From mark.snegg@onwe.co.za Sun Oct 17 00:11:32 1999
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From: "Mark Snegg" <mark.snegg@onwe.co.za>
To: "Classics List" <classics@u.washington.edu>
Subject: Re: semi-classical query
Date: Sun, 17 Oct 1999 09:04:29 +0200
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Alfred Kriman wrote :

> LNSc = LNS/cos(T).
>
>cos is the trigonometric cosine function, T is an angle proportional to
>the time away from true local noon:
>
> T = 15deg. * (time away from true noon in units of hours)
>
>Thus, at "10:30" and at "1:30", T = 15deg. * 1.5 =  22.5 deg.;
>cos(T) = 0.924 and the corrected value of LNS is LNSc = LNS/.924
>= 1.08 * LNS.  The corrected value LNSc is the one you want to use as
>you would the measured shadow length at noon.  By "10:30", of course,
>I mean 1h30m before true local noon (computed half-way between sunrise
>and sunset).

This assumes that the effect of the sun rising or setting is negligible - which
would only be true very close to noon. It must be taken into account if the
measurement is done an hour or two before or after true noon. The sun has two
motions : E to W and up and down in the sky.

This additional correction depends on the latitude. At the latitude of Toronto,
43deg 42min, the sun will be at a height of 46deg 18min at true noon on the
equinox. Assuming that the rate of ascent and descent is constant, then one hour
after noon the sun will have set by 7deg 43 min. This will increase the length
of the shadow by about 13%. This additional correction has to be applied before
using the NS component of the shadow to calculate the length at noon.

I would think that a better solution (if it's practically possible ) would be to
take the measurements with the three different classes at noon, but the day
before the equinox, on the equinox, and the day after the equinox. This would
introduce an error of only a fraction of a percent, which is well within the
margins of error for the experiment.

Mark Snegg


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