tion as the tube starts to
oscillate and a listener hears a little click.

The frequency of the alternating current which the tube produces depends
upon the tuned circuit formed by _L_ and _C_. Suppose that
this frequency is not the same as that to which the receiving antenna is
tuned. What will happen?

There will be impressed on the grid of the tube two alternating e. m.
f.'s, one due to the tube's own oscillations and the other incoming from
the distant transmitting station. The two e. m. f. 's are both active at
once so that at each instant the e. m. f. of the grid is really the sum
of these two e. m. f.'s. Suppose at some instant both e. m.
f.'s are acting to make the grid positive. A little later one of them
will be trying to make the grid negative while the other is still trying
to make it positive. And later still when the first e. m. f. is ready
again to make the grid positive the second will be trying to make it
negative.

It's like two men walking along together but with different lengths of
step. 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 left. A little later, but just for an instant,
they are in step again. And so it goes. They are in step for a moment
and then completely out of step. Suppose one of them makes ten steps in
the time that the other makes nine. In that time they will be once in
step and once completely out of step. If one makes ten steps while the
other does eight this will happen twice.

The same thing happens in the audion detector circuit when two e. m.
f.'s which differ slightly in frequency are simultaneously impressed on
the grid. If one e. m. f. passes through ten complete cycles while the
other is making eight cycles, then during that time they will twice be
exactly in step, that is, "in phase" as we say. Twice in that time they
will be exactly out of step, that is, exactly "opposite in phase." Twice
in that time the two e. m. f.'s will aid each other in their effects on
the grid and twice they will exactly oppose. Unless they are equal in
amplitude there will still be a net e. m. f. even when they are exactly
opposed. 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 time.

The listener will then hear a note of a frequency equal to the
difference between the frequen