Controlling a current with another - home-made alternatives to the transistor?
There is the magnetic amplifier.  I think that it looks pretty easy to build, and works rather well.

Here's a good book about mag amps: Magnetic Amplifiers, Paul Mali, 1960, 101 pages, found in Pete Millet's truly awesome book collection. From this book:



"Basically, the principle of the simple saturable reactor can be stated in two parts: As magnetic core saturates, current to load increases; as magnetic core desaturates, current to load decreases." (p.28)

Another picture illustrates this:



When you vary the DC current (control circuit), you drive the core into or out of saturation, controlling the slope if the output-to-input transfer characteristic (AC load circuit).

Note that because the underlying principle is an inductor, you can control AC load currents only. For DC applications, it is possible to control an AC current and rectify the output, using a diode rectifier and a smoothing capacitor.

Besides the rather exotic applications in early military technology, avionics or high voltage transmission, there are at least two examples where saturable inductors were used by the millions in consumer devices:


Post-regulation in switch-mode power supplies - actually an applicaton where an AC current is controlled to create, after being rectified, a stabilized DC voltage.
Circuits for correcting the otherwise distorted geometry ("cushion shape") of a picture on a CRT display. Here, the AC current to the picture tube's deflection coils is modified by a controlled saturable inductor.