The following is from Secrets of the Aether:

Resonance

Distributed frequency is equal to resonance.  Viewing resonance in just one dimension of frequency is like viewing area in just one dimension of length.  The true meaning of resonance is lost when we change its dimensions.  The unit of resonance indicates there are two distinct dimensions of frequency involved. 

\[rson = fre{q^2} \tag{6.39}\]

Modern physics does not measure capacitance and inductance as square roots, yet the resonance equation usually expresses as:

\[F = \frac{1}{{2\pi \sqrt {LC} }} \tag{6.40}\]

where $F$ is the “resonant frequency,” $L$ is the inductance and $C$ is the capacitance. (“Resonant frequency” is redundant and incorrect.  It is like saying “surface length.”)  Equation (6.40) loses much of its meaning by making it appear the inductance and capacitance measurements are square roots and expressing the resonance in terms of frequency.  It is as though modern physics has not yet discovered the unit of resonance.

To make the math of resonance compatible with the rest of physics, the correct expression would keep the natural measurements of inductance and capacitance and notate the result as frequency squared.  In the Aether Physics Model, equation (6.41) arises as a different equation (6.40) from the Standard Model resonance equation.

\[rson = \frac{1}{{4\pi  \cdot indc \cdot capc}} \tag{6.41}\]

Equation (6.41) differs from the Standard Model resonance equation by a factor of $\sqrt \pi  $ and yet it produces true resonance in physical experiments.  This is not to say the Standard Model resonance equation is wrong.  It is merely incomplete.  There are actually three resonance equations, which are related through the Pythagorean Theorem.

We express the three resonance equations in terms of a common denominator of ${4{\pi ^2}}$ and in quantum measurements units:

\[rson1 = \frac{1}{{4{\pi ^2} \cdot indc \cdot capc}} \tag{6.42}\]

\[rson2 = \frac{{\pi  - 1}}{{4{\pi ^2} \cdot indc \cdot capc}} \tag{6.43}\]

\[rson3 = \frac{\pi }{{4{\pi ^2} \cdot indc \cdot capc}} \tag{6.44}\]

Equations (6.42) to (6.44) are related such that:

\[rson1 + rson2 = rson3 \tag{6.45}\]

The rson1 equation is identical to the Standard Model equation for resonance (6.40), and is associated with the highest potential.  The rson3 equation is the true resonance of an inductive-capacitive circuit and is identical to equation (6.41).  Both rson2 and rson3 equations resonate with potential near zero. 

The resonance unit indicates that resonance must measure as a distributed quantity in order for us to arrive at the correct value.  The design of present measurement equipment measures resonance in only one dimension of frequency. 

Because familiarity with the time domain exists at the macro level of existence, modern physics also measures the quantum realm in the time domain.  The reciprocal of time is frequency, not resonance.  It is a significant error that modern physics does not recognize resonance as a distributed unit. 

The quantum realm exists in a five-dimensional space-resonance as opposed to a four-dimensional space-time.  If physicists wish to understand quantum existence properly, then we must design measurement equipment to measure directly in the resonance domain.  Presently, Fourier analysis attempts to account for this shortcoming by mathematically converting time domain measurements into frequency domain data. 

I made the following post to the Pupman Tesla Coil mailing list on March 8, 2018:

If you are looking for a truly fascinating coil design with ground breaking potential, try building a magnifier with three tertiary coils on a common grounded frame. From my decades of studying Tesla literature, this is how Tesla built the flying triangle, which has since been perfected by US black projects. Back in the 1990s, there was more Tesla information on the Internet and BBS forums, which has since disappeared. One such report was of Tesla having built a model flying triangle configuration in his lab.
 
There is one primary and secondary coil, which drives three tertiary coils. All are grounded to a single aluminum frame, which is not in contact with Earth ground. The tertiary coils are each 1/3 out of phase with each other, and have variable inductance or variable capacitance to finely adjust the resonance.
 
The three tertiary coils develop a rotating magnetic field around the entire coil setup, which creates what I call a space bubble. The space in this macro rotating magnetic field becomes gravitationally separated from the space around it. By changing the characteristics of the of the rotating magnetic field space bubble, you can build a free moving vehicle that can navigate through space with reduced gravitational influence from the Earth. The orientation of the tertiary coils with respect to the Earth ground plane is what keeps the system from tumbling. With the tertiary coils perpendicular to the Earth ground plane, the rotating magnetic field orientation will also have an axis perpendicular to the Earth ground plane.
 
I believe Tesla's first model was an open frame. The rotating magnetic field space bubble will exist whether the frame is open, or whether it is completely enclosed around the Tesla coil system. However, a closed frame system should be more stable, as the conductive frame will give the rotating magnetic field space bubble a more reliable structure.
 
This is something I have been planning on for years, but have not yet put together. The key component of this system will be the design of the tertiary coils to be in 1/3 phase with each other and also to have a controllable variable inductance or controllable variable capacitance with just the right range of adjustment. 
 
I followed up with the following comment:
 
Thanks, Jim, for the link to Antonio's work. This just clarified for me how the three tertiary coils should be tuned. A tertiary coil would be way out of tune with the resonating primary and secondary power supply if it was tuned to 1/3 wavelength. Instead, there should be three, quarter-wave steps and a missing step, such that the tertiary coils would fire X-X-X-O, or 1/4, 1/2, 3/4, 0. This makes sense since a magnetic field, whether rotating or not, is asymmetrical. 
And it is more than just the magnetic field that is at play, here. Tertiary coils are acting strongly on the electrostatic field, in addition to the magnetic field. They are pushing electrons and ions. When three tertiary coils are mounted to a common ground, and tuned to produce maximum potential in succession, they will push the ions circularly, and perpendicular to the axis of the frame. This is what creates a rotating magnetic field plasma. The plasma will likely be double layered, with negative ions moving in one direction, and positive ions moving in the opposite direction.
The resulting plasma is the space bubble that surrounds the frame and coils. Naturally, the aim for tuning is to minimize streamer production and keep as much of the energy as possible within the system.

Frequency 

Angular frequency is a cycle of repetition and refers to the angles covered by a frequency.   Thus angular frequency is equal to:

APM MO1

A bicycle wheel turning at the rate of five cycles per second will scan an angle of 10π radians per second.  Angular frequency is in units of radians per second.  

When a cycle completes, it does so in a given period of time.  The period of time to complete a cycle is the reciprocal of the frequency:

APM MO2

A bicycle wheel turning at five cycles per second will have a period of 1/5 second.  Or in other words, the time it takes to turn the wheel once at five cycles per second will be 1/5 second.

Not all cycles are stationary and go in circles.  Quite often a cycle is associated with a velocity.  As a bicycle wheel turns and completes one cycle, the rider of the bike will travel a distance.  This distance is called the "wavelength" when applied to photons.  The distance the bicycle rider will travel will depend on its velocity per frequency:

APM MO3

So if the rider travels five feet per second, and the wheel turns at five cycles per second, then the rider has traveled one foot (the bicycle would be very small!).  

doublecoilnew01

bipolarcone01

The above pictures are of a double coned coil I acquired on eBay. The seller purchased it from the estate of a deceased FBI agent.  I was informed by one of the bidders, who owns a similar coil without the wires that it was designed by Nikola Tesla, himself. The wooden frame he owns was given to his father by Nikola Tesla as payment (Tesla had no money at the time). 

Each cone is 6" in diameter and 6" in height.  Each cone has approx. 127ft of wire.  The end to end inductance of the secondary is 2.36mH.  The quarter wave length frequency calculates to 1.937MHz for a straight solenoid but this coil resonates at about 1.12MHz as determined by a frequency counter and oscilloscope. 

The two cones are connected in the middle such that the entire length is one wire.  There is no tapping point between the two coils.  I had to replace the copper primary due to age and wear but I am keeping the old copper tubing as verification for the coil's age.  This coil was likely built in the early 1900s and is identical in layout to Tesla's patent schematics from the late 1890s. 

Rumor has it that this coil exhibits antigravity properties.  I have not seen antigravity effects when applying a standard spark gap discharge to the primary.

David Thomson's Coil Formula

As is explained in the Aether Physics Model, Coulomb's constant is equal to:

\[{k_C} = \frac{{c \cdot Cd \cdot {\mu _0}}}{{{\varepsilon _0}}} \tag{1.1}\]

From this, inductance can be defined as:

induct2(1.2)

In equation (1.2) 1 meter equals 1 henry.  .003 meter equals 3 mH, and so on.  The relationship of length to inductance is clearly shown in reference to Coulomb's constant.  Wheeler's formula (for the inductance of an air core solenoid coil) outputs inductance in terms of thousand inches. 

induct4(1.3)

where N is the number of turns, R is the radius in inches, and H is the length of windings in inches.

Equation (1.3) outputs in length, just what the Coulomb's constant formula requires.  So if the units of Wheeler's formula are converted to meter and the two formulas are combined then:

induct5(1.4)

and this can be simplified to:

induct6(1.5)

The values and units generated in equation (1.5) are accurate to the same degree as Wheeler's formula for inductance since it incorporates Wheeler's formula unchanged.  The exact value of Cd is equal to:

induct7(1.6)

where the values are Coulomb's constant, light speed, permeability, and permittivity.

A practical simplification of the formula (1.5) is:

induct8(1.7)

where the value N is a number, and R and H are in inches, and the result is in henry.

If you use MathCAD or another program, which automatically converts inches to meters, then use equation (1.8):

induct9(1.8)

If you're looking for an inductance formula where the input is in meters instead of inches, you can use this formula:

induct10(1.9)

Formula (1.9) can be used for either solenoid or flat spiral coils.  For flat spiral coils use the average radius for R and the width of the coil windings for H.  Both R and H are in meters.  N is the number of turns.