On the other hand suppose the gangs came from different parts of the town and disliked each other. He wouldn't have nearly the trouble. Each gang would be yelling at the other as they went along: "You'd better beat it. He knows all right, all right, who broke that bush down by the gate. Just wait till he catches you." They'd get out a little easier, each in the hope the other crowd would catch it from the owner. There's a case where their mutual relations, their mutual inductance, makes the job easier. That's true of coils with inductance. Suppose you wind two inductance coils and connect them in series. If they are at right angles to each other as in Fig. 46a they have no effect on each other. There is no mutual inductance. But if they are parallel and wound the same way like the coils of Fig. 46b they will act like a single coil of greater inductance. If the coils are parallel but wound in opposite directions as in Fig. 46c they will have less inductance because of their mutual inductance. You can check these statements for yourself if you'll refer back to Letter 10 and see what happens in the same way as I told you in discussing Fig. 28. [Illustration: Fig 46a] [Illustration: Fig 46b] If the coils are neither parallel nor at right angles there will be some mutual inductance but not as much as if they were parallel. By turning the coils we can get all the variations in mutual relations from the case of Fig. 46b to that of Fig. 46c. That's what we arrange to do in a variable inductance of the variometer type. [Illustration: Fig 46c] There is another way of varying the mutual inductance. We can make one coil slide inside another. If it is way inside, the total inductance which the two coils offer is either larger than the sum of what they can offer separately or less, depending upon whether the windings are in the same direction or opposite. As we pull the coil out the mutual effect becomes less and finally when it is well outside the mutual inductance is very small. Now we have several methods of varying capacity and inductance and therefore we are ready to vary the frequency of our audion oscillator; that is, "tune" it, as we say. In my next letter I shall show you why we tune. Now for the rule which I promised. The frequency to which a circuit is tuned depends upon the product of the number of mil-henries in the coil and the number of microfarads in the condenser. Change the coil and the condenser as much as you want but keep this product the same and the frequency will be the same. [Footnote 5: More accurately the number is 6,286,000,000,000.] LETTER 13 TUNING DEAR RADIO ENTHUSIAST: