reduction in the number of electrons which are hopping around in the negative plate trying to keep out of each other's way4 ,when we connect a wire between the plates we let some of these extra electrons of the negative plate pass along to the positive plate where they will be welcome4 ,and the moment a couple of them start off on that errand along comes another sulphate ion in the solution and lands two more electrons on the plate4 ,that's how the battery keeps on discharging4 ,we mustn't let it get too much discharged for the lead sulphate is not soluble1 as ,i just told you1 and it will coat up that plate until there isn't much chance of getting the process to reverse4 ,that's why we are so careful not to let the discharge process go on too long before we reverse it and charge4 ,that's why1 when the car battery has been used pretty hard to start the car1 ,i like to run quite a while to let the generator charge the battery again4 ,when the battery charges1 the process reverses and we get spongy lead on the negative plate and lead peroxide on the positive plate4 ,you've learned enough for one day4 ,write me your questions and ,i'll answer and then go on in my next letter to tell how the audion works4 ,you know about conduction of electricity in wires2 that is1 about the electron stream1 and about batteries which can cause the stream4 ,now you are ready for the most wonderful little device known to science3 the audion4 ,,letter #e ,,getting ,,electrons ,,from ,a ,,heated ,,wire ,,dear ,,son3 ,i was pleased to get your letter and its questions4 ,yes1 a proton is a speck of electricity of the kind we call positive and an electron is of the kind we call negative4 ,you might remember this simple law2 ,like kinds of electricity repel1 and unlike attract4 ,the word ion#b is used to describe any atom1 or part of a molecule which can travel by itself and has more or less than its proper number of electrons4 ,by proper number of electrons ,i mean proper for the number of protons which it has4 ,if an ion has more electrons than protons it is negative2 if the inequality is the other way around it is positive4 ,an atom or molecule has neither more nor less protons than electrons4 ,it is neutral or uncharged1 as we say4 ,no1 not every substance which will dissolve will dissociate or split up into positive and negative ions4 ,the salt which you eat will1 but the sugar will not4 ,if you want a name for those substances which will dissociate in solution1 call them electrolytes4 ,to make a battery we must always use an electrolyte4 ,yes1 it is hard to think of a smooth piece of metal or a wire as full of holes4 ,even in the densest solids like lead the atoms are quite far apart and there are large spaces between the nuclei and the planetary electrons of each atom4 ,i hope this clears up the questions in your mind for ,i want to get along to the vacuum tube4 ,by a vacuum we mean a space which has very few atoms or molecules in it1 just as few as we can possibly get1 with the best methods of pumping and exhausting4 ,for the present let's suppose that we can get all the gas molecules1 that is1 all the air1 out of a little glass bulb4 ,the audion is a glass bulb like an electric light bulb which has in it a thread1 or filament1 of metal4 ,the ends of this filament extend out through the glass so that we may connect a battery to them and pass a current of electricity through the wire4 ,if we do so the wire gets hot4 ,what do we mean when we say the wire gets hot8 ,we mean that it feels hot4 ,it heats the glass bulb and we can feel it4 ,but what do we mean in words of electrons and atoms8 ,to answer this we must start back a little way4 ,in every bit of matter in our world the atoms and molecules are in very rapid motion4 ,in gases they can move anywhere2 and do4 ,that's why odors travel so fast4 ,in liquids most of the molecules or atoms have to do their moving without getting out of the dish or above the surface4 ,not all of them stay in1 however1 for some are always getting away from the liquid and going out into the air above4 ,that is why a dish of water will dry up so quickly4 ,the faster the molecules are going the better chance they have of jumping clear away from the water like fish jumping in the lake at sundown4 ,heating the liquid makes its molecules move faster and so more of them are able to jump clear of the rest of the liquid4 ,that's why when we come in wet we hang our clothes where they will get warm4 ,the water in them evaporates more quickly when it is heated because all we mean by heating is speeding up the molecules4 ,in a solid body the molecules can't get very far away from where they start but they keep moving back and forth and around and around4 ,the hotter the body is1 the faster are its molecules moving4 ,generally they move a little farther when the body is hot than when it is cold4 ,that means they must have a little more room and that is why a body is larger when hot than when cold4 ,it expands with heating because its molecules are moving more rapidly and slightly farther4 ,when a wire is heated its molecules and atoms are hurried up and they dash back and forth faster than before4 ,now you know that a wire1 like the filament of a lamp1 gets hot when the electricity is turned on1 that is1 when there is a stream of electrons passing through it4 ,why does it get hot8 ,because when the electrons stream through it they bump and jostle their way along like rude boys on a crowded sidewalk4 ,the atoms have to step a bit more lively to keep out of the way4 ,these more rapid motions of the atoms we recognize by the wire growing hotter4 ,that is why an electric current heats a wire through which it is flowing4 ,now what happens to the electrons1 the rude boys who are dodging their way along the sidewalk8 ,some of them are going so fast and so carelessly that they will have to dodge out into the gutter and off the sidewalk entirely4 ,the more boys that are rushing along and the faster they are going the more of them will be turned aside and plunge off the sidewalks4 ,the greater and faster the stream of electrons1 that is the more current which is flowing through the wire1 the more electrons will be emitted1 that is1 thrown out of the wire4 ,if you could watch them you would see them shooting out of the wire1 here1 there1 and all along its length1 and going in every direction4 ,the number which shoot out each second isn't very large until they have stirred things up so that the wire is just about red hot4 ,what becomes of them8 ,sometimes they don't get very far away from the wire and so come back inside again4 ,they scoot off the sidewalk and on again just as boys do in dodging their way along4 ,some of them start away as if they were going for good4 ,if the wire is in a vacuum tube1 as it is in the case of the audion1 they can't get very far away4 ,of course there is lots of room2 but they are going so fast that they need more room just as older boys who run fast need a larger play ground than do the little tots4 ,by and by there gets to be so many of them outside that they have to dodge each other and some of them are always dodging back into the wire while new electrons are shooting out from it4 ,when there are just as many electrons dodging back into the wire each second as are being emitted from it the vacuum in the tube has all the electrons it can hold4 ,we might say it is saturated with electrons1 which means1 in slang1 full up4 ,if any more electrons are to get out of the filament just as many others which are already outside have to go back inside4 ,or else they have got to be taken away somewhere else4 ,what ,i have just told you about electrons getting away from a heated wire is very much like what happens when a liquid is heated4 ,the molecules of the liquid get away from the surface4 ,if we cover a dish of liquid which is being heated the liquid molecules can't get far away and very soon the space between the surface of the liquid and the cover gets saturated with them4 ,then every time another molecule escapes from the surface of the liquid there must be some molecule which goes back into the liquid4 ,there is then just as much condensation back into liquid as there is evaporation from it4 ,that's why in cooking they put covers over the vessels when they don't want the liquid all to boil away4 ,sometimes we speak of the vacuum tube in the same words we would use in describing evaporation of a liquid4 ,the molecules of the liquid which have escaped form what is called a vapor of the liquid4 ,as you know there is usually considerable water vapor in the air4 ,we say then that electrons are boiled out of the filament and that there is a vapor of electrons in the tube4 ,that is enough for this letter4 ,next time ,i shall tell you how use is made of these electrons which have been boiled out and are free in the space around the filament4 ,footnote #b3 ,if the reader has omitted ,letters #c and #d he should omit this paragraph and the next4 ,,letter #f ,,the ,,audion ,,dear ,,son3 ,in my last letter ,i told how electrons are boiled out of a heated filament4 ,the hotter the filament the more electrons are emitted each second4 ,if the temperature is kept steady1 or constant as we say1 then there are emitted each second just the same number of electrons4 ,when the filament is enclosed in a vessel or glass bulb these electrons which get free from it cannot go very far away4 ,some of them1 therefore1 have to come back to the filament and the number which returns each second is just equal to the number which is leaving4 ,you realize that this is what is happening inside an ordinary electric light bulb when its filament is being heated4 ,illustration3 ,fig #d ,an ordinary electric light bulb1 however1 is not an audion although it is like one in the emission of electrons from its filament4 ,that reminds me that last night as ,i was waiting for a train ,i picked up one of the ,radio ,supplements which so many newspapers are now running4 ,there was a column of enquiries4 ,one letter told how its writer had tried to use an ordinary electric light bulb to receive radio signals4 ,he had plenty of electrons in it but no way to control them and make their motions useful4 ,in an audion besides the filament there are two other things4 ,one is a little sheet or plate of metal with a connecting wire leading out through the glass walls and the other is a little wire screen shaped like a gridiron and so called a grid4 ,it also has a connecting wire leading through the glass4 ,fig4 #d shows an audion4 ,it will be most convenient1 however1 to represent an audion as in ,fig4 #e4 ,there you see the filament1 ,f1 with its two terminals brought out from the tube1 the plate1 ,p1 and between these the grid1 ,g4 ,illustration3 ,fig #e ,these three parts of the tube are sometimes called elements4 ,usually1 however1 they are called electrodes and that is why the audion is spoken of as the three-electrode vacuum tube4 ,an electrode is what we call any piece of metal or wire which is so placed as to let us get at electrons 7or ions7 to control their motions4 ,let us see how it does so4 ,to start with1 we shall forget the grid and think of a tube with only a filament and a plate in it--a two-electrode tube4 ,we shall represent it as in ,fig4 #f and show the battery which heats the filament by some lines as at ,a4 ,in this way of representing a battery each cell is represented by a short heavy line and a longer lighter line4 ,the heavy line stands for the negative plate and the longer line for the positive plate4 ,we shall call the battery which heats the filament the filament battery or sometimes the ,a-battery4 ,as you see1 it is formed by several battery cells connected in series4 ,illustration3 ,fig #f ,sometime later ,i may tell you how to connect battery cells together and why4 ,for the present all you need to remember is that two batteries are in series if the positive plate of one is connected to the negative plate of the other4 ,if the batteries are alike they will pull an electron just twice as hard as either could alone4 ,illustration3 ,pl4 ,,iv4--,radiotron 7,courtesy of ,radio ,corporation of ,america74 ,to heat the filament of an audion1 such as you will probably use in your set1 will require three storage-battery cells1 like the one ,i described in my fourth letter1 all connected in series4 ,we generally use storage batteries of about the same size as those in the automobile4 ,if you will look at the automobile battery you will see that it is made of three cells connected in series4 ,that battery would do very well for the filament circuit4 ,by the way1 do you know what a circuit is8 ,the word comes from the same ,latin word as our word circus4 ,the ,romans were very fond of chariot racing at their circuses and built race tracks around which the chariots could go4 ,a circuit1 therefore1 is a path or track around which something can race2 and an electrical circuit is a path around which electrons can race4 ,the filament1 the ,a-battery and the connecting wires of ,fig4 #f form a circuit4 ,illustration3 ,fig #g ,let us imagine another battery formed by several cells in series which we shall connect to the tube as in ,fig4 #g4 ,all the positive and negative terminals of these batteries are connected in pairs1 the positive of one cell to the negative of the next1 except for one positive and one negative4 ,the remaining positive terminal is the positive terminal of the battery which we are making by this series connection4 ,we then connect this positive terminal to the plate and the negative terminal to the filament as shown in the figure4 ,this new battery we shall call the plate battery or the ,b-battery4 ,now what's going to happen8 ,the ,b-battery will want to take in electrons at its positive terminal and to send them out at its negative terminal4 ,the positive is connected to the plate in the vacuum tube of the figure and so draws some of the electrons of the plate away from it4 ,where do these electrons come from8 ,they used to belong to the atoms of the plate but they were out playing in the space between the atoms1 so that they came right along when the battery called them4 ,that leaves the plate with less than its proper number of electrons2 that is1 leaves it positive4 ,so the plate immediately draws to itself some of the electrons which are dodging about in the vacuum around it4 ,do you remember what was happening in the tube8 ,the filament was steadily going on emitting electrons although there were already in the tube so many electrons that just as many crowded back into the filament each second as the filament sent out4 ,the filament was neither gaining nor losing electrons1 although it was busy sending them out and welcoming them home again4 ,when the ,b-battery gets to work all this is changed4 ,the ,b-battery attracts electrons to the plate and so reduces the crowd in the tube4 ,then there are not as many electrons crowding back into the filament as there were before and so the filament loses more than it gets back4 ,suppose that1 before the ,b-battery was connected to the plate1 each tiny length of the filament was emitting #ajjj electrons each second but was getting #ajjj back each second4 ,there was no net change4 ,now1 suppose that the ,b-battery takes away #ajj of these each second4 ,then only #ijj get back to the filament and there is a net loss from the filament of #ajj4 ,each second this tiny length of filament sends into the vacuum #ajj electrons which are taken out at the plate4 ,from each little bit of filament there is a stream of electrons to the plate4 ,millions of electrons1 therefore1 stream across from filament to plate4 ,that is1 there is a current of electricity between filament and plate and this current continues to flow as long as the ,a-battery and the ,b-battery do their work4 ,the negative terminal of the ,b-battery is connected to the filament4 ,every time this battery pulls an electron from the plate its negative terminal shoves one out to the filament4 ,you know from my third and fourth letters that electrons are carried through a battery from its positive to its negative terminal4 ,you see1 then1 that there is the same stream of electrons through the ,b-battery as there is through the vacuum between filament and plate4 ,this same stream passes also through the wires which connect the battery to the tube4 ,the path followed by the stream of electrons includes the wires1 the vacuum and the battery in series4 ,we call this path the plate circuit4 ,we can connect a telephone receiver1 or a current-measuring instrument1 or any thing we wish which will pass a stream of electrons1 so as to let this same stream of electrons pass through it also4 ,all we have to do is to connect the instrument in series with the other parts of the plate circuit4 ,i'll show you how in a minute1 but just now ,i want you to understand that we have a stream of electrons1 for ,i want to tell you how it may be controlled4 ,suppose we use another battery and connect it between the grid and the filament so as to make the grid positive4 ,that would mean connecting the positive terminal of the battery to the grid and the negative to the filament as shown by the ,c-battery of ,fig4 #h4 ,this figure also shows a current-measuring instrument in the plate circuit4 ,what effect is this ,c-battery1 or grid-battery1 going to have on the current in the plate circuit8 ,making the grid positive makes it want electrons4 ,it will therefore act just as we saw that the plate did and pull electrons across the vacuum towards itself4 ,illustration3 ,fig #h ,what happens then is something like this3 ,electrons are freed at the filament2 the plate and the grid both call them and they start off in a rush4 ,some of them are stopped by the wires of the grid but most of them go on by to the plate4 ,the grid is mostly open space1 you know1 and the electrons move as fast as lightning4 ,they are going too fast in the general direction of the grid to stop and look for its few and small wires4 ,when the grid is positive the grid helps the plate to call electrons away from the filament4 ,making the grid positive1 therefore1 increases the stream of electrons between filament and plate2 that is1 increases the current in the plate circuit4 ,we could get the same effect so far as concerns an increased plate current by using more batteries in series in the plate circuit so as to pull harder4 ,but the grid is so close to the filament that a single battery cell in the grid circuit can call electrons so strongly that it would take several extra battery cells in the plate circuit to produce the same effect4 ,illustration3 ,fig #i ,if we reverse the grid battery1 as in ,fig4 #i1 so as to make the grid negative1 then1 instead of attracting electrons the grid repels them4 ,nowhere near as many electrons will stream across to the plate when the grid says1 ,no1 go back4 ,the grid is in a strategic position and what it says has a great effect4 ,when there is no battery connected to the grid it has no possibility of influencing the electron stream which the plate is attracting to itself4 ,we say1 then1 that the grid is uncharged or is at zero potential1 meaning that it is zero or nothing in possibility4 ,but when the grid is charged1 no matter how little1 it makes a change in the plate current4 ,when the grid says ,come on1 even though very softly1 it has as much effect on the electrons as if the plate shouted at them1 and a lot of extra electrons rush for the plate4 ,but when the grid whispers ,go back1 many electrons which would otherwise have gone streaking off to the plate crowd back toward the filament4 ,that's how the audion works4 ,there is an electron stream and a wonderfully sensitive way of controlling the stream4 ,,letter #g ,,how ,,to ,,measure ,,an ,,electron ,,stream 7,this letter may be omitted on the first reading47 ,,dear ,,youth3 ,if we are to talk about the audion and how its grid controls the current in the plate circuit we must know something of how to measure currents4 ,an electric current is a stream of electrons4 ,we measure it by finding the rate at which electrons are traveling along through the circuit4 ,what do we mean by the word rate8 ,you know what it means when a speedometer says twenty miles an hour4 ,if the car should keep going just as it was doing at the instant you looked at the speedometer it would go twenty miles in the next hour4 ,its rate is twenty miles an hour even though it runs into a smash the next minute and never goes anywhere again except to the junk heap4 ,it's the same when we talk of electric currents4 ,we say there is a current of such and such a number of electrons a second going by each point in the circuit4 ,we don't mean that the current isn't going to change1 for it may get larger or smaller1 but we do mean that if the stream of electrons keeps going just as it is there will be such and such a number of electrons pass by in the next second4 ,in most of the electrical circuits with which you will deal you will find that electrons must be passing along in the circuit at a most amazing rate if there is to be any appreciable effect4 ,when you turn on the #dj-watt light at your desk you start them going through the filament of the lamp at the rate of about two and a half billion billion each second4 ,you have stood on the sidewalk in the city and watched the people stream past you4 ,just suppose you could stand beside that narrow little sidewalk which the filament offers to the electrons and count them as they go by4 ,we don't try to count them although we do to-day know about how many go by in a second if the current is steady4 ,if some one asks you how old you are you don't say ,about five hundred million seconds2 you tell him in years4 ,when some one asks how large a current is flowing in a wire we don't tell him six billion billion electrons each second2 we tell him one ampere4 ,just as we use years as the units in which to count up time so we use amperes as the units in which to count up streams of electrons4 ,when a wire is carrying a current of one ampere the electrons are streaming through it at the rate of about #f1jjj1jjj1jjj1jjj1jjj1jjj a second4 ,don't try to remember this number but do remember that an ampere is a unit in which we measure currents just as a year is a unit in which we measure time4 ,an ampere is a unit in which we measure streams of electrons just as miles per hour is a unit in which we measure the speed of trains or automobiles4 ,if you wanted to find the weight of something you would take a scale and weigh it1 wouldn't you8 ,you might take that spring balance which hangs out in the kitchen4 ,but if the spring balance said the thing weighed five pounds how would you know if it was right8 ,of course you might take what ever it was down town and weigh it on some other scales but how would you know those scales gave correct weight8 ,the only way to find out would be to try the scales with weights which you were sure were right and see if the readings on the scale correspond to the known weights4 ,then you could trust it to tell you the weight of something else4 ,that's the way scales are tested4 ,in fact that's the way that the makers know how to mark them in the first place4 ,they put on known weights and marked the lines and figures which you see4 ,what they did was called calibrating the scale4 ,you could make a scale for yourself if you wished1 but if it was to be reliable you would have to find the places for the markings by applying known weights1 that is1 by calibration4 ,how would you know that the weights you used to calibrate your scale were really what you thought them to be8 ,you would have to find some place where they had a weight that everybody would agree was correct and then compare your weight with that4 ,you might1 for example1 send your pound weight to the ,bureau of ,standards in ,washington and for a small payment have the ,bureau compare it with the pound which it keeps as a standard4 ,that is easy where one is interested in a pound4 ,but it is a little different when one is interested in an ampere4 ,you can't make an ampere out of a piece of platinum as you can a standard pound weight4 ,an ampere is a stream of electrons at about the rate of six billion billion a second4 ,no one could ever count anywhere near that many1 and yet everybody who is concerned with electricity wants to be able to measure currents in amperes4 ,how is it done8 ,first there is made an instrument which will have something in it to move when electrons are flowing through the instrument4 ,we want a meter for the flow of electrons4 ,in the basement we have a meter for the flow of gas and another for the flow of water4 ,each of these has some part which will move when the water or the gas passes through4 ,but they are both arranged with little gear wheels so as to keep track of all the water or gas which has flowed through2 they won't tell the rate at which the gas or water is flowing4 ,they are like the odometer on the car which gives the trip mileage or the total mileage4 ,we want a meter like the speedometer which will indicate at each instant just how fast the electrons are streaming through it4 ,there are several kinds of meters but ,i shall not try to tell you now of more than one4 ,the simplest to understand is called a hot-wire meter4 ,you already know that an electron stream heats a wire4 ,suppose a piece of fine wire is fastened at the two ends and that there are binding posts also fastened to these ends of the wire so that the wire may be made part of the circuit where we want to know the electron stream4 ,then the same stream of electrons will flow through the fine wire as through the other parts of the circuit4 ,because the wire is fine it acts like a very narrow sidewalk for the stream of electrons and they have to bump and jostle pretty hard to get through4 ,that's why the wire gets heated4 ,you know that a heated wire expands4 ,this wire expands4 ,it grows longer and because it is held firmly at the ends it must bow out at the center4 ,the bigger the rate of flow of electrons the hotter it gets2 and the hotter it gets the more it bows out4 ,at the center we might fasten one end--the short end--of a little lever4 ,a small motion of this short end of the lever will mean a large motion of the other end1 just like a teeter board when one end is longer than the other2 the child on the long end travels further than the child on the short end4 ,the lever magnifies the motion of the center of the hot wire part of our meter so that we can see it easier4 ,illustration3 ,fig #aj ,there are several ways to make such a meter4 ,the one shown in ,fig4 #aj is as easy to understand as any4 ,we shape the long end of the lever like a pointer4 ,then the hotter the wire the farther the pointer moves4 ,if we could put this meter in an electric circuit where we knew one ampere was flowing we could put a numeral #a opposite where the pointer stood4 ,then if we could increase the current until there were two amperes flowing through the meter we could mark that position of the pointer #b and so on4 ,that's the way we would calibrate the meter4 ,after we had done so we would call it an ammeter because it measures amperes4 ,years ago people would have called it an amperemeter but no one who is up-to-date would call it so to-day4 ,illustration3 ,fig #aa ,if we had a very carefully made ammeter we would send it to the ,bureau of ,standards to be calibrated4 ,at the ,bureau they have a number of meters which they know are correct in their readings4 ,they would put one of their meters and ours into the same circuit so that both carry the same stream of electrons as in ,fig4 #aa4 ,then whatever the reading was on their meter could be marked opposite the pointer on ours4 ,now ,i want to tell you how the physicists at the ,bureau know what is an ampere4 ,several years ago there was a meeting or congress of physicists and electrical engineers from all over the world who discussed what they thought should be the unit in which to measure current4 ,they decided just what they would call an ampere and then all the countries from which they came passed laws saying that an ampere should be what these scientists had recommended4 ,to-day1 therefore1 an ampere is defined by law4 ,to tell when an ampere of current is flowing requires the use of two silver plates and a solution of silver nitrate4 ,silver nitrate has molecules made up of one atom of silver combined with a group of atoms called nitrate4 ,you remember that the molecule of copper sulphate1 discussed in our third letter1 was formed by a copper atom and a group called sulphate4 ,nitrate is another group something like sulphate for it has oxygen atoms in it1 but it has three instead of four1 and instead of a sulphur atom there is an atom of nitrogen4 ,when silver nitrate molecules go into solution they break up into ions just as copper sulphate does4 ,one ion is a silver atom which has lost one electron4 ,this electron was stolen from it by the nitrate part of the molecule when they dissociated4 ,the nitrate ion1 therefore1 is formed by a nitrogen atom1 three oxygen atoms1 and one extra electron4 ,if we put two plates of silver into such a solution nothing will happen until we connect a battery to the plates4 ,then the battery takes electrons away from one plate and gives electrons to the other4 ,some of the atoms in the plate which the battery is robbing of electrons are just like the silver ions which are moving around in the solution4 ,that's why they can go out into the solution and play with the nitrate ions each of which has an extra electron which it stole from some silver atom4 ,but the moment silver ions leave their plate we have more silver ions in the solution than we do sulphate ions4 ,the only thing that can happen is for some of the silver ions to get out of the solution4 ,they aren't going back to the positive silver plate from which they just came4 ,they go on toward the negative plate where the battery is sending an electron for every one which it takes away from the positive plate4 ,there start off towards the negative plate1 not only the ions which just came from the positive plate1 but all the ions that are in the solution4 ,the first one to arrive gets an electron but it can't take it away from the silver plate4 ,and why should it8 ,as soon as it has got this electron it is again a normal silver atom4 ,so it stays with the other atoms in the silver plate4 ,that's what happens right along4 ,for every atom which is lost from the positive plate there is one added to the negative plate4 ,the silver of the positive plate gradually wastes away and the negative plate gradually gets an extra coating of silver4 ,every time the battery takes an electron away from the positive plate and gives it to the negative plate there is added to the negative plate an atom of silver4 ,if the negative plate is weighed before the battery is connected and again after the battery is disconnected we can tell how much silver has been added to it4 ,suppose the current has been perfectly steady1 that is1 the same number of electrons streaming through the circuit each second4 ,then if we know how long the current has been running we can tell how much silver has been deposited each second4 ,the law says that if silver is being deposited at the rate of #j4jjaaah gram each second then the current is one ampere4 ,that's a small amount of silver1 only about a thousandth part of a gram1 and you know that it takes #bh4ce grams to make an ounce4 ,it's a very small amount of silver but it's an enormous number of atoms4 ,how many8 ,six billion billion1 of course1 for there is deposited one atom for each electron in the stream4 ,in my next letter ,i'll tell you how we measure the pull which batteries can give to electrons1 and then we shall be ready to go on with more about the audion4 ,,letter #h ,,electron-,,moving-,,forces 7,this letter may be omitted on the first reading47 ,,dear ,,young ,,man3 ,i trust you have a fairly good idea that an ampere means a stream of electrons at a certain definite rate and hence that a current of say #c amperes means a stream with three times as many electrons passing along each second4 ,in the third and fourth letters you found out why a battery drives electrons around a conducting circuit4 ,you also found that there are several different kinds of batteries4 ,batteries differ in their abilities to drive electrons and it is therefore convenient to have some way of comparing them4 ,we do this by measuring the electron-moving-force or electromotive force which each battery can exert4 ,to express electromotive force and give the results of our measurements we must have some unit4 ,the unit we use is called the volt4 ,the volt is defined by law and is based on the suggestions of the same body of scientists who recommended the ampere of our last letter4 ,they defined it by telling how to make a particular kind of battery and then saying that this battery had an electromotive force of a certain number of volts4 ,one can buy such standard batteries1 or standard cells as they are called1 or he can make them for himself4 ,to be sure that they are just right he can then send them to the ,bureau of ,standards and have them compared with the standard cells which the ,bureau has4 ,i don't propose to tell you much about standard cells for you won't have to use them until you come to study physics in real earnest4 ,they are not good for ordinary purposes because the moment they go to work driving electrons the conditions inside them change so their electromotive force is changed4 ,they are delicate little affairs and are useful only as standards with which to compare other batteries4 ,and even as standard batteries they must be used in such a way that they are not required to drive any electrons4 ,illustration3 ,fig #ab ,let's see how it can be done4 ,suppose two boys sit opposite each other on the floor and brace their feet together4 ,then with their hands they take hold of a stick and pull in opposite directions4 ,if both have the same stick-motive-force the stick will not move4 ,now suppose we connect the negative feet--,i mean negative terminals--of two batteries together as in ,fig4 #ab4 ,then we connect their positive terminals together by a wire4 ,in the wire there will be lots of free electrons ready to go to the positive plate of the battery which pulls the harder4 ,if the batteries are equal in electromotive force these electrons will stay right where they are4 ,there will be no stream of electrons and yet we'll be using one of the batteries to compare with the other4 ,that is all right1 you think1 but what are we to do when the batteries are not just equal in e4 m4 f48 7e4 m4 f4 is code for electromotive force74 ,i'll tell you1 because the telling includes some other ideas which will be valuable in your later reading4 ,illustration3 ,fig #ac ,suppose we take batteries which aren't going to be injured by being made to work--storage batteries will do nicely--and connect them in series as in ,fig4 #ac4 ,when batteries are in series they act like a single stronger battery1 one whose e4 m4 f4 is the sum of the e4 m4 f4's of the separate batteries4 ,connect these batteries to a long fine wire as in ,fig4 #ad4 ,there is a stream of electrons along this wire4 ,next connect the negative terminal of the standard cell to the negative terminal of the storage batteries1 that is1 brace their feet against each other4 ,then connect a wire to the positive terminal of the standard cell4 ,this wire acts just like a long arm sticking out from the positive plate of this cell4 ,illustration3 ,fig #ad ,touch the end of the wire1 which is p of ,fig4 #ad1 to some point as a on the fine wire4 ,now what do we have8 ,right at a1 of course1 there are some free electrons and they hear the calls of both batteries4 ,if the standard battery1 ,s of the figure1 calls the stronger they go to it4 ,in that case move the end p nearer the positive plate of the battery ,b1 so that it will have a chance to exert a stronger pull4 ,suppose we try at c and find the battery ,b is there the stronger4 ,then we can move back to some point1 say b1 where the pulls are equal4 ,to make a test like this we put a sensitive current-measuring instrument in the wire which leads from the positive terminal of the standard cell4 ,we also use a long fine wire so that there can never be much of an electron stream anyway4 ,when the pulls are equal there will be no current through this instrument4 ,as soon as we find out where the proper setting is we can replace ,s by some other battery1 say ,x1 which we wish to compare with ,s4 ,we find the setting for that battery in the same way as we just did for ,s4 ,suppose it is at d in ,fig4 #ad while the setting for ,s was at b4 ,we can see at once that ,x is stronger than ,s4 ,the question1 however1 is how much stronger4 ,perhaps it would be better to try to answer this question by talking about e4 m4 f4's4 ,it isn't fair to speak only of the positive plate which calls1 we must speak also of the negative plate which is shooing electrons away from itself4 ,the idea of e4 m4 f4 takes care of both these actions4 ,the steady stream of electrons in the fine wire is due to the e4 m4 f4 of the battery ,b1 that is to the pull of the positive terminal and the shove of the negative4 ,if the wire is uniform1 that is the same throughout its length1 then each inch of it requires just as much e4 m4 f4 as any other inch4 ,two inches require twice the e4 m4 f4 which one inch requires4 ,we know how much e4 m4 f4 it takes to keep the electron stream going in the part of the wire from n to b4 ,it takes just the e4 m4 f4 of the standard cell1 ,s1 because when that had its feet braced at n it pulled just as hard at b as did the big battery ,b4 ,suppose the distance n to d 7usually written nd7 is twice as great as that from n to b 7nb74 ,that means that battery ,x has twice the e4 m4 f4 of battery ,s4 ,you remember that ,x could exert the same force through the length of wire nd1 as could the large battery4 ,that is twice what cell ,s can do4 ,therefore if we know how many volts to call the e4 m4 f4 of the standard cell we can say that ,x has an e4 m4 f4 of twice as many volts4 ,if we measured dry batteries this way we should find that they each had an e4 m4 f4 of about #a4df volts4 ,a storage battery would be found to have about #b4d volts when fully charged and perhaps as low as #b4a volts when we had run it for a while4 ,that is the way in which to compare batteries and to measure their e4 m4 f4's1 but you see it takes a lot of time4 ,it is easier to use a voltmeter which is an instrument for measuring e4 m4 f4's4 ,here is how one could be made4 ,first there is made a current-measuring instrument which is quite sensitive1 so that its pointer will show a deflection when only a very small stream of electrons is passing through the instrument4 ,we could make one in the same way as we made the ammeter of the last letter but there are other better ways of which ,i'll tell you later4 ,then we connect a good deal of fine wire in series with the instrument for a reason which ,i'll tell you in a minute4 ,the next and last step is to calibrate4 ,we know how many volts of e4 m4 f4 are required to keep going the electron stream between n and b--we know that from the e4 m4 f4 of our standard cell4 ,suppose then that we connect this new instrument1 which we have just made1 to the wire at n and b as in ,fig4 #ae4 ,some of the electrons at n which are so anxious to get away from the negative plate of battery ,b can now travel as far as b through the wire of the new instrument4 ,they do so and the pointer swings around to some new position4 ,opposite that we mark the number of volts which the standard battery told us there was between n and b4 ,illustration3 ,fig #ae ,if we move the end of the wire from b to d the pointer will take a new position4 ,opposite this we mark twice the number of volts of the standard cell4 ,we can run it to a point e where the distance ne is one-half nb1 and mark our scale with half the number of volts of the standard cell1 and so on for other positions along the wire4 ,that's the way we calibrate a sensitive current-measuring instrument 7with its added wire1 of course7 so that it will read volts4 ,it is now a voltmeter4 ,if we connect a voltmeter to the battery ,x as in ,fig4 #af the pointer will tell us the number of volts in the e4 m4 f4 of ,x1 for the pointer will take the same position as it did when the voltmeter was connected between n and d4 ,there is only one thing to watch out for in all this4 ,we must be careful that the voltmeter is so made that it won't offer too easy a path for electrons to follow4 ,we only want to find how hard a battery can pull an electron1 for that is what we mean by e4 m4 f4 ,of course1 we must let a small stream of electrons flow through the voltmeter so as to make the pointer move4 ,that is why voltmeters of this kind are made out of a long piece of fine wire or else have a coil of fine wire in series with the current-measuring part4 ,the fine wire makes a long and narrow path for the electrons and so there can be only a small stream4 ,usually we describe this condition by saying that a voltmeter has a high resistance4 ,illustration3 ,fig #af ,fine wires offer more resistance to electron streams than do heavy wires of the same length4 ,if a wire is the same diameter all along1 the longer the length of it which we use the greater is the resistance which is offered to an electron stream4 ,you will need to know how to describe the resistance of a wire or of any part of an electric circuit4 ,to do so you tell how many ohms of resistance it has4 ,the ohm is the unit in which we measure the resistance of a circuit to an electron stream4 ,i can show you what an ohm is if ,i tell you a simple way to measure a resistance4 ,suppose you have a wire or coil of wire and want to know its resistance4 ,connect it in series with a battery and an ammeter as shown in ,fig4 #ag4 ,the same electron stream passes through all parts of this circuit and the ammeter tells us what this stream is in amperes4 ,now connect a voltmeter to the two ends of the coil as shown in the figure4 ,the voltmeter tells in volts how much e4 m4 f4 is being applied to force the current through the coil4 ,divide the number of volts by the number of amperes and the quotient 7answer7 is the number of ohms of resistance in the coil4 ,illustration3 ,fig #ag ,suppose the ammeter shows a current of one ampere and the voltmeter an e4 m4 f4 of one volt4 ,then dividing #a by #a gives #a4 ,that means that the coil has a resistance of one ohm4 ,it also means one ohm is such a resistance that one volt will send through it a current of one ampere4 ,you can get lots of meaning out of this4 ,for example1 it means also that one volt will send a current of one ampere through a resistance of one ohm4 ,how many ohms would the coil have if it took #e volts to send #b amperes through it4 ,solution3 ,divide #e by #b and you get #b4e4 ,therefore the coil would have a resistance of #b4e ohms4 ,try another4 ,if a coil of resistance three ohms is carrying two amperes what is the voltage across the terminals of the coil8 ,for #a ohm it would take #a volt to give a current of #a ampere1 wouldn't it8 ,for #c ohms it takes three times as much to give one ampere4 ,to give twice this current would take twice #c volts4 ,that is1 #b amperes in #c ohms requires #bx#c volts4 ,here's one for you to try by yourself4 ,if an e4 m4 f4 of #h volts is sending current through a resistance of #b ohms1 how much current is flowing8 ,notice that ,i told the number of ohms and the number of volts1 what are you going to tell8 ,don't tell just the number2 tell how many and what4 ,,letter #i ,,the ,,audion-,,characteristic ,,my ,,dear ,,young ,,student3 ,although there is much in ,letters #g and #h which it is well to learn and to think about1 there are only three of the ideas which you must have firmly grasped to get the most out of this letter which ,i am now going to write you about the audion4 ,first3 ,electric currents are streams of electrons4 ,we measure currents in amperes4 ,to measure a current we may connect into the circuit an ammeter4 ,second3 ,electrons move in a circuit when there is an electron-moving-force1 that is an electromotive force or e4 m4 f4 ,we measure e4 m4 f4's in volts4 ,to measure an e4 m4 f4 we connect a voltmeter to the two points between which the e4 m4 f4 is active4 ,third3 ,what current any particular e4 m4 f4 will cause depends upon the circuit in which it is active4 ,circuits differ in the resistance which they offer to e4 m4 f4's4 ,for any particular e4 m4 f4 7that is for any given e4 m4 f47 the resulting current will be smaller the greater the resistance of the circuit4 ,we measure resistance in ohms4 ,to measure it we find the quotient of the number of volts applied to the circuit by the number of amperes which flow4 ,in my sixth letter ,i told you something of how the audion works4 ,it would be worth while to read again that letter4 ,you remember that the current in the plate circuit can be controlled by the e4 m4 f4 which is applied to the grid circuit4 ,there is a relationship between the plate current and the grid voltage which is peculiar or characteristic to the tube4 ,so we call such a relationship a characteristic4 ,let us see how it may be found and what it will be4 ,connect an ammeter in the plate- or ,b-circuit1 of the tube so as to measure the plate-circuit current4 ,you will find that almost all books use the letter ,i to stand for current4 ,the reason is that scientists used to speak of the intensity of an electric current so that ,i really stands for intensity4 ,we use ,i to stand for something more than the word current4 ,it is our symbol for whatever an ammeter would read1 that is for the amount of current4 ,illustration3 ,fig #ah ,another convenience in symbols is this3 ,we shall frequently want to speak of the currents in several different circuits4 ,it saves time to use another letter along with the letter ,i to show the circuit to which we refer4 ,for example1 we are going to talk about the current in the ,b-circuit of the audion1 so we call that current ,i,b4 ,we write the letter ,b below the line on which ,i stands4 ,that is why we say the ,b is subscript1 meaning written below4 ,when you are reading to yourself be sure to read ,i,b as eye-bee or else as eye-subscript-bee4 ,i,b therefore will stand for the number of amperes in the plate circuit of the audion4 ,in the same way ,ia would stand for the current in the filament circuit4 ,we are going to talk about e4 m4 f4's also4 ,the letter ,e stands for the number of volts of e4 m4 f4 in a circuit4 ,in the filament circuit the battery has ,e,a volts4 ,in the plate circuit the e4 m4 f4 is ,e,b volts4 ,if we put a battery in the grid circuit we can let ,e,c represent the number of volts applied to the grid-filament or ,c-circuit4 ,the characteristic relation which we are after is one between grid voltage1 that is ,e,c1 and plate current1 that is ,i,b4 ,so we call it the ,e,c--,i,b characteristic4 ,the dash between the letters is not a subtraction sign but merely a dash to separate the letters4 ,now we'll find the ee-see-eye-bee characteristic4 ,connect some small dry cells in series for use in the grid circuit4 ,then connect the filament to the middle cell as in ,fig4 #ai4 ,take the wire which comes from the grid and put a battery clip on it1 then you can connect the grid anywhere you want along this series of batteries4 ,see ,fig4 #ah4 ,in the figure this movable clip is represented by an arrow head4 ,you can see that if it is at a the battery will make the grid positive4 ,if it is moved to b the grid will be more positive4 ,on the other hand if the clip is at o there will be no e4 m4 f4 applied to the grid4 ,if it is at c the grid will be made negative4 ,between grid and filament there is placed a voltmeter which will tell how much e4 m4 f4 is applied to the grid1 that is1 tell the value of ,e,c1 for any position whatever of the clip4 ,we shall start with the filament heated to a deep red4 ,the manufacturers of the audion tell the purchaser what current should flow through the filament so that there will be the proper emission of electrons4 ,there are easy ways of finding out for one's self but we shall not stop to describe them4 ,the makers also tell how many volts to apply to the plate1 that is what value ,e,b should have4 ,we could find this out also for ourselves but we shall not stop to do so4 ,illustration3 ,fig #ai ,now we set the battery clip so that there is no voltage applied to the grid2 that is1 we start with ,e,c equal to zero4 ,then we read the ammeter in the plate circuit to find the value of ,i,b which corresponds to this condition of the grid4 ,next we move the clip so as to make the grid as positive as one battery will make it1 that is we move the clip to a in ,fig4 #ai4 ,we now have a different value of ,e,c and will find a different value of ,i,b when we read the ammeter4 ,next move the clip to apply two batteries to the grid4 ,we get a new pair of values for ,e,c and ,i,b1 getting ,e,c from the voltmeter and ,i,b from the ammeter4 ,as we continue in this way1 increasing ,e,c1 we find that the current ,i,b increases for a while and then after we have reached a certain value of ,e,c the current ,i,b stops increasing4 ,adding more batteries and making the grid more positive doesn't have any effect on the plate current4 ,illustration3 ,fig #bj ,before ,i tell you why this happens ,i want to show you how to make a picture of the pairs of values of ,e,c and ,i,b which we have been reading on the voltmeter and ammeter4 ,imagine a city where all the streets are at right angles and the north and south streets are called streets and numbered while the east and west thorofares are called avenues4 ,i'll draw the map as in ,fig4 #bj4 ,right through the center of the city goes ,main ,street4 ,but the people who laid out the roads were mathematicians and instead of calling it ,main ,street they called it ,zero ,street4 ,the first street east of ,zero ,st4 we should have called ,east ,first ,street but they called it ,positive #a ,st4 and the next beyond ,positive #b ,st41 and so on4 ,west of the main street they called the first street ,negative #a ,st4 and so on4 ,when they came to name the avenues they were just as precise and mathematical4 ,they called the main avenue ,zero ,ave4 and those north of it ,positive #a ,ave41 ,positive #b ,ave4 and so on4 ,of course1 the avenues south of ,zero ,ave4 they called ,negative4 ,the ,town ,council went almost crazy on the subject of numbering2 they numbered everything4 ,the silent policeman which stood at the corner of ,positive #b ,st4 and ,positive #a ,ave4 was marked that way4 ,half way between ,positive #b ,st4 and ,positive #c ,st4 there was a garage which set back about two-tenths of a block from ,positive #a ,ave4 ,the ,council numbered it and called it ,positive #b4e ,st4 and ,positive #a4b ,ave4 ,most of the people spoke of it as ,plus #b4e ,st4 and ,plus #a4b ,ave4 ,sometime later there was an election in the city and a new ,council was elected4 ,the members were mostly young electricians and the new ,highway ,commissioner was a radio enthusiast4 ,at the first meeting the ,council changed the names of all the avenues to ,mil-amperes#c and of all the streets to ,volts4 ,then the ,highway ,commissioner who had just been taking a set of voltmeter and ammeter readings on an audion moved that there should be a new road known as ,audion ,characteristic4 ,he said the road should pass through the following points3 ,zero ,volt and ,plus #a4j ,mil-ampere ,plus #b4j ,volts and ,plus #a4g ,mil-amperes ,plus #d4j ,volts and ,plus #b4f ,mil-amperes ,plus #f4j ,volts and ,plus #c4d ,mil-amperes ,plus #h4j ,volts and ,plus #d4c ,mil-amperes ,and so on4 ,fig4 #ba shows the new road4 ,illustration3 ,fig #ba ,one member of the ,council jumped up and said ,but what if the grid is made negative8 ,the ,commissioner had forgotten to see what happened so he went home to take more readings4 ,he shifted the battery clip along1 starting at c of ,fig4 #bb4 ,at the next meeting of the ,council he brought in the following list of readings and hence of points on his proposed road4 ,minus #a4j ,volts and ,plus #j4f ,mil-ampere #b4j #j4d #c4j #j4b #d4j #j4a #e4j #j4j ,then he showed the other members of the ,council on the map of ,fig4 #bc how the ,audion ,characteristic would look4 ,illustration3 ,fig #bb ,there was considerable discussion after that and it appeared that different designs and makes of audions would have different characteristic curves4 ,they all had the same general form of curve but they would pass through different sets of points depending upon the design and upon the ,b-battery voltage4 ,it was several meetings later1 however1 before they found out what effects were due to the form of the curve4 ,right after this they found that they could get much better results with their radio sets4 ,now look at the audion characteristic4 ,making the grid positive1 that is going on the positive side of the zero volts in our map1 makes the plate current larger4 ,you remember that ,i told you in ,letter #f how the grid1 when positive1 helped call electrons away from the filament and so made a larger stream of electrons in the plate circuit4 ,the grid calls electrons away from the filament4 ,it can't call them out of it2 they have to come out themselves as ,i explained to you in the fifth letter4 ,illustration3 ,fig #bc ,you can see that as we make the grid more and more positive1 that is1 make it call louder and louder1 a condition will be reached where it won't do it any good to call any louder1 for it will already be getting all the electrons away from the filament just as fast as they are emitted4 ,making the grid more positive after that will not increase the plate current any4 ,that's why the characteristic flattens off as you see at high values of grid voltage4 ,the arrangement which we pictured in ,fig4 #bb 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 cell4 ,i want to show you a way which will4 ,you'll find it very useful to know and it is easily understood for it is something like the arrangement of ,fig4 #ad in the preceding letter4 ,illustration3 ,fig #bd ,connect the cells as in ,fig4 #bd to a fine wire4 ,about the middle of this wire connect the filament4 ,as before use a clip on the end of the wire from the grid4 ,if the grid is connected to a in the figure there is applied to the grid circuit that part of the e4 m4 f4 of the battery which is active in the length of wire between o and a4 ,the point a is nearer the positive plate of the battery than is the point o4 ,so the grid will be positive and the filament negative4 ,on the other hand1 if the clip is connected at b the grid will be negative with respect to the filament4 ,we can1 therefore1 make the grid positive or negative depending on which side of o we connect the clip4 ,how large the e4 m4 f4 is which will be applied to the grid depends1 of course1 upon how far away from o the clip is connected4 ,suppose you took the clip in your hand and slid it along in contact with the wire1 first from o to a and then back again through o to b and so on back and forth4 ,you would be making the grid alternately positive and negative1 wouldn't you8 ,that is1 you would be applying to the grid an e4 m4 f4 which increases to some positive value and then1 decreasing to zero1 reverses1 and increases just as much1 only to decrease to zero1 where it started4 ,if you do this over and over again1 taking always the same time for one round trip of the clip you will be impressing on the grid circuit an alternating e4 m4 f4 ,what's going to happen in the plate circuit8 ,when there is no e4 m4 f4 applied to the grid circuit1 that is when the grid potential 7possibilities7 is zero1 there is a definite current in the plate circuit4 ,that current we can find from our characteristic of ,fig4 #bc for it is where the curve crosses ,zero ,volts4 ,as the grid becomes positive the current rises above this value4 ,when the grid is made negative the current falls below this value4 ,the current1 ,i,b1 then is made alternately greater and less than the current when ,e,c is zero4 ,you might spend a little time thinking over this1 seeing what happens when an alternating e4 m4 f4 is applied to the grid of an audion1 for that is going to be fundamental to our study of radio4 ,footnote #c3 ,a mil-ampere is a thousandth of an ampere just as a millimeter is a thousandth of a meter4 ,,letter #aj ,,condensers ,,and ,,coils ,,dear ,,son3 ,in the last letter we learned of an alternating e4 m4 f4 ,the way of producing it1 which ,i described1 is very crude and ,i want to tell how to make the audion develop an alternating e4 m4 f4 for itself4 ,that is what the audion does in the transmitting set of a radio telephone4 ,but an audion can't do it all alone4 ,it must have associated with it some coils and a condenser4 ,you know what ,i mean by coils but you have yet to learn about condensers4 ,a condenser is merely a gap in an otherwise conducting circuit4 ,it's a gap across which electrons cannot pass so that if there is an e4 m4 f4 in the circuit1 electrons will be very plentiful on one side of the gap and scarce on the other side4 ,if there are to be many electrons waiting beside the gap there must be room for them4 ,for that reason we usually provide waiting-rooms for the electrons on each side of the gap4 ,metal plates or sheets of tinfoil serve nicely for this purpose4 ,look at ,fig4 #be4 ,you see a battery and a circuit which would be conducting except for the gap at ,c4 ,on each side of the gap there is a sheet of metal4 ,the metal sheets may be separated by air or mica or paraffined paper4 ,the combination of gap1 plates1 and whatever is between1 provided it is not conducting1 is called a condenser4 ,let us see what happens when we connect a battery to a condenser as in the figure4 ,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 condenser4 ,one plate of the condenser1 therefore1 becomes positive while the other plate becomes negative4 ,illustration3 ,fig #be ,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 plate4 ,the same thing happens at the other condenser plate4 ,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 away4 ,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 circuit4 ,the battery has not enough e4 m4 f4 to drive any more electrons4 ,why8 ,because the condenser has now just enough e4 m4 f4 with which to oppose the battery4 ,it would be well to learn at once the right words to use in describing this action4 ,we say that the battery sends a charging current around its circuit and charges the condenser until it has the same e4 m4 f4 ,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 other4 ,just at this first instant the charging current1 therefore1 is large but it decreases rapidly1 for the moment electrons start to pile up on one plate of the condenser and to leave the other1 an e4 m4 f4 builds up on the condenser4 ,this e4 m4 f41 of course1 opposes that of the battery so that the net e4 m4 f4 acting to move electrons round the circuit is no longer that of the battery1 but is the difference between the e4 m4 f4 of the battery and that of the condenser4 ,and so1 with each added electron1 the e4 m4 f4 of the condenser increases until finally it is just equal to that of the battery and there is no net e4 m4 f4 to act4 ,what would happen if we should then disconnect the battery8 ,the condenser would be left with its extra electrons in the negative plate and with its positive plate lacking the same number of electrons4 ,that is1 the condenser would be left charged and its e4 m4 f4 would be of the same number of volts as the battery4 ,illustration3 ,fig #bf ,now suppose we connect a short wire between the plates of the condenser as in ,fig4 #bf4 ,the electrons rush home from the negative plate to the positive plate4 ,as fast as electrons get home the e4 m4 f4 decreases4 ,when they are all back the e4 m4 f4 has been reduced to zero4 ,sometimes we say that the condenser discharges4 ,the discharge current starts with a rush the moment the conducting path is offered between the two plates4 ,the e4 m4 f4 of the condenser falls1 the discharge current grows smaller1 and in a very short time the condenser is completely discharged4 ,illustration3 ,fig #bg ,that's what happens when there is a short conducting path for the discharge current4 ,if that were all that could happen ,i doubt if there would be any radio communication to-day4 ,but if we connect a coil of wire between two plates of a charged condenser1 as in ,fig4 #bg1 then something of great interest happens4 ,to understand you must know something more about electron streams4 ,suppose we should wind a few turns of wire on a cylindrical core1 say on a stiff cardboard tube4 ,we shall use insulated wire4 ,now start from one end of the coil1 say a1 and follow along the coiled wire for a few turns and then scratch off the insulation and solder onto the coil two wires1 b1 and c1 as shown in ,fig4 #bh4 ,the further end of the coil we shall call d4 ,now let's arrange a battery and switch so that we can send a current through the part of the coil between a and b4 ,arrange also a current-measuring instrument so as to show if any current is flowing in the part of the coil between c and d4 ,for this purpose we shall use a kind of current-measuring instrument which ,i have not yet explained4 ,it is different from the hot-wire type described in ,letter #g for it will show in which direction electrons are streaming through it4 ,the diagram of ,fig4 #bh indicates the apparatus of our experiment4 ,when we close the switch1 ,s1 the battery starts a stream of electrons from a towards b4 ,just at that instant the needle1 or pointer1 of the current instrument moves4 ,the needle moves1 and thus shows a current in the coil cd2 but it comes right back again1 showing that the current is only momentary4 ,let's say this again in different words4 ,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 ab4 ,illustration3 ,fig #bh ,one thing this current-measuring instrument tells us is the direction of the electron stream through itself4 ,it shows that the momentary stream of electrons goes through the coil from d to c1 that is in the opposite direction to the stream in the part ab4 ,now prepare to do a little close thinking4 ,read over carefully all ,i have told you about this experiment4 ,you see that the moment the battery starts a stream of electrons from a towards b1 something causes a momentary1 that is a temporary1 movement of electrons from d to c4 ,we say that starting a stream of electrons from a to b sets up or induces a stream of electrons from d to c4 ,what will happen then if we connect the battery between a and d as in ,fig4 #bi8 ,electrons will start streaming away from a towards b1 that is towards d4 ,but that means there will be a momentary stream from d towards c1 that is towards a4 ,our stream from the battery causes this oppositely directed stream4 ,in the usual words we say it induces in the coil an opposing stream of electrons4 ,this opposing stream doesn't last long1 as we saw1 but while it does last it hinders the stream which the battery is trying to establish4 ,illustration3 ,fig #bi ,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 steadily4 ,in other words a current in a coil builds up slowly1 because while it is building up it induces an effect which opposes somewhat its own building up4 ,did you ever see a small boy start off somewhere1 perhaps where he shouldn't be going1 and find his conscience starting to trouble him at once4 ,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 pace4 ,when he started he stirred up his conscience and that opposed him4 ,nobody else was hindering his going4 ,it was all brought about by his own actions4 ,the opposition which he met was self-induced4 ,he was hindered at first by a self-induced effect of his own conscience4 ,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 e4 m4 f4 ,and any path in which such an effect will be produced we say has self-inductance4 ,usually we shorten this term and speak of inductance4 ,there is another way of looking at it4 ,we know habits are hard to form and equally hard to break4 ,it's hard to get electrons going around a coil and the self-inductance of a circuit tells us how hard it is4 ,the harder it is the more self-inductance we say that the coil or circuit has4 ,of course1 we need a unit in which to measure self-inductance4 ,the unit is called the henry4 ,but that is more self-inductance than we can stand in most radio circuits1 so we find it convenient to measure in smaller units called mil-henries which are thousandths of a henry4 ,you ought to know what a henry#d is1 if we are to use the word1 but it isn't necessary just now to spend much time on it4 ,the opposition which one's self-induced conscience offers depends upon how rapidly one starts4 ,it's volts which make electrons move and so the conscience which opposes them will be measured in volts4 ,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 volt4 ,don't try to remember this now2 you can come back to it later4 ,there is one more effect of inductance which we must know before we can get very far with our radio4 ,suppose an electron stream is flowing through a coil because a battery is driving the electrons along4 ,now let the battery be removed or disconnected4 ,you'd expect the electron stream to stop at once but it doesn't4 ,it keeps on for a moment because the electrons have got the habit4 ,illustration3 ,fig #bh ,if you look again at ,fig4 #bh you will see what ,i mean4 ,suppose the switch is closed and a steady stream of electrons is flowing through the coil from a to b4 ,there will be no current in the other part of the coil4 ,now open the switch4 ,there will be a motion of the needle of the current-measuring instrument1 showing a momentary current4 ,the direction of this motion1 however1 shows that the momentary stream of electrons goes through the coil from c to d4 ,do you see what this means8 ,the moment the battery is disconnected there is nothing driving the electrons in the part ab and they slow down4 ,immediately1 and just for an instant1 a stream of electrons starts off in the part cd in the same direction as if the battery was driving them along4 ,now look again at ,fig4 #bi4 ,if the battery is suddenly disconnected there is a momentary rush of electrons in the same direction as the battery was driving them4 ,just as the self-inductance of a coil opposes the starting of a stream of electrons1 so it opposes the stopping of a stream which is already going4 ,illustration3 ,fig #bi ,so far we haven't said much about making an audion produce alternating e4 m4 f4's and thus making it useful for radio-telephony4 ,before radio was possible all these things that ,i have just told you1 and some more too1 had to be known4 ,it took hundreds of good scientists years of patient study and experiment to find out those ideas about electricity which have made possible radio-telephony4 ,two of these ideas are absolutely necessary for the student of radio-communication4 ,first3 ,a condenser is a gap in a circuit where there are waiting-rooms for the electrons4 ,second3 ,electrons form habits4 ,it's hard to get them going through a coil of wire1 harder than through a straight wire1 but after they are going they don't like to stop4 ,they like it much less if they are going through a coil instead of a straight wire4 ,in my next letter ,i'll tell you what happens when we have a coil and a condenser together in a circuit4 ,footnote #d3 ,the henry has nothing to do with a well-known automobile4 ,it was named after ,joseph ,henry1 a professor years ago at ,princeton ,university4 ,,letter #aa ,a ,c-,w ,,transmitter ,,dear ,,son3 ,illustration3 ,fig #bh ,let's look again at the coils of ,fig4 #bh which we studied in the last letter4 ,i have reproduced them here so you won't have to turn back4 ,when electrons start from a towards b there is a momentary stream of electrons from d towards c4 ,if the electron stream through ab were started in the opposite direction1 that is from b to a the induced stream in the coil cd would be from c towards d4 ,illustration3 ,fig #cj ,it all reminds me of two boys with a hedge or fence between them as in ,fig4 #cj4 ,one boy is after the other4 ,suppose you were being chased2 you know what you'd do4 ,if your pursuer started off with a rush towards one end of the hedge you'd beat it towards the other4 ,but if he started slowly and cautiously you would start slowly too4 ,you always go in the opposite direction1 dodging back and forth along the paths which you are wearing in the grass on opposite sides of the hedge4 ,if he starts to the right and then slows up and starts back1 you will start to your right1 slow up1 and start back4 ,suppose he starts at the center of the hedge4 ,first he dodges to the right1 and then back through the center as far to the left1 then back again and so on4 ,you follow his every change4 ,illustration3 ,fig #ca ,i am going to make a picture of what you two do4 ,let's start with the other fellow4 ,he dodges or alternates back and forth4 ,some persons would say he oscillates back and forth in the same path4 ,as he does so he induces you to move4 ,i am on your side of the hedge with a moving-picture camera4 ,my camera catches both of you4 ,fig4 #ca shows the way the film would look if it caught only your heads4 ,the white circle represents the tow-head on my side of the hedge and the black circle1 young ,brown who lives next door4 ,of course1 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 on4 ,see ,fig4 #cb4 ,illustration3 ,fig #cb ,now suppose you are an electron in coil cd of ,fig4 #cc and ,brownie is one in coil ab4 ,your motions are induced by his4 ,what's true of you two is true of all the other electrons4 ,i have separated the coils a little in this sketch so that you can think of a hedge between4 ,i don't know how one electron can affect another on the opposite side of this hedge but it can4 ,and ,i don't know anything really about the hedge1 which is generally called the ether4 ,the hedge isn't air4 ,the effect would be the same if the coils were in a vacuum4 ,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 molecule1 every proton and every electron4 ,illustration3 ,fig #cc ,why and how electrons can affect one another when they are widely separated is one of the great mysteries of science4 ,we don't know any more about it than about why there are electrons4 ,let's accept it as a fundamental fact which we can't as yet explain4 ,illustration3 ,fig #cd ,and now we can see how to make an audion produce an alternating current or as we sometimes say make an audion oscillator4 ,we shall set up an audion with its ,a-battery as in ,fig4 #cd4 ,between the grid and the filament we put a coil and a condenser4 ,notice that they are in parallel1 as we say4 ,in the plate-filament circuit we connect the ,b-battery and a switch1 ,s1 and another coil4 ,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 you4 ,the moment any current flows in coil ab there will be a current flow in the coil cd4 7,an induced electron stream47 ,of course1 as long as the switch in the ,b-battery is open no current can flow4 ,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 b4 ,you know what that does to the coil cd4 ,it induces an electron stream from d towards c4 ,where do these electrons come from8 ,why1 from the grid and the plate #a of the condenser4 ,where do they go8 ,most of them go to the waiting-room offered by plate #b of the condenser and some1 of course1 to the filament4 ,what is the result8 ,the grid becomes positive and the filament negative4 ,illustration3 ,fig #ce ,this is the crucial moment in our study4 ,can you tell me what is going to happen to the stream of electrons in the plate circuit8 ,remember that just at the instant when we closed the switch the grid was neither positive nor negative4 ,we were at the point of zero volts on the audion characteristic of ,fig4 #ce4 ,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 ,st4 crosses ,audion ,characteristic4 ,but this jump in plate current makes the grid positive as we have just seen4 ,so the grid will help the plate call electrons and that will make the current in the plate circuit still larger1 that is1 result in a larger stream of electrons from a to b4 ,this increase in current will be matched by an increased effect in the coil cd1 for you remember how you and ,brownie behaved4 ,and that will pull more electrons away from plate #a of the condenser and send them to the waiting-room of #b4 ,all this makes the grid more positive and so makes it call all the more effectively to help the plate move electrons4 ,illustration3 ,pl4 ,v4--,variometer 7top7 and ,variable ,condenser 7bottom7 of the ,general ,radio ,company4 ,voltmeter and ,ammeter of the ,weston ,instrument ,company4 ,we started something that time4 ,it's going on all by itself4 ,the grid is getting more positive1 the plate current is getting bigger1 and so the grid is getting more positive and the plate current still bigger4 ,is it ever going to stop8 ,yes4 ,look at the audion characteristic4 ,there comes a time when making the grid a little more positive won't have any effect on the plate-circuit current4 ,so the plate current stops increasing4 ,there is nothing now to keep pulling electrons away from plate #a and crowding them into waiting-room #b4 ,why shouldn't the electrons in this waiting-room go home to that of plate #a8 ,there is now no reason and so they start off with a rush4 ,of course1 some of them came from the grid and as fast as electrons get back to the grid it becomes less and less positive4 ,as the grid becomes less and less positive it becomes less and less helpful to the plate4 ,if the grid doesn't help1 the plate alone can't keep up this stream of electrons4 ,all the plate can do by itself is to maintain the current represented by the intersection of zero volts and the audion characteristic4 ,the result is that the current in the plate circuit1 that is1 of course1 the current in coil ab1 becomes gradually less4 ,about the time all the electrons1 which had left the grid and plate #a of the condenser1 have got home the plate current is back to the value corresponding to ,e,c#j4 ,the plate current first increases and then decreases1 but it doesn't stop decreasing when it gets back to zero-grid value4 ,and the reason is all due to the habit forming tendencies of electrons in coils4 ,to see how this comes about1 let's tell the whole story over again4 ,in other words let's make a review and so get a sort of flying start4 ,illustration3 ,fig #cd ,when we close the battery switch1 ,s in ,fig4 #cd1 we allow a current to flow in the plate circuit4 ,this current induces a current in the coil cd and charges the condenser which is across it1 making plate #a positive and plate #b negative4 ,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 characteristic4 ,that's the end of the increase in current4 ,now the condenser discharges1 sending electrons through the coil cd and making the grid less positive until finally it is at zero potential1 that is neither positive nor negative4 ,while the condenser is discharging the electrons in the coil cd get a habit of flowing from c toward d1 that is from plate #b to plate #a4 ,if it wasn't for this habit the electron stream in cd would stop as soon as the grid had reduced to zero voltage4 ,because of the habit1 however1 a lot of electrons that ought to stay on plate #b get hurried along and land on plate #a4 ,it is a little like the old game of crack the whip4 ,some electrons get the habit and can't stop quickly enough so they go tumbling into waiting-room #a and make it negative4 ,that means that the condenser not only discharges but starts to get charged in the other direction with plate #a negative and plate #b positive4 ,the grid feels the effect of all this1 because it gets extra electrons if plate #a gets them4 ,in fact the voltage effective between grid and filament is always the voltage between the plates of the condenser4 ,the audion characteristic tells us what is the result4 ,as the grid becomes negative it opposes the plate1 shooing electrons back towards the filament and reducing the plate current still further4 ,but you have already seen in my previous letter what happens when we reduce the current in coil ab4 ,there is then induced in coil cd an electron stream from c to d4 ,this induced current is in just the right direction to send more electrons into waiting-room #a and so to make the grid still more negative4 ,and the more negative the grid gets the smaller becomes the plate current until finally the plate current is reduced to zero4 ,look at the audion characteristic again and see that making the grid sufficiently negative entirely stops the plate current4 ,when the plate current stops1 the condenser in the grid circuit is charged1 with plate #a negative and #b positive4 ,it was the plate current which was the main cause of this change for it induced the charging current in coil cd4 ,so1 when the plate current becomes zero there is nothing to prevent the condenser from discharging4 ,its discharge makes the grid less and less negative until it is zero volts and there we are--back practically where we started4 ,the plate current is increasing and the grid is getting positive1 and we're off on another cycle as we say4 ,during a cycle the plate current increases to a maximum1 decreases to zero1 and then increases again to its initial value4 ,illustration3 ,fig #cf ,this letter has a longer continuous train of thought than ,i usually ask you to follow4 ,but before ,i stop ,i want to give you some idea of what good this is in radio4 ,what about the current which flows in coil cd8 ,it's an alternating current1 isn't it8 ,first the electrons stream from d towards c1 and then back again from c towards d4 ,suppose we set up another coil like ,,cd in ,fig4 #cf4 ,it would have an alternating current induced in it4 ,if this coil was connected to an antenna there would be radio waves sent out4 ,the switch ,s could be used for a key and kept closed longer or shorter intervals depending upon whether dashes or dots were being set4 ,i'll tell you more about this later1 but in this diagram are the makings of a ,c-,w ,transmitter1 that is a continuous wave transmitter for radio-telegraphy4 ,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 described4 ,,letter #ab ,,inductance ,,and ,,capacity ,,dear ,,sir3 ,in the last letter ,i didn't stop to draw you a picture of the action of the audion oscillator which ,i described4 ,i am going to do it now and you are to imagine me as using two pencils and drawing simultaneously two curves4 ,one curve shows what happens to the current in the plate circuit4 ,the other shows how the voltage of the grid changes4 ,both curves start from the instant when the switch is closed2 and the two taken together show just what happens in the tube from instant to instant4 ,fig4 #cg shows the two curves4 ,you will notice how ,i have drawn them beside and below the audion characteristic4 ,the grid voltage and the plate current are related1 as ,i have told you1 and the audion characteristic is just a convenient way of showing the relationship4 ,if we know the current in the plate circuit we can find the voltage of the grid and vice versa4 ,as time goes on1 the plate current grows to its maximum and decreases to zero and then goes on climbing up and down between these two extremes4 ,the grid voltage meanwhile is varying alternately1 having its maximum positive value when the plate current is a maximum and its maximum negative value when the plate current is zero4 ,look at the two curves and see this for yourself4 ,illustration3 ,fig #cg ,now ,i want to tell you something about how fast these oscillations occur4 ,we start by learning two words4 ,one is cycle with which you are already partly familiar and the other is frequency4 ,take cycle first4 ,starting from zero the current increases to a maximum1 decreases to zero1 and is ready again for the same series of changes4 ,we say the current has passed through a cycle of values4 ,it doesn't make any difference where we start from4 ,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 over1 then we have followed through a cycle of values4 ,once you get the idea of a cycle1 and the markings on the curves in ,fig4 #ca will help you to understand1 then the other idea is easy4 ,by frequency we mean the number of cycles each second4 ,the electric current which we use in lighting our house goes through sixty cycles a second4 ,that means the current reverses its direction #abj times a second4 ,in radio we use alternating currents which have very high frequencies4 ,in ship sets the frequency is either #ejj1jjj or #a1jjj1jjj cycles per second4 ,amateur transmitting sets usually have oscillators which run at well over a million cycles per second4 ,the longer range stations use lower frequencies4 ,you'll find1 however1 that the newspaper announcements of the various broadcast stations do not tell the frequency but instead tell the wave length4 ,i am not going to stop now to explain what that means but ,i am going to give you a simple rule4 ,divide #cjj1jjj1jjj by the wave length and you'll have the frequency4 ,for example1 ships are supposed to use wave lengths of #cjj meters or #fjj meters4 ,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 sets4 ,dividing by six hundred gives #ejj1jjj or just half the frequency4 ,you can remember that sets transmitting with long waves have low frequencies1 but sets with short waves have high frequencies4 ,the frequency and the wave length don't change in the same way4 ,they change in opposite ways or inversely1 as we say4 ,the higher the frequency the shorter the wave length4 ,i'll tell you about wave lengths later4 ,first let's see how to control the frequency of an audion oscillator like that of ,fig4 #ch4 ,illustration3 ,fig #ch ,it takes time to get a full-sized stream going through a coil because of the inductance of the coil4 ,that you have learned4 ,and also it takes time for such a current to stop completely4 ,therefore1 if we make the inductance of the coil small1 keeping the condenser the same1 we shall make the time required for the current to start and stop smaller4 ,that will mean a higher frequency for there will be more oscillations each second4 ,one rule1 then1 for increasing the frequency of an audion oscillator is to decrease the inductance4 ,later in this letter ,i shall tell you how to increase or decrease the inductance of a coil4 ,before ,i do so1 however1 ,i want to call your attention to the other way in which we can change the frequency of an audion oscillator4 ,let's see how the frequency will depend upon the capacity of the condenser4 ,if a condenser has a large capacity it means that it can accommodate in its waiting-room a large number of electrons before the e4 m4 f4 of the condenser becomes large enough to stop the stream of electrons which is charging the condenser4 ,if the condenser in the grid circuit of ,fig4 #ch 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 zero4 ,therefore1 the charging current will have to flow a long time to store up the necessary number of electrons4 ,you will get the same idea1 of course1 if you think about the electrons in the lower room4 ,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 maximum4 ,it can't do that until enough electrons have left the upper room and been stored away in the lower4 ,therefore the charging current will have to flow for a long time if the capacity is large4 ,we have1 therefore1 the other rule for increasing the frequency of an audion oscillator1 that is1 decrease the capacity4 ,these rules can be stated the other way around4 ,to decrease the frequency we can either increase the capacity or increase the inductance or do both4 ,but what would happen if we should decrease the capacity and increase the inductance8 ,decreasing the capacity would make the frequency higher1 but increasing the inductance would make it lower4 ,what would be the net effect8 ,that would depend upon how much we decreased the capacity and how much we increased the inductance4 ,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 frequency4 ,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 frequency4 ,i'll give you a rule for this1 after ,i have told you some more things about capacities and inductances4 ,first as to inductances4 ,a short straight wire has a very small inductance1 indeed4 ,the longer the wire the larger will be the inductance but unless the length is hundreds of feet there isn't much inductance anyway4 ,a coiled wire is very different4 ,a coil of wire will have more inductance the more turns there are to it4 ,that isn't the whole story but it's enough for the moment4 ,let's see why4 ,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 path4 ,look again at the coils of ,figs4 #bh and #bi which we discussed in the tenth letter4 ,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 ab4 ,illustration3 ,fig #ci ,if we should turn these coils as in ,fig4 #ci 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 stopped4 ,look at the circuit of the oscillating audion in ,fig4 #ch4 ,if we should turn these coils at right angles to each other we would stop the oscillation4 ,electrons only influence other electrons which are in parallel paths4 ,when we want a large inductance we wind the coil so that there are many parallel paths4 ,then when the battery starts to drive an electron along1 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 driven4 ,the battery1 of course1 starts to drive all the electrons1 not only those nearest its negative terminal but those all along the wire4 ,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 direction4 ,it is not an exceptional state of affairs4 ,suppose a lot of boys are being driven out of a yard where they had no right to be playing4 ,suppose also that a boy can resist and lag back twice as much if some other boy urges him to do so4 ,make it easy and imagine three boys4 ,the first boy lags back not only on his own account but because of the urging of the other boys4 ,that makes him three times as hard to start as if the other boys didn't influence him4 ,the same is true of the second boy and also of the third4 ,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 with4 ,if there were two boys it would be four times as hard as for one boy4 ,if there were four in the group it would be sixteen times1 and if five it would be twenty-five times4 ,the difficulty increases much more rapidly than the number of boys4 ,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 coil4 ,if there are five turns there will be twenty-five times as much inductance1 as for a single turn2 and so on4 ,you see that we can change the inductance of a coil very easily by changing the number of turns4 ,i'll tell you two things more about inductance because they will come in handy4 ,the first is that the inductance will be larger if the turns are large circles4 ,you can see that for yourself because if the circles were very small we would have practically a straight wire4 ,the other fact is this4 ,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 said1 ,aw1 don't go2 he can't put you off2 the other half would have said ,come on1 let's get out4 ,if he did that he would have a coil without any inductance1 that is1 he would have only the natural inertia of the electrons to deal with4 ,we would say that he had made a coil with pure resistance or else that he had made a non-inductive resistance4 ,illustration3 ,fig #dj ,how would he do it8 ,easy enough after one learns how1 but quite ingenious4 ,take the wire and fold it at the middle4 ,start with the middle and wind the coil with the doubled wire4 ,fig4 #dj 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 direction4 ,it is just as if the boys were paired off1 a goody-goody and a tough nut together4 ,they both shout at once opposite advice and neither has any effect4 ,i have told you all except one of the ways in which we can affect the inductance of a circuit4 ,you know now all the methods which are important in radio4 ,so let's consider how to make large or small capacities4 ,first ,i want to tell you how we measure the capacity of a condenser4 ,we use units called microfarads4 ,you remember that an ampere means an electron stream at the rate of about six billion billion electrons a second4 ,a millionth of an ampere would1 therefore1 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 by4 ,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 circuit4 ,that is what would happen if there weren't any waiting-rooms in the circuit4 ,if there was a condenser then that number of electrons would leave one waiting-room and would enter the other4 ,well1 suppose that just as the last electron of this enormous number#e entered its waiting-room we should know that the voltage of the condenser was just one volt4 ,then we would say that the condenser had a capacity of one microfarad4 ,if it takes half that number to make the condenser oppose further changes in the contents of its waiting-rooms1 with one volt's worth of opposition1 that is1 one volt of e4 m4 f41 then the condenser has only half a microfarad of capacity4 ,the number of microfarads of capacity 7abbreviated mf47 is a measure of how many electrons we can get away from one plate and into the other before the voltage rises to one volt4 ,what must we do then to make a condenser with large capacity8 ,either of two things2 either make the waiting-rooms large or put them close together4 ,if we make the plates of a condenser larger1 keeping the separation between them the same1 it means more space in the waiting-rooms and hence less crowding4 ,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-room1 that is the higher the e4 m4 f4 of the condenser4 ,the other way to get a larger capacity is to bring the plates closer together1 that is to shorten the gap4 ,look at it this way3 ,the closer the plates are together the nearer home the electrons are4 ,their home is only just across a little gap2 they can almost see the electronic games going on around the nuclei they left4 ,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 homes4 ,that's why it's always easier1 and takes less voltage1 to get the same number of electrons moved from one plate to the other of a condenser which has only a small space between plates4 ,it takes less voltage and that means that the condenser has a smaller e4 m4 f4 for the same number of electrons4 ,it also means that before the e4 m4 f4 rises to one volt we can get more electrons moved around if the plates are close together4 ,and that means larger capacity4 ,there is one thing to remember in all this3 ,it doesn't make any difference how thick the plates are4 ,it all depends upon how much surface they have and how close together they are4 ,most of the electrons in the plate which is being made negative are way over on the side toward their old homes1 that is1 toward the plate which is being made positive4 ,and most of the homes1 that is1 atoms which have lost electrons1 are on the side of the positive plate which is next to the gap4 ,that's why ,i said the electrons could almost see their old homes4 ,illustration3 ,fig #da ,all this leads to two very simple rules for building condensers4 ,if you have a condenser with too small a capacity and want one1 say1 twice as large1 you can either use twice as large plates or bring the plates you already have twice as close together2 that is1 make the gap half as large4 ,generally1 of course1 the gap is pretty well fixed4 ,for example1 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 mica4 ,so we increase the size of the plates4 ,we can do that either by using larger plates or other plates and connecting it as in ,fig4 #da so that the total waiting-room space for electrons is increased4 ,illustration3 ,pl4 ,,vi4--,low-power ,transmitting ,tube1 ,u ,v #bjb 7,courtesy of ,radio ,corporation of ,america74 ,illustration3 ,fig #db ,if you have got these ideas you can understand how we use both sides of the same plate in some types of condensers4 ,look at ,fig4 #db4 ,there are two plates connected together and a third between them4 ,suppose electrons are pulled from the outside plates and crowded into the middle plate4 ,some of them go on one side and some on the other1 as ,i have shown4 ,the negative signs indicate electrons and the plus signs their old homes4 ,if we use more plates as in ,fig4 #dc we have a larger capacity4 ,illustration3 ,fig #dc ,illustration3 ,fig #dd ,what if we have two plates which are not directly opposite one another1 like those of ,fig4 #dd8 ,what does the capacity depend upon8 ,imagine yourself an electron on the negative plate4 ,look off toward the positive plate and see how big it seems to you4 ,the bigger it looks the more capacity the condenser has4 ,when the plates are right opposite one another the positive plate looms up pretty large4 ,but if they slide apart you don't see so much of it2 and if it is off to one side about all you see is the edge4 ,if you can't see lots of atoms which have lost electrons and so would make good homes for you1 there is no use of your staying around on that side of the plate2 you might just as well be trying to go back home the long way which you originally came4 ,that's why in a variable plate condenser there is very little capacity when no parts of the plates are opposite each other1 and there is the greatest capacity when they are exactly opposite one another4 ,illustration3 ,fig #de ,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 inductance4 ,fig4 #de shows the simplest way but it has some disadvantages which ,i won't try now to explain4 ,we make a long coil and then take off taps4 ,we can make connections between one end of the coil and any of the taps4 ,the more turns there are included in the part of the coil which we are using the greater is the inductance4 ,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 them4 ,then we have an inductance the value of which we can vary step-by-step in a convenient manner4 ,another way to make a variable inductance is to make what is called a variometer4 ,i dislike the name because it doesn't meter anything4 ,if properly calibrated it would of course meter inductance1 but then it should be called an inducto-meter4 ,do you remember the gang of boys that fellow had to drive off his property8 ,what if there had been two different gangs playing there8 ,how much trouble he has depends upon whether there is anything in common between the gangs4 ,suppose they are playing in different parts of his property and so act just as if the other crowd wasn't also trespassing4 ,he could just add the trouble of starting one gang to the trouble of starting the other4 ,it would be very different if the gangs have anything in common4 ,then one would encourage the other much as the various boys of the same gang encourage each other4 ,he would have a lot more trouble4 ,and this extra trouble would be because of the relations between gangs1 that is1 because of their mutual inductance4 ,on the other hand suppose the gangs came from different parts of the town and disliked each other4 ,he wouldn't have nearly the trouble4 ,each gang would be yelling at the other as they went along3 ,you'd better beat it4 ,he knows all right1 all right1 who broke that bush down by the gate4 ,just wait till he catches you4 ,they'd get out a little easier1 each in the hope the other crowd would catch it from the owner4 ,there's a case where their mutual relations1 their mutual inductance1 makes the job easier4 ,that's true of coils with inductance4 ,suppose you wind two inductance coils and connect them in series4 ,if they are at right angles to each other as in ,fig4 #df;a they have no effect on each other4 ,there is no mutual inductance4 ,but if they are parallel and wound the same way like the coils of ,fig4 #df;b they will act like a single coil of greater inductance4 ,if the coils are parallel but wound in opposite directions as in ,fig4 #df;c they will have less inductance because of their mutual inductance4 ,you can check these statements for yourself if you'll refer back to ,letter #aj and see what happens in the same way as ,i told you in discussing ,fig4 #bh4 ,illustration3 ,fig #df;a ,illustration3 ,fig #df;b ,if the coils are neither parallel nor at right angles there will be some mutual inductance but not as much as if they were parallel4 ,by turning the coils we can get all the variations in mutual relations from the case of ,fig4 #df;b to that of ,fig4 #df;c4 ,that's what we arrange to do in a variable inductance of the variometer type4 ,illustration3 ,fig #df;c ,there is another way of varying the mutual inductance4 ,we can make one coil slide inside another4 ,if it is way inside1 the total inductance which the two coils offer is either larger than the sum of what they can offer separately or less1 depending upon whether the windings are in the same direction or opposite4 ,as we pull the coil out the mutual effect becomes less and finally when it is well outside the mutual inductance is very small4 ,now we have several methods of varying capacity and inductance and therefore we are ready to vary the frequency of our audion oscillator2 that is1 tune it1 as we say4 ,in my next letter ,i shall show you why we tune4 ,now for the rule which ,i promised4 ,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 condenser4 ,change the coil and the condenser as much as you want but keep this product the same and the frequency will be the same4 ,footnote #e3 ,more accurately the number is #f1bhf1jjj1jjj1jjj4 ,,letter #ac ,,tuning ,,dear ,,radio ,,enthusiast3 ,i want to tell you about receiving sets and their tuning4 ,in the last letter ,i told you what determines the frequency of oscillation of an audion oscillator4 ,it was the condenser and inductance which you studied in connection with ,fig4 #cf4 ,that's what determines the frequency and also what makes the oscillations4 ,all the tube does is to keep them going4 ,let's see why this is so4 ,illustration3 ,fig #dg;a ,start first1 as in ,fig4 #dg;a1 with a very simple circuit of a battery and a non-inductive resistance1 that is1 a wire wound like that of ,fig4 #dj in the previous letter1 so that it has no inductance4 ,the battery must do work forcing electrons through that wire4 ,it has the ability1 or the energy as we say4 ,illustration3 ,fig #dg;b ,now connect a condenser to the battery as in ,fig4 #dg;b4 ,the connecting wires are very short2 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 plate4 ,the battery displaces a certain number of electrons in the waiting-rooms of the condenser4 ,how many1 depends upon how hard it can push and pull1 that is on its e4 m4 f41 and upon how much capacity the condenser has4 ,illustration3 ,fig #dg;c ,remove the battery and connect the charged condenser to the resistance as in ,fig4 #dg;c4 ,the electrons rush home4 ,they bump and jostle their way along1 heating the wire as they go4 ,they have a certain amount of energy or ability to do work because they are away from home and they use it all up1 bouncing along on their way4 ,when once they are home they have used up all the surplus energy which the battery gave them4 ,try it again1 but this time1 as in ,fig4 #dg;d1 connect the charged condenser to a coil which has inductance4 ,the electrons don't get started as fast because of the inductance4 ,but they keep going because the electrons in the wire form the habit4 ,the result is that about the time enough electrons have got into plate #b 7which was positive71 to satisfy all its lonely protons1 the electrons in the wire are streaming along at a great rate4 ,a lot of them keep going until they land on this plate and so make it negative4 ,illustration3 ,fig #dg;d ,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 fact4 ,there is nothing to keep electrons going to the #b plate except this habit4 ,and there are plenty of stay-at-home electrons to stop them as they rush along4 ,they bump and jostle1 but some of them are stopped or else diverted so that they go bumping around without getting any nearer plate #b4 ,of course1 they spend all their energy this way1 getting every one all stirred up and heating the wire4 ,some of the energy which the electrons had when they were on plate #a is spent1 therefore1 and there aren't as many electrons getting to plate #b4 ,when they turn around and start back1 as you know they do1 the same thing happens4 ,the result is that each successive surge of electrons is smaller than the preceding4 ,their energy is being wasted in heating the wire4 ,the stream of electrons gets smaller and smaller1 and the voltage of the condenser gets smaller and smaller1 until by-and-by there isn't any stream and the condenser is left uncharged4 ,when that happens1 we say the oscillations have damped out4 ,illustration3 ,fig #dh ,that's one way of starting oscillations which damp out--to start with a charged condenser and connect an inductance across it4 ,there is another way which leads us to some important ideas4 ,look at ,fig4 #dh4 ,there is an inductance and a condenser4 ,near the coil is another coil which has a battery and a key in circuit with it4 ,the coils are our old friends of ,fig4 #cc in ,letter #aj4 ,suppose we close the switch ,s4 ,it starts a current through the coil ab which goes on steadily as soon as it really gets going4 ,while it is starting1 however1 it induces an electron stream in coil cd4 ,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 battery4 ,illustration3 ,fig #di ,now take away this coil ab with its battery and substitute the oscillator of ,fig4 #cf4 ,what's going to happen8 ,we have two circuits in which oscillations can occur4 ,see ,fig4 #di4 ,one circuit is associated with an audion and some batteries which keep supplying it with energy so that its oscillations are continuous4 ,the other circuit is near enough to the first to be influenced by what happens in that circuit4 ,we say it is coupled to it1 because whatever happens in the first circuit induces an effect in the second circuit4 ,suppose first that in each circuit the inductance and capacity have such values as to produce oscillations of the same frequency4 ,then the moment we start the oscillator we have the same effect in both circuits4 ,let me draw the picture a little differently 7,fig4 #ej7 so that you can see this more easily4 ,i have merely made the coil ab in two parts1 one of which can affect cd in the oscillator and the other the coil ,l of the second circuit4 ,but suppose that the two circuits do not have the same natural frequencies1 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 other4 ,it is like learning to dance4 ,you know about how well you and your partner would get along if you had one frequency of oscillation and she had another4 ,that's what happens in a case like this4 ,illustration3 ,fig #ej ,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 it4 ,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 direction4 ,it is practically impossible under these conditions to get a stream of any size going in circuit ,l-,c4 ,it is equally hard if ,l-,c has smaller capacity and inductance than ab so that it naturally oscillates faster4 ,i'll tell you exactly what it is like4 ,suppose you and your partner are trying to dance without any piano or other source of music4 ,she has one tune running through her head and she dances to that1 except as you drag her around the floor4 ,you are trying to follow another tune4 ,as a couple you have a difficult time going anywhere under these conditions4 ,but it would be all right if you both had the same tune4 ,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 tune1 that is the same natural frequency of oscillation4 ,illustration3 ,fig #ea ,this can be shown very easily by a simple experiment4 ,suppose we set up our circuit ,l-,c with an ammeter in it1 so as to be able to tell how large an electron stream is oscillating in that circuit4 ,let us also make the condenser a variable one so that we can change the natural frequency or tune of the circuit4 ,now let's see what happens to the current as we vary this condenser1 changing the capacity and thus changing the tune of the circuit4 ,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 plates4 ,if we do1 we find one position of these plates1 that is one setting1 corresponding to one value of capacity in the condenser1 where the current in the circuit is a maximum4 ,this is the setting of the condenser for which the circuit has the same tune or natural frequency as the circuit cd4 ,sometimes we say that the circuits are now in resonance4 ,we also refer to the curve of values of current and condenser positions as a tuning curve4 ,such a curve is shown in ,fig4 #ea4 ,illustration3 ,fig #eb ,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 work4 ,we can either adjust the capacity as we just did1 or we can adjust the inductance4 ,in that case we use a variable inductance as in ,fig4 #eb4 ,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 time4 ,when we do we get these mil-henries of inductance from a coil which we call a loading coil4 ,that's why your friends add a loading coil when they want to tune for the long wave-length stations1 that is1 those with a low frequency4 ,when our circuit ,l-,c of ,fig4 #di is tuned to the frequency of the oscillator we get in it a maximum current4 ,there is a maximum stream of electrons1 and hence a maximum number of them crowded first into one and then into the other plate of the condenser4 ,and so the condenser is charged to a maximum voltage1 first in one direction and then in the other4 ,illustration3 ,fig #ec ,now connect the circuit ,l-,c to the grid of an audion4 ,if the circuit is tuned we'll have the maximum possible voltage applied between grid and filament4 ,in the plate circuit we'll get an increase and then a decrease of current4 ,you know that will happen for ,i prepared you for this moment by the last page of my ninth letter4 ,i'll tell you more about that current in the plate circuit in a later letter4 ,i am connecting a telephone receiver in the plate circuit1 and also a condenser1 the latter for a reason to be explained later4 ,the combination appears then as in ,fig4 #ec4 ,that figure shows a ,c-,w transmitter and an audion detector4 ,this is the sort of a detector we would use for radio-telephony1 but the transmitter is the sort we would use for radio-telegraphy4 ,we shall make some changes in them later4 ,illustration3 ,fig #ed ,whenever we start the oscillating current in the transmitter we get an effect in the detector circuit1 of which ,i'll tell you more later4 ,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 closed4 ,this is how we do it4 ,at the sending station1 that is1 wherever we locate the transmitter1 we make a condenser using the earth1 or ground1 as one plate4 ,we do the same thing at the receiving station where the detector circuit is located4 ,to these condensers we connect inductances and these inductances we couple to our transmitter and receiver as shown in ,fig4 #ed4 ,the upper plate of the condenser in each case is a few horizontal wires4 ,the lower plate is the moist earth of the ground and we arrange to get in contact with that in various ways4 ,one of the simplest methods is to connect to the water pipes of the city water-system4 ,now we have our radio transmitting-station and a station for receiving its signals4 ,you remember we can make dots and dashes by the key or switch in the oscillator circuit4 ,when we depress the key we start the oscillator going4 ,that sets up oscillations in the circuit with the inductance and the capacity formed by the antenna4 ,if we want a real-sized stream of electrons up and down this antenna lead 7the vertical wire71 we must tune that circuit4 ,that is why ,i have shown a variable inductance in the circuit of the transmitting antenna4 ,what happens when these electrons surge back and forth between the horizontal wires and the ground1 ,i don't know4 ,i do know1 however1 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 circuit4 ,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 station4 ,wherever you put up a receiving station you will get the effect4 ,it will be much smaller1 however1 the farther the two stations are apart4 ,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 explain1 but ,i shall tell you what we mean by wave length4 ,somehow energy1 the ability to do work1 travels out from the sending antenna in all directions4 ,wherever you put up your receiving station you get more or less of this energy4 ,of course1 energy is being sent out only while the key is depressed and the oscillator going4 ,this energy travels just as fast as light1 that is at the enormous speed of #ahf1jjj miles a second4 ,if you use meters instead of miles the speed is #cjj1jjj1jjj meters a second4 ,now1 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 antenna8 ,suppose the current is oscillating one million times a second4 ,then it takes one-millionth of a second for one oscillation4 ,in that time the energy will have traveled away from the antenna one-millionth part of the distance it will travel in a whole second4 ,that is one-millionth of #cjj million meters or #cjj meters4 ,the distance which energy will go in the time taken by one oscillation of the source of that energy is the wave length4 ,in the case just given that distance is #cjj meters4 ,the wave length1 then1 of #cjj meters corresponds to a frequency of one million4 ,in fact if we divide #cjj million meters by the frequency we get the wave length1 and that's the same rule as ,i gave you in the last letter4 ,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 significance1 or signal significance4 ,we shall have to learn quite a little about the telephone itself and about the human voice4 ,,letter #ad ,,why ,,and ,,how ,,to ,,use ,a ,,detector ,,dear ,,son3 ,in the last letter we got far enough to sketch1 in ,fig4 #ed1 a radio transmitting station and a receiving station4 ,we should never1 however1 use just this combination because the transmitting station is intended to send telegraph signals and the receiving station is best suited to receiving telephonic transmission4 ,but let us see what happens4 ,illustration3 ,fig #ed ,when the key in the plate circuit of the audion at the sending station is depressed an alternating current is started4 ,this induces an alternating current in the neighboring antenna circuit4 ,if this antenna circuit1 which is formed by a coil and a condenser1 is tuned to the frequency of oscillations which are being produced in the audion circuit then there is a maximum current induced in the antenna4 ,as soon as this starts the antenna starts to send out energy in all directions1 or radiate energy as we say4 ,how this energy1 or ability to do work1 gets across space we don't know4 ,however it may be1 it does get to the receiving station4 ,it only takes a small fraction of a second before the antenna at the receiving station starts to receive energy1 because energy travels at the rate of #ahf1jjj miles a second4 ,the energy which is received does its work in making the electrons in that antenna oscillate back and forth4 ,if the receiving antenna is tuned to the frequency which the sending station is producing1 then the electrons in the receiving antenna oscillate back and forth most widely and there is a maximum current in this circuit4 ,the oscillations of the electrons in the receiving antenna induce similar oscillations in the tuned circuit which is coupled to it4 ,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 electrons4 ,the condenser in that circuit charges and discharges alternately4 ,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 negative4 ,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 down4 ,now what happens inside the audion8 ,as the grid becomes more and more positive the current in the plate circuit increases4 ,when the grid no longer grows more positive but rather becomes less and less positive the current in the plate circuit decreases4 ,as the grid becomes of zero voltage and then negative1 that is as the grid reverses its polarity1 the plate current continues to decrease4 ,when the grid stops growing more negative and starts to become less so1 the plate current stops decreasing and starts to increase4 ,all this you know1 for you have followed through such a cycle of changes before4 ,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 changes4 ,the plate current increases and decreases alternately1 becoming greater and less than it would be if the grid were not interfering4 ,these variations in its intensity take place very rapidly1 that is with whatever high frequency the sending station operates4 ,what happens to the plate current on the average8 ,the plate current1 you remember1 is a stream of electrons from the filament to the plate 7on the inside of the tube71 and from the plate back through the ,b-battery to the filament 7on the outside of the tube74 ,the grid alternately assists and opposes that stream4 ,when it assists1 the electrons in the plate circuit are moved at a faster rate4 ,when the grid becomes negative and opposes the plate the stream of electrons is at a slower rate4 ,the stream is always going in the same direction but it varies in its rate depending upon the changes in grid potential4 ,illustration3 ,fig #ee ,when the grid is positive1 that is for half a cycle of the alternating grid-voltage1 the stream is larger than it would be if the plate current depended only on the ,b-battery4 ,for the other half of a cycle it is less4 ,the question ,i am raising is this3 ,do more electrons move around the plate circuit if there is a signal coming in than when there is no incoming signal8 ,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 signals4 ,there are just three possible answers to this question4 ,the first answer is3 ,no1 there is a smaller number of electrons passing through the plate circuit each second if the grid is being affected by an incoming signal4 ,the second is3 ,the signal doesn't make any difference in the total number of electrons which move each second from filament to plate4 ,and the third answer is3 ,yes1 there is a greater total number each second4 ,illustration3 ,fig #ef ,any one of the three answers may be right4 ,it all depends on the characteristic of the tube as we are operating it1 and that depends not only upon the type and design of tube but also upon what voltages we are using in our batteries4 ,suppose the variations in the voltage of the grid are as represented in ,fig4 #ee1 and that the characteristic of the tube is as shown in the same figure4 ,then obviously the first answer is correct4 ,you can see for yourself that when the grid becomes positive the current in the plate circuit can't increase much anyway4 ,for the other half of the cycle1 that is1 while the grid is negative1 the current in the plate is very much decreased4 ,the decrease in one half-cycle is larger than the increase during the other half-cycle1 so that on the average the current is less when the signal is coming in4 ,the dotted line shows the average current4 ,suppose that we take the same tube and use a ,b-battery of lower voltage4 ,the characteristic will have the same shape but there will not be as much current unless the grid helps1 so that the characteristic will be like that of ,fig4 #ef4 ,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 case4 ,illustration3 ,fig #eg ,you can see the result4 ,when the grid becomes positive it helps and increases the plate current4 ,when it becomes negative it opposes and decreases the plate current4 ,but the increase just balances the decrease1 so that on the average the current is unchanged1 as shown by the dotted line4 ,on the other hand1 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 potential4 ,for this case1 as shown in ,fig4 #eg1 the plate current is larger on the average when there is an incoming signal4 ,if we want to know whether or not there is any incoming signal we will not use the tube in the second condition1 that of ,fig4 #ef1 because it won't tell us anything4 ,on the other hand why use the tube under the first conditions where we need a large plate battery8 ,if we can get the same result1 that is an indication when the other station is signalling1 by using a small battery let's do it that way for batteries cost money4 ,for that reason we shall confine ourselves to the study of what takes place under the conditions of ,fig4 #eg4 ,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 greater1 on the average4 ,we are ready to see what effect this has on the telephone receiver4 ,and to do this requires a little study of how the telephone receiver works and why4 ,illustration3 ,fig #eh ,i shall not stop now to tell you much about the telephone receiver for it deserves a whole letter all to itself4 ,you know that a magnet attracts iron4 ,suppose you wind a coil of insulated wire around a bar magnet or put the magnet inside such a coil as in ,fig4 #eh4 ,send a stream of electrons through the turns of the coil--a steady stream such as comes from the battery shown in the figure4 ,the strength of the magnet is altered4 ,for one direction of the electron stream through the coil the magnet is stronger4 ,for the opposite direction of current the magnet will be weaker4 ,illustration3 ,fig #ei ,fig4 #ei shows a simple design of telephone receiver4 ,it is formed by a bar magnet1 a coil about it through which a current can flow1 and a thin disc of iron4 ,the iron disc1 or diaphragm1 is held at its edges so that it cannot move as a whole toward the magnet4 ,the center can move1 however1 and so the diaphragm is bowed out in the form shown in the smaller sketch4 ,now connect a battery to the receiver winding and allow a steady stream of electrons to flow4 ,the magnet will be either strengthened or weakened4 ,suppose the stream of electrons is in the direction to make it stronger--,i'll give you the rule later4 ,then the diaphragm is bowed out still more4 ,if we open the battery circuit and so stop the stream of electrons the diaphragm will fly back to its original position1 for it is elastic4 ,the effect is very much that of pushing in the bottom of a tin pan and letting it fly back when you remove your hand4 ,next reverse the battery4 ,the magnet does not pull as hard as it would if there were no current4 ,the diaphragm is therefore not bowed out so much4 ,suppose that instead of reversing the current by reversing the battery we arrange to send an alternating current through the coil4 ,that will have the same effect4 ,for one direction of current flow1 the diaphragm is attracted still more by the magnet but for the other direction it is not attracted as much4 ,the result is that the center of the diaphragm moves back and forth during one complete cycle of the alternating current in the coil4 ,the diaphragm vibrates back and forth in tune with the alternating current in the receiver winding4 ,as it moves away from the magnet it pushes ahead of it the neighboring molecules of air4 ,these molecules then crowd and push the molecules of air which are just a little further away from the diaphragm4 ,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 ear4 ,when the molecules of air next your ear receive the push they in turn push against your eardrum4 ,in the meantime what has happened8 ,the current in the telephone receiver has reversed its direction4 ,the diaphragm is now pulled toward the magnet and the adjacent molecules of air have even more room than they had before4 ,so they stop crowding each other and follow the diaphragm in the other direction4 ,the molecules of air just beyond these1 on the way toward your ear1 need crowd no longer and they also move back4 ,of course1 they go even farther than their old positions for there is now more room on the other side4 ,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 outward4 ,as they move away they make a little vacuum there and the eardrum puffs out4 ,that goes on over and over again just as often as the alternating current passes through one cycle of values4 ,and you1 unless you are thinking particularly of the scientific explanations1 say that you hear a musical note4 ,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 scale4 ,if we started with a very low-frequency alternating current1 say one of fifteen or twenty cycles per second1 you wouldn't say you heard a note at all4 ,you would hear a sort of a rumble4 ,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 note4 ,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 second4 ,then1 perhaps about twenty-thousand cycles a second1 you find you hear only a little sound like wind or like steam escaping slowly from a jet or through a leak4 ,a few thousand cycles more each second and you don't hear anything at all4 ,you know that for radio-transmitting stations we use audion oscillators which are producing alternating currents with frequencies of several hundred-thousand cycles per second4 ,it certainly wouldn't do any good to connect a telephone receiver in the antenna circuit at the receiving station as in ,fig4 #fj4 ,we couldn't hear so high pitched a note4 ,illustration3 ,fig #fj ,even if we could1 there are several reasons why the telephone receiver wouldn't work at such high frequencies4 ,the first is that the diaphragm can't be moved so fast4 ,it has some inertia1 you know1 that is1 some unwillingness to get started4 ,if you try to start it in one direction and1 before you really get it going1 change your mind and try to make it go in the other direction1 it simply isn't going to go at all4 ,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 high1 certainly not if it is above about #bj1jjj cycles a second4 ,the other reason is that there will only be a very feeble current in the coil anyway1 no matter what you do1 if the frequency is high4 ,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 paths4 ,the result is that they have a great unwillingness to get started and an equal unwillingness to stop4 ,their unwillingness is much more than if the wire was long and straight4 ,it is also made very much greater by the presence of the iron core4 ,an alternating e4 m4 f4 of high frequency hardly gets the electrons started at all before it's time to get them going in the opposite direction4 ,there is very little movement to the electrons and hence only a very small current in the coil if the frequency is high4 ,if you want a rule for it you can remember that the higher the frequency of an alternating e4 m4 f4 the smaller the electron stream which it can set oscillating in a given coil4 ,of course1 we might make the e4 m4 f4 stronger1 that is pull and shove the electrons harder1 but unless the coil has a very small inductance or unless the frequency is very low we should have to use an e4 m4 f4 of enormous strength to get any appreciable current4 ,condensers are just the other way in their action4 ,if there is a condenser in a circuit1 where an alternating e4 m4 f4 is active1 there is lots of trouble if the frequency is low4 ,if1 however1 the frequency is high the same-sized current can be maintained by a smaller e4 m4 f4 than if the frequency is low4 ,you see1 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 room4 ,unless there is a large current1 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 e4 m4 f4 ,because the electrons do not push back very hard a small e4 m4 f4 can drive them back and forth4 ,ordinarily we say that a condenser impedes an alternating current less and less the higher is the frequency of the current4 ,and as to inductances1 we say that an inductance impedes an alternating current more and more the higher is the frequency4 ,now we are ready to study the receiving circuit of ,fig4 #ed4 ,i showed you in ,fig4 #eg how the current through1 the tube will vary as time goes on4 ,it increases and decreases with the frequency of the current in the antenna of the distant transmitting station4 ,we have a picture1 or graph1 as we say1 of how this plate current varies4 ,it will be necessary to study that carefully and to resolve it into its components1 that is to separate it into parts1 which1 added together again will give the whole4 ,to show you what ,i mean ,i am going to treat first a very simple case involving money4 ,suppose a boy was started by his father with #ej cents of spending money4 ,he spends that and runs #ej cents in debt4 ,the next day his father gives him a dollar4 ,half of this he has to spend to pay up his yesterday's indebtedness4 ,this he does at once and that leaves him #ej cents ahead4 ,but again he buys something for a dollar and so runs #ej cents in debt4 ,day after day this cycle is repeated4 ,we can show what happens by the curve of ,fig4 #fa;a4 ,illustration3 ,fig #fa;a ,on the other hand1 suppose he already had #fj cents which1 he was saving for some special purpose4 ,this he doesn't touch1 preferring to run into debt each day and to pay up the next1 as shown in ,fig4 #fa;a4 ,then we would represent the story of this #fj cents by the graph of ,fig4 #fa;b4 ,illustration3 ,fig #fa;b ,now suppose that instead of going in debt each day he uses part of this #fj cents4 ,each day after the first his father gives him a dollar1 just as before4 ,he starts then with #fj cents as shown in ,fig4 #fa;c1 increases in wealth to #a4aj1 then spends #a4jj1 bringing his funds down to #aj cents4 ,then he receives #a4jj from his father and the process is repeated cyclically4 ,illustration3 ,fig #fa;c ,if you saw the graph of ,fig4 #fa;c you would be able to say that1 whatever he actually did1 the effect was the same as if he had two pockets1 in one of which he kept #fj cents all the time as shown in ,fig4 #fa;b4 ,in his other pocket he either had money or he was in debt as shown in ,fig4 #fa;a4 ,if you did that you would be resolving the money changes of ,fig4 #fa;c into the two components of ,figs4 #fa;a and b4 ,that is what ,i want you to do with the curve of ,fig4 #eg which ,i am reproducing here1 redrawn as ,fig4 #fb;a4 ,you see it is really the result of adding together the two curves of ,figs4 #fb;b and c1 which are shown on the following page4 ,illustration3 ,fig #fb;a ,we can think1 therefore1 of the current in the plate circuit as if it were two currents added together1 that is1 two electron streams passing through the same wire4 ,one stream is steady and the other alternates4 ,illustration3 ,fig #fb;b ,now look again at the diagram of our receiving set which ,i am reproducing as ,fig4 #fc4 ,when the signal is incoming there flow in the plate circuit two streams of electrons1 one steady and of a value in mil-amperes corresponding to that of the graph in ,fig4 #fb;b1 and the other alternating as shown in ,fig4 #fb;c4 ,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 wire4 ,on the other hand it cannot pass the gap of the condenser4 ,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 them4 ,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 time4 ,illustration3 ,fig #fb;c ,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 condenser4 ,of course1 at that same instant an equal number leave the other plate and start off toward the ,b-battery and the filament4 ,an instant later1 when the current in the plate circuit is small1 electrons start to come out of the plate and to join the stream through the receiver so that this stream is kept steady4 ,illustration3 ,fig #fc ,this steady stream of electrons1 which is passing through the receiver winding1 is larger than it would be if there was no incoming radio signal4 ,the result is a stronger pull on the diaphragm of the receiver4 ,the moment the signal starts this diaphragm is pulled over toward the magnet and it stays pulled over as long as the signal lasts4 ,when the signal ceases it flies back4 ,we would hear then a click when the signal started and another when it stopped4 ,if we wanted to distinguish dots from dashes this wouldn't be at all satisfactory4 ,so in the next letter ,i'll show you what sort of changes we can make in the apparatus4 ,to understand what effect these changes will have you need1 however1 to understand pretty well most of this letter4 ,,letter #ae ,,radio-,,telephony ,,dear ,,lad3 ,before we start on the important subject matter of this letter let us make a short review of the preceding two letters4 ,an oscillating audion at the transmitting station produces an effect on the plate current of the detector audion at the receiving station4 ,there is impressed upon the grid of the detector an alternating e4 m4 f4 which has the same frequency as the alternating current which is being produced at the sending station4 ,while this e4 m4 f4 is active1 and of course it is active only while the sending key is held down1 there is more current through the winding of the telephone receiver and its diaphragm is consequently pulled closer to its magnet4 ,what will happen if the e4 m4 f4 which is active on the grid of the detector is made stronger or weaker8 ,the pull on the receiver diaphragm will be stronger or weaker and the diaphragm will have to move accordingly4 ,if the pull is weaker the elasticity of the iron will move the diaphragm away from the magnet1 but if the pull is stronger the diaphragm will be moved toward the magnet4 ,every time the diaphragm moves it affects the air in the immediate neighborhood of itself and that air in turn affects the air farther away and so the ear of the listener4 ,therefore if there are changes in the intensity or strength of the incoming signal there are going to be corresponding motions of the receiver diaphragm4 ,and something to listen1 too1 if these changes are frequent enough but not so frequent that the receiver diaphragm has difficulty in following them4 ,there are many ways of affecting the strength of the incoming signal4 ,suppose1 for example1 that we arrange to decrease the current in the antenna of the transmitting station4 ,that will mean a weaker signal and a smaller increase in current through the winding of the telephone receiver at the other station4 ,on the other hand if the signal strength is increased there is more current in this winding4 ,illustration3 ,fig #fd ,suppose we connect a fine wire in the antenna circuit as in ,fig4 #fd and have a sliding contact as shown4 ,suppose that when we depress the switch in the oscillator circuit and so start the oscillations that the sliding contact is at o as shown4 ,corresponding to that strength of signal there is a certain value of current through the receiver winding at the other station4 ,now let us move the slider1 first to a and then back to b and so on1 back and forth4 ,you see what will happen4 ,we alternately make the current in the antenna larger and smaller than it originally was4 ,when the slider is at b there is more of the fine wire in series with the antenna1 hence more resistance to the oscillations of the electrons1 and hence a smaller oscillating stream of electrons4 ,that means a weaker outgoing signal4 ,when the slider is at a there is less resistance in the antenna circuit and a larger alternating current4 ,illustration3 ,fig #fe ,illustration3 ,fig #ff ,a picture of what happens would be like that of ,fig4 #fe4 ,the signal varies in intensity1 therefore1 becoming larger and smaller alternately4 ,that means the voltage impressed on the grid of the detector is alternately larger and smaller4 ,and hence the stream of electrons through the winding of the telephone receiver is alternately larger and smaller4 ,and that means that the diaphragm moves back and forth in just the time it takes to move the slider back and forth4 ,instead of the slider we might use a little cup almost full of grains of carbon4 ,the carbon grains lie between two flat discs of carbon4 ,one of these discs is held fixed4 ,the other is connected to the center of a thin diaphragm of steel and moves back and forth as this diaphragm is moved4 ,the whole thing makes a telephone transmitter such as you have often talked to4 ,illustration3 ,fig #fg;a ,wires connect to the carbon discs as shown in ,fig4 #ff4 ,a stream of electrons can flow through the wires and from grain to grain through the carbon button1 as we call it4 ,the electrons have less difficulty if the grains are compressed1 that is the button then offers less resistance to the flow of current4 ,if the diaphragm moves back1 allowing the grains to have more room1 the electron stream is smaller and we say the button is offering more resistance to the current4 ,illustration3 ,fig #fg;b ,you can see what happens4 ,suppose some one talks into the transmitter and makes its diaphragm go back and forth as shown in ,fig4 #fg;a4 ,then the current in the antenna varies1 being greater or less1 depending upon whether the button offers less or more resistance4 ,the corresponding variations in the antenna current are shown in ,fig4 #fg;b4 ,in the antenna at the receiving station there are corresponding variations in the strength of the signal and hence corresponding variations in the strength of the current through the telephone receiver4 ,i shall show graphically what happens in ,fig4 #fh4 ,you see that the telephone receiver diaphragm does just the same motions as does the transmitter diaphragm4 ,that means that the molecules of air near the receiver diaphragm are going through just the same kind of motions as are those near the transmitter diaphragm4 ,when these air molecules affect your eardrum you hear just what you would have heard if you had been right there beside the transmitter4 ,that's one way of making a radio-telephone4 ,it is not a very efficient method but it has been used in the past4 ,before we look at any of the more recent methods we can draw some general ideas from this method and learn some words that are used almost always in speaking of radio-telephones4 ,in any system of radio-telephony you will always find that there is produced at the transmitting station a high-frequency alternating current and that this current flows in a tuned circuit one part of which is the condenser formed by the antenna and the ground 7or something which acts like a ground74 ,this high-frequency current1 or radio-current1 as we usually say1 is varied in its strength4 ,it is varied in conformity with the human voice4 ,if the human voice speaking into the transmitter is low pitched there are slow variations in the intensity of the radio current4 ,if the voice is high pitched there are more rapid variations in the strength of the radio-frequency current4 ,that is why we say the radio-current is modulated by the human voice4 ,illustration3 ,fig #fh ,the signal which radiates out from the transmitting antenna carries all the little variations in pitch and loudness of the human voice4 ,when this signal reaches the distant antenna it establishes in that antenna circuit a current of high frequency which has just the same variations as did the current in the antenna at the sending station4 ,the human voice isn't there4 ,it is not transmitted4 ,it did its work at the sending station by modulating the radio-signal1 modulating the carrier current1 as we sometimes say4 ,but there is speech significance hidden in the variations in strength of the received signal4 ,if a telephone-receiver diaphragm can be made to vibrate in accordance with the variations in signal intensity then the air adjacent to that diaphragm will be set into vibration and these vibrations will be just like those which the human voice set up in the air molecules near the mouth of the speaker4 ,all the different systems of receiving radio-telephone signals are merely different methods of getting a current which will affect the telephone receiver in conformity with the variations in signal strength4 ,getting such a current is called detecting4 ,there are many different kinds of detectors but the vacuum tube is much to be preferred4 ,the cheapest detector1 but not the most sensitive1 is the crystal4 ,if you understand how the audion works as a detector you will have no difficulty in understanding the crystal detector4 ,the crystal detector consists of some mineral crystal and a fine-wire point1 usually platinum4 ,crystals are peculiar things4 ,like everything else they are made of molecules and these molecules of atoms4 ,the atoms are made of electrons grouped around nuclei which1 in turn1 are formed by close groupings of protons and electrons4 ,the great difference between crystals and substances which are not crystalline1 that is1 substances which don't have a special natural shape1 is this3 ,in crystals the molecules and atoms are all arranged in some orderly manner4 ,in other substances1 substances without special form1 amorphous substances1 as we call them1 the molecules are just grouped together in a haphazard way4 ,illustration3 ,fig #fi ,for some crystals we know very closely indeed how their molecules or rather their individual atoms are arranged4 ,sometime you may wish to read how this was found out by the use of ,x-rays4#f ,take the crystal of common salt for example4 ,that is well known4 ,each molecule of salt is formed by an atom of sodium and one of chlorine4 ,in a crystal of salt the molecules are grouped together so that a sodium atom always has chlorine atoms on every side of it1 and the other way around1 of course4 ,suppose you took a lot of wood dumb-bells and painted one of the balls of each dumb-bell black to stand for a sodium atom1 leaving the other unpainted to stand for a chlorine atom4 ,now try to pile them up so that above and below each black ball1 to the right and left of it1 and also in front and behind it1 there shall be a white ball4 ,the pile which you would probably get would look like that of ,fig4 #fi4 ,i have omitted the gripping part of each dumbell because ,i don't believe it is there4 ,in my picture each circle represents the nucleus of an atom4 ,i haven't attempted to show the planetary electrons4 ,other crystals have more complex arrangements for piling up their molecules4 ,now suppose we put two different kinds of substances close together1 that is1 make contact between them4 ,how their electrons will behave will depend entirely upon what the atoms are and how they are piled up4 ,some very curious effects can be obtained4 ,illustration3 ,fig #gj ,the one which interests us at present is that across the contact points of some combinations of substances it is easier to get a stream of electrons to flow one way than the other4 ,the contact doesn't have the same resistance in the two directions4 ,usually also the resistance depends upon what voltage we are applying to force the electron stream across the point of contact4 ,the one way to find out is to take the voltage-current characteristic of the combination4 ,to do so we use the same general method as we did for the audion4 ,and when we get through we plot another curve and call it1 for example1 a platinum-galena characteristic4 ,fig4 #gj shows the set-up for making the measurements4 ,there is a group of batteries arranged so that we can vary the e4 m4 f4 applied across the contact point of the crystal and platinum4 ,a voltmeter shows the value of this e4 m4 f4 and an ammeter tells the strength of the electron stream4 ,each time we move the slider we get a new pair of values for volts and amperes4 ,as a matter of fact we don't get amperes or even mil-amperes2 we get millionths of an ampere or microamperes1 as we say4 ,we can plot the pairs of values which we measure and make a curve like that of ,fig4 #ga4 ,illustration3 ,fig #ga ,when the voltage across the contact is reversed1 of course1 the current reverses4 ,part of the curve looks something like the lower part of an audion characteristic4 ,illustration3 ,fig #gb ,now connect this crystal in a receiving circuit as in ,fig4 #gb4 ,we use an antenna just as we did for the audion and we tune the antenna circuit to the frequency of the incoming signal4 ,the receiving circuit is coupled to the antenna circuit and is tuned to the same frequency4 ,whatever voltage there may be across the condenser of this circuit is applied to the crystal detector4 ,we haven't put the telephone receiver in the circuit yet4 ,i want to wait until you have seen what the crystal does when an alternating voltage is applied to it4 ,illustration3 ,fig #gc ,we can draw a familiar form of sketch as in ,fig4 #gc to show how the current in the crystal varies4 ,you see that there flows through the crystal a current very much like that of ,fig4 #fb;a4 ,and you know that such a current is really equivalent to two electron streams1 one steady and the other alternating4 ,the crystal detector gives us much the same sort of a current as does the vacuum tube detector of ,fig4 #ed4 ,the current isn't anywhere near as large1 however1 for it is microamperes instead of mil-amperes4 ,our crystal detector produces the same results so far as giving us a steady component of current to send through a telephone receiver4 ,so we can connect a receiver in series with the crystal as shown in ,fig4 #gd4 ,because the receiver would offer a large impedance to the high-frequency current1 that is1 seriously impede and so reduce the high-frequency current1 we connect a condenser around the receiver4 ,illustration3 ,fig #gd ,there is a simple crystal detector circuit4 ,if the signal intensity varies then the current which passes through the receiver will vary4 ,if these variations are caused by a human voice at the sending station the crystal will permit one to hear from the telephone receiver what the speaker is saying4 ,that is just what the audion detector does very many times better4 ,in the letter on how to experiment you'll find details as to the construction of a crystal-detector set4 ,excellent instructions for an inexpensive set are contained in ,bull4 ,no4 #abj of the ,bureau of ,standards4 ,a copy can be obtained by sending ten cents to the ,commissioner of ,public ,documents1 ,washington1 ,d4 ,c4 ,footnote #f3 ,cf4 ,within the ,atom1 ,chapter ,x4 ,,letter #af ,,the ,,human ,,voice ,,dear ,,sir3 ,the radio-telephone does not transmit the human voice4 ,it reproduces near the ears of the listener similar motions of the air molecules and hence causes in the ears of the listener the same sensations of sound as if he were listening directly to the speaker4 ,this reproduction takes place almost instantaneously so great is the speed with which the electrical effects travel outward from the sending antenna4 ,if you wish to understand radio-telephony you must know something of the mechanism by which the voice is produced and something of the peculiar or characteristic properties of voice sounds4 ,illustration3 ,fig #ge ,the human voice is produced by a sort of organ pipe4 ,imagine a long pipe connected at one end to a pair of fire-bellows1 and closed at the other end by two stretched sheets of rubber4 ,fig4 #ge is a sketch of what ,i mean4 ,corresponding to the bellows there is the human diaphragm1 the muscular membrane separating the thorax and abdomen1 which expands or contracts as one breathes4 ,corresponding to the pipe is the windpipe4 ,corresponding to the two stretched pieces of rubber are the vocal cords1 ,l and ,r1 shown in cross section in ,fig4 #gg4 ,they are part of the larynx and do not show in ,fig4 #gf 7,pl4 viii7 which shows the wind pipe and an outside view of the larynx4 ,illustration3 ,fig #gg ,when the sides of the bellows are squeezed together the air molecules within are crowded closer together and the air is compressed4 ,the greater the compression the greater1 of course1 is the pressure with which the enclosed air seeks to escape4 ,that it can do only by lifting up1 that is by blowing out1 the two elastic strips which close the end of the pipe4 ,the air pressure1 therefore1 rises until it is sufficient to push aside the elastic membranes or vocal cords and thus to permit some of the air to escape4 ,it doesn't force the membranes far apart1 just enough to let some air out4 ,but the moment some air has escaped there isn't so much inside and the pressure is reduced just as in the case of an automobile tire from which you let the air escape4 ,what is the result8 ,the membranes fly back again and close the opening of the pipe4 ,what got out1 then1 was just a little puff of air4 ,the bellows are working all the while1 however1 and so the space available for the remaining air soon again becomes so crowded with air molecules that the pressure is again sufficient to open the membranes4 ,another puff of air escapes4 ,this happens over and over again while one is speaking or singing4 ,hundreds of times a second the vocal cords vibrate back and forth4 ,the frequency with which they do so determines the note or pitch of the speaker's voice4 ,what determines the significance of the sounds which he utters8 ,this is a most interesting question and one deserving of much more time than ,i propose to devote to it4 ,to give you enough of an answer for your study of radio-telephony ,i am going to tell you first about vibrating strings for they are easier to picture than membranes like the vocal cords4 ,suppose you have a stretched string1 a piece of rubber band or a wire will do4 ,you pluck it1 that is pull it to one side4 ,when you let go it flies back4 ,because it has inertia#g it doesn't stop when it gets to its old position but goes on through until it bows out almost as far on the other side4 ,illustration3 ,pl4 ,,vii4--,photographs of ,vibrating ,strings4 ,it took some work to pluck this string1 not much perhaps2 but all the work which you did in deforming it1 goes to the string and becomes its energy1 its ability to do work4 ,this work it does in pushing the air molecules ahead of it as it vibrates4 ,in this way it uses up its energy and so finally comes again to rest4 ,its vibrations damp out1 as we say1 that is die down4 ,each swing carries it a smaller distance away from its original position4 ,we say that the amplitude1 meaning the size1 of its vibration decreases4 ,the frequency does not4 ,it takes just as long for a small-sized vibration as for the larger4 ,of course1 for the vibration of large amplitude the string must move faster but it has to move farther so that the time required for a vibration is not changed4 ,first the string crowds against each other the air molecules which are in its way and so leads to crowding further away1 just as fast as these molecules can pass along the shove they are receiving4 ,that takes place at the rate of about #aajj feet a second4 ,when the string swings back it pushes away the molecules which are behind it and so lets those that were being crowded follow it4 ,you know that they will4 ,air molecules will always go where there is the least crowding4 ,following the shove1 therefore1 there is a chance for the molecules to move back and even to occupy more room than they had originally4 ,the news of this travels out from the string just as fast as did the news of the crowding4 ,as fast as molecules are able they move back and so make more room for their neighbors who are farther away2 and these in turn move back4 ,do you want a picture of it8 ,imagine a great crowd of people and at the center some one with authority4 ,the crowd is the molecules of air and the one with authority is one of the molecules of the string which has energy4 ,whatever this molecule of the string says is repeated by each member of the crowd to his neighbor next farther away4 ,first the string says3 ,go back and each molecule acts as soon as he gets the word4 ,and then the string says3 ,come on and each molecule of air obeys as soon as the command reaches him4 ,over and over this happens1 as many times a second as the string makes complete vibrations4 ,illustration3 ,fig #gh ,if we should make a picture of the various positions of one of these air molecules much as we pictured ,brownie in ,letter #i it would appear as in ,fig4 #gh;a where the central line represents the ordinary position of the molecule4 ,that's exactly the picture also of the successive positions of an electron in a circuit which is carrying an alternating current4 ,first it moves in one direction along the wire and then back in the opposite direction4 ,the electron next to it does the same thing almost immediately for it does not take anywhere near as long for such an effect to pass through a crowd of electrons4 ,if we make the string vibrate twice as fast1 that is1 have twice the frequency1 the story of an adjacent particle of air will be as in ,fig4 #gh;b4 ,unless we tighten the string1 however1 we can't make it vibrate as a whole and do it twice as fast4 ,we can make it vibrate in two parts or even in more parts1 as shown in ,fig4 #gi of ,pl4 ,,vii4 ,when it vibrates as a whole1 its frequency is the lowest possible1 the fundamental frequency as we say4 ,when it vibrates in two parts each part of the string makes twice as many vibrations each second4 ,so do the adjacent molecules of air and so does the eardrum of a listener4 ,the result is that the listener hears a note of twice the frequency that he did when the string was vibrating as a whole4 ,he says he hears the octave of the note he heard first4 ,if the string vibrates in three parts and gives a note of three times the frequency the listener hears a note two octaves above the fundamental note of which the string is capable4 ,it is entirely possible1 however1 for a string to vibrate simultaneously in a number of ways and so to give not only its fundamental note but several others at the same time4 ,the photographs#h of ,fig4 #hj of ,pl4 ,,vii illustrate this possibility4 ,what happens then to the molecules of air which are adjacent to the vibrating string8 ,they must perform quite complex vibrations for they are called upon to move back and forth just as if there were several strings all trying to push them with different frequencies of vibration4 ,look again at the pictures1 of ,fig4 #hj and see that each might just as well be the picture of several strings placed close together1 each vibrating in a different way4 ,each of the strings has a different frequency of vibration and a different maximum amplitude1 that is1 greatest size of swing away from its straight position4 ,illustration3 ,fig #ha ,suppose instead of a single string acting upon the adjacent molecules we had three strings4 ,suppose the first would make a nearby molecule move as in ,fig4 #ha;,a1 the second as in ,fig4 #ha;,b1 and the third as in ,fig4 #ha;,c4 ,it is quite evident that the molecule can satisfy all three if it will vibrate as in ,fig4 #ha;,d4 ,now take it the other way around4 ,suppose we had a picture of the motion of a molecule and that it was not simple like those shown in ,fig4 #gh but was complex like that of ,fig4 #ha;,d4 ,we could say that this complex motion was made up of three parts1 that is1 had three component simple motions1 each represented by one of the three other graphs of ,fig4 #ha4 ,that means we can resolve any complex vibratory motion into component motions which are simple4 ,it means more than that4 ,it means that the vibrating string which makes the neighboring molecules of air behave as shown in ,fig4 #ha;,d is really acting like three strings and is producing simultaneously three pure musical notes4 ,now suppose we had two different strings1 say a piano string in the piano and a violin string on its proper mounting4 ,suppose we played both instruments and some musician told us they were in tune4 ,what would he mean8 ,he would mean that both strings vibrated with the same fundamental frequency4 ,they differ1 however1 in the other notes which they produce at the same time that they produce their fundamental notes4 ,that is1 they differ in the frequencies and amplitudes of these other component vibrations or overtones which are going on at the same time as their fundamental vibrations4 ,it is this difference which lets us tell at once which instrument is being played4 ,that brings us to the main idea about musical sounds and about human speech4 ,the pitch of any complex sound is the pitch of its fundamental or lowest sound2 but the character of the complex sound depends upon all the overtones or harmonics which are being produced and upon their relative frequencies and amplitudes4 ,illustration3 ,fig #hb ,the organ pipe which ends in the larynx produces a very complex sound4 ,i can't show you how complex but ,i'll show you in ,fig4 #hb the complicated motion of an air molecule which is vibrating as the result of being near an organ pipe4 7,organ pipes differ--this is only one case47 ,you can see that there are a large number of pure notes of various intensities1 that is1 strengths1 which go to make up the sound which a listener to this organ pipe would hear4 ,the note from the human pipe is much more complex4 ,when one speaks there are little puffs of air escaping from his larynx4 ,the vocal cords vibrate as ,i explained4 ,and the molecules of air near the larynx are set into very complex vibrations4 ,these transmit their vibrations to other molecules until those in the mouth are reached4 ,in the mouth1 however1 something very important happens4 ,did you ever sing or howl down a rain barrel or into a long pipe or hallway and hear the sound8 ,it sounds just about the same no matter who does it4 ,the reason is that the long column of air in the pipe or barrel is set into vibration and vibrates according to its own ideas of how fast to do it4 ,it has a natural frequency of its own4 ,if in your voice there is a note of just that frequency it will respond beautifully4 ,in fact it resonates1 or sings back1 when it hears this note4 ,the net result is that it emphasizes this note so much that you don't hear any of the other component notes of your voice--all you hear is the rain barrel4 ,we say it reinforces one of the component notes of your voice and makes it louder4 ,that same thing happens in the mouth cavity of a speaker4 ,the size and shape of the column of air in the mouth can be varied by the tongue and lip positions and so there are many different possibilities of resonance4 ,depending on lip and tongue1 different frequencies of the complex sound which comes from the larynx are reinforced4 ,you can see that for yourself from ,fig4 #hc which shows the tongue positions for three different vowel sounds4 ,you can see also from ,fig4 #hd1 which shows the mouth positions for the different vowels1 how the size and shape of the mouth cavity is changed to give different sounds4 ,these figures are in ,pl4 ,,viii4 ,the pitch of the note need not change as every singer knows4 ,you can try that also for yourself by singing the vowel sound of ahh and then changing the shape of your mouth so as to give the sound ah--aw--ow--ou4 ,the pitch of the note will not change because the fundamental stays the same4 ,the speech significance of the sound1 however1 changes completely because the mouth cavity resonates to different ones of the higher notes which come from the larynx along with the fundamental note4 ,now you can see what is necessary for telephonic transmission4 ,each and every component note which enters into human speech must be transmitted and accurately reproduced by the receiver4 ,more than that1 all the proportions must be kept just the same as in the original spoken sound4 ,we usually say that there must be reproduced in the air at the receiver exactly the same wave form as is present in the air at the transmitter4 ,if that isn't done the speech won't be natural and one cannot recognize voices although he may understand pretty well4 ,if there is too much distortion of the wave form1 that is if the relative intensities of the component notes of the voice are too much altered1 then there may even be a loss of intelligibility so that the listener cannot understand what is being said4 ,what particular notes are in the human voice depends partly on the person who is speaking4 ,you know that the fundamental of a bass voice is lower than that of a soprano4 ,besides the fundamental1 however1 there are a lot of higher notes always present4 ,this is particularly true when the spoken sound is a consonant1 like s or f or v4 ,the particular notes1 which are present and are important1 depend upon what sound one is saying4 ,usually1 however1 we find that if we can transmit and reproduce exactly all the notes which lie between a frequency of about #bjj cycles a second and one of about #bjjj cycles a second the reproduced speech will be quite natural and very intelligible4 ,for singing and for transmitting instrumental music it is necessary to transmit and reproduce still higher notes4 ,what you will have to look out for1 therefore1 in a receiving set is that it does not cut out some of the high notes which are necessary to give the sound its naturalness4 ,you will also have to make sure that your apparatus does not distort1 that is1 does not receive and reproduce some notes or voice frequencies more efficiently than it does some others which are equally necessary4 ,for that reason when you buy a transformer or a telephone receiver it is well to ask for a characteristic curve of the apparatus which will show how the action varies as the frequency of the current is varied4 ,the action or response should1 of course1 be practically the same at all the frequencies within the necessary part of the voice range4 ,footnote #g3 ,cf4 ,chap4 ,,vi of ,the ,realities of ,modern ,science4 ,footnote #h3 ,my thanks are due to ,professor ,d4 ,c4 ,miller and to the ,macmillan ,company for permission to reproduce ,figs4 #gi to #hc inclusive from that interesting book1 ,the ,science of ,musical ,sounds4 ,,letter #ag ,,grid ,,batteries ,,and ,,grid ,,condensers ,,for ,,detectors ,,dear ,,son3 ,you remember the audion characteristics which ,i used in ,figs4 #ee1 #ef and #eg of ,letter #ad to show you how an incoming signal will affect the current in the plate circuit4 ,look again at these figures and you will see that these characteristics all had the same general shape but that they differed in their positions with reference to the main streets of zero volts on the grid and zero mil-amperes in the plate circuit4 ,changing the voltage of the ,b-battery in the plate circuit changed the position of the characteristic4 ,we might say that changing the ,b-battery shifted the curve with reference to the axis of zero volts on the grid4 ,illustration3 ,fig #ef ,illustration3 ,fig #fc ,in the case of the three characteristics which we are discussing the shift was made by changing the ,b-battery4 ,increasing ,b-voltage shifts characteristic to the left4 ,it is possible1 however1 to produce such a shift by using a ,c-battery1 that is1 a battery in the grid circuit1 which makes the grid permanently negative 7or positive1 depending upon how it is connected74 ,this battery either helps or hinders the plate battery1 and because of the strategic position of the grid right near the filament one volt applied to the grid produces as large an effect as would several volts in the plate battery4 ,usually1 therefore1 we arrange to shift the characteristic by using a ,c-battery4 ,illustration3 ,fig #he ,suppose for example that we had an audion in the receiving circuit of ,fig4 #fc and that its characteristic under these conditions is given by ,fig4 #ef4 ,i've redrawn the figures to save your turning back4 ,the audion will not act as a detector because an incoming signal will not change the average value of the current in the plate circuit4 ,if1 however1 we connect a ,c-battery so as to make the grid negative1 we can shift this characteristic so that the incoming signal will be detected4 ,we have only to make the grid sufficiently negative to reduce the plate current to the value shown by the line oa in ,fig4 #he4 ,then the signal will be detected because1 while it makes the plate current alternately larger and smaller than this value oa1 it will result1 on the average1 in a higher value of the plate current4 ,illustration3 ,fig #hf ,you see that what we have done is to arrange the point on the audion characteristic about which the tube is to work by properly choosing the value of the grid voltage ,e,c4 ,there is an important method of using an audion for a detector where we arrange to have the grid voltage change steadily1 getting more and more negative all the time the signal is coming in4 ,before ,i tell how it is done ,i want to show you what will happen4 ,suppose we start with an audion detector1 for which the characteristic is that of ,fig4 #ef1 but arranged as in ,fig4 #hf to give the grid any potential which we wish4 ,the batteries and slide wire resistance which are connected in the grid circuit are already familiar to you4 ,when the slider is set as shown in ,fig4 #hf the grid is at zero potential and we are at the point #a of the characteristic shown in ,fig4 #hg4 ,now imagine an incoming signal1 as shown in that same figure1 but suppose that as soon as the signal has stopped making the grid positive we shift the slider a little so that the ,c-battery makes the grid slightly negative4 ,we have shifted the point on the characteristic about which the tube is being worked by the incoming signal from point #a to point #b4 ,illustration3 ,fig #hg ,every time the incoming signal makes one complete cycle of changes we shift the slider a little further and make the grid permanently more negative4 ,you can see what happens4 ,as the grid becomes more negative the current in the plate circuit decreases on the average4 ,finally1 of course1 the grid will become so negative that the current in the plate circuit will be reduced to zero4 ,under these conditions an incoming signal finally makes a large change in the plate current and hence in the current through the telephone4 ,the method of shifting a slider along1 every time the incoming signal makes a complete cycle1 is impossible to accomplish by hand if the frequency of the signal is high4 ,it can be done automatically1 however1 no matter how high the frequency if we use a condenser in the grid circuit as shown in ,fig4 #hh4 ,illustration3 ,fig #hh ,when the incoming signal starts a stream of electrons through the coil ,l of ,fig4 #hh and draws them away from plate #a of the condenser ,c it is also drawing electrons away from the #a plate of the condenser ,cg which is in series with the grid4 ,as electrons leave plate #a of this condenser others rush away from the grid and enter plate #b4 ,this means that the grid doesn't have its ordinary number of electrons and so is positive4 ,if the grid is positive it will be pleased to get electrons2 and it can do so at once1 for there are lots of electrons streaming past it on their way to the plate4 ,while the grid is positive1 therefore1 there is a stream of electrons to it from the filament4 ,fig4 #hi shows this current4 ,all this takes place during the first half-cycle of the incoming signal4 ,during the next half-cycle electrons are sent into plate #a of the condenser ,c and also into plate #a of the grid condenser ,cg4 ,as electrons are forced into plate #a of the grid condenser those in plate #b of that condenser have to leave and go back to the grid where they came from4 ,that is all right1 but while they were away the grid got some electrons from the filament to take their places4 ,the result is that the grid has now too many electrons1 that is1 it is negatively charged4 ,illustration3 ,fig #hi ,an instant later the signal e4 m4 f4 reverses and calls electrons away from plate #a of the grid condenser4 ,again electrons from the grid rush into plate #b and again the grid is left without its proper number and so is positive4 ,again it receives electrons from the filament4 ,the result is still more electrons in the part of the grid circuit which is formed by the grid1 the plate #b of the grid condenser and the connecting wire4 ,these electrons can't get across the gap of the condenser ,cg and they can't go back to the filament any other way4 ,so there they are1 trapped4 ,finally there are so many of these trapped electrons that the grid is so negative all the time as almost entirely to oppose the efforts of the plate to draw electrons away from the filament4 ,illustration3 ,pl4 ,,viii4--,to ,illustrate the ,mechanism for the ,production of the ,human ,voice4 ,then the plate current is reduced practically to zero4 ,that's the way to arrange an audion so that the incoming signal makes the largest possible change in plate current4 ,we can tell if there is an incoming signal because it will block the tube1 as we say4 ,the plate-circuit current will be changed from its ordinary value to almost zero in the short time it takes for a few cycles of the incoming signal4 ,we can detect one signal that way1 but only one because the first signal makes the grid permanently negative and blocks the tube so that there isn't any current in the plate circuit and can't be any4 ,if we want to put the tube in condition to receive another signal we must allow these electrons1 which originally came from the filament1 to get out of their trapped position and go back to the filament4 ,illustration3 ,fig #ij ,to do so we connect a very fine wire between plates #a and #b of the grid condenser4 ,we call that wire a grid-condenser leak because it lets the electrons slip around past the gap4 ,by using a very high resistance1 we can make it so hard for the electrons to get around the gap that not many will do so while the signal is coming in4 ,in that case we can leave the leak permanently across the condenser as shown in ,fig4 #ij4 ,of course1 the leak must offer so easy a path for the electrons that all the trapped electrons can get home between one incoming signal and the next4 ,one way of making a high resistance like this is to draw a heavy pencil line on a piece of paper1 or better a line with ,india ink1 that is ink made of fine ground particles of carbon4 ,the leak should have a very high resistance1 usually one or two million ohms if the condenser is about #j4jjb microfarad4 ,if it has a million ohms we say it has a megohm of resistance4 ,this method of detecting with a leaky grid-condenser and an audion is very efficient so far as telling the listener whether or not a signal is coming into his set4 ,it is widely used in receiving radio-telephone signals although it is best adapted to receiving the telegraph signals from a spark set4 ,i don't propose to stop to tell you how a spark-set transmitter works4 ,it is sufficient to say that when the key is depressed the set sends out radio signals at the rate usually of #ajjj signals a second4 ,every time a signal reaches the receiving station the current in the telephone receiver is sudden reduced2 and in the time between signals the leak across the grid condenser brings the tube back to a condition where it can receive the next signal4 ,while the sending key is depressed the current in the receiver is decreasing and increasing once for every signal which is being transmitted4 ,for each decrease and increase in current the diaphragm of the telephone receiver makes one vibration4 ,what the listener then hears is a musical note with a frequency corresponding to that number of vibrations a second1 that is1 a note with a frequency of one thousand cycles per second4 ,he hears a note of frequency about that of two octaves above middle ,c on the piano4 ,there are usually other notes present at the same time and the sound is not like that of any musical instrument4 ,illustration3 ,fig #ia ,if the key is held down a long time for a dash the listener hears this note for a corresponding time4 ,if it is depressed only about a third of that time so as to send a dot1 the listener hears the note for a shorter time and interprets it to mean a dot4 ,in ,fig4 #ia ,i have drawn a sketch to show the e4 m4 f4 which the signals from a spark set impress on the grid of a detector and to show how the plate current varies if there is a condenser and leak in the grid circuit4 ,i have only shown three signals in succession4 ,if the operator sends at the rate of about twenty words a minute a dot is formed by about sixty of these signals in succession4 ,the frequency of the alternations in one of the little signals will depend upon the wave length which the sending operator is using4 ,if he uses the wave length of #fjj meters1 as ship stations do1 he will send with a radio frequency of #ejj1jjj cycles a second4 ,since the signals are at the rate of a thousand a second each one is made up of #ejj complete cycles of the current in the antenna4 ,it would be impracticable therefore to show you a complete picture of the signal from a spark set4 ,i have1 however1 lettered the figure quite completely to cover what ,i have just told you4 ,if the grid-condenser and its leak are so chosen as to work well for signals from a #ejj-;cycle spark set they will also work well for the notes in human speech which are about #ajjj cycles a second in frequency4 ,the detecting circuit will not1 however1 work so well for the other notes which are in the human voice and are necessary to speech4 ,for example1 if notes of about #bjjj cycles a second are involved in the speech which is being transmitted1 the leak across the condenser will not work fast enough4 ,on the other hand1 for the very lowest notes in the voice the leak will work too fast and such variations in the signal current will not be detected as efficiently as are those of #ajjj cycles a second4 ,you can see that there is always a little favoritism on the part of the grid-condenser detector4 ,it doesn't exactly reproduce the variations in intensity of the radio signal which were made at the sending station4 ,it distorts a little4 ,as amateurs we usually forgive it that distortion because it is so efficient4 ,it makes so large a change in the current through the telephone when it receives a signal that we can use it to receive much weaker signals1 that is1 signals from smaller or more distant sending stations1 than we can receive with the arrangement described in ,letter #ad4 ,,letter #ah ,,amplifiers ,,and ,,the ,,regenerative ,,circuit ,,my ,,dear ,,receiver3 ,there is one way of making an audion even more efficient as a detector than the method described in the last letter4 ,and that is to make it talk to itself4 ,suppose we arrange a receiving circuit as in ,fig4 #ib4 ,it is exactly like that of ,fig4 #ij of the previous letter except for the fact that the current in the plate circuit passes through a little coil1 ,lt1 which is placed near the coil ,l and so can induce in it an e4 m4 f4 which will correspond in intensity and wave form to the current in the plate circuit4 ,if we should take out the grid condenser and its leak this circuit would be like that of ,fig4 #ed in ,letter #ac which we used for a generator of high-frequency alternating currents4 ,you remember how that circuit operates4 ,a small effect in the grid circuit produces a large effect in the plate circuit4 ,because the plate circuit is coupled to the grid circuit the grid is again affected and so there is a still larger effect in the plate circuit4 ,and so on1 until the current in the plate circuit is swinging from zero to its maximum possible value4 ,what happens depends upon how closely the coils ,l and ,lt are coupled1 that is1 upon how much the changing current in one can affect the other4 ,if they are turned at right angles to each other1 so that there is no possible mutual effect we say there is zero coupling4 ,start with the coils at right angles to each other and turn ,lt so as to bring its windings more and more parallel to those of ,l4 ,if we want ,lt to have a large effect on ,l its windings should be parallel and also in the same direction just as they were in ,fig4 #ed of ,letter #ac to which we just referred4 ,as we approach nearer to that position the current in ,lt induces more and more e4 m4 f4 in coil ,l4 ,for some position of the two coils1 and the actual position depends on the tube we are using1 there will be enough effect from the plate circuit upon the grid circuit so that there will be continuous oscillations4 ,illustration3 ,fig #ib ,we want to stop just short of this position4 ,there will then be no continuous oscillations2 but if any changes do take place in the plate current they will affect the grid4 ,and these changes in the grid voltage will result in still larger changes in the plate current4 ,now suppose that there is coming into the detector circuit of ,fig4 #ib a radio signal with1 speech significance4 ,the current in the plate circuit varies accordingly4 ,so does the current in coil ,lt which is in the plate circuit4 ,but this current induces an e4 m4 f4 in coil ,l and this adds to the e4 m4 f4 of the incoming signal so as to make a greater variation in the plate current4 ,this goes on as long as there is an incoming signal4 ,because the plate circuit is coupled to the grid circuit the result is a larger e4 m4 f4 in the grid circuit than the incoming signal could set up all by itself4 ,you see now why ,i said the tube talked to itself4 ,it repeats to itself whatever it receives4 ,it has a greater strength of signal to detect than if it didn't repeat4 ,of course1 it detects also just as ,i told you in the preceding letter4 ,in adjusting the coupling of the two coils of ,fig4 #ib we stopped short of allowing the tube circuit to oscillate and to generate a high frequency4 ,if we had gone on increasing the coupling we should have reached a position where steady oscillations would begin4 ,usually this is marked by a little click in the receiver4 ,the reason is that when the tube oscillates the average current in the plate circuit is not the same as the steady current which ordinarily flows between filament and plate4 ,there is a sudden change1 therefore1 in the average current in the plate circuit when the tube starts to oscillate4 ,you remember that what affects the receiver is the average current in the plate circuit4 ,so the receiver diaphragm suddenly changes position as the tube starts to oscillate and a listener hears a little click4 ,the frequency of the alternating current which the tube produces depends upon the tuned circuit formed by ,l and ,c4 ,suppose that this frequency is not the same as that to which the receiving antenna is tuned4 ,what will happen8 ,there will be impressed on the grid of the tube two alternating e4 m4 f4's1 one due to the tube's own oscillations and the other incoming from the distant transmitting station4 ,the two e4 m4 f4 's are both active at once so that at each instant the e4 m4 f4 of the grid is really the sum of these two e4 m4 f4's4 ,suppose at some instant both e4 m4 f4's are acting to make the grid positive4 ,a little later one of them will be trying to make the grid negative while the other is still trying to make it positive4 ,and later still when the first e4 m4 f4 is ready again to make the grid positive the second will be trying to make it negative4 ,it's like two men walking along together but with different lengths of step4 ,even if they start together with their left feet they are soon so completely out of step that one is putting down his right foot while the other is putting down his left4 ,a little later1 but just for an instant1 they are in step again4 ,and so it goes4 ,they are in step for a moment and then completely out of step4 ,suppose one of them makes ten steps in the time that the other makes nine4 ,in that time they will be once in step and once completely out of step4 ,if one makes ten steps while the other does eight this will happen twice4 ,the same thing happens in the audion detector circuit when two e4 m4 f4's which differ slightly in frequency are simultaneously impressed on the grid4 ,if one e4 m4 f4 passes through ten complete cycles while the other is making eight cycles1 then during that time they will twice be exactly in step1 that is1 in phase as we say4 ,twice in that time they will be exactly out of step1 that is1 exactly opposite in phase4 ,twice in that time the two e4 m4 f4's will aid each other in their effects on the grid and twice they will exactly oppose4 ,unless they are equal in amplitude there will still be a net e4 m4 f4 even when they are exactly opposed4 ,the result of all this is that the average current in the plate circuit of the detector will alternately increase and decrease twice during this time4 ,the listener will then hear a note of a frequency equal to the difference between the frequencies of the two e4 m4 f4's which are being simultaneously impressed on the grid of the detector4 ,suppose the incoming signal has a frequency of #ajj1jjj cycles a second but that the detector tube is oscillating in its own circuit at the rate of #ii1jjj cycles per second1 then the listener will hear a note of #ajjj cycles per second4 ,one thousand times each second the two e4 m4 f4's will be exactly in phase and one thousand times each second they will be exactly opposite in phase4 ,the voltage applied to the grid will be a maximum one thousand times a second and alternately a minimum4 ,we can think of it1 then1 as if there were impressed on the grid of the detector a high-frequency signal which varied in intensity one thousand times a second4 ,this we know will produce a corresponding variation in the current through the telephone receiver and thus give rise to a musical note of about two octaves above middle ,c on the piano4 ,this circuit of ,fig4 #ib will let us detect signals which are not varying in intensity4 ,and consequently this is the method which we use to detect the telegraph signals which are sent out by such a continuous wave transmitter as ,i showed you at the end of ,letter #ac4 ,when the key of a ,c-,w transmitter is depressed there is set up in the distant receiving-antenna an alternating current4 ,this current doesn't vary in strength4 ,it is there as long as the sender has his key down4 ,because1 however1 of the effect which ,i described above there will be an audible note from the telephone receiver if the detector tube is oscillating at a frequency within two or three thousand cycles of that of the transmitting station4 ,this method of receiving continuous wave signals is called the heterodyne method4 ,the name comes from two ,greek words1 dyne meaning force and the other part meaning different4 ,we receive by combining two different electron-moving-forces1 one produced by the distant sending-station and the other produced locally at the receiving station4 ,neither by itself will produce any sound1 except a click when it starts4 ,both together produce a musical sound in the telephone receiver2 and the frequency of that note is the difference of the two frequencies4 ,there are a number of words used to describe this circuit with some of which you should be familiar4 ,it is sometimes called a feed-back circuit because part of the output of the audion is fed back into its input side4 ,more generally it is known as the regenerative circuit because the tube keeps on generating an alternating current4 ,the little coil which is used to feed back into the grid circuit some of the effects from the plate circuit is sometimes called a tickler coil4 ,it is not necessary to use a grid condenser in a feed-back circuit but it is perhaps the usual method of detecting where the regenerative circuit is used4 ,the whole value of the regenerative circuit so far as receiving is concerned is in the high efficiency which it permits4 ,one tube can do the work of two4 ,we can get just as loud signals by using another tube instead of making one do all the work4 ,in the regenerative circuit the tube is performing two jobs at once4 ,it is detecting but it is also amplifying4#i ,by amplifying we mean making an e4 m4 f4 larger than it is without changing the shape of its picture1 that is without changing its wave form4 ,to show just what we mean by amplifying we must look again at the audion and see how it acts4 ,you know that a change in the grid potential makes a change in the plate current4 ,let us arrange an audion in a circuit which will tell us a little more of what happens4 ,fig4 #ic shows the circuit4 ,this circuit is the same as we used to find the audion characteristic except that there is a clip for varying the number of batteries in the plate circuit and a voltmeter for measuring their e4 m4 f4 ,we start with the grid at zero potential and the usual number of batteries in the plate circuit4 ,the voltmeter tells us the e4 m4 f4 ,we read the ammeter in the plate circuit and note what that current is4 ,then we shift the slider in the grid circuit so as to give the grid a small potential4 ,the current in the plate circuit changes4 ,we can now move the clip on the ,b-batteries so as to bring the current in this circuit back to its original value4 ,of course1 if we make the grid positive we move the clip so as to use fewer cells of the ,b-battery4 ,on the other hand if we make the grid negative we shall need more e4 m4 f4 in the plate circuit4 ,in either case we shall find that we need to make a very much larger change in the voltage of the plate circuit than we have made in the voltage of the grid circuit4 ,illustration3 ,fig #ic ,usually we perform the experiment a little differently so as to get more accurate results4 ,we read the voltmeter in the plate circuit and the ammeter in that circuit4 ,then we change the number of batteries which we are using in the plate circuit4 ,that changes the plate current4 ,the next step is to shift the slider in the grid circuit until we have again the original value of current in the plate circuit4 ,suppose that the tube is ordinarily run with a plate voltage of #dj volts and we start with that e4 m4 f4 on the plate4 ,suppose that we now make it #ej volts and then vary the position of the slider in the grid circuit until the ammeter reads as it did at the start4 ,next we read the voltage impressed on the grid by reading the voltmeter in the grid circuit4 ,suppose it reads #b volts4 ,what does that mean8 ,illustration3 ,fig #id ,it means that two volts in the grid circuit have the same effect on the plate current as ten volts in the plate circuit4 ,if we apply a volt to the grid circuit we get five times as large an effect in the plate circuit as we would if the volt were applied there4 ,we get a greater effect1 the effect of more volts1 by applying our voltage to the grid4 ,we say that the tube acts as an amplifier of voltage because we can get a larger effect than the number of volts which we apply would ordinarily entitle us to4 ,now let's take a simple case of the use of an audion as an amplifier4 ,suppose we have a receiving circuit with which we find that the signals are not easily understood because they are too weak4 ,let this be the receiving circuit of ,fig4 #hh which ,i am reproducing here as part of ,fig4 #id4 ,we have replaced the telephone receiver by a transformer4 ,a transformer is two coils1 or windings1 coupled together4 ,an alternating current in one will give rise to an alternating current in the other4 ,you are already familiar with the idea but this is our first use of the word4 ,usually we call the first coil1 that is the one through which the alternating current flows1 the primary and the second coil1 in which a current is induced1 the secondary4 ,the secondary of this transformer is connected to the grid circuit of another vacuum tube1 to the plate circuit of which is connected another transformer and the telephone receiver4 ,the result is a detector and one stage of amplification4 ,the primary of the first transformer1 so we shall suppose1 has in it the same current as would have been in the telephone4 ,this alternating current induces in the secondary an e4 m4 f4 which has the same variations as this current4 ,this e4 m4 f4 acts on the grid of the second tube1 that is on the amplifier4 ,because the audion amplifies1 the e4 m4 f4 acting on the telephone receiver is larger than it would have been without the use of this audion4 ,and hence there is a greater response on the part of its diaphragm and a louder sound4 ,in setting up such a circuit as this there are several things to watch4 ,for some of these you will have to rely on the dealer from whom you buy your supplies and for the others upon yourself4 ,but it will take another letter to tell you of the proper precautions in using an audion as an amplifier4 ,illustration3 ,fig #ie ,in the circuit which ,i have just described an audion is used to amplify the current which comes from the detector before it reaches the telephone receiver4 ,sometimes we use an audion to amplify the e4 m4 f4 of the signal before impressing it upon the grid of the detector4 ,fig4 #ie shows a circuit for doing that4 ,in the case of ,fig4 #id we are amplifying the audio-frequency current4 ,in that of ,fig4 #ie it is the radio-frequency effect which is amplified4 ,the feed-back or regenerative circuit of ,fig4 #ib is a one-tube circuit for doing the same thing as is done with two tubes in ,fig #ie4 ,footnote #i3 ,there is always some amplification taking place in an audion detector but the regenerative circuit amplifies over and over again until the signal is as large as the tube can detect4 ,,letter #ai ,,the ,,audion ,,amplifier ,,and ,,its ,,connections ,,dear ,,son3 ,in our use of the audion we form three circuits4 ,the first or ,a-circuit includes the filament4 ,the ,b-circuit includes the part of the tube between filament and plate4 ,the ,c-circuit includes the part between filament and grid4 ,we sometimes speak of the ,c-circuit as the input circuit and the ,b-circuit as the output circuit of the tube4 ,this is because we can put into the grid-filament terminals an e4 m4 f4 and obtain from the plate-filament circuit an effect in the form of a change of current4 ,illustration3 ,fig #if ,suppose we had concealed in a box the audion and circuit of ,fig4 #if and that only the terminals which are shown came through the box4 ,we are given a battery and an ammeter and asked to find out all we can as to what is between the terminals ,f and ,g4 ,we connect the battery and ammeter in series with these terminals4 ,no current flows through the circuit4 ,we reverse the battery but no current flows in the opposite direction4 ,then we reason that there is an open-circuit between ,f and ,g4 ,as long as we do not use a higher voltage than that of the ,c-battery which is in the box no current can flow4 ,even if we do use a higher voltage than the negative ,c-battery of the hidden grid-circuit there will be a current only when the external battery is connected so as to make the grid positive with respect to the filament4 ,now suppose we take several cells of battery and try in the same way to find what is hidden between the terminals ,p and ,f4 ,we start with one battery and the ammeter as before and find that if this battery is connected so as to make ,p positive with respect to ,f1 there is a feeble current4 ,we increase the battery and find that the current is increased4 ,two cells1 however1 do not give exactly twice the current that one cell does1 nor do three give three times as much4 ,the current does not increase proportionately to the applied voltage4 ,therefore we reason that whatever is between ,p and ,f acts like a resistance but not like a wire resistance4 ,then1 we try another experiment with this hidden audion4 ,we connect a battery to ,g and ,f1 and note what effect it has on the current which our other battery is sending through the box between ,p and ,f4 ,there is a change of current in this circuit1 just as if our act of connecting a battery to ,g-,f had resulted in connecting a battery in series with the ,p-,f circuit4 ,the effect is exactly as if there is inside the box a battery which is connected into the hidden part of the circuit ,p-,f4 ,this concealed battery1 which now starts to act1 appears to be several times stronger than the battery which is connected to ,g-,f4 ,sometimes this hidden battery helps the ,b-battery which is on the outside2 and sometimes it seems to oppose1 for the current in the ,p-,f circuit either increases or decreases1 depending upon how we connect the battery to ,g and ,f4 ,the hidden battery is always larger than our battery connected to ,g and ,f4 ,if we arrange rapidly to reverse the battery connected to ,g-,f it appears as if there is inside the box in the ,p-,f circuit an alternator1 that is1 something which can produce an alternating e4 m4 f4 ,all this1 of course1 is merely a review statement of what we already know4 ,these experiments are interesting1 however1 because they follow somewhat those which were performed in studying the audion and finding out how to make it do all the wonderful things which it now can4 ,as far as we have carried our series of experiments the box might contain two separate circuits4 ,one between ,g and ,f appears to be an open circuit4 ,the other appears to have in it a resistance and a battery 7or else an alternator74 ,the e4 m4 f4 of the battery1 or alternator1 as the case may be1 depends on what source of e4 m4 f4 is connected to ,g-,f4 ,whatever that e4 m4 f4 is1 there is a corresponding kind of e4 m4 f4 inside the box but one several times larger4 ,illustration3 ,fig #ig ,we might1 therefore1 pay no further attention to what is actually inside the box or how all these effects are brought about4 ,we might treat the entire box as if it was formed by two separate circuits as shown in ,fig4 #ig4 ,if we do so1 we are replacing the box by something which is equivalent so far as effects are concerned1 that is we are replacing an actual audion by two circuits which together are equivalent to it4 ,the men who first performed such experiments wanted some convenient way of saying that if an alternator1 which has an e4 m4 f4 of ,v volts1 is connected to ,f and ,g1 the effect is the same as if a much stronger alternator is connected between ,f and ,p4 ,how much stronger this imaginary alternator is depends upon the design of the audion4 ,for some audions it might be five times as strong1 for other designs #f4e or almost any other number1 although usually a number of times less than #dj4 ,they used a little ,greek letter called mu to stand for this number which depends on the design of the tube4 ,then they said that the hidden alternator in the output circuit was mu times as strong as the actual alternator which was applied between the grid and the filament4 ,of course1 instead of writing the sound and name of the letter they used the letter ,greek3 m itself4 ,and that is what ,i have done in the sketch of ,fig4 #ig4 ,now we are ready to talk about the audion as an amplifier4 ,the first thing to notice is the fact that we have an open circuit between ,f and ,g4 ,this is true as long as we don't apply an e4 m4 f4 large enough to overcome the ,c-battery of ,fig4 #if and thus let the grid become positive and attract electrons from the filament4 ,we need then spend no further time thinking about what will happen in the circuit ,g-,f1 for there will be no current4 ,as to the circuit ,f-,p1 we can treat it as a resistance in series with which there is a generator ,greek3 m times as strong as that which is connected to ,f and ,g4 ,the next problem is how to get the most out of this hidden generator4 ,we call the resistance which the tube offers to the passage of electrons between ,p and ,f the internal resistance of the plate circuit of the tube4 ,how large it is depends upon the design of tube4 ,in some tubes it may be five or six thousand ohms1 and in others several times as high4 ,in the large tubes used in high-powered transmitting sets it is much less4 ,since it will be different in different cases we shall use a symbol for it and say that it is ,rp ohms4 ,then one rule for using an audion as an amplifier is this3 ,to get the most out of an audion see that the telephone1 or whatever circuit or piece of apparatus is connected to the output terminals1 shall have a resistance of ,rp ohms4 ,when the resistance of the circuit1 which an audion is supplying with current1 is the same as the internal resistance of the output side of the tube1 then the audion gives its greatest output4 ,that is the condition for the greatest amount of energy each second1 or the greatest power as we say4 ,that rule is why we always select the telephone receivers which we use with an audion and always ask carefully as to their resistance when we buy4 ,sometimes1 however1 it is not practicable to use receivers of just the right resistance4 ,where we connect the output side of an audion to some other circuit1 as where we let one audion supply another1 it is usually impossible to follow this rule without adding some special apparatus4 ,this leads to the next rule3 ,if the telephone receiver1 or the circuit1 which we wish to connect to the output of an audion1 does not have quite nearly a resistance of ,rp ohms we use a properly designed transformer as we have already done in ,figs4 #id and #ie4 ,a transformer is two separate coils coupled together so that an alternating current in the primary will induce an alternating current in the secondary4 ,of course1 if the secondary is open-circuited then no current can flow but there will be induced in it an e4 m4 f4 which is ready to act if the circuit is closed4 ,transformers have an interesting ability to make a large resistance look small or vice versa4 ,to show you why1 ,i shall have to develop some rules for transformers4 ,suppose you have an alternating e4 m4 f4 of ten volts applied to the primary of an iron-cored transformer which has ten turns4 ,there is one volt applied to each turn4 ,now1 suppose the secondary has only one turn4 ,that one turn has induced in it an alternating e4 m4 f4 of one volt4 ,if there are more turns of wire forming the secondary1 then each turn has induced in it just one volt4 ,but the e4 m4 f4's of all these turns add together4 ,if the secondary has twenty turns1 there is induced in it a total of twenty volts4 ,so the first rule is this3 ,in a transformer the number of volts in each turn of wire is just the same in the secondary as in the primary4 ,if we want a high-voltage alternating e4 m4 f4 all we have to do is to send an alternating current through the primary of a transformer which has in the secondary1 many times more turns of wire than it has in the primary4 ,from the secondary we obtain a higher voltage than we impress on the primary4 ,you can see one application of this rule at once4 ,when we use an audion as an amplifier of an alternating current we send the current which is to be amplified through the primary of a transformer1 as in ,fig4 #id4 ,we use a transformer with many times more turns on the secondary than on the primary so as to apply a large e4 m4 f4 to the grid of the amplifying tube4 ,that will mean a large effect in the plate circuit of the amplifier4 ,you remember that the grid circuit of an audion with a proper value of negative ,c-battery is really open-circuited and no current will flow in it4 ,for that case we get a real gain by using a step-up transformer1 that is1 one with more turns in the secondary than in the primary4 ,it looks at first as if a transformer would always give a gain4 ,if we mean a gain in energy it will not although we may use it1 as we shall see in a minute1 to permit a vacuum tube to work into an output circuit more efficiently than it could without the transformer4 ,we cannot have any more energy in the secondary circuit of a transformer than we give to the primary4 ,suppose we have a transformer with twice as many turns on the secondary as on the primary4 ,to the primary we apply an alternating e4 m4 f4 of a certain number of volts4 ,in the secondary there will be twice as many volts because it has twice as many turns4 ,the current in the secondary1 however1 will be only half as large as is the current in the primary4 ,we have twice the force in the secondary but only half the electron stream4 ,it is something like this3 ,you are out coasting and two youngsters ask you to pull them and their sleds up hill4 ,you pull one of them all the way and do a certain amount of work4 ,on the other hand suppose you pull them both at once but only half way up4 ,you pull twice as hard but only half as far and you do the same amount of work as before4 ,illustration3 ,fig #ih ,we can't get more work out of the secondary of a transformer than we do in the primary4 ,if we design the transformer so that there is a greater pull 7e4 m4 f47 in the secondary the electron stream in the secondary will be correspondingly smaller4 ,you remember how we measure resistance4 ,we divide the e4 m4 f4 7number of volts7 by the current 7number of amperes7 to find the resistance 7number of ohms74 ,suppose we do that for the primary and for the secondary of the transformer of ,fig4 #ih which we are discussing4 ,see what happens in the secondary4 ,there is only half as much voltage but twice as much current4 ,it looks as though the secondary had one-fourth as much resistance as the primary4 ,and so it has1 but we usually call it impedance instead of resistance because straight wires resist but coils or condensers impede alternating e4 m4 f4's4 ,illustration3 ,fig #ii ,before we return to the question of using a transformer in an audion circuit let us turn this transformer around as in ,fig4 #ii and send the current through the side with the larger number of windings4 ,let's talk of primary and secondary just as before but1 of course1 remember that now the primary has twice the turns of the secondary4 ,on the secondary side we shall have only half the current1 but there will be twice the e4 m4 f4 ,the resistance of the secondary then is four times that of the primary4 ,now return to the amplifier of ,fig4 #id and see what sort of a transformer should be between the plate circuit of the tube and the telephone receivers4 ,suppose the internal resistance of the tube is #ab1jjj ohms and the resistance of the telephones is #c1jjj ohms4 ,suppose also that the resistance 7really impedance7 of the primary side of the transformer which we just considered is #ab1jjj ohms4 ,the impedance of its secondary will be a quarter of this or #c1jjj ohms4 ,if we connect such a transformer in the circuit1 as shown1 we shall obtain the greatest output from the tube4 ,in the first place the primary of the transformer has a number of ohms just equal to the internal resistance of the tube4 ,the tube1 therefore1 will give its best to that transformer4 ,in the second place the secondary of the transformer has a resistance just equal to the telephone receivers so it can give its best to them4 ,the effect of the transformer is to make the telephones act as if they had four times as much resistance and so were exactly suited to be connected to the audion4 ,this whole matter of the proper use of transformers is quite simple but very important in setting up vacuum-tube circuits4 ,to overlook it in building or buying your radio set will mean poor efficiency4 ,whenever you have two parts of a vacuum-tube circuit to connect together be sure and buy only a transformer which is designed to work between the two impedances 7or resistances7 which you wish to connect together4 ,there is one more precaution in connection with the purchase of transformers4 ,they should do the same thing for all the important frequencies which they are to transmit4 ,if they do not1 the speech or signals will be distorted and may be unintelligible4 ,if you take the precautions which ,i have mentioned your radio receiving set formed by a detector and one amplifier will look like that of ,fig4 #id4 ,that is only one possible scheme of connections4 ,you can use any detector circuit which you wish1#aj one with a grid condenser and leak1 or one arranged for feed-back ,in either case your amplifier may well be as shown in the figure4 ,illustration3 ,fig #ajj ,the circuit ,i have described uses an audion to amplify the audio-frequency currents which come from the detector and are capable of operating the telephones4 ,in some cases it is desirable to amplify the radio signals before applying them to the detector4 ,this is especially true where a loop antenna is being used4 ,loop antennas are smaller and more convenient than arials and they also have certain abilities to select the signals which they are to receive because they receive best from stations which lie along a line drawn parallel to their turns4 ,unfortunately1 however1 they are much less efficient and so require the use of amplifiers4 ,with a small loop made by ten turns of wire separated by about a quarter of an inch and wound on a square mounting1 about three feet on a side1 you will usually require two amplifiers4 ,one of these might be used to amplify the radio signals before detection and the other to amplify after detection4 ,to tune the loop for broadcasts a condenser of about #j4jjje mf4 will be needed4 ,the diagram of ,fig4 #ajj shows the complete circuit of a set with three stages of radio-amplification and none of audio4 ,footnote #aj3 ,except for patented circuits4 ,see p4 #bbd4 ,,letter #bj ,,telephone ,,receivers ,,and ,,other ,,electromagnetic ,,devices ,,dear ,,son3 ,in an earlier letter when we first introduced a telephone receiver into a circuit ,i told you something of how it operates4 ,i want now to tell why and also of some other important devices which operate for the same reason4 ,you remember that a stream of electrons which is starting or stopping can induce the electrons of a neighboring parallel circuit to start off in parallel paths4 ,we do not know the explanation of this4 ,nor do we know the explanation of another fact which seems to be related to this fact of induction and is the basis for our explanations of magnetism4 ,illustration3 ,fig #aja ,if two parallel wires are carrying steady electron streams in the same general direction the wires attract each other4 ,if the streams are oppositely directed the wires repel each other4 ,fig4 #aja illustrates this fact4 ,if the streams are not at all in the same direction1 that is1 if they are at right angles1 they have no effect on each other4 ,illustration3 ,fig #ajb ,these facts1 of the attraction of electron streams which are in the same direction and repulsion of streams in opposite directions1 are all that one need remember to figure out for himself what will happen under various conditions4 ,for example1 if two coils of wire are carrying currents what will happen is easily seen4 ,fig4 #ajb shows the two coils and a section through them4 ,illustration3 ,fig #ajc ,looking at this cross section we seem to have four wires1 #a and #b of coil ,a and #c and #d of coil ,b4 ,you see at once that if the coils are free to move they will move into the dotted positions shown in ,fig #ajb1 because wire #a attracts wire #c and repels wire #d1 while wire #b attracts wire #d and repels wire #c4 ,if necessary1 and if they are free to move1 the coils will turn completely around to get to this position4 ,i have shown such a case in ,fig4 #ajc4 ,wires which are not carrying currents do not behave in this way4 ,the action is due1 but how we don't yet know1 to the motions of the electrons4 ,as far as we can explain it to-day1 the attraction of two wires which are carrying currents is due to the attraction of the two streams of electrons4 ,of course these electrons are part of the wires4 ,they can't get far away from the stay-at-home electrons and the nuclei of the atoms which form the wires4 ,in fact it is these nuclei which keep the wandering electrons within the wires4 ,the result is that if the streams of electrons are to move toward each other the wires must go along with them4 ,if the wires are held firmly the electron streams cannot approach one another for they must stay in the wires4 ,wires1 therefore1 perform the important service of acting as paths for electrons which are traveling as electric currents4 ,there are other ways in which electrons can be kept in a path1 and other means beside batteries for keeping them going4 ,it doesn't make any difference so far as the attraction or the repulsion is concerned why they are following a certain path or why they stay in it4 ,so far as we know two streams of electrons1 following parallel paths1 will always1 behave just like the two streams of ,fig4 #aja4 ,illustration3 ,fig #ajd ,suppose1 for example1 there were two atoms which were each formed by a nucleus and a number of electrons swinging around about the nucleus as pictured in ,fig4 #ajd4 ,the electrons are going of their own accord and the nucleus keeps them from flying off at a tangent1 the way mud flies from the wheel of an automobile4 ,suppose these two atoms are free to turn but not to move far from their present positions4 ,they will turn so as to make their electron paths parallel just as did the loops of ,fig4 #ajb4 ,illustration3 ,fig #aje ,now1 ,i don't say that there are any atoms at all like the ones ,i have pictured4 ,there is still a great deal to be learned about how electrons act inside different kinds of atoms4 ,we do know1 however1 that the atoms of iron act just as if they were tiny loops with electron streams4 ,illustration3 ,fig #ajf ,suppose we had several loops and that they were lined up like the three loops in ,fig4 #aje4 ,you can see that they would all attract the other loop1 on the right in the figure4 ,on the other hand if they were grouped in the triangle of ,fig4 #ajf they would barely affect the loop because they would be pulling at cross purposes4 ,if a lot of the tiny loops of the iron atoms are lined up so as to act together and attract other loops1 as in the first figure1 we say the iron is magnetized and is a magnet4 ,in an ordinary piece of iron1 however1 the atoms are so grouped that they don't pull together but like the loops of our second figure pull in different directions and neutralize each other's efforts so that there is no net effect4 ,illustration3 ,pl4 ,,ix4--,western ,electric ,loud ,speaking ,receiver4 ,crystal ,detector ,set of the ,general ,electric ,co4 ,audibility ,meter of ,general ,radio ,co4 ,and like the loops of ,fig4 #ajf the atoms in an unmagnetized piece of iron are pretty well satisfied to stay as they are without all lining up to pull together4 ,to magnetize the iron we must force some of these atomic loops to turn part way around4 ,that can be done by bringing near them a strong magnet or a coil of wire which is carrying a current4 ,then the atoms are forced to turn and if enough turn so that there is an appreciable effect then the iron is magnetized4 ,the more that are properly turned the stronger is the magnet4 ,one end or pole we call north-seeking and the other south-seeking1 because a magnetized bar of iron acts like a compass needle4 ,illustration3 ,fig #ajg ,a coil of wire1 carrying a current1 acts just like a magnet because its larger loops are all ready to pull together4 ,i have marked the coil of ,fig4 #ajg with ,n and ,s for north and south4 ,if the electron stream in it is reversed the polarity is reversed4 ,there is a simple rule for this4 ,partially close your left hand so that the fingers form loops4 ,let the thumb stick out at right angles to these loops4 ,if the electron streams are flowing around the loops of a coil in the same direction as your fingers point then your thumb is the ,n pole and the coil will repel the north poles of other loops or magnets in the direction in which your thumb points4 ,if you know the polarity already there is a simple rule for the repulsion or attraction4 ,like poles repel1 unlike poles attract4 ,from what has been said about magnetism you can now understand why in a telephone receiver the current in the winding can make the magnet stronger4 ,it does so because it makes more of the atomic loops of the iron turn around and help pull4 ,on the other hand if the current in the winding is reversed it will turn some of the loops which are already helping into other positions where they don't help and may hinder4 ,if the current in the coil is to help1 the electron stream in it must be so directed that the north pole of the coil is at the same end as the north pole of the magnet4 ,this idea of the attraction or repulsion of electron streams1 whether in coils of wire or in atoms of iron and other magnetizable substances1 is the fundamental idea of most forms of telephone receivers1 of electric motors1 and of a lot of other devices which we call electromagnetic4 ,the ammeters and voltmeters which we use for the measurement of audion characteristics and the like are usually electromagnetic instruments4 ,ammeters and voltmeters are alike in their design4 ,both are sensitive current-measuring instruments4 ,in the case of the voltmeter1 as you know1 we have a large resistance in series with the current-measuring part for the reason of which ,i told in ,letter #h4 ,in the case of ammeters we sometimes let all the current go through the current-measuring part but generally we let only a certain fraction of it do so4 ,to pass the rest of the current we connect a small resistance in parallel with the measuring part4 ,in both types of instruments the resistances are sometimes hidden away under the cover4 ,both instruments must1 of course1 be calibrated as ,i have explained before4 ,in the electromagnetic instruments there are several ways of making the current-measuring part4 ,the simplest is to let the current1 or part of it1 flow through a coil which is pivoted between the ,n and ,s poles of a strong permanent magnet4 ,a spring keeps the coil in its zero position and if the current makes the coil turn it must do so against this spring4 ,the stronger the current in the coil the greater the interaction of the loops of the coil and those of the iron atoms and hence the further the coil will turn4 ,a pointer attached to the coil indicates how far2 and the number of volts or amperes is read off from the calibrated scale4 ,such instruments measure direct-currents1 that is1 steady streams of electrons in one direction4 ,to measure an alternating current or voltage we can use a hot-wire instrument or one of several different types of electromagnetic instruments4 ,perhaps the simplest of these is the so-called plunger type4 ,the alternating current flows in a coil2 and a piece of soft iron is so pivoted that it can be attracted and moved into the coil4 ,soft iron does not make a good permanent magnet4 ,if you put a piece of it inside a coil which is carrying a steady current it becomes a magnet but about as soon as you interrupt the current the atomic loops of the iron stop pulling together4 ,almost immediately they turn into all sorts of positions and form little self-satisfied groups which don't take any interest in the outside world4 7,that isn't true of steel1 where the atomic loops are harder to turn and to line up1 but are much more likely to stay in their new positions47 ,because the plunger in an alternating-current ammeter is soft iron its loops line up with those of the coil no matter which way the electron stream happens to be going in the coil4 ,the atomic magnets in the iron turn around each time the current reverses and they are always1 therefore1 lined up so that the plunger is attracted4 ,if the plunger has much inertia or if the oscillations of the current are reasonably frequent the plunger will not move back and forth with each reversal of the current but will take an average position4 ,the stronger the a-c 7alternating current7 the farther inside the coil will be this position of the plunger4 ,the position of the plunger becomes then a measure of the strength of the alternating current4 ,instruments for measuring alternating e4 m4 f4's and currents1 read in volts and in amperes4 ,so far ,i haven't stopped to tell what we mean by one ampere of alternating current4 ,you know from ,letter #g what we mean by an ampere of d-c 7direct current74 ,it wasn't necessary to explain before because ,i told you only of hot-wire instruments and they will read the same for either d-c or a-c4 ,when there is an alternating current in a wire the electrons start1 rush ahead1 stop1 rush back1 stop1 and do it all over again and again4 ,that heats the wire in which it happens4 ,if an alternating stream of electrons1 which are doing this sort of thing1 heats a wire just exactly as much as would a d-c of one ampere1 then we say that the a-c has an effective value of one ampere4 ,of course part of the time of each cycle the stream is larger than an ampere but for part it is less4 ,if the average heating effect is the same the a-c is said to be one ampere4 ,in the same way1 if a steady e4 m4 f4 7a d-c e4 m4 f47 of one volt will heat a wire to which it is applied a certain amount and if an alternating e4 m4 f4 will have the same heating effect in the same time1 then the a-c e4 m4 f4 is said to be one volt4 ,another electromagnetic instrument which we have discussed but of which more should be said is the iron-cored transformer4 ,we consider first what happens in one of the coils of the transformer4 ,the inductance of a coil is very much higher if it has an iron core4 ,the reason is that then the coil acts as if it had an enormously larger number of turns4 ,all the atomic loops of the core add their effects to the loops of the coil4 ,when the current starts it must line up a lot of these atomic loops4 ,when the current stops and these loops turn back into some of their old self-satisfied groupings1 they affect the electrons in the coil4 ,where first they opposed the motion of these electrons1 now they insist on its being continued for a moment longer4 ,i'll prove that by describing two simple experiments2 and then we'll have the basis for understanding the effect of an iron core in a transformer4 ,illustration3 ,fig #cc ,look again at ,fig4 #cc of ,letter #i which ,i am reproducing for convenience4 ,we considered only what would happen in coil cd if a current was started in coil ab4 ,suppose instead of placing the coils as shown in that figure they are placed as in ,fig4 #ajh4 ,because they are at right angles there will be no effect in cd when the current is started in ab4 ,let the current flow steadily through ab and then suddenly turn the coils so that they are again parallel as shown by the dotted positions4 ,we get the same temporary current in cd as we would if we should place the coils parallel and then start the current in ab4 ,illustration3 ,fig #ajh ,the other experiment is this3 ,starting with the coils lined up as in the dotted position of ,fig4 #ajh and the current steadily flowing in ab1 we suddenly turn them into positions at right angles to each other4 ,there is the same momentary current in cd as if we had left them lined up and had opened the switch in the circuit of ab4 ,illustration3 ,fig #aji ,now we know that the atomic loops of iron behave in the same general way as do loops of wire which are carrying currents4 ,let us replace the coil ab by a magnet as shown in ,fig4 #aji4 ,first we start with the magnet at right angles to the coil cd4 ,suddenly we turn it into the dotted position of that figure4 ,there is the same momentary current in cd as if we were still using the coil ab instead of a magnet4 ,if now we turn the magnet back to a position at right angles to cd1 we observe the opposite direction of current in cd4 ,these effects are more noticeable the more rapidly we turn the magnet4 ,the same is true of turning the coil4 ,the experiment of turning the magnet illustrates just what happens in the case of a transformer with1 an iron core except that instead of turning the entire magnet the little atomic loops do the turning inside the core4 ,in the secondary of an iron-cored transformer the induced current is the sum of two currents both in the same direction at each instant4 ,one current is caused by the starting or stopping of the current in the primary4 ,the other current is due to the turning of the atomic loops of the iron atoms so that more of them line up with the turns of the primary4 ,these atomic loops1 of course1 are turned by the current in the primary4 ,there are so many of them1 however1 that the current due to their turning is usually the more important part of the total current4 ,in all transformers the effect is greater the more rapidly the current changes direction and the atomic loops turn around4 ,for the same size of electron stream in the primary1 therefore1 there is induced in the secondary a greater e4 m4 f4 the greater is the frequency with which the primary current alternates4 ,where high frequencies are dealt with it isn't necessary to have iron cores because the effect is large enough without the help of the atomic loops4 ,and even if we wanted their help it wouldn't be easy to obtain1 for they dislike to turn so fast and it takes a lot of power to make them do so4 ,we know that fact because we know that an iron core increases the inductance and so chokes the current4 ,for low frequencies1 however1 that is those frequencies in the audio range1 it is usually necessary to have iron cores so as to get enough effect without too many turns of wire4 ,the fact that iron decreases the inductance and so seriously impedes alternating currents leads us to use iron-core coils where we want high inductance4 ,such coils are usually called choke coils or retard coils4 ,of their use we shall see more in a later letter where we study radio-telephone transmitters4 ,,letter #ba ,,your ,,receiving ,,set ,,and ,,how ,,to ,,experiment ,,my ,,dear ,,student3 ,in this letter ,i want to tell you how to experiment with radio apparatus4 ,the first rule is this3 ,start with a simple circuit1 never add anything to it until you know just why you are doing so1 and do not box it up in a cabinet until you know how it is working and why4 ,your antenna at the start had better be a single wire about #be feet high and about #ge feet long4 ,this antenna will have capacity of about #j4jjja m4 f4 ,if you want an antenna of two wires spaced about three feet apart ,i would make it about #ge feet long4 ,bring down a lead from each wire1 twisting them into a pigtail to act like one wire except near the horizontal part of the antenna4 ,illustration3 ,fig #aaj ,your ground connection can go to a water pipe4 ,to protect the house and your apparatus from lightning insert a fuse and a little carbon block lightning arrester such as are used by the telephone company in their installations of house phones4 ,you can also use a so-called vacuum lightning arrester4 ,in either case the connections will be as shown in ,fig4 #aaa4 ,if you use a loop antenna1 of course1 no arrester is needed4 ,at first ,i would plan to receive signals between #aej meters and #cfj meters4 ,this will include the amateurs who work between #afj and #bjj m41 the special amateurs who send ,c-,w telegraph at #bge m41 and the broadcasting stations which operate at #cfj m4 ,this range will give you plenty to listen to while you are experimenting4 ,in addition you will get some ship signals at #cjj m4 ,illustration3 ,fig #aaa ,to tune the antenna to any of the wave lengths in this range you can use a coil of #ge turns wound on a cardboard tube of three and a half inches in diameter4 ,you can wind this coil of bare wire if you are careful1 winding a thread along with the wire so as to keep the successive turns separated4 ,in that case you will need to construct a sliding contact for it4 ,that is the simplest form of tuner4 ,on the other hand you can wind with single silk covered wire and bring out taps at the #j1 #b1 #d1 #f1 #h1 #aj1 #ad1 #bj1 #bh1 #cf1 #dd1 #ef1 #ff1 and #geth turns4 ,to make a tap drill a small hole through the tube1 bend the wire into a loop about a foot long and pull this loop through the hole as shown in ,fig4 #aaj4 ,then give the wire a twist1 as shown1 so that it can't pull out1 and proceed with your winding4 ,use #bf s4 s4 c4 wire4 ,you will need about #hj feet and might buy #bjj to have enough for the secondary coil4 ,make contacts to the taps by two rotary switches as shown in ,fig4 #aab4 ,you can buy switch arms and contacts studs or a complete switch mounted on a small panel of some insulating compound4 ,let switch s#a make the contacts for taps between #ad and #ge turns1 and let switch s#b make the other contacts4 ,for the secondary coil use the same size of wire and of core4 ,wind #fj turns1 bringing out a tap at the middle4 ,to tune the secondary circuit you will need a variable condenser4 ,you can buy one of the small ones with a maximum capacity of about #j4jjjc mf41 one of the larger ones with a maximum capacity of #j4jjje mf41 or even the larger size which has a maximum capacity of #j4jja mf4 ,i should prefer the one of #j4jjje mf4 ,you will need a crystal detector--,i should try galena first--and a so-called cat's whisker with which to make contact with the galena4 ,for these parts and for the switch mentioned above you can shop around to advantage4 ,for telephone receivers ,i would buy a really good pair with a resistance of about #bejj ohms4 ,buy also a small mica condenser of #j4jjb mf4 for a blocking condenser4 ,your entire outfit will then look as in ,fig4 #aab4 ,the switch ,s is a small knife switch4 ,to operate1 leave the switch ,s open1 place the primary and secondary coils near together as in the figure and listen4 ,the tuning is varied1 while you listen1 by moving the slider of the slide-wire tuner or by moving the switches if you have connected your coil for that method4 ,make large changes in the tuning by varying the switch s#a and then turn slowly through all positions of s#b1 listening at each position4 ,illustration3 ,fig #aab ,when a signal is heard adjust to the position of s#a and s#b which gives the loudest signal and then closing ,s start to tune the secondary circuit4 ,to do this1 vary the capacity of the condenser in the secondary circuit4 ,don't change the primary tuning until you have tuned the secondary and can get the signal with good volume1 that is loud4 ,you will want to vary the position of the primary and secondary coils1 that is1 vary their coupling1 for you will get sharper tuning as they are drawn farther apart4 ,sharper tuning means less interference from other stations which are sending on wave lengths near that which you wish to receive4 ,reduce the coupling1 therefore1 and then readjust the tuning4 ,it will usually be necessary to make a slight change in both circuits1 in one case with switch s#a and in the other with the variable condenser4 ,as soon as you can identify any station which you hear sending make a note of the position of the switches s#a and s#b1 and of the setting of the condenser in the secondary circuit4 ,in that way you will acquire information as to the proper adjustments to receive certain wave-lengths4 ,this is calibrating your set by the known wave-lengths of distant stations4 ,after learning to receive with this simple set ,i should recommend buying a good audion tube4 ,ask the seller to supply you with a blue print of the characteristic#aa of the tube taken under the conditions of filament current and plate voltage which he recommends for its use4 ,buy a storage battery and a small slide-wire rheostat1 that is variable resistance1 to use in the filament circuit4 ,buy also a bank of dry batteries of the proper voltage for the plate circuit of the tube4 ,at the same time you should buy the proper design of transformer to go between the plate circuit of your tube and the pair of receivers which you have4 ,it will usually be advisable to ask the dealer to show you a characteristic curve for the transformer1 which will indicate how well the transformer operates at the different frequencies in the audio range4 ,it should operate very nearly the same for all frequencies between #bjj and #bejj cycles4 ,the next step is to learn to use the tube as a detector4 ,connect it into your secondary circuit instead of the crystal detector4 ,use the proper value of ,c-battery as determined from your study of the characteristic of the tube4 ,one or two small dry cells1 which have binding-post terminals are convenient ,c-batteries4 ,if you think you will need a voltage much different from that obtained with a whole number of batteries you can arrange to supply the grid as we did in ,fig4 #hf of ,letter #ah4 ,in that case you can use a few feet of #cj ,german-silver wire and make connections to it with a suspender clip4 ,learn to receive with the tube and be particularly careful not to let the filament have too much current and burn out4 ,now buy some more apparatus4 ,you will need a grid condenser of about #j4jjjb mf4 ,the grid leaks to go with it you can make for yourself4 ,i would use a piece of brown wrapping paper and two little metal eyelets4 ,the eyelets can be punched into the paper4 ,between them coat the paper with carbon ink1 or with lead pencil marks4 ,a line about an inch long ought to serve nicely4 ,you will probably wish to make several grid leaks to try4 ,when you get satisfactory operation in receiving by the grid-condenser method the leak will probably be somewhere between a megohm and two megohms4 ,for this method you will not want a ,c-battery1 but you will wish to operate the detector with about as high a voltage as the manufacturers will recommend for the plate circuit4 ,in this way the incoming signal1 which decreases the plate current1 can produce the largest decrease4 ,it is also possible to start with the grid slightly positive instead of being as negative as it is when connected to the negative terminal of the ,a-battery4 ,there will then be possible a greater change in grid voltage4 ,to do so connect the grid as in ,fig4 #aae to the positive terminal of the ,a-battery4 ,illustration3 ,fig #aac ,about this time ,i would shop around for two or three small double-pole double-throw switches4 ,those of the #e-;ampere size will do4 ,with these you can arrange to make comparisons between different methods of receiving4 ,suppose1 for example1 you connect the switches as shown in ,fig4 #aac so that by throwing them to the left you are using the audion and to the right the crystal as a detector4 ,you can listen for a minute in one position and then switch and listen for a minute in the other position1 and so on back and forth4 ,that way you can tell whether or not you really are getting better results4 ,if you want a rough measure of how much better the audion is than the crystal you might see1 while you are listening to the audion1 how much you can rob the telephone receiver of its current and still hear as well as you do when you switch back to the crystal4 ,the easiest way to do this is to put a variable resistance across the receiver as shown in ,fig4 #aac4 ,adjust this resistance until the intensity of the signal when detected by the audion is the same as for the crystal4 ,you adjust this variable resistance until it by-passes so much of the current1 which formerly went through the receiver1 that the audibility of the signal is reduced until it is the same as for the crystal detector4 ,carefully made resistances for such a purpose are sold under the name of audibility meters4 ,you can assemble a resistance which will do fairly well if you will buy a small rheostat which will give a resistance varying by steps of ten ohms from zero to one hundred ohms4 ,at the same time you can buy four resistance spools of one hundred ohms each and perhaps one of #ejj ohms4 ,the spools need not be very expensive for you do not need carefully adjusted resistances4 ,assemble them so as to make a rheostat with a range of #j-ajjj ohms by steps of #aj ohms4 ,the cheapest way to mount is with ,fahnestock clips as illustrated in ,fig4 #aad4 ,after a while1 however1 you will probably wish to mount them in a box with a rotary switch on top4 ,illustration3 ,fig #aad ,to study the effect of the grid condenser you can arrange switches so as to insert this condenser and its leak and at the same time to cut out the ,c-battery4 ,fig4 #aae shows how4 ,you can measure the gain in audibility at the same time4 ,illustration3 ,pl4 ,x4--,audio-frequency ,transformer and ,banked-wound ,coil4 7,courtesy of ,pacent ,electric ,co47 ,illustration3 ,fig #aae ,after learning to use the audion as a detector1 both by virtue of its curved characteristic and by the grid-condenser method1 ,i would suggest studying the same tube as an amplifier4 ,first ,i would learn to use it as an audio-frequency amplifier4 ,set up the crystal detector circuit4 ,use your audio-frequency transformer the other way around so as to step up to the grid4 ,put the telephone in the plate circuit4 ,choose your ,c-battery for amplification and not detection and try to receive4 ,you will get better results if you can afford another iron-core transformer4 ,if you can1 buy one which will work between the plate circuit of one vacuum tube and the grid circuit of another similar tube4 ,then you will have the right equipment when you come to make a two-stage audio-frequency amplifier4 ,if you buy such a transformer use the other transformer between plate and telephones as you did before and insert the new one as shown in ,fig4 #aaf4 ,this circuit also shows how you can connect the switches so as to see how much the audion is amplifying4 ,illustration3 ,fig #aaf ,the next step is to use the audion as an amplifier of the radio-signal before its detection4 ,use the proper ,c-battery for an amplifier1 as determined from the blue print of the tube characteristic4 ,connect the tube as shown in ,fig4 #aag4 ,you will see that in this circuit we are using a choke coil to keep the radio-frequency current out of the battery part of the plate circuit and a small condenser1 another one of #j4jjb mf41 to keep the battery current from the crystal detector4 ,you can see from the same figure how you can arrange the switches so as to find whether or not you are getting any gain from the amplifier4 ,now you are ready to receive those ,c-,w senders at #bge meters4 ,you will need to wind another coil like the secondary coil you already have4 ,here is where you buy another condenser4 ,you will need it later4 ,if before you bought the #j4jjje size1 this time buy the #j4jja size or vice versa4 ,wind also a small coil for a tickler4 ,about #bj turns of #bf wire on a core of #c-a_/b in4 diameter will do4 ,connect the tickler in the plate circuit of the audion4 ,connect to the grid your new coil and condenser and set the audion circuit so that it will induce a current in the secondary circuit which supplies the crystal4 ,fig4 #aah shows the hook-up4 ,illustration3 ,fig #aag ,you will see that you are now supplying the crystal with current from two sources1 namely the distant source of the incoming signals and the local oscillator which you have formed4 ,the crystal will detect the beat note between these two currents4 ,to receive the #bge meters signals you will need to make several adjustments at the same time4 ,in the first place ,i would set the tuning of the antenna circuit and of the crystal circuit about where you think right because of your knowledge of the settings for other wave lengths4 ,then ,i would get the local oscillator going4 ,you can tell whether or not it is going if you suddenly increase or decrease the coupling between the tickler coil and the input circuit of the audion4 ,if this motion is accompanied by a click in the receivers the tube is oscillating4 ,illustration3 ,fig #aah ,now you must change the frequency at which it is oscillating by slowly changing the capacity in the tuned input circuit of the tube4 ,unless the antenna circuit is properly tuned to the #bge meter signal you will get no results4 ,if it is1 you will hear an intermittent musical note for some tune of your local oscillator4 ,this note will have the duration of dots and dashes4 ,you will have to keep changing the tuning of your detector circuit and of the antenna4 ,for each new setting very slowly swing the condenser plates in the oscillator circuit and see if you get a signal4 ,it will probably be easier to use the stand-by position1 which ,i have described1 with switch ,s open in the secondary circuit of ,fig4 #aah4 ,in that case you have only to tune your antenna to #bge meters and then you will pick up a note when your local oscillator is in tune4 ,after you have done so you can tune the secondary circuit which supplies the crystal4 ,if you adopt this method you will want a close coupling between the antenna and the crystal circuit4 ,you will always want a very weak coupling between the oscillator circuit and the detector circuit4 ,you will also probably want a weaker coupling between tickler and tube input than you are at first inclined to believe will be enough4 ,patience and some skill in manipulation is always required for this sort of experiment4 ,when you have completed this experiment in heterodyne receiving1 using a local oscillator1 you are ready to try the regenerative circuit4 ,this has been illustrated in ,fig4 #ib of ,letter #ah and needs no further description4 ,you will have the advantage when you come to this of knowing very closely the proper settings of the antenna circuit and the secondary tuned circuit4 ,you will need then only to adjust the coupling of the tickler and make finer adjustments in your tuning4 ,after you have completed this series of experiments you will be something of an adept at radio and are in a position to plan your final set4 ,for this set you will need to purchase certain parts complete from reputable dealers because many of the circuits which ,i have described are patented and should not be used except as rights to use are obtained by the purchase of licensed apparatus which embodies the patented circuits4 ,knowing how radio receivers operate and why1 you are now in a good condition to discuss with dealers the relative merits and costs of receiving sets4 ,illustration3 ,fig #aai ,before you actually buy a completed set you may want to increase the range of frequency over which you are carrying out your experiments4 ,to receive at longer wave-lengths you will need to increase the inductance of your antenna so that it will be tuned to a lower frequency4 ,this is usually called loading and can be done by inserting a coil in the antenna4 ,to obtain smaller wave-lengths decrease the effective capacity of the antenna circuit by putting another condenser in series with the antenna4 ,usually1 therefore1 one connects into his antenna circuit both a condenser and a loading coil4 ,by using a variable condenser the effective capacity of the antenna system may be easily changed4 ,the result is that this series condenser method becomes the easiest method of tuning and the slide wire tuner is not needed4 ,fig4 #aai shows the circuit4 ,for quite a range of wave-lengths we may use the same loading coil and tune the antenna circuit entirely by this series condenser4 ,for some other range of wave-lengths we shall then need a different loading coil4 ,in a well-designed set the wave-length ranges overlap4 ,the calculation of the size of loading coil is quite easy but requires more arithmetic than ,i care to impose on you at present4 ,i shall therefore merely give you illustrations based on the assumption that your antenna has a capacity of #j4jjja or of #j4jjjb mf4 and that the condensers which you have bought are #j4jjje and #j4jja for their maxima4 ,in ,table ,i there is given1 for each of several values of the inductance of the primary coil1 the shortest and the longest wave-lengths which you can expect to receive4 ,the table is in two parts1 the first for an antenna of capacity #j4jjja mf4 and the second for one of #j4jjjb mf4 ,yours will be somewhere between these two limits4 ,the shortest wave-length depends upon the antenna and not upon the condenser which you use in series with it for tuning4 ,it also depends upon how much inductance there is in the coil which you have in the antenna circuit4 ,the table gives values of inductance in the first column1 and of minimum wave-length in the second4 ,the third column shows what is the greatest wave-length you may expect if you use a tuning condenser of #j4jjje mf42 and the fourth column the slightly large wave-length which is possible with the larger condenser4 ,,table ,i ,part #a4 7,for antenna of #j4jjja mf47 ,inductance in ,shortest wave-length ,longest wave-length in meters mil-henries4 in meters4 with #j4jjje mf4 with #j4jja mf4 #j4aj #ajc #afi #agi #j4bj #adf #bch #bec #j4dj #bjg #ccg #ceh #j4he #cjj #dij #eae #a4hj #djj #gjj #gfj #b4jj #dbj #gej #hjj #d4jj #fjj #ajhj #aacj #e4jj #ffj #abjj #abfj #aj4jj #ijj #agjj #agij #cj4jj #afjj #bijj #cajj ,part #b4 7,for antenna of #j4jjjb mf47 #j4aj #afi #bbe #bdj #j4af #baj #bhe #cje #j4bj #bdj #cbj #cdj #j4be #bgj #cee #chj #j4dj #cdj #dej #dhj #j4fj #dbj #eej #eij #j4hj #dhj #fcj #fhj #a4bj #ehe #gge #hdj #a4hj #gbj #iej #ajbj #c4jj #icj #abbj #acbj #e4jj #abjj #afjj #agjj #h4jj #aejj #bjjj #baej #ab4jj #ahej #bdjj #bfej #af4jj #baej #bhjj #cjej ,from ,table ,i you can find how much inductance you will need in the primary circuit4 ,a certain amount you will need to couple the antenna and the secondary circuit4 ,the coil which you wound at the beginning of your experiments will do well for that4 ,anything more in the way of inductance1 which the antenna circuit requires to give a desired wave-length1 you may consider as loading4 ,in ,table ,,ii are some data as to winding coils on straight cores to obtain various values of inductance4 ,your #bf s4 s4 c4 wire will wind about #ed turns to the inch4 ,i have assumed that you will have this number of turns per inch on your coils and calculated the inductance which you should get for various numbers of total turns4 ,the first part of the table is for a core of #c4e inches in diameter and the second part for one of #e inches4 ,the first column gives the inductance in mil-henries4 ,the second gives number of turns4 ,the third and fourth are merely for convenience and give the approximate length in inches of the coil and the approximate total length of wire which is required to wind it4 ,i have allowed for bringing out taps4 ,in other words #eej feet of the wire will wind a coil of #aj4b inches with an inductance of #h4jj mil-henries1 and permit you to bring out taps at all the lower values of inductance which are given in the table4 ,table ,,ii ,part #a4 7,for a core of #c4e in4 diam47 ,inductance in ,number ,length ,feet of wire mil-henries4 of turns4 in inches4 required4 #j4aj #be #j4df #be #j4af #cd #j4fc #cf #j4bj #ci #j4gb #db #j4be #dd #j4ha #di #j4dj #eh #a4jg #fc #j4fj #ge #a4ch #hj #j4hj #ib #a4gj #ajj #j4he #if #a4gh #ajd #a4jj #ajh #b4jj #aah #a4bj #abc #b4bh #acc #a4hj #afd #c4jc #agf #b4jj #ahj #c4cc #aij #c4jj #bdb #d4dh #bej #d4jj #cjd #e4fb #caj #e4jj #cff #f4gg #cgj #h4jj #eej #aj4bj #eej ,part #b4 7,for core of #e4j in4 diam47 #b4jj #abj #b4bb #afj #c4jj #aeh #b4ic #bae #d4jj #aid #c4eh #bfe #e4jj #bbh #d4bb #caj #h4jj #cbd #f4jj #dej #aj4jj #chd #g4aj #ecj #ab4jj #dej #h4cj #fbe ,the coil which you wound at the beginning of your experiment had only #ge turns and was tapped so that you could1 by manipulating the two switches of ,fig4 #aab1 get small variations in inductance4 ,in ,table ,,iii is given the values of the inductance which is controlled by the switches of that figure1 the corresponding number of turns1 and the wave-length to which the antenna should then be tuned4 ,i am giving this for two values of antenna capacity1 as ,i have done before4 ,by the aid of these three tables you should have small difficulty in taking care of matters of tuning for all wave-lengths below about #cjjj meters4 ,if you want to get longer waves than that you had better buy a few banked-wound coils4 ,these are coils in which the turns are wound over each other but in such a way as to avoid in large part the capacity effects which usually accompany such winding4 ,you can try winding them for yourself but ,i doubt if the experience has much value until you have gone farther in the study of the mathematical theory of radio than this series of letters will carry you4 ,,table ,,iii ,circuit of ,fig4 #aab ,number ,inductance in ,wave length with antenna of of turns4 mil-henries4 #j4jjja mf4 #j4jjjb mf4 #ad #j4jd #abj #agj #bj #j4jg #afj #bbj #bh #j4ab #baj #bij #cf #j4ah #bej #cfj #dd #j4be #cjj #dbj #ef #j4ch #cgj #ebj #ge #j4fj #dfj #fej ,in the secondary circuit there is only one capacity1 that of the variable condenser4 ,if it has a range of values from about #j4jjjje mf4 to #j4jjje mf4 your coil of #fj turns and #j4db mf4 permits a range of wave-lengths from #bgj to #hfj m4 ,using half the coil the range is #aej to #dhj m4 ,with the larger condenser the ranges are respectively #bgj to #abbj and #bgj to #fgj4 ,for longer wave-lengths load with inductance4 ,four times the inductance will tune to double these wave-lengths4 ,footnote #aa3 ,if you can afford to buy1 or if you can borrow1 ammeters and voltmeters of the proper range you should take the characteristic yourself4 ,,letter #bb ,,high-,,powered ,,radio-,,telephone ,,transmitters ,,my ,,dear ,,experimenter3 ,this letter is to summarize the operations which must be performed in radio-telephone transmission and reception2 and also to describe the circuit of an important commercial system4 ,to transmit speech by radio three operations are necessary4 ,first1 there must be generated a high-frequency alternating current2 second1 this current must be modulated1 that is1 varied in intensity in accordance with the human voice2 and third1 the modulated current must be supplied to an antenna4 ,for efficient operation1 of course1 the antenna must be tuned to the frequency which is to be transmitted4 ,there is also a fourth operation which is usually performed and that is amplification4 ,wherever the electrical effect is smaller than desired1 or required for satisfactory transmission1 vacuum tubes are used as amplifiers4 ,of this ,i shall give you an illustration later4 ,three operations are also essential in receiving4 ,first1 an antenna must be so arranged and tuned as to receive energy from the distant transmitting station4 ,there is then in the receiving antenna a current similar in wave form to that in the transmitting antenna4 ,second1 the speech significance of this current must be detected1 that is1 the modulated current must be demodulated4 ,a current is then obtained which has the same wave form as the human voice which was the cause of the modulation at the distant station4 ,the third operation is performed by a telephone receiver which makes the molecules of air in its neighborhood move back and forth in accordance with the detected current4 ,as you already know a fourth operation may be carried on by amplifiers which give on their output sides currents of greater strength but of the same forms as they receive at their input terminals4 ,in transmitting and in receiving equipment two or more of these operations may be performed by the same vacuum tube as you will remember from our discussion of the regenerative circuit for receiving4 ,for example1 also1 in any receiving set the vacuum tube which detects is usually amplifying4 ,in the regenerative circuit for receiving continuous waves by the heterodyne method the vacuum tube functions as a generator of high-frequency current and as a detector of the variations in current which occur because the locally-generated current does not keep in step with that generated at the transmitting station4 ,another example of a vacuum tube performing simultaneously two different functions is illustrated in ,fig4 #abj which shows a simple radio-telephone transmitter4 ,the single tube performs in itself both the generation of the radio-frequency current and its modulation in accordance with the output of the carbon-button transmitter4 ,this audion is in a feed-back circuit1 the oscillation frequency of which depends upon the condenser ,c and the inductance ,l4 ,the voice drives the diaphragm of the transmitter and thus varies the resistance of the carbon button4 ,this varies the current from the battery1 ,ba1 through the primary1 ,t#a1 of the transformer ,t4 ,the result is a varying voltage applied to the grid by the secondary ,t#b4 ,the oscillating current in the plate circuit of the audion varies accordingly because it is dependent upon the grid voltage4 ,the condenser ,cr offers a low impedance to the radio-frequency current to which the winding ,t#b of audio-frequency transformer offers too much4 ,illustration3 ,fig #abj ,in this case the tube is both generator and modulator4 ,in some cases these operations are separately performed by different tubes4 ,this was true of the transmitting set used in #aiae when the engineers of the ,bell ,telephone ,system talked by radio from ,arlington1 near ,washington1 ,d4 ,c41 to ,paris and ,honolulu4 ,i shall not draw out completely the circuit of their apparatus but ,i shall describe it by using little squares to represent the parts responsible for each of the several operations4 ,first there was a vacuum tube oscillator which generated a small current of the desired frequency4 ,then there was a telephone transmitter which made variations in a direct-current flowing through the primary of a transformer4 ,the e4 m4 f4 from the secondary of this transformer and the e4 m4 f4 from the radio-frequency oscillator were both impressed upon the grid of an audion which acted as a modulator4 ,the output of this audion was a radio-frequency current modulated by the voice4 ,the output was amplified by a two-stage audion amplifier and supplied through a coupling coil to the large antenna of the ,u4 ,s4 ,navy ,station at ,arlington4 ,fig4 #aba shows the system4 ,illustration3 ,fig #aba ,the audion amplifiers each consisted of a number of tubes operating in parallel4 ,when tubes are operated in parallel they are connected as shown in ,fig4 #abb so that the same e4 m4 f4 is impressed on all the grids and the same plate-battery voltage on all the plates4 ,as the grids vary in voltage there is a corresponding variation of current in the plate circuit of each tube4 ,the total change of the current in the plate-battery circuit is1 then1 the sum of the changes in all the plate-filament circuits of the tubes4 ,this scheme of connections gives a result equivalent to that of a single tube with a correspondingly larger plate and filament4 ,illustration3 ,fig #abb ,parallel connection is necessary because a single tube would be overheated in delivering to the antenna the desired amount of power4 ,you remember that when the audion is operated as an amplifier the resistance to which it supplies current is made equal to its own internal resistance of ,rp4 ,that means that there is in the plate circuit just as much resistance inside the tube as outside4 ,hence there is the same amount of work done each second in forcing the current through the tube as through the antenna circuit1 if that is what the tube supplies4 ,work per second is power2 the plate battery is spending energy in the tube at the same rate as it is supplying it to the antenna where it is useful for radiation4 ,illustration3 ,pl4 ,,xi4--,broadcasting ,equipment1 ,developed by the ,american ,telephone and ,telegraph ,company and the ,western ,electric ,company4 ,all the energy expended in the tube appears as heat4 ,it is due to the blows which the electrons strike against the plate when they are drawn across from the filament4 ,these impacts set into more rapid motion the molecules of the plate2 and the temperature of the tube rises4 ,there is a limit to the amount the temperature can rise without destroying the tube4 ,for that reason the heat produced inside it must not exceed a certain limit depending upon the design of the tube and the method of cooling it as it is operated4 ,in the ,arlington experiments1 which ,i mentioned a moment ago1 the tubes were cooled by blowing air on them from fans4 ,we can find the power expended in the plate circuit of a tube by multiplying the number of volts in its battery by the number of amperes which flows4 ,suppose the battery is #bej volts and the current #j4jb amperes1 then the power is #e watts4 ,the watt is the unit for measuring power4 ,tubes are rated by the number of watts which can be safely expended in them4 ,you might ask1 when you buy an audion1 what is a safe rating for it4 ,the question will not be an important one1 however1 unless you are to set up a transmitting set since a detector is usually operated with such small plate-voltage as not to have expended in it an amount of power dangerous to its life4 ,in recent transmitting sets the tubes are used in parallel for the reasons ,i have just told1 but a different method of modulation is used4 ,the generation of the radio-frequency current is by large-powered tubes which are operated with high voltages in their plate circuits4 ,the output of these oscillators is supplied to the antenna4 ,the intensity of the oscillations of the current in these tubes is controlled by changing the voltage applied in their plate circuits4 ,you can see from ,fig4 #abc that if the plate voltage is changed the strength of the alternating current is changed accordingly4 ,it is the method used in changing the voltage which is particularly interesting4 ,illustration3 ,fig #abc ,the high voltages which are used in the plate circuits of these high-powered audions are obtained from generators instead of batteries4 ,you remember from ,letter #bj that an e4 m4 f4 is induced in a coil when the coil and a magnet are suddenly changed in their positions1 one being turned with reference to the other4 ,a generator is a machine for turning a coil so that a magnet is always inducing an e4 m4 f4 in it4 ,it is formed by an armature carrying coils and by strong electromagnets4 ,the machine can be driven by a steam or gas engine1 by a water wheel1 or by an electric motor4 ,generators are designed either to give steady streams of electrons1 that is for d-c currents1 or to act as alternators4 ,illustration3 ,fig #abd ,suppose we have1 as shown in ,fig4 #abd1 a d-c generator supplying current to a vacuum tube oscillator4 ,the current from the generator passes through an iron-cored choke coil1 marked ,la in the figure4 ,between this coil and the plate circuit we connect across the line a telephone transmitter4 ,to make a system which will work efficiently we shall have to suppose that this transmitter has a high resistance1 say about the same as the internal resistance1 ,rp1 of the tube and also that it can carry as large a current4 ,of the current which comes from the generator about one-half goes to the tube and the rest to the transmitter4 ,if the resistance of the transmitter is increased it can't take as much current4 ,the coil1 ,la1 however1 because of its inductance1 tends to keep the same amount of current flowing through itself4 ,for just an instant then the current in ,la keeps steady even though the transmitter doesn't take its share4 ,the result is more current for the oscillating tube4 ,on the other hand if the transmitter takes more current1 because its resistance is decreased1 the choke coil1 ,la1 will momentarily tend to keep the current steady so that what the transmitter takes must be at the expense of the oscillating tube4 ,that's one way of looking at what happens4 ,we know1 however1 from ,fig4 #abc that to get an increase in the amplitude of the current in the oscillating tube we must apply an increased voltage to its plate circuit4 ,that is what really happens when the transmitter increases in resistance and so doesn't take its full share of the current4 ,the reason is this3 ,when the transmitter resistance is increased the current in the transmitter decreases4 ,just for a moment it looks as though the current in ,la is going to decrease4 ,that's the way it looks to the electrons2 and you know what electrons do in an inductive circuit when they think they shall have to stop4 ,they induce each other to keep on for a moment4 ,for a moment they act just as if there was some extra e4 m4 f4 which was acting to keep them going4 ,we say1 therefore1 that there is an extra e4 m4 f41 and we call this an e4 m4 f4 of self-induction4 ,all this time there has been active on the plate circuit of the tube the e4 m4 f4 of the generator4 ,to this there is added at the instant when the transmitter resistance increases1 the e4 m4 f4 of self-induction in the coil1 ,la and so the total e4 m4 f4 applied to the tube is momentarily increased4 ,this increased e4 m4 f41 of course1 results in an increased amplitude for the alternating current which the oscillator is supplying to the transmitting antenna4 ,when the transmitter resistance is decreased1 and a larger current should flow through the choke coil1 the electrons are asked to speed up in going through the coil4 ,at first they object and during that instant they express their objection by an e4 m4 f4 of self-induction which opposes the generator voltage4 ,for an instant1 then1 the voltage of the oscillating tube is lowered and its alternating-current output is smaller4 ,illustration3 ,fig #abe ,for the purpose of bringing about such threatened changes in current1 and hence such e4 m4 f4's of self-induction1 the carbon transmitter is not suitable because it has too small a resistance and too small a current carrying ability4 ,the plate circuit of a vacuum tube will serve admirably4 ,you know from the audion characteristic that without changing the plate voltage we can1 by applying a voltage to the grid1 change the current through the plate circuit4 ,now if it was a wire resistance with which we were dealing and we should be able to obtain a change in current without changing the voltage acting on this wire we would say that we had changed the resistance4 ,we can say1 therefore1 that the internal resistance of the plate circuit of a vacuum tube can be changed by what we do to the grid4 ,in ,fig4 #abe ,i have substituted the plate circuit of an audion for the transmitter of ,fig4 #abd and arranged to vary its resistance by changing the potential of the grid4 ,this we do by impressing upon the grid the e4 m4 f4 developed in the secondary of a transformer1 to the primary of which is connected a battery and a carbon transmitter4 ,the current through the primary varies in accordance with the sounds spoken into the transmitter4 ,and for all the reasons which we have just finished studying there are similar variations in the output current of the oscillating tube in the transmitting set of ,fig4 #abe4 ,in this latter figure you will notice a small air-core coil1 ,l,r1 between the oscillator and the modulator tube4 ,this coil has a small inductance but it is enough to offer a large impedance to radio-frequency currents4 ,the result is1 it does not let the alternating currents of the oscillating tube flow into the modulator4 ,these currents are confined to their own circuit1 where they are useful in establishing similar currents in the antenna4 ,on the other hand1 the coil ,l,r doesn't seriously impede low-frequency currents and therefore it does not prevent variations in the current which are at audio-frequency4 ,it does not interfere with the changes in current which accompany the variations in the resistance of the plate circuit of the modulator4 ,that is1 it has too little impedance to act like ,la and so it permits the modulator to vary the output of the oscillator4 ,illustration3 ,fig #abf ,the oscillating circuit of ,fig4 #abe includes part of the antenna4 ,it differs also from the others ,i have shown in the manner in which grid and plate circuits are coupled4 ,i'll explain by ,fig4 #abf4 ,the transmitting set which ,i have just described involves many of the principles of the most modern sets4 ,if you understand its operation you can probably reason out for yourself any of the other sets of which you will hear from time to time4 ,,letter #bc ,,amplification ,,at ,,intermediate ,,frequencies ,,dear ,,son3 ,in the matter of receiving ,i have already covered all the important principles4 ,there is one more system1 however1 which you will need to know4 ,this is spoken of either as the super-heterodyne or as the intermediate-frequency amplification method of reception4 ,the system has two important advantages4 ,first1 it permits sharper tuning and so reduces interference from other radio signals4 ,second1 it permits more amplification of the incoming signal than is usually practicable4 ,first as to amplification3 ,we have seen that amplification can be accomplished either by amplifying the radio-frequency current before detection or by amplifying the audio-frequency current which results from detection4 ,there are practical limitations to the amount of amplification which can be obtained in either case4 ,an efficient multi-stage amplifier for radio-frequencies is difficult to build because of what we call capacity effects4 ,consider for example the portion of circuit shown in ,fig4 #abg4 ,the wires a and b act like small plates of condensers4 ,what we really have1 is a lot of tiny condensers which ,i have shown in the figure by the light dotted-lines4 ,if the wires are transmitting high-frequency currents these condensers offer tiny waiting-rooms where the electrons can run in and out without having to go on to the grid of the next tube4 ,there are other difficulties in high-frequency amplifiers4 ,this one of capacity effects between parallel wires is enough for the present4 ,it is perhaps the most interesting because it is always more or less troublesome whenever a pair of wires is used to transmit an alternating current4 ,illustration3 ,fig #abg ,in the case of a multi-stage amplifier of audio-frequency current there is always the possibility of the amplification of any small variations in current which may naturally occur in the action of the batteries4 ,there are always small variations in the currents from batteries1 due to impurities in the materials of the plates1 air bubbles1 and other causes4 ,ordinarily we don't observe these changes because they are too small to make an audible sound in the telephone receivers4 ,suppose1 however1 that they take place in the battery of the first tube of a series of amplifiers4 ,any tiny change of current is amplified many times and results in a troublesome noise in the telephone receiver which is connected to the last tube4 ,in both types of amplifiers there is1 of course1 always the chance that the output circuit of one tube may be coupled to and induce some effect in the input circuit of one of the earlier tubes of the series4 ,this will be amplified and result in a greater induction4 ,in other words1 in a circuit where there is large amplification1 there is always the difficulty of avoiding a feed-back of energy from one tube to another so that the entire group acts like an oscillating circuit1 that is regeneratively4 ,much of this difficulty can be avoided after experience4 ,if a multi-stage amplifier is to be built for a current which does not have too high a frequency the capacity effects and the other difficulties due to high-frequency need not be seriously troublesome4 ,if the frequency is not too high1 but is still well above the audible limit1 the noises due to variations in battery currents need not bother for they are of quite low frequency4 ,currents from #bj1jjj to #fj1jjj cycles a second are1 therefore1 the most satisfactory to amplify4 ,suppose1 however1 one wishes to amplify the signals from a radio-broadcasting station4 ,the wave-length is #cfj meters and the frequency is about #hcd1jjj cycles a second4 ,the system of intermediate-frequency amplification solves the difficulty and we shall see how it does so4 ,illustration3 ,fig #abh ,at the receiving station a local oscillator is used4 ,this generates a frequency which is about #cj1jjj cycles less than that of the incoming signal4 ,both currents are impressed on the grid of a detector4 ,the result is1 in the output of the detector1 a current which has a frequency of #cj1jjj cycles a second4 ,the intensity of this detected current depends upon the intensity of the incoming signal4 ,the beat note current of #cj1jjj cycles varies1 therefore1 in accordance with the voice which is modulating at the distant sending station4 ,the speech significance is now hidden in a current of a frequency intermediate between radio and audio4 ,this current may be amplified many times and then supplied to the grid of a detector which obtains from it a current of audio-frequency which has a speech significance4 ,in ,fig4 #abh ,i have indicated the several operations4 ,we can now see why this method permits sharper tuning4 ,the whole idea of tuning1 of course1 is to arrange that the incoming signal shall cause the largest possible current and at the same time to provide that any signals at other wave-lengths shall cause only negligible currents4 ,what we want a receiving set to do is to distinguish between two signals which differ slightly in wave-length and to respond to only one of them4 ,suppose we set up a tuned circuit formed by a coil and a condenser and try it out for various frequencies of signals4 ,you know how it will respond from our discussion in connection with the tuning curve of ,fig4 #ea of ,letter #ac4 ,we might find from a number of such tests that the best we can expect any tuned circuit to do is to discriminate between signals which differ about ten percent in frequency1 that is1 to receive well the desired signal and to fail practically entirely to receive a signal of a frequency either ten percent higher or the same amount lower4 ,for example1 if the signal is at #cj1jjj cycles a tuned circuit might be expected to discriminate against an interfering signal of #cc1jjj4 ,if the signal is at #cjj1jjj cycles a tuned circuit might discriminate against an interfering signal of #ccj1jjj cycles1 but an interference at #cjc1jjj cycles would be very troublesome indeed4 ,it couldn't be tuned out at all4 ,now suppose that the desired signal is at #cjj1jjj cycles and that there is interference at #cjc1jjj cycles4 ,we provide a local oscillator of #bgj1jjj cycles a second1 receive by this super-heterodyne method which ,i have just described1 and so obtain an intermediate frequency4 ,in the output of the first detector we have then a current of #cjj1jjj--bgj1jjj or #cj1jjj cycles due to the desired signal and also a current of #cjc1jjj--bgj1jjj or #cc1jjj cycles due to the interference4 ,both these currents we can supply to another tuned circuit which is tuned for #cj1jjj cycles a second4 ,it can receive the desired signal but it can discriminate against the interference because now the latter is ten percent off the tune of the signal4 ,you see the question is not one of how far apart two signals are in number of cycles per second4 ,the question always is3 ,how large in percent is the difference between the two frequencies8 ,the matter of separating two effects of different frequencies is a question of the interval between the frequencies4 ,to find the interval between two frequencies we divide one by the other4 ,you can see that if the quotient is larger than #a4a or smaller than #j4i the frequencies differ by ten percent or more4 ,the higher the frequency the larger the number of cycles which is represented by a given size of interval4 ,while ,i am writing of frequency intervals ,i want to tell you one thing more of importance4 ,you remember that in human speech there may enter1 and be necessary1 any frequency between about #bjj and #bjjj cycles a second4 ,that we might call the range of the necessary notes in the voice4 ,whenever we want a good reproduction of the voice we must reproduce all the frequencies in this range4 ,suppose we have a radio-current of #ajj1jjj cycles modulated by the frequencies in the voice range4 ,we find in the output of our transmitting set not only a current of #ajj1jjj cycles but currents in two other ranges of frequencies4 ,one of these is above the signal frequency and extends from #ajj1bjj to #ajb1jjj cycles4 ,the other is the same amount below and extends from #ih1jjj to #ii1hjj cycles4 ,we say there is an upper and a lower band of frequencies4 ,all these currents are in the complex wave which comes from the radio-transmitter4 ,for this statement you will have to take my word until you can handle the form of mathematics known as trigonometry4 ,when we receive at the distant station we receive not only currents of the signal frequency but also currents whose frequencies lie in these side-bands4 ,no matter what radio-frequency we may use we must transmit and receive side-bands of this range if we use the apparatus ,i have described in the past letters4 ,you can see what that means4 ,suppose we transmit at a radio-frequency of #ej1jjj cycles and modulate that with speech4 ,we shall really need all the range from #dh1jjj cycles to #eb1jjj cycles for one telephone message4 ,on the other hand if we modulated a #ejj1jjj cycle wave by speech the side-bands are from #dih1jjj to #dii1hjj and #ejj1bjj to #ejb1jjj cycles4 ,if we transmit at #ej1jjj cycles1 that is1 at #fjjj meters1 we really need all the range between #eggj meters and #fbej meters1 as you can see by the frequencies of the side-bands4 ,at #ajj1jjj cycles we need only the range of wave-lengths between #bidj m4 and #cjfj m4 ,if the radio-frequency is #ejj1jjj cycles we need a still smaller range of wave-lengths to transmit the necessary side-bands4 ,then the range is from #eih m4 to #fjc m4 ,in the case of the transmission of speech by radio we are interested in having no interference from other signals which are within #bjjj cycles of the frequency of our radio-current no matter what their wave-lengths may be4 ,the part of the wave-length range which must be kept clear from interfering signals becomes smaller the higher the frequency which is being modulated4 ,you can see that very few telephone messages can be sent in the long-wave-length part of the radio range and many more1 although not very many after all1 in the short wave-length part of the radio range4 ,you can also see why it is desirable to keep amateurs in the short wave-length part of the range where more of them can transmit simultaneously without interfering with each other or with commercial radio stations4 ,there is another reason1 too1 for keeping amateurs to the shortest wave-lengths4 ,transmission of radio signals over short distances is best accomplished by short wave-lengths but over long distances by the longer wave-lengths4 ,for trans-oceanic work the very longest wave-lengths are best4 ,the long-haul stations1 therefore1 work in the frequency range immediately above #aj1jjj cycles a second and transmit with wave lengths of #cj1jjj m4 and shorter4 ,illustration3 ,pl4 ,,xii4--,broadcasting ,station of the ,american ,telephone and ,telegraph ,company on the ,roof of the ,walker-,lispenard ,bldg4 in ,new ,york ,city ,where the ,long-distance ,telephone ,lines ,terminate4 ,,letter #bd ,,by ,,wire ,,and ,,by ,,radio ,,dear ,,boy3 ,the simplest wire telephone-circuit is formed by a transmitter1 a receiver1 a battery1 and the connecting wire4 ,if two persons are to carry on a conversation each must have this amount of equipment4 ,the apparatus might be arranged as in ,fig4 #abi4 ,this set-up1 however1 requires four wires between the two stations and you know the telephone company uses only two wires4 ,let us find the principle upon which its system operates because it is the solution of many different problems including that of wire-to-radio connections4 ,illustration3 ,fig #abi ,imagine four wire resistances connected together to form a square as in ,fig4 #acj4 ,suppose there are two pairs of equal resistances1 namely ,r#a and ,r#b1 and ,z#a and ,z#b4 ,if we connect a generator1 ,g1 between the junctions a and b there will be two separate streams of electrons1 one through the ,r-side and the other through the ,z-side of the circuit4 ,these streams1 of course1 will not be of the same size for the larger stream will flow through the side which offers the smaller resistance4 ,illustration3 ,fig #acj ,half the e4 m4 f4 between a and b is used up in sending the stream half the distance4 ,half is used between a and the points c and d1 and the other half between c and d and the other end4 ,it doesn't make any difference whether we follow the stream from a to c or from a to d1 it takes half the e4 m4 f4 to keep this stream going4 ,points c and d1 therefore1 are in the same condition of being half-way electrically from a to b4 ,the result is that there can be no current through any wire which we connect between c and d4 ,suppose1 therefore1 that we connect a telephone receiver between c and d4 ,no current flows in it and no sound is emitted by it4 ,now suppose the resistance of ,z#b is that of a telephone line which stretches from one telephone station to another4 ,suppose also that ,z#a is a telephone line exactly like ,z#b except that it doesn't go anywhere at all because it is all shut up in a little box4 ,we'll call ,z#a an artificial telephone line4 ,we ought to call it1 as little children would say1 a make-believe telephone line4 ,it doesn't fool us but it does fool the electrons for they can't tell the difference between the real line ,z#b and the artificial line ,z#a4 ,we can make a very good artificial line by using a condenser and a resistance4 ,the condenser introduces something of the capacity effects which ,i told you were always present in a circuit formed by a pair of wires4 ,illustration3 ,fig #aca ,at the other telephone station let us duplicate this apparatus1 using the same real line in both cases4 ,instead of just any generator of an alternating e4 m4 f4 let us use a telephone transmitter4 ,we connect the transmitter through a transformer4 ,the system then looks like that of ,fig4 #aca4 ,when some one talks at station #a there is no current through his receiver because it is connected to c and d1 while the e4 m4 f4 of the transmitter is applied to a and b4 ,the transmitter sets up two electron streams between a and b1 and the stream which flows through the ,z-side of the square goes out to station #b4 ,at this station the electrons have three paths between d and b4 ,i have marked these by arrows and you see that one of them is through the receiver4 ,the current which is started by the transmitter at station #a will therefore operate the receiver at station #b but not at its own station4 ,of course station #b can talk to #a in the same way4 ,the actual set-up used by the telephone company is a little different from that which ,i have shown because it uses a single common battery at a central office between two subscribers4 ,the general principle1 however1 is the same4 ,illustration3 ,fig #acb ,it won't make any difference if we use equal inductance coils1 instead of the ,r-resistances1 and connect the transmitter to them inductively as shown in ,fig4 #acb4 ,so far as that is concerned we can also use a transformer between the receiver and the points c and d1 as shown in the same figure4 ,illustration3 ,fig #acc ,we are now ready to put in radio equipment at station #b4 ,in place of the telephone receiver at station #b we connect a radio transmitter4 ,then whatever a person at station #a says goes by wire to #b and on out by radio4 ,in place of the telephone transmitter at station #b we connect a radio receiver4 ,whatever that receives by radio is detected and goes by wire to the listener at station #a4 ,in ,fig4 #acc ,i have shown the equipment of station #b4 ,there you have the connections for wire to radio and vice versa4 ,one of the most interesting developments of recent years is that of wired wireless or carrier-current telephony over wires4 ,suppose that instead of broadcasting from the antenna at station #b we arrange to have its radio transmitter supply current to a wire circuit4 ,we use this same pair of wires for receiving from the distant station4 ,we can do this if we treat the radio transmitter and receiver exactly like the telephone instruments of ,fig4 #acb and connect them to a square of resistances4 ,one of these resistances is1 of course1 the line between the stations4 ,i have shown the general arrangement in ,fig4 #acd4 ,you see what the square of resistances1 or bridge really does for us4 ,it lets us use a single pair of wires for messages whether they are coming or going4 ,it does that because it lets us connect a transmitter and also a receiver to a single pair of wires in such a way that the transmitter can't affect the receiver4 ,whatever the transmitter sends out goes along the wires to the distant receiver but doesn't affect the receiver at the sending station4 ,this bridge permits this whether the transmitter and receiver are radio instruments or are the ordinary telephone instruments4 ,illustration3 ,fig #acd ,by its aid we may send a modulated high-frequency current over a pair of wires and receive from the same pair of wires the high-frequency current which is generated and modulated at the distant end of the line4 ,it lets us send and receive over the same pair of wires the same sort of a modulated current as we would supply to an antenna in radio-telephone transmitting4 ,it is the same sort of a current but it need not be anywhere near as large because we aren't broadcasting2 we are sending directly to the station of the other party to our conversation4 ,if we duplicate the apparatus we can use the same pair of wires for another telephone conversation without interfering with the first4 ,of course1 we have to use a different frequency of alternating current for each of the two conversations4 ,we can send these two different modulated high-frequency currents over the same pair of wires and separate them by tuning at the distant end just as well as we do in radio4 ,i won't sketch out for you the tuned circuits by which this separation is made4 ,it's enough to give you the idea4 ,in that way1 a single pair of wires can be used for transmitting1 simultaneously and without any interference1 several different telephone conversations4 ,it takes very much less power than would radio transmission and the conversations are secret4 ,the ordinary telephone conversation can go on at the same time without any interference with those which are being carried by the modulations in high-frequency currents4 ,a total of five conversations over the same pair of wires is the present practice4 ,this method is used between many of the large cities of the ,u4 ,s4 because it lets one pair of wires do the work of five4 ,that means a saving1 for copper wire costs money4 ,of course1 all the special apparatus also costs money4 ,you can see1 therefore1 that this method wouldn't be economical between cities very close together because all that is saved by not having to buy so much wire is spent in building special apparatus and in taking care of it afterwards4 ,for long lines1 however1 by not having to buy five times as much wire1 the ,bell ,company saves more than it costs to build and maintain the extra special apparatus4 ,i implied a moment ago why this system is called a carrier-current system2 it is because the high-frequency currents carry in their modulations the speech significance4 ,sometimes it is called a system of multiplex telephony because it permits more than one message at a time4 ,this same general principle is also applied to the making of a multiplex system of telegraphy4 ,in the multiplex telephone system we pictured transmitting and receiving sets very much like radio-telephone sets4 ,if instead of transmitting speech each transmitter was operated as a ,c-,w transmitter then it would transmit telegraph messages4 ,in the same frequency range there can be more telegraph systems operated simultaneously without interfering with each other1 for you remember how many cycles each radio-telephone message requires4 ,for that reason the multiplex telegraph system which operates by carrier-currents permits as many as ten different telegraph messages simultaneously4 ,you remember that ,i told you how capacity effects rob the distant end of a pair of wires of the alternating current which is being sent to them4 ,that is always true but the effect is not very great unless the frequency of the alternating current is high4 ,it's enough1 however1 so that every few hundred miles it is necessary to connect into the circuit an audion amplifier4 ,this is true of carrier currents especially1 but also true of the voice-frequency currents of ordinary telephony4 ,the latter1 however1 are not weakened1 that is1 attenuated1 as much and consequently do not need to be amplified as much to give good intelligibility at the distant receiver4 ,illustration3 ,fig #ace ,in a telephone circuit over such a long distance as from ,new ,york ,city to ,san ,francisco it is usual to insert amplifiers at about a dozen points along the route4 ,of course1 these amplifiers must work for transmission in either direction1 amplifying speech on its way to ,san ,francisco or in the opposite direction4 ,at each of the amplifying stations1 or repeater stations1 as they are usually called1 two vacuum tube amplifiers are used1 one for each direction4 ,to connect these with the line so that each may work in the right direction there are used two of the bridges or resistance squares4 ,you can see from the sketch of ,fig4 #ace how an alternating current from the east will be amplified and sent on to the west1 or vice versa4 ,illustration3 ,fig #acf ,there are a large number of such repeater stations in the ,united ,states along the important telephone routes4 ,in ,fig4 #acf ,i am showing you the location of those along the route of the famous transcontinental telephone-circuit4 ,this shows also a radio-telephone connection between the coast of ,california and ,catalina ,island4 ,conversations have been held between this island and a ship in the ,atlantic ,ocean1 as shown in the sketch4 ,the conversation was made possible by the use of the vacuum tube and the bridge circuit4 ,part of the way it was by wire and part by radio4 ,wire and radio tie nicely together because both operate on the same general principles and use much of the same apparatus4 ,blank ,page ,,index ,a-battery for tubes1 #db ,accumulator1 #bi ,acid1 action of hydrogen in1 #g ,air1 constitution of1 #aj ,ammeter1 alternating current1 #bjf2 calibration of1 #ec2 construction of1 #bje ,ampere1 #di1 #ed ,amplification1 #ahb2 one stage of1 #ahe ,amplitude of vibration1 #aee ,antenna current variation1 #ada ,arlington tests1 #bcc ,artificial telephone line1 #beb ,atom1 conception of1 #f2 nucleus of1 #aj2 neutral1 #cd ,atomic number1 #ac ,atoms1 difference between1 #ab2 kinds of1 #f1 #aj2 motion of1 #ce ,attenuation of current in wires1 #bei ,audibility meter1 #bah ,audio-frequency amplifier1 #ahe2 limitations of1 #ahe ,audion1 #ce1 #dj1 #db ,audion1 amplifier1 #ahb2 detector1 theory of1 #abf2 modulator1 #bcb2 oscillator1 theory of1 #hi2 frequency control of1 #ii ,b-battery for tubes1 #dc2 effect upon characteristic1 #abh ,banked wound 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