The diagram drawn by crazycut06 shows best
what the circuit does. (bottom diagram)
In Tesla's day there was no easy way to
produce oscillations so some rather unusual
mechanical devices were devised. It is a
capacitive discharge circuit as was
previously
identified by Magluvin and it does function as
a push-push exciter. The speed of rotation of
the switching system would have been very
critical, particularly if a True AC Output needed
to be attained. It would have been very difficult
indeed to generate a signal with any frequency
stability or waveform purity. The circuit is interesting
as an example of the innovative genius of Tesla but
would have very little application today.
To assist the capacitors better storing the
inductive kick of the two O inductors (O and
O'), a diode could be installed at the bottom end
of the inductors just before the connection
points to the brushes. The diodes would permit
the capacitors to charge to the higher potential
of the flyback pulses and also prevent the stored
charge from leaking off back through the inductors
to the main supply. This technique is known as
Resonant Charging.
The brushes could be replaced with either MOSFETs
or Thyristors (SCRs) which are alternately triggered
ON with some dead time between triggers. The output
taken from secondary winding L would most likely be
a series of high voltage discharges very much like from
an ignition coil but at a much higher frequency. At some
critical switching rate the output may even be AC if
synchronized with the resonance of the O inductors and
the capacitors.
Nowadays we are able to perform the similar function
to Tesla's circuit with semiconductor power oscillators
or an oscillator followed by a power amplifier stage.
If Tesla were alive today with all of the miraculous
semiconductor devices we have at our disposal he'd
show us a thing or two!