These are photos of a saturable reactor used to control the power to 
a neon plant bombarder.  The large center winding is the DC control 
winding.  The two outer windings are the current windings, designed 
in this case to handle 60 amps.  They are wound magnetically additive
so that their fields travel around the outside of the core and do not
penetrate the control leg.  DC applied to the control winding adds flux to
both control leg cores, enough to saturate them.  As the core saturates, the 
inductance of the coils drop and pass more current.  When the core is 
fully saturated, the current is limited only by the DC resistance of the 
windings and the external series load.

The small white winding visible in Photo 3 is a test winding I put on the core
to measure the turns of each winding.  A small amount of AC from a variac 
is applied to each winding and the voltage induced in the test winding is 
measured.  Since I know the nubmer of turns of the test winding and I know the
applied voltage, it is a simple matter of computing the ratio to determine
the number of windings on each leg.