Let stand for velocity, & for wave length, f for frequency, and, as previously given, R resistance, L inductance, C capacity, X reactance, X, inductive reactance, Xe condensive reactance. Then:

which of course is maximum when the second expression under

the radical is equal to zero, or when 2′′fL =

I

27fC. This condi

tion of the circuit is called resonance. Two circuits are said to be in resonance when they have the same wave length.

The frequency at which this maximum current occurs is called the critical frequency; it can be found from the last expression to be

which can be further simplified to λ=1884: VLC, where L is microhenries and C is microfarads. This is important because "tuning" is merely changing the wave length, and this shows that it is accomplished by varying either capacity or inductance, or both.

Varying the wave length by changing the inductance is one of the methods that is used in sending signals. A continuous wave is sent out. When the key is pressed it changes the inductance of the circuit, therefore the wave length. The receiving station

is tuned to receive only that wave length which is radiated when the key is pressed.

With this in mind the elementary idea of the "arc sets," such as are used at high-power stations can be easily understood. Fig. 11 gives the elementary layout.

Even before radio existed it was known that an arc produced by D. C. would set up electric oscillations, if in circuit with an inductance and a condenser; and that these oscillations were

produced continuously if the circuit was properly adjusted. It can be seen from the figure that the arc has an inductance in circuit with it. The aerial and the ground or ballast with air between form the condenser, which is shown dotted in the figure. The circuit is completed through the two grounds.

The large inductance serves two purposes. It prevents rush of current back over the line, and it blows out the arc. It has nothing to do with the LC of the set. It is not a part of the radiating circuit. The current that passes through it is unidirectional. The radiating circuit is everything to the right of the dotted line AB. It is a complete circuit in itself, as stated above.

The key in small sets is so connected that when it is closed it short circuits part of the small inductance of the radiating circuit, thus changing the inductance. In large sets it is inductively coupled, as shown in Fig. 11. Due to transformer action current is set up in the key circuit when the key is closed. This current creates its own field, which in turn reacts on the already existing field of the coil in the radiating circuit, changing the inductance of this circuit, due to the change of magnetic flux. Consequently, the wave length is changed. This interaction of two coils on each other is called "mutual inductance" to distinguish from selfinductance already described.

The key can be operated locally, or if connected through proper relay, messages can be sent from a distance. For instance, an operator in Washington can send signals out over the station at Annapolis.

A second method of making signals with these electromagnetic waves is to have a key which completes the circuit. Then waves are only sent out when the key is pressed. The system is used with spark sets.

"Spark sets" require A. C. in the primary circuit. The inductor type of alternator is used to supply the current. The frequency is 500 cycles per second. This frequency is only in the primary and secondary circuits. The radiating circuit depends on its own Lc for its frequency, just as in the previous set. Fig. 12 shows the elementary layout.

The frequency of the primary and secondary circuits is 500, so that when the key is pressed the condenser is charged 1000 times per second; once for each alternation. But this frequency is much lower than the oscillations set up by the condenser, after being charged. These oscillations are set up in the spark or oscillating circuit. The frequency of this circuit depends upon its inductance and capacity. Only once during each alternation is the condenser charged to high enough potential to break down the spark gap, but having broken it down it sets up high frequency oscillations in that circuit. The LC of the spark circuit is the same as the LC of the radiating circuit; that is, the two circuits are of the same frequency or the same tune, or in resonance. So the spark circuit transfers energy to the radiating circuit. Having done that, oscillations are no longer required in the spark circuit. quenched spark gap is used to prevent further oscillations. The radiating circuit is left free to oscillate at its natural frequency. It radiates waves depending for their length on the LC of the radiating circuit. There is a loss of energy, so the waves are not sustained. They gradually diminish in amplitude. A group of waves ranging from maximum amplitude to minimum is called a wave train. There is one wave train radiated for each alternation of the primary circuit; therefore, 1000 wave trains per second. The traffic regulations do not permit of wave trains of less than 15 waves per train, which corresponds to a log decrement of two-tenths.

The

If the propagation of waves is understood, the methods of receiving them and distinguishing dots and dashes naturally follow. All tones depend upon the frequency of vibration or the frequency of the wave. Low tones are of low frequency, and higher frequencies produce a higher tone or pitch. When the frequency is above 20,000 the tones are inaudible, but the vibrations are there just the same. Radio receiving consists of changing the high frequency of the incoming waves to a frequency that can be heard. Undamped or continuous waves can be made audible by setting up local vibrations in the receiving circuit at slightly different frequency; resulting in the production of beats at audio frequency. The frequency of the beats is the difference between that of the incoming waves and the local waves. This is the heterodyne principle.

Damped waves are readily heard because each wave train as it comes in gives one impulse. The current is rectified and one click of the telephone diaphragm results. The frequency of the wave trains is one within the range of audibility.

For amplifying, rectifying, and production of beats by setting up local oscillations, the vacuum tube, which is also called by various names, such as audion, ultra-audion, audodyne, etc., is used. There is no short cut to familiarity with the vacuum tube. There are several books on the subject for those who are interested.

The above notes are extracts from talks and lectures given to reserve officers and to midshipmen who were having their first fling at A. C. during the last year. I hope they may be of some use to officers in general, and especially to those preparing for examination.