Editing Apps/DysonPotential (section)

====Dyson's Figures====

In his effort to illustrate the behavior of equipotential contours in the space exterior to various ''anchor rings'', Dyson evaluated his expression for the potential up through <math>~\mathcal{O}(\tfrac{a^2}{c^2})</math>; that is, he evaluated the function,
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<math>~V_2 \equiv V_\mathrm{Dyson}\biggr|_{\mathcal{O}(a^2/c^2)}</math>
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<math>~=</math>
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<math>~
\frac{4K(\mu)}{R+R_1}\biggl[1 - \frac{1}{8}\biggl(\frac{a^2}{c^2}\biggr) \cos^2\biggl( \frac{\psi}{2}\biggr)\biggr]
+ 
\frac{(R + R_1)E(\mu)}{RR_1}\biggl[\frac{1}{8}\biggl(\frac{a^2}{c^2}\biggr) \cos\psi \biggr] \, .
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Figures 1, 2, 3, &amp; 6 from [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson (1893a)] &#8212; replicated immediately below &#8212; show his resulting set of contours for six cases:  Tori (anchor rings) having aspect ratios of <math>~a/c = 0, 1/5, 2/5, 1</math>.   Click on an image to view the contour plot at higher resolution.  In what follows we present results from our own evaluation of this "V<sub>2</sub>" function for the single case of an anchor ring having <math>~a/c = 2/5</math>.


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'''Figures 1, 2, 3, &amp; 6 extracted without modification from pp. 63-66 of <br />
{{ Dyson1893figure }}
<!--
[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184
-->
<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />
[[File:PermissionsRectYellow.png|75px|link=Appendix/Permissions#Dyson1893]]
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[[File:RoverDinfty.png|300px|center|The Potential Exterior to an Anchor Ring; R/d = infinity]]
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[[File:RoverD5over1.png|300px|center|The Potential Exterior to an Anchor Ring; R/d = 5]]
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[[File:RoverD5over2.png|300px|center|The Potential Exterior to an Anchor Ring; R/d = 1.667]]
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[[File:RoverDunity.png|300px|center|The Potential Exterior to an Anchor Ring; R/d = 1]]
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