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Thank you Frank. The attachment you intended did not make it along with the 
email; but I do appreciate your narrative 

Sent from my iPad

> On Sep 21, 2014, at 7:21 PM, Frank Reed  wrote:
> 
> It turns out that the 18° magic number for the altitude of the Sun below the 
horizon as the definition of astronomical twilight has been standard "since 
antiquity". Also of interest, the times of twilight seem to have been of 
greater concern to meteorologists (such as they were a century ago) than to 
astronomers or navigators. It appears that astronomical twilight was defined 
very early, civil twilight more recently (c.1800 but not settled even in 
1916), and nautical twilight some time after that --when? The definitive 
analysis of twilight and the history of the concept, up until then, was 
written by H. H. Kimball in 1916 and published in the "Monthly Weather 
Review". I am attaching a copy of the paper. Kimball also discussed the 
varying arbitrary definitions of sunrise and sunset that were in use in the 
nineteenth century. He notes that older German sources defined sunrise and 
sunset as the instant when the geocentric sun has an altitude of zero degrees 
(H_c=0° in navigator's terms). There's lots of interesting material in the 
article. For example, he notes that the brightness of twilight when the Sun 
is about 8° 40' below the horizon is comparable to a sky with a Full Moon (at 
the zenith, but at any moderately high altitude would be equivalent). This, 
incidentally, confirms something that many navigators know but it's not often 
stated plainly in the textbooks: a Full Moon night is comparable to nautical 
twilight.
> By the way, the crepuscular arch described in Kimball's paper is the shadow 
of the Earth on the atmosphere, which apparently figured in some early 
definitions of civil twilight. There was a  [LINK: 
http://www.skyandtelescope.com/astronomy-news/observing-news/earths-shadow-07292014/] 
recent article on the Sky & Telescope web site describing it.
> -FER
>  
> 
> [PLAIN TEXT VERSION OF MESSAGE AUTO-GENERATED. ORIGINAL MAY INCLUDE MORE CONTENT]
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> Attached File: http://fer3.com/arc/imgx/On-twilight.pdf
> 
> 
> : 
> http://fer3.com/arc/m2.aspx/History-Twilight-FrankReed-sep-2014-g28683
> 
> 
> 

   

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