NavList:

Hello Peter,

It is very likely that what you have are "time sights". Historically this was known as finding the "true time" (at least in English). These calculations were usually listed in navigation manuals under the generic title "longitude by chronometer". A time sight is a sundial sight. It effectively converts a sextant into a sundial. By a straight-forward mathematical calculation, the altitude of the Sun is converted into local hour angle. This then is added or subtracted from 12:00 depending on whether the sight was made in the morning or afternoon, and then the equation of time is added/subtracted to allow comparison with the "mean time" displayed by a chronometer.

The simplest geometry for a time sight is found on the equator at either equinox. On those dates, the Sun rises vertically from the east, climbs to the zenith, and then sets vertically, due west. If you measure the Sun's altitude with a sextant at the equator on the equinox, after the usual corrections, the altitude directly yields the exact local apparent time at the usual rate of 15° per hour. Specifically, the Sun's zenith distance is identical to the LAT, so if the Sun is 30° high in the morning, then its zd is 60° which tells us that we are four hours from noon. Since it's morning, it must be four hours before noon or 8:00am. We could use a sundial for exactly the same purpose, but sundials don't work at sea, and sextants are more accurate.

Clearly this simple equatorial equinox case has to be generalized. The actual calculation that yields LAT from the altitude is the most basic spherical triangle problem. Draw the ZPS (zenith-pole-Sun) triangle. The angle between the arcs ZP and ZS is the local apparent time that we're looking for. The arc PS is the Sun's "polar distance" (90 +/- Dec). This is a known quantity from almanac pages. The arc ZS is just the zenith distance: 90 - Corrected Alt. We know this because we have measured it. And finally the arc ZP is the co-latitude: 90 - Lat. The latitude is potentially uncertain. This latter uncertainty means that we need to be careful about taking our sights as near to due east/west (on the "Prime Vertical") as possible. I'll have more to say about that in another message. The actual method used to "work" this triangle problem varies a little from one navigational culture to another, but it really doesn't matter much. We're simply solving a spherical triangle. In my experience, by far the most popular method was what has come to be known (in later decades) as a "haversine" solution. In the calculations that you're examining, look for three angles added up and then divided by two... and also four logarithms added up (there are a few other steps but you can look for these first). If you see that pattern, then you probably have some examples of standard time sights worked by the usual haversine method.

Noon Sun sights for latitude and "time sights" in the morning and afternoon for longitude were the "bread and butter" of 19th century celestial navigation. This was "normal" celestial navigation back then. Star sights were for eccentrics. I teach a class in this methodology called, appropriately enough, "Celestial Navigation: 19th Century Methods" (you can read the description on my web site at http://ReedNavigation.com). You can find many examples of this methodology in old navigation notebooks and scrap paper. Have a look at my NavList post from this past winter on "scrap paper" sights here:
http://fer3.com/arc/m2.aspx/Scrap-paper-with-time-sights-c1870-FrankReed-feb-2013-g22446
and see if this resembles the pages that you have been looking over. Look for follow-up posts under that same subject. Lars Bergman put together a great spreadsheet showing his alanysis of all of those scribbled sights and also determined that they were more likely taken c.1855. There's a great deal of fun in old calculations like this, and it's amazing how much information can be teased out of them. By the way, if you don't think you can figure out how to attach your own scans, please email your files to me at fer@fer3.com, and I will post them for you.

-FER

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