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When we think of a celestial fix today, we think of two or more lines of
position (LOPs). Those lines of position can be at any angle (more or less).
With those LOPs, we make a simultaneous estimation of our latitude and longitude
at a given time.  Before the days of Thomas Sumner (ca. 1830), things were very
different.  The idea of a celestial line of position had not yet been conceived.
There was a very strong mindset that latitude and longitude were to be
determined separately, and usually not at the same time.

It has long been relatively easy to determine latitude, either from Polaris or
from a meridian transit of the Sun (or of some other body).

Determining longitude was a separate and distinct process.  Many of you have
read "The Search for Longitude".  It is all about the need to develop an
accurate timepiece so that longitude could be found.  The process by which
longitude was found once you had accurate time was called a "Time Sight".
Basically, if you know local time, and you know UT, then you know your
longitude.  The chronometer gives you UT. A Time Sight of the Sun gives you the
meridian angle of the Sun, which, given a nautical almanac, is equivalent to
local time.

The formula was derived from the Law of Cosines.  I don't have it in front of
me, but the idea is to measure altitude, assume your latitude, then solve for
meridian angle (t).  Then use meridian angle to solve for longitude. This
requires accurate time, which is perhaps another reason why it was called a Time
Sight. I believe the formula can be found in any copy of Bowditch before the
1995 Edition, and in other texts as well.

The separate estimates of latitude and longitude were combined to give a point
estimate of one's position. It was nearly always a running fix.

Ideally, time sights of the Sun were taken at the time of the Sun's Prime
Vertical crossing, which is the time at which the Sun is due east or due west of
the observer.  Not only does this give the best cut at longitude, it is also the
time at which the rate of change of the azimuth of the Sun is minimal. That
makes Prime Vertical crossing a good time to check your compass as well.

My apologies to the group if I am simply restating what is common knowledge.

Chuck Taylor

 47 deg 55.161 min N
122 deg 11.176 min W

   

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