Peter, whatever happened with Eric P. Dollard?

[Nhopa]

What is the big deal? Eric Dollard has done this demonstration almost 30 yars-ago, and the first time before anyone else.

[Kokomoj0]

Could this be what tesla had in mind?


the earth as a spherical capacitor inside the air as an outer spherical capacitor with the coils connecting the whole thing as a gigantic resonant tank?

and does anyone have an opinion on what naudin did here?

You may notice that the Magnetic energy is in Space CONJUCTION with the Dielectric energy

appears he replicated Erics setup in part.

see the rest here

Has anyone talked with him about this and how he made those conclusions?

I know Eric got higher voltage, but according to naudin as shown above greater power out as well?

Find that a bit difficult to accept.

[garrettm4]

Versor Operators Decoded, With Respect to DC & AC Circuits Pt2

Continuing with Part 2

Versor Operators; Rotation about an Axis:

With the above cliff notes on exponentiation and roots of unity we can now perform a more advanced and elucidated study of a Dollard type versor operator, but first, we should cover a few basic concepts of what a versor is and historically where it came from.

For this purpose, one needs go no further than a quick study of William Rowan Hamilton, the discoverer of quaternions. Hamilton during the year 1843, discovered a new mathematical entity which he called a quaternion and from which formed a new branch of mathematical thought that extended the complex numbers, with new imaginary axes “j” & “k” (“i” is the familiar imaginary axis from high school). This expanded the usual Argand diagram with two new axes that have a 90° separation to the Re and Im axes while also having a 90° separation between themselves, j & k. New terms were spawned from the mind of Hamilton to describe the unique concepts and entities contained in this seemingly odd branch of mathematics. Notably the most important, for our discussion, are “scalar”, “tensor” “vector” & “versor”. Without going too deep into this topic, we will only cover the versor and a few of its associated relations.

Hamilton’s Versor

In Hamilton’s branch of math, each Quaternion has a Tensor, which is a measure of its magnitude; this being similar to the length of a Vector is a measure of a Vectors' magnitude. The Versor is a Quaternion having a Tensor of 1, Tensors by Hamilton’s definition are “signless numbers” or more simply a positive number. The term Versor was derived by Hamilton from the Latin vertere, "to turn".

In general a Versor can be associated with a plane, an axis and an angle. When a versor and a vector which lies in the plane of the versor are multiplied, the result is a new vector of the same length but turned by the angle of the versor. When the arc of a versor has the magnitude of a right angle (π/2), it is then called a Right Versor. Right Versors have a zero Scalar part, and thus, are Vectors of length one, or Unit Vectors.

Outside the context of quaternion theory, in normal algebra and geometry, the term Versor is often used for a Right Versor. In this case, a Versor is defined as a Unit Vector indicating the orientation of a directed axis in a Cartesian coordinate system.

Dollard type Versors

It can be seen that the Dollard DC & AC versors share many commonalties with Hamilton’s Quaternion Versor, but despite this, they generally have little to no relation to one another. The Dollard versors, from what I understand, are used to indicate the orientation of (or rotate) a vector magnitude’s position in a Cartesian coordinate system, and possibly polar or spherical coordinate systems as well. These versors form what could be called a Unit Vector, where the vector magnitude is always equal to unity.

In the case of both the DC & AC versors, their associated Unit Vector always equals a magnitude of one, also, the possible “directions” of travel are associated with the number of axes present. This is where we get the accompanying roots of the Unit Vector. The number of possible directions become the exponent n of the unit vector and the corresponding roots derived, are from the number of potential positions, these derived roots represent the angle of rotation.

The DC Versor h, 180° Rotation (or Mirror Image Operator)

Thus, if there are only two possible directions on the real axis, as seen from the origin (+1 & -1), such as in the DC circuit (consumption and production of active power) we have:

With the real axis as the only number system used, we have only two directions of travel, thus the versor operator h has only two possible positions with corresponding values +1 & -1. Despite any arbitrary power of h (-1), there is a periodicity or repeating nature of the values for h, which can be seen as a cycling through or rotation of the positions that h can have. For simplicity, only h^1 (or h) & h^0 are needed to describe -1, 180° rotation (from +1) & +1, 0° rotation (from +1). The pattern of periodicity for h was discussed earlier under the topic “roots of unity”.

The AC Versor k, 90° Rotation (or Quadrant Operator)

Note: When dealing with Mr Dollard's AC versor k, the usual Argand diagram would need to be turned 90° to the left so that the positive real axis is on top. Everything I have written in this post, related to versor k, is in direct reference to this subtle change of perspective! i.e. the horizontal or "x" axis is now the imaginary axis and the corresponding vertical or "y" axis is now the real axis.

Similarly, if there are four possible directions along the real & imaginary axes, as seen from the origin (+1, -1, +j & -j), such as in the AC circuit (production of active & reactive power and consumption of active & reactive power) we have:

With the real & imaginary axes, as the number systems used, we have four directions of travel, thus the versor operator k has four possible positions with corresponding values +1, -1, +j & -j. Despite any arbitrary power of k (+j), there is a periodicity or repeating nature of the values for k, which can be seen as a cycling through or rotation of the positions that k can have. For simplicity, only k^1, k^0, k^2 & k^3 are needed to describe +j, 90° rotation (from +1), +1, 0° rotation (from +1), -1, 180° rotation (from +1) and –j, 90° rotation (from +1). The pattern of periodicity for k was discussed earlier under the topic “roots of unity”.

Something of great interest to this concept, is the fact that if an arbitrary vector is multiplied by k^1, the rotation is always equal to one -90° (or +270°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^1, it would be rotated -90°, or now positioned at (j,-1). When a vector is multiplied by k^0, the rotation always equals 0°, or no rotation (even if it were 360°, there was no apparent change of position), where a vector of (j,1) is multiplied by k^0, it would still be positioned at (j,1). When a vector is multiplied by k^2, the rotation is always equal to one +180° (or -180°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^2, it would now be positioned at (-j,-1). When a vector is multiplied by k^3, the rotation is always equal to one -270° (or +90°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^3, it would now be positioned at (-j,1).

Note: The coordinates used for the above arbitrary vectors, is in the standard format where (x,y) denotes the exact position on the grid, and where the length or MAGNITUDE of the vector is determined as the distance from the origin (0,0) to that point.

The notion of whether the RESULTANT rotation, by k^n, is NEGATIVE (-) or POSITIVE (+), has strictly to do with the "NORMAL" direction of rotation of the arbitrary vector. In the special case of vectors E & I, the INDUCTIONS of the Magnetic & Dielectric fields, we find that they counter rotate, and thus form a pair of counter rotating vectors, having a double frequency PRODUCT (EI=P) called Power. E is said to rotate Clock-Wise (CW) and I is said to rotate Counter-Clock-Wise (CCW) with this distinction made, a rotation by versor k can now be found to have produced a forward (leading) or backward (lagging) effect on the vector's arbitrary position, with respect to its normal direction of rotation.

I hope this helps anyone who was a bit unsure as to what Mr. Dollard’s versors were all about, granted there is quite a lot of regurgitation of various other concepts I feel that they were necessary to cover before a good grasp of the versor (as a unit vector) concept could be had.

Continued in Part 3, The subtopic of "AC Power" is discussed in minor detail, which shows the relevant "cause & effect" brought about by a rotation by versor k.

Garrett M

[garrettm4]

Versor Operators Decoded, With Respect to DC & AC Circuits Pt1

Foreword:

I thought I would share what I understand about the DC & AC versor operators of Mr. Dollard and while I can’t speak for Mr. Dollard or say that I am 100% right, this post is intended to assist anyone who would like a “beginner’s guide” on the subject (sadly this is all I am capable of at the moment). I feel that Mr. Dollard takes for granted, his understanding of exponentiation and use of versors in relation to degrees of rotation, much like breathing or walking most people don’t even have to think to do these things. Thus this is written for your “common man”, who like myself (I’m a high school dropout), were never given a good education and lack the fundamentals of more advanced math principles. This is by no means a formal study, but instead, can be looked at as a primer on the subject, at least until a better treatment by Mr. Dollard is available.

If you already have a good grasp of the Dollard type versos then this whole post can be skipped over.

Roots & Powers; Exponentiation Cliff Notes:

To fully understand the machinery of a versor operator of the type used by Mr. Dollard, one must first understand the subject of “exponentiation” (also known less formally as roots and powers of a number) or at least have available a basic reference sheet of what each degree of power or root does.

So as not to be confused with the versor operators used latter on, we will use the letter b as our variable and n as our root or power. This exercise requires only basic high school algebra, and will be found to give good insight into the workings of a versor operator.


Here we have b, or some “arbitrary number”, to the nth power, n being another “arbitrary number”. Where b & n are assumed to be whole real numbers and where b is not equal to zero.

Depending upon what “arbitrary number” n represents, changes a whole host of things with how b is treated. Shown below are some simple common numbers that n could represent, and from understanding these seven different powers of b we can start to gain some insight into versors and also what to do when confronted by these in other mathematical situations.


Here we have a few arbitrary values of n, some of which may seem familiar and others very foreign.

Let’s start off with the case of b^1

Here it is understood algebraically that any number raised to the exponent 1 is simply the same number. (In the case of Mr. Dollard’s DC Versor, h=-1 and AC versor k=+j)

Next, we have the case of b^0

Here it is understood algebraically that any nonzero number raised to the exponent 0 will ALWAYS equal POSITIVE UNITY +1. As was shown above for b^1, and referenced with b^0, any number (aside from zero) be it negative or positive divided into itself will always be a positive one.

Moving on to b^(1/2) and b^(1/n)

Here it is understood algebraically that any number raised to the exponent (1/n) represents the root of that number, where n=2 is the “square root”, n=3 the “cube root”, n=4 the forth root etc. This relation b^(1/n) has use with both the DC & AC versor operators, h & k, which will be discussed further on.

Continuing to b^-1

Here it is understood algebraically that any number raised to the exponent -1 is simply the reciprocal of the number itself.

Taking this concept further b^-(1/2) and b^-(1/n)

Here it is understood algebraically that any number raised to the exponent –(1/n) is simply the reciprocal of the root of that number.

It can be seen that these less common “powers” of b can save quite a bit of space when writing an equation and are generally used in calculus for this very reason. Also it can be seen that when using “fractional” powers (1/n) instead of roots (numbers inside a radical), you gain a greater understanding of what is going on mathematically and are less likely to be confused when in unfamiliar circumstances, i.e. fractional powers are roots and negative powers are reciprocals. The cases of b^n where n>2 or b^-n where b<-2 and where b is not equal 0, are very simple cases, which I don’t think need even the slightest explanation, as they are the most commonly understood form of powers (at least for positive powers equal to or greater than 2 this is the case). This topic could be taken much further but I don’t feel there is anything to gain with respect to understanding of the versor operators used by Mr. Dollard in doing so. The most vaguely understood cases of n have been shown and given proper, albeit very simple, explanations with some minor references to the DC & AC versor operators h & k for use further on in this post.

The Roots of Unity; Negative & Imaginary Numbers Cliff Notes:

It turns out the subject “roots of unity” has a lot to do with a Dollard type versor operator and a whole host of other branches of science. With what we just covered on exponentiation we can now briefly cover this primer before finally getting to the versors.


In a nut shell, any number that equals 1 when raised to some power of n is a so called “root of unity”.

When we go to solve for b we get

Here things start to get interesting with regards to Mr. Dollard’s work and his versors.

For the purpose of this post, we will limit the values of n, in the above, to only 2 & 4, as these have the most relevance to the Dollard DC & AC versors.

In the case of n=2 we have

Here we are confronted with the “square root” of unity. From this problem, we get two possible solutions or roots, b=1 & b=-1.

As we all blink our eyes and breathe without giving a second thought, we also take for granted the concept of negative numbers. If we represent positive numbers extending to the right of zero, we can represent negative numbers extending to the left all of which is along a single axis where the angle of measure between both sides is always 180°, as shown below.



The above expression and diagram give some general insight into the DC versor h. The base value of h in the case of Mr. Dollard’s DC versor is always -1, h^1=h=-1. In this special case h^-1, h, h^1, … etc. (all odd non-fractional powers of h^n where n=1+x2) equal -1, or 180° rotation (from +1) and for h^-2, h^0, h^2, … etc. (all even non-fractional powers of h^n where n=0+x2) equal +1 or 0° rotation (from +1).

In the case of n=4 we have

Here we are confronted with the “fourth root” of unity. From this problem, we get four possible solutions or roots, b=+1, b=-1, b=+j=(sqrt-1) & b=-j=-(sqrt-1).

It turns out that a mathematician named Gauss extended the concept of the real axis by placing j or (sqrt-1) as halfway between +1 and -1, having an angle of 90° from the line -1 and +1. If the division of unity into plus and minus is 180°, a second division leads to an axis which intersects this line at an angle of 90°. We now have two axes, the horizontal representing positive and negative real numbers, and the vertical representing positive and negative imaginary numbers. These two axes form the complex coordinate system, any number inside this plane, is a number having a real and an imaginary part.



The above expression and diagram give some general insight into the AC versor k. The base value of k in the case of Mr. Dollards AC versor is always +j, k^1=k=+j, also the diagram above would need to be turned 90° to the left so that the positive real axis is on top. In this special case, k, k^1, k^5, … etc. (all odd non-fractional powers of k^n where n= 1+x4) equal +j, or 90°, rotation (from +1), for k^0, k^4, k^8 … etc. (all even non-fractional powers of k^n where n= 0+x4) equal +1 or 0° rotation (from +1), for k^2, k^6, k^10… etc. (all even non-fractional powers of k^n where n= 2+x4) equal -1 or 180° rotation (from +1), for k^3, k^7, k^11… etc. (all odd non-fractional powers of k^n where n= 3+x4) equal -j or 90° rotation (from +1). Note that negative values for exponents are not shown, but would follow the same pattern, if I’m not mistaken, as for the positive values as they are only reciprocals, i.e. 1/j=j & 1/-1=-1.

Continued in Part 2

[m786]

In Eric's notes, intro to tesla coils, he states that for plasma work you need an "image coil" between the secondary and ground to provide 180 degree phase shift. I would prefer not to build two tesla coils as he seems to suggest later on for plasma work, since I'm not positive of all the design parameters. Would a simple coil with 1/2 wavelength resonance work as an image coil? Or does "image coil" literally mean that the coil is a "mirror image" of the secondary and extra coil? I've been searching for a definition of an image coil and I'm not finding much.

Does anyone know the definition of the term "image coil"?

Thanks!

Hi,
He mentioned AFC - automatic frequency and phase control.Probably need to keep resonance all the time or need to check phase between 2 coils, even load changed. to do that he have 2 same secondary coils. He is measuring phase of 2 secondary coils and based on that is controlling a voltage controled oscillator - VCO.VCO is generating a main fequency and as well a synchronization pulses for pulse modulation of main frequency.Phase discriminator is checking a difference in phase and frequency of 2 signals.It is used in nearly all RF receivers.

On Page 13 of that book is :

"To confine the energy an image coil
(180 degree shift) must be connected to the earth terminal. Making this
arrangement in a horseshoe configuration produces intense dielectric
flux and displacement current that is quite usefull for plasma work."

The electrical length is 360 degrees at the fundamental of oscillation.
I think that image coil is to keep total electrical lenght in 360 degree. then need to control a phase of that 2 coils to get strongest effect.

[skaght]

&quot;image coil&quot;

In Eric's notes, intro to tesla coils, he states that for plasma work you need an "image coil" between the secondary and ground to provide 180 degree phase shift. I would prefer not to build two tesla coils as he seems to suggest later on for plasma work, since I'm not positive of all the design parameters. Would a simple coil with 1/2 wavelength resonance work as an image coil? Or does "image coil" literally mean that the coil is a "mirror image" of the secondary and extra coil? I've been searching for a definition of an image coil and I'm not finding much.

Does anyone know the definition of the term "image coil"?

Thanks!

[Nhopa]

Thank you dR-Green for the help with my questions. I guess no.:2, the "well as a ground" still needs to be resolved. It seems to me from the foregoing discussions, that the best answers to questions is experimenting. After all Tesla's Colorado Springs Notes are about experimenting. Tesla did'n have all the answers but deducted many from the various experiments. I also apologize for my mistake about the diameter to lenght ratios of the secondery coil. Most of the "extra" coils have a D to L ratio of larger than 1. For example from the Notes on p.110: 2' dia to 6' lg, p.160: 6' dia to 12' lg. However the cage type "extra" coil shown on a few pages in the Notes are indeed close to the 1:1 ratio.
I agree for first hand information one must be going to the source. In our case the real McCoys are the Colorado Spring Notes and Eric Dollard's publications on the subject.
@skaght: Things can be confusing and that is the reason why I have lots of questions. I would recommend obtaining a copy of the Notes as an onhand reference together with Eric's various publications on the subject.

[garrettm4]

Hallelujah!

Four Quadrant Energy Exchange in Magnetic & Dielectric Fields of Induction, Part One:

WOW!

That mega post by Mr. Dollard answered quite a few complex and downright perplexing issues that I was trying to resolve when doing the math on impulse discharges (of L or C or both one into the other)! Also the concept of the battery as having characteristics of both a capacitor and inductor rings true with me, I have been trying to resolve how to analyze the storage battery (in the electrical sense, or non-chemical sense) for quite some time and came to similar but not quite as refined results. I think one word would sum up my opinion of what was recently posted, Hallelujah! I feel as if that post filled in a fair bit of what I was unsure about in my post "Question On Plank, Q with Respect to an Impulse Discharge of L or C into r".

Furthermore, we now have new insight into the whole negative resistance / negative conductance situation, I personally HATE the term NEGATIVE RESISTANCE -r (generally this is actually a non-linear/non-ohmic resistance and has nothing to do with excess energy), negative ohms is acceptable by my standards though. With whats presented by Mr. Dollard we at least can now call negative ohms & siemens, Receptance H & Acceptance S, something that makes me very happy indeed. This should elucidate, if the concept is fully understood and used properly, interesting phenomena in an electrical circuit whereby there is an excess of energy (or the "load" acts as a "source").

Finally we see some use of a versor operator and its application and (inferred) theory of its use mathematically in electrical situations! I think there's a lot yet to be said or done with this mathematical tool. Hopefully we will get another post with its usage soon from Mr. Dollard.

In conclusion I feel everyone should read that post a few times over, it has some gold nuggets that are sure to give new insight and potential use in future "practical" real life situations.

Garrett M

[dR-Green]

I'm trying to understand the secondary coil design. It sounds like Nhopa is saying that Tesla's colorado springs notes describe a long thin secondary, yet Eric's notes in intro to tesla coils describe the secondary as a spiral or short fat coil. Anyone want to weigh in on which is correct? The picture on the front of Eric's intro to tesla coils looks like a long thin coil, so I'm totally confused on what is correct.

The Colorado Springs coil (the one in most pictures) secondary is 15 metres diameter and about 2m high. Or short and fat.

A flat spiral coil is another coil altogether. In context it means you can either build one or the other.

May I recommend going to the source of the information rather than interpreting interpretations

[edit] I suppose the simple answer to your original question if you don't want to have to make an extra coil is to make a flat spiral coil instead.

[skaght]

I'm trying to understand the secondary coil design. It sounds like Nhopa is saying that Tesla's colorado springs notes describe a long thin secondary, yet Eric's notes in intro to tesla coils describe the secondary as a spiral or short fat coil. Anyone want to weigh in on which is correct? The picture on the front of Eric's intro to tesla coils looks like a long thin coil, so I'm confused on what is correct.

[mikrovolt]

I thought it was an avalanche through a lump transmission line into a thyratron tube giving a longitudinal asymptotic pulse.

This seems aggressive yet very smooth compared to the erratic transverse kW sized sparks that I keep seeing on this thread.

What would be wrong with an Lwave of 80 volts 50mA on 160M ?

[dR-Green]

1. In my design the weight of primary coil is the same as the secondary coil. Should the primary coil be one turn copper strip or two? I can make the strip half wide and twice the length. Does it matters? Looking the surface areas the secondary coil has 18.8% more surface area than the primarycoil.
2. I have an unused dug well on the property with some water in it. Would it function as an acceptable ground if I would lower into the water a heavy cable with some metal weight on the end?
3. Will a tennis ball covered with aluminum foil work as a spherical metal capacitor?
4. The radio station for which I am designing the crystal receiver is transmitting @ 1,476 Kc/sec with 60KW power. I am located 110 miles from it, am I too far from this station?
5. Is it important which direction the "extra" coil is wound with respect to the secondary coil? Secondary coil is wound in the same direction as the primary coil.
6. In order to make the spiral coil a smaller diameter, would it make much difference if I wound 3 turns on top of each other in each groove instead of the two as Eric has done it for the Longitudinal Wave demonstration video?
Thank you in advance for any suggestion or recommendation.

This is my opinion

1. Two. Best to keep it in accordance with the patent and Eric's design to start with.

2. I don't know, but I'm inclined to think that won't be up to some people's standards. Although it may still work.

3. Yes a tennis ball will work, but probably not very well due to being small and low capacitance. You might be able to overcome this with the use of the metal plate near it.

4. You'll probably hear the radio, but in relation with question 2 you probably won't be lighting up a 100 watt bulb any time soon

5. Extra coil should be wound in the same direction. I don't think this is required with a flat spiral coil.

6. Read from page 120 of the CS Notes. I believe the purpose of the layered turns is to set up series capacitance in order to overcome the undesirable parallel capacitance that's a result of the spaced turns. Or something to that effect. You can try 3 but I don't think anyone knows the answer as to whether it will be better or worse, unless the posted equations can predict it or someone has actually done it and seen the differences for themselves.

[dR-Green]

So far I have not seen any reference in the Notes that the secondary coil should be n=1, that is diameter to lenght ratio of 1. All the secondary coils described in the Notes are much longer than their diameter.

I think you will find that it's the diameter of the secondary that's much greater than its height/length (15 metres diameter x about 2m high) The extra coil is equal diameter to height ratio.

Also I read somewhere in the CS Notes, a greater surface area of secondary will result in a greater pressure than an equal number of turns with thinner wire. I think, I didn't make a note of what page it was so I can't easily find it again. That reference MIGHT be somewhere around page 60.

@skaght: In my opinion you are probably complicating it through trying to simplify it. Beware the illusion of something becoming simpler through removing parts - reality is one continuous whole, not a collection of parts. That is, Eric wants people to do it "properly" and is answering things on that basis, so you won't get a simple answer. If you just build it then you won't need to ask the question

[Nhopa]

Practical questions con't

1. In my design the weight of primary coil is the same as the secondary coil. Should the primary coil be one turn copper strip or two? I can make the strip half wide and twice the length. Does it matters? Looking the surface areas the secondary coil has 18.8% more surface area than the primarycoil.
2. I have an unused dug well on the property with some water in it. Would it function as an acceptable ground if I would lower into the water a heavy cable with some metal weight on the end?
3. Will a tennis ball covered with aluminum foil work as a spherical metal capacitor?
4. The radio station for which I am designing the crystal receiver is transmitting @ 1,476 Kc/sec with 60KW power. I am located 110 miles from it, am I too far from this station?
5. Is it important which direction the "extra" coil is wound with respect to the secondary coil? Secondary coil is wound in the same direction as the primary coil.
6. In order to make the spiral coil a smaller diameter, would it make much difference if I wound 3 turns on top of each other in each groove instead of the two as Eric has done it for the Longitudinal Wave demonstration video?
Thank you in advance for any suggestion or recommendation.

[Nhopa]

Coil design

Okay, so I feel a bit foolish having tried to build circuits emulating Dollards work before reading all of his references and papers. I'm working my way through his work on tesla's oscillating current transformer and I'm wondering if anyone has built a DC tesla coil transformer with the secondary having an n=1 (length to diameter ratio)? It sounds like a short fat secondary is critical to reproduce the unique effects.

My primary interest is in the production of the dielectric field, not in transmitting, so I'm not sure I need the three coil arrangement. I'm guessing if I balance the secondary and primary with regards to surface area, make the secondary n=1, wrap it on a proper form and drive it properly with a DC capacitive discharge that I may start to see the special effects. Any thoughts from anyone?

The following discussion will reference Nikola Tesla's Colorado Springs Notes 1899-1900, from now on just called the Notes. So far I have not seen any reference in the Notes that the secondary coil should be n=1, that is diameter to lenght ratio of 1. All the secondary coils described in the Notes are much longer than their diameter. On the other hand the so called "extra" or Tesla coils are closer to that 1:1 ratio, as can be seen from some of the photographs in the Notes. With the "extra" coil Tesla has achived extremely high e.m.f.. I think the extra coil is necessary for the reproduction of unique effects. Although, you are not interested in transmitting/receiving but to best achieve it Tesla prefers the use of "flat spiral form of coil...", page 66 of the Notes. Teasla indicates in a couple of places in the Notes that the copper masses in the primary and secondary should be equal, for example page 193. On the other hand in Eric Dollard's book "Condensed Intro to Tesla Transformers", page 16, Eric is recommending the use of equal surface area rather than weight because of the skin effect. Eric also used the surface area method in costructing his transmitter/receiver antennas used in his Longitudinal Waves demonstration video. In my coil calculations I equated the weight of primary to the secondary coil as Tesla did then when I compared the surface areas, my secondary has 18.8% more surface than my primary flat copper strip coil. I am sure the calculation can be set up so to find a good close compromise between surfaces and weights.