That is not the way in fact, the device oh Hans Coler does not use bi-filiar coils (Aryton-Perry), it uses two opposite coils to produce resonance, I could find even other great explication:

Excitation
1 The oscillators can be alternately pulse each other at least as two, or multiple group.
2 The oscillators are pulsed by a moving permanent magnet (rotating). (Motor-generator)
The oscillator may only induces short to generate a magnetic field and an output power.
Then the oscillators must contact can oscillate freely to generate an accelerated ZPE flux.
All power generators require excitation by radiation, which is mostly produced by radon doped iron, or by fast-moving permanent magnet.

When the oscillator is energized, increasing the amplitude and the magnets are moved slightly (up to 9mm) to resonance offset, and the best focus ZPE-wave apart. At maximum amplitude of the switch is opened.
If the generator does not start, or runs poorly, a small DC voltage should be switched serially in both circuits. The Spannungeinspeisestelle must be connected in parallel with a capacitor at 330 uF.
Left: A version with only a magnetic bar. The two halves of the winding are drawn only to illustrate the connections of the magnetic core is not of a continuous winding, but rather as a cut. The number of turns must not be too high.
Right: jump start. Pulse supply with a battery a transformer to the non-inductive coil. The diode is poled with the pole changing according to the flow of the connected solenoid, and directs the pulses equal.

More info here:
http://translate.google.com/translate?hl=en&sl=de&tl=en&u=http%3A%2F%2Fwww.freie-energy.de%2Fhtml%2Farchiv.htm&sandbox=1

Now you are confusing terms.  Canceling inductance and building a resonant circuit are completely different concepts.  An Ayrton-Perry winding is not bifilar.  Bifilar windings suffer significant parasitic capacitance.  Ayrton-Perry resistor windings have extremely low parasitic capacitance and very low parasitic inductance.

If you enjoy playing with a Coler machine then have fun.  Coler was unable to demonstrate his claims.  No one has successfully replicated Coler's claims.  You are chasing a myth.

I guess is possible to build a resonant circuit using in some parts a inductance cancelled, and Aryton-Perry is a type of bi-filiar winding, the thing is the device Hans Coler use a work system wich is very difficult to understand.

The apparatus was tested in 1926 by Professor M. Klose from the Technische Hochschule Berlin-Charlottenburg and Professor WO Schumann of the Technical University of Munich, who confirmed that it was working properly, but were not able to explain how the energy was produced.

Franz Haid of Siemens-Schukert could replicate it, the device was seen by Dr. Kurt Mie of Berlin Technische Hochschule and Herr Fehr (Haber’s assistant at the K.W.I.) who reported that the device apparently worked, and they could detect no fraud.

A resonant circuit alternately stores energy in a magnetic and electrostatic potentials. 
Ayrton-Perry is not a type of bifilar winding.  Bifilar windings consist of two adjacent conductors wound directly next to each other in order to establish maximum mutual inductance.  The close parallel arrangement creates substantial capacitance.  Ayrton-Perry windings consist of two oppositely rotating helixes.  The mutual inductance of an Ayrton-Perry winding is lower than for a bifilar winding on the same form.  At the same time, the mutual capacitance is orders of magnitude lower than for a bifilar winding. 

Bifilar windings are particularly useful in 1:1 transformer applications where maximizing the mutual versus self-inductance is more important than other considerations such as: mutual capacitance or breakdown voltage.  They are used extensively in common mode chokes and low voltage power transformers.

Ayrton-Perry windings are particularly useful for realizing low parasitic power resistors.

The alleged Coler replications of 85 years ago are themselves nowhere to be found.  Coler failed to reproduce working for the British after WWII.  Coler had claimed 5kW.  He couldn't demonstrate 1mW.

Hi policijarj2,

I have modified and embedded the two drawings you uploaded on the two bifilar coil windings.

So to answer your dilemma, there are two possibilities for bifilar coils to connect them in series: either the two wires (run close to each other) aid each other magnetically or they oppose each other fields.

In my edited picture you can see that in the upper bifi coil the end of coil A is connected to the end of coil B and the inputs are the start of coil A and B.

In the bottom bifi coil (Tesla drawing) the end of coil A is connected to the start of coil B and the inputs are the start of coil A and the end of coil B.

If you happen to have an L meter, you can simply measure the difference between the two coil connections, no need to wind two different bifi coils, it is enough to wind only one bifi coil with two wires and play with the wire end and start connections as shown.

Gyula

ok I got it, and what function has this kind of a Coupling coil?:

I wanted to point out that the replication seen in these photos did not work and was made by the two austrian guys of the hcrs lab:
www.hcrs.at/COLER.HTM