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As I understand the matter, the path of the sun in the ecliptic, as
plotted on a plane surface between the tropics of Cancer and Capricorn,
takes the form of a sine curve, therefore - knowing the obliquity of the
ecliptic, the declination may be calculated by spherical trigonometry. To
do this, however, it appears also necessary that the Sun's Longitude, or
place east/west of the vernal equinox in the ecliptic be known, as can be
calculated or proportioned from a knowledge of both the time and date
that the Sun enters the various zodiacal signs, a fact once published in
the nautical almanac, allowing thirty degrees of longitude per sign.
Actually were mixing a little astrology with navigation here, as was not
so unusual in bygone times.

My old standby, Arnold's Lunarian poses this problem and it's solution at
some length and it appears to have been a method used by some navigators,
although it certainly does not obviate the need for some form of
tabulation - at least as far as the obliquity of the ecliptic, the
date/time of the Sun's entry into the various signs, and trigonometric
functions are concerned. It is perhaps also interesting to note that
certain navigation tables provided the sun's declination for a number of
years at noon on each day - Norie's Tables, 1904 edition, includes a
table of the Sun's declination for the years 1888 - 1891 and also allows
for several additional years by the application of a correction, although
there is a precaution stated to the effect that this table should be used
only if there is no NA aboard.

At one point in time, I prepared a tabulation of the Sun's declination at
noon for each anticipated
day of a forthcoming voyage, together with certain other basic data, so
as to have this information available and with me in the event of a
sudden separation of ship and me. I know very little about Bligh's small
boat voyage, but it seems that if he wound up with a sextant, there must
have been some other form of navigational data available to him - or
perhaps he was just well prepared,

On Wed, 19 May 2004 09:38:46 -0700 William Allen 
writes:
> Fred,
>
> Could you please give a little more explanation on using the sine
> curve
> to approximate declination?  Maybe a short example?
>
> Thanks,
> Bill Allen
>
> -----Original Message-----
> From: Navigation Mailing List
> [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM] On Behalf Of Fred
> Hebard
> Sent: Tuesday, May 18, 2004 3:21 PM
> To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> Subject: Re: HMS Bounty
>
> On May 18, 2004, at 5:44 PM, George Huxtable wrote:
>
> > How could he have
> > done this without a table of day-by-day Sun declination, that only
> the
> > ephemeris or some other nautical table could provide?
>
>
> Although not accurate to the minute, one can estimate the sun's
> declination by means of a sine curve running from the equinox as
> zero
> degrees to the solstice as 90, with an amplitude of 23.5 degrees.
> The
> ellipticity of the earth's orbit is accounted for, more or less, by
> the
> varying number of days between the various equinoxes and solstices.
> Of
> course, how does one estimate a sine?  If one remembers the Taylor
> expansion for it, that would be one way.  It's more likely, from
> subsequent references in George Huxtable's post, that Captain Bligh
> had
> a short table of declinations.  An adequate one could fit on one
> page.
>
> Making heroes out of the mutineers is undoubtedly stretching the
> truth
> on the Bounty mutiny.  But, as captain, it was Bligh's fault, just
> as
> in any other catastrophe on a ship.  Apparently, however, his charms
> were no match for those of some of the Tahitian maidens!
>
> I told some of the boys who work with me the story of the Hawaiian
> girls swimming out to Cook's ship to "welcome" him and his crew.
> Some
> of those boys are not too unlike some of Cook's sailors I would
> think.
> One of them was ready to go to Hawaii on the spot!  He had missed
> that
> Cook got there 230 years ago.
>
> Fred Hebard
>

   

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