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    Re: The Sun does not stop for anyone
    From: Frank Reed
    Date: 2016 Dec 17, 07:02 -0800

    David C, you wrote:
    "My intention is to use the sights in various ways:

    • Intercept - to check the accuracy
    • Long by Chron
    • Sumner two-point method on a plane chart
    • Longitude by Equal Altitudes"

    Hmm. Check accuracy? The intercept calculation is intrinsically less accurate than a time sight calculation (by the way, I have been meaning to say: the expression "long by chron" is decidedly archaic and misleading --just call it a time sight calculation or a local time calculation). The time sight yields the exact longitude of a point on the circle of position for a specified latitude. And if the latitude is known exactly, as it certainly is in land-based experiments, then the longitude is exact for that given altitude. The two-point method (Sumner) is no different in accuracy compared to the intercept computation. If you want something to check accuracy, then you can just do any old computer simulation. If you do an "intercept method" for your observing location with an intercept of zero, then your safe since this is identical to any computer simulation if done right.

    The method here that stands apart, the technique of which we can say "one of these things is not like the others," is the longitude by equal altitudes. Longitude by equal altitudes works effectively in the modern world, but there are ways to make it much easier and significantly more accurate. First you should be taking a.m. and p.m. sights in intervals that overlap as nearly as possible, That is, they should have the same distance from noon at the beginning and end of the time period during which you're shooting. But there's no need to duplicate the exact times. Instead shoot five or six altitudes from 30 to 20 minutes before noon and then shoot five or six altitudes from 20 to 30 minutes after noon. 

    After you have taken your a.m. and p.m. sights, plot them against UT/GMT as accurately as you can. Then draw the best line you can through the a.m. sights. Then draw the best line you can through the p.m. sights. If they're close enough to noon that you can see the curvature in the plot, then you should draw a nice parabola through the whole bunch. We can discuss details on that another time. Now match up the before noon and after noon lines (or curves). A really nice way to do this (my own methodology) is to plot the sights on transparencies or semi-transparent graph paper, run your lines through them, and then lightly fold the paper in half while holding it up to a light. Align the lines --not the individual sights-- perfectly on top of each other, and then make a hard crease in the paper at that alignment. You can now read off the UT of the middle time. This middle time will not necessarily be noon. You need to correct for motion of the vessel towards or away from the Sun, which should properly include motion of the Sun's declination though that's nearly zero this week. There's a short computation or a table for this, or alternatively you can adjust each of your sights. When you're done, you have the UT corresponding to local apparent noon, 12:00:00. Add or subtract the equation of time from either of these as appropriate, and then the difference is longitude in time. Convert to degrees, and you're done.

    Frank Reed

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