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	<id>https://wiki.naturalphilosophy.org/index.php?action=history&amp;feed=atom&amp;title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow</id>
	<title>A Cosmic Lens May Explain the Hubble Flow - Revision history</title>
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	<updated>2026-07-22T06:00:57Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=308241&amp;oldid=prev</id>
		<title>ClaudeBot: infobox: unlink bare volume/issue numbers (removes redlinks to numeric titles)</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=308241&amp;oldid=prev"/>
		<updated>2026-07-21T13:18:34Z</updated>

		<summary type="html">&lt;p&gt;infobox: unlink bare volume/issue numbers (removes redlinks to numeric titles)&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 09:18, 21 July 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| published = 2007&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| published = 2007&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| journal = [[Proceedings of the NPA]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| journal = [[Proceedings of the NPA]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>ClaudeBot</name></author>
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	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=16350&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=16350&amp;oldid=prev"/>
		<updated>2017-01-01T16:54:10Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:54, 1 January 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Infobox paper&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Infobox paper&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| title = A Cosmic Lens May Explain the Hubble Flow  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| title = A Cosmic Lens May Explain the Hubble Flow  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| author = [[Glen W&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. &lt;/del&gt;Deen]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| author = [[Glen W Deen]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| keywords = [[dark matter]], [[Hubble flow]], [[cosmology]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| keywords = [[dark matter]], [[Hubble flow]], [[cosmology]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| published = 2007&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| published = 2007&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l14&quot;&gt;Line 14:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 14:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Cosmic lenses obtain their refracting properties from the hypothesis that the speed of light is a slightly slower constant inside the lens than outside. The title of this paper expresses its original goal, but that goal was not achieved in this paper because the target galaxies chosen for the analysis are too near to the Milky Way Galaxy (MWG). The MWG&amp;#039;s lens cannot project local group galaxy images if they are inside its focal distance. Instead, a model for a spherical cosmic lens is presented that is constrained by the observed distances to the galaxies M31 and NGC 5128. These galaxies were chosen because the angular orientations of M31 are almost exactly equal to those of the inverted mirror image of NGC 5128, and that fits my claim that NGC 5128 is the negative-time projection of M31&amp;#039;s dark- matter halo. Another observation in support of this claim is that these two galaxy images are nearly 180? apart in the sky. The model initially converged to the following solution using Microsoft Excel&amp;#039;s Solver: lens radius R = 280.94 pc, index of refraction n = 1.00044563, and the distance to the unseen real object responsible for projecting both images, xo1 = 0.34475 Mpc. But closer examination revealed that this was not a unique solution. The ambiguity should be resolved as other conjugate galaxy pairs are included in the analysis.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Cosmic lenses obtain their refracting properties from the hypothesis that the speed of light is a slightly slower constant inside the lens than outside. The title of this paper expresses its original goal, but that goal was not achieved in this paper because the target galaxies chosen for the analysis are too near to the Milky Way Galaxy (MWG). The MWG&amp;#039;s lens cannot project local group galaxy images if they are inside its focal distance. Instead, a model for a spherical cosmic lens is presented that is constrained by the observed distances to the galaxies M31 and NGC 5128. These galaxies were chosen because the angular orientations of M31 are almost exactly equal to those of the inverted mirror image of NGC 5128, and that fits my claim that NGC 5128 is the negative-time projection of M31&amp;#039;s dark- matter halo. Another observation in support of this claim is that these two galaxy images are nearly 180? apart in the sky. The model initially converged to the following solution using Microsoft Excel&amp;#039;s Solver: lens radius R = 280.94 pc, index of refraction n = 1.00044563, and the distance to the unseen real object responsible for projecting both images, xo1 = 0.34475 Mpc. But closer examination revealed that this was not a unique solution. The ambiguity should be resolved as other conjugate galaxy pairs are included in the analysis.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Cosmic Lens May Explain the Hubble Flow&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cosmic lens explain hubble flow&lt;/ins&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Maintenance script</name></author>
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	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=13310&amp;oldid=prev</id>
		<title>DeHilster at 19:15, 30 December 2016</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=13310&amp;oldid=prev"/>
		<updated>2016-12-30T19:15:31Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 15:15, 30 December 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l12&quot;&gt;Line 12:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Cosmic lenses obtain their refracting properties from the hypothesis that the speed of light is a slightly slower constant inside the lens than outside. The title of this paper expresses its original goal, but that goal was not achieved in this paper because the target galaxies chosen for the analysis are too near to the Milky Way Galaxy (MWG). The MWG&#039;s lens cannot project local group galaxy images if they are inside its focal distance. Instead, a model for a spherical cosmic lens is presented that is constrained by the observed distances to the galaxies M31 and NGC 5128. These galaxies were chosen because the angular orientations of M31 are almost exactly equal to those of the inverted mirror image of NGC 5128, and that fits my claim that NGC 5128 is the negative-time projection of M31&#039;s dark- matter halo. Another observation in support of this claim is that these two galaxy images are nearly 180? apart in the sky. The model initially converged to the following solution using Microsoft Excel&#039;s Solver: lens radius R = 280.94 pc, index of refraction n = 1.00044563, and the distance to the unseen real object responsible for projecting both images, xo1 = 0.34475 Mpc. But closer examination revealed that this was not a unique solution. The ambiguity should be resolved as other conjugate galaxy pairs are included in the analysis.[[Category:Scientific Paper]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Cosmic lenses obtain their refracting properties from the hypothesis that the speed of light is a slightly slower constant inside the lens than outside. The title of this paper expresses its original goal, but that goal was not achieved in this paper because the target galaxies chosen for the analysis are too near to the Milky Way Galaxy (MWG). The MWG&#039;s lens cannot project local group galaxy images if they are inside its focal distance. Instead, a model for a spherical cosmic lens is presented that is constrained by the observed distances to the galaxies M31 and NGC 5128. These galaxies were chosen because the angular orientations of M31 are almost exactly equal to those of the inverted mirror image of NGC 5128, and that fits my claim that NGC 5128 is the negative-time projection of M31&#039;s dark- matter halo. Another observation in support of this claim is that these two galaxy images are nearly 180? apart in the sky. The model initially converged to the following solution using Microsoft Excel&#039;s Solver: lens radius R = 280.94 pc, index of refraction n = 1.00044563, and the distance to the unseen real object responsible for projecting both images, xo1 = 0.34475 Mpc. But closer examination revealed that this was not a unique solution. The ambiguity should be resolved as other conjugate galaxy pairs are included in the analysis.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|Cosmic Lens May Explain the Hubble Flow&lt;/ins&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>DeHilster</name></author>
	</entry>
	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=1210&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=A_Cosmic_Lens_May_Explain_the_Hubble_Flow&amp;diff=1210&amp;oldid=prev"/>
		<updated>2016-12-30T02:06:28Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Infobox paper&lt;br /&gt;
| title = A Cosmic Lens May Explain the Hubble Flow &lt;br /&gt;
| author = [[Glen W. Deen]]&lt;br /&gt;
| keywords = [[dark matter]], [[Hubble flow]], [[cosmology]]&lt;br /&gt;
| published = 2007&lt;br /&gt;
| journal = [[Proceedings of the NPA]]&lt;br /&gt;
| volume = [[5]]&lt;br /&gt;
| number = [[1]]&lt;br /&gt;
| pages = 35-42&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Abstract==&lt;br /&gt;
&lt;br /&gt;
Cosmic lenses obtain their refracting properties from the hypothesis that the speed of light is a slightly slower constant inside the lens than outside. The title of this paper expresses its original goal, but that goal was not achieved in this paper because the target galaxies chosen for the analysis are too near to the Milky Way Galaxy (MWG). The MWG&amp;#039;s lens cannot project local group galaxy images if they are inside its focal distance. Instead, a model for a spherical cosmic lens is presented that is constrained by the observed distances to the galaxies M31 and NGC 5128. These galaxies were chosen because the angular orientations of M31 are almost exactly equal to those of the inverted mirror image of NGC 5128, and that fits my claim that NGC 5128 is the negative-time projection of M31&amp;#039;s dark- matter halo. Another observation in support of this claim is that these two galaxy images are nearly 180? apart in the sky. The model initially converged to the following solution using Microsoft Excel&amp;#039;s Solver: lens radius R = 280.94 pc, index of refraction n = 1.00044563, and the distance to the unseen real object responsible for projecting both images, xo1 = 0.34475 Mpc. But closer examination revealed that this was not a unique solution. The ambiguity should be resolved as other conjugate galaxy pairs are included in the analysis.[[Category:Scientific Paper]]&lt;/div&gt;</summary>
		<author><name>Maintenance script</name></author>
	</entry>
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