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George H, you wrote:
"It's Layton (faithfully  copied by Walden) who confusingly uses those "
symbols to separate the parts of  an angle, rather than the conventional symbols
for degrees, minutes, and  seconds."

It wasn't confusing to Layton! In fact, it was quite common to  write angles
this way (with dots or double dots as separators) in the 19th  century.

Regarding Layton's interpolation of Sun declination, you  wrote:
"But his procedure for interpolating seems remarkably  ham-handed."

I hope my earlier posting convinced you that it wasn't  unusual, let alone
ham-handed, but I've had another thought. From a post-20th  century perspective,
we're accustomed to interpolating for declination based on  chronometer time
(GMT), but the 19th century approach was oriented towards local  time and
specifically Local Apparent Time. So a navigator would look up the  declination
for Greenwich Apparent Noon, adjust for his longitude to get the  declination
for Local Apparent Noon and then adjust to the time on his watch  (which would
have been set to local time). Naturally since the ship is moving,  this
declination is not as good as what you would get by going straight off the  GMT, but
the difference was not important from a practical  standpoint.

Regarding the logarithmic calculation of the time sight (to  determine Local
Apparent Time), you wrote:
"What Layton has done is this-  Being completely familiar with that
calculation, which he has gone through day  after day, he has a good idea of the sort
of time interval that will result. He  knows, without doing any calculation,
that the log hav of the result will always  be somewhere in the range between
about 8.7 and 9.7. So he simply ignores those  numbers preceding the decimal
point (and the decimal point itself) in his  calculation. He concentrates
entirely on the numbers that follow thedecimal  point, knowing that he can guess the
other part from his experience. It saves a  few seconds in the calculation."

Another thing worth remembering here is  that the result of the time sight is
already known within 15 minutes or so.  After all, this sight is just telling
us the local time. And we know that more  or less from the time of the noon
sight which is probably when everyone's  watches would have been set. That is,
when you take the time sight, you write  down your best estimate of local time
from your watch. When you work the  calculation, you know that the answer is
going to be very close to the time  you've written down.

-FER
42.0N 87.7W, or 41.4N  72.1W.
www.HistoricalAtlas.com/lunars

   

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