RE: Solid State Tesla Coil Book Available

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Loudner, Godfrey by way of Terry Fritz <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>

Hello Ed

I think I know what you mean. The books on electricity and magnetism from
the old days explored topics in great depth and the some of the exercises
bordered on research problems in my humble opinion. The same is true of
mathematics. Just take a look at Whittaker and Watson's "A Course Of Modern
Analysis". Some of the exercises have never been solved by students or
professors. Only Whittaker and Watson knew how to solve them. Dunford and
Schwartz's books "Linear Operators" has an exercise that could not be solved
by students or the authors themselves! Many years went by until the young
mathematical genius and student Robert Langlands presented a solution at
Yale. Langlands is presently one of the greatest living mathematicians. This
is why I stock my reference library with such books. I can't find a
reference to the book you mentioned, but I do have a copy of Smythe's
"Static and Dynamic Electricity". I'm certainly going to look through the
exercises to find the one you mentioned.

Closed-form solutions are regarded in mathematics as those solutions which
are expressible, with a finite number of elementary arithmetic operations,
in terms of elementary functions such a cos(z), sinh(z), ln(z), ect. The
theory of differential Galois groups tell us that some integrals such as
those defining the Legendre functions cannot be expressed in closed-form.
Functions not expressible in closed-form are called transcendental. To
determine if the function defined by the capacitance formula is
transcendental or not could be settled by computing a certain Galois group.
To compute the Galois group, a large number of symmetries would have to be
determined. I consider the problem to be overwhelming. However I do consider
the capacitance formula to be successful. The formula is very elegant and
values can be easily obtained with computers. It is a very successful
solution. 

Godfrey Loudner     

> -----Original Message-----
> From:	Tesla list [SMTP:tesla-at-pupman-dot-com]
> Sent:	Thursday, December 27, 2001 12:35 PM
> To:	tesla-at-pupman-dot-com
> Subject:	Re: Solid State Tesla Coil Book Available
> 
> Original poster: "Ed Phillips by way of Terry Fritz <twftesla-at-qwest-dot-net>"
> <evp-at-pacbell-dot-net>
> 
> Tesla list wrote:
> > 
> > Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz
> <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>
> > 
> > Tesla list wrote:
> > >
> > > Original poster: "Loudner, Godfrey by way of Terry Fritz
> > <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>
> > 
> > > Software packages such as Mathematica can calculate values of the
> > > capacitance formula to any degree of accuracy. Unfortunately the
> Mathematica
> > > package cost about $1,600 (half that to an educational institution).
> > 
> > To just evaluate a formula, there are certainly less expensive
> > alternatives...
> > 
> > > Anyway I'm playing around with approximation theory to see if I can
> extract
> > > a useful algebraic formula that approximates the capacitance formula
> given
> > > in Moon and Spencer. If I'm lucky, I'll share the result with the
> list.
> > 
> > What is the formula? Is it ideally exact or just an empirical
> > approximation?
> > 
> > Antonio Carlos M. de Queiroz
> 
> 	If I remember correctly (it's been over 50 years) calculation of the
> capacitance of an isolated torus was a student's problem in Smythe's
> "Electricity and Magnetism".  Solution involved Legendre integrals and I
> never saw a successful answer.  There may be no closed-form solution.
> 
> Ed
> 
>