OVERVIEW of docs in this Smythe folder

OVERVIEW of docs in this Smythe folder PhL 12.9.10 I downloaded Smythe Nov 5, 2009 after seeing the book referenced many times. 1. Smythe Section 5_27 on oblate spheroidal coordinates.doc created 12.3.09 I was interested in oblate coordinates at first just to do the charged disk, and later to do the on-axis Green's function for the disk in hopes of getting from there to the charged bowl. I had no real place to look that had details on oblates, but Smythe had a lot! So in this doc, I am just "taking notes" as I scan through Smythe's section on oblates. He talks about the "oblate harmonics" which I prefer to call the oblate atomic forms (at least one form, the one most used). He uses the atomic form to solve a problem of a metal iris in a uniform E field on one side. I studied this pretty hard and wrote a separate doc on the subject. The issue of parameterization was at first confusing to me. I did some Maple plots of the potential and remember being quite pleased with them. He then does torque on a disk in an E field, and then the Neumann Problem for a spheroid (ie, prescribed σ on spheroid). As a special case of that he gets a 1/R expansion in oblates which I later derived elsewhere. He then briefly does prolates, and his only problem is a prolate haystack in an E field of some sort. Then he is off on cylindricals. 2. Smythe hole in plate problems created 12.3.09 This doc has a 2 page overview. I had trouble with parameterization in the hole region. I solved this problem "my way" and duplicated his answer. I then solved the problem of the "charged iris" doing it the same "my way" and got an answer that is probably meaningful in terms of the central region of a huge disk. 3. Smythe General, and Review of Chapter 5 created 12.29.09 Between this and the last doc I did a Christmas Cape Cod visit. Here I learn about Smythe the person, and various editions of his book (mine is 1932) "Static and Dynamic Electricity" which is completely out of print (somebody wants $300 for the paperback!). I display all the chapter titles, and see that Chapter 5 is about "Three dimensional potential distributions". I then survey the very long sub-contents of this Chapter which is 107 pages of pretty dense stuff. I then do a "walk through" of this entire chapter, taking notes. He has an interesting opening section discussing a condition a surface must satisfy to be an equipotential, reminds me a little of Stackel matrix stuff, and we are off into the ellipsoidals. He has some strange-looking formulas using variable θ, and out pops the Kelvin charge distribution on an ellipsoid, and then the potential of same. I actually do his θ integral and get this result. Then he is off on images, then the Neumann sphere problem, then a Cone Dirichlet problem using what I later call "the cone method". But on page 155 Smythe does mention n = ip - 1/2, and I comment on this in my spherical atoms section of the general atoms doc. Now he starts on Green's Functions using what I now call the Smythian Form method. First is Green's for a cone where I ran into the Π function, a shifting of the Γ function. Next comes Green's for a conical box. Then the oblates which I took notes in the above separate file for. Then onto cylindricals. He does Green's for a cylindrical box. He ends with a list of references which includes Hobson, Jeans, Planck, Stratton, Ramsey, Watson on Bessel, and of course Maxwell. 4. Green's Functions using the Smythe Method created 1.1.10 This doc (56 pages) takes a detailed look at some of the sections mentioned in the general review doc above. Emphasis is on: the cone and conical box Green's problems, I then do the sphere Green's using this method (instead of the usual image method). I compare the Smythian Form method to Stak's list of Green's methods. I review his oblates stuff, and do details of the Neumann spheroid problem. I then do my own Dirichlet spheroid problem in section 8, and of course the special case of the charged spheroid and I compare that to the charged ellipsoid. 5. Green's Functions using the Smythe Method META created 6.24.10 This 13 page meta doc summarized the above doc, and also has a nice 1 page overview written 12.4.10 which I won't replicate here.