NavList:

   

Reply

Referring to Frank Reed's earlier message-

| > By 1800, there were
| > many practical methods for clearing lunars available which reduced the
total
| > time for the calculation (from beginning to end, including calculating
local
| > apparent time) to twenty minutes or even less.

Mike Daly asked-

| Is there a good reference for this?  Something suitable for Wikipedia?
| I'm reworking some of the history stuff for navigation and would like to
| specify the time reducing from hours to minutes from Maskelyne's first
| voyage to the regular use of lunars in the early 19th c.

The working-time reduced instantly when the precomputed tables for lunar
distance appeared in the 1767 issue of the Nautical Almanac (long before the
early 19th c.!) After that, there may have been a bit more speeding-up, in
streamlining of the "clearing" process, but it was only marginal.

Until that date, it was necessary to predict the position of the Moon in
ecliptic lat and long, from a complex calculation involving looking up many
harmonic constituents from tables which had been provided by Mayer, then
calculate the position of the Sun (for example) in a similar but less
complex way, and then get the great circle distance between those positions.
You can follow such a procedure in Maskelyne's "British Mariner's
Guide",(first ed. 1763), a procedure for which he claims to give "complete
and easy instructions". Complete they may have been, but far from easy. I am
not surprised that they took several hours. What amazes me is that anyone
could get the right answer after all that longhand arithmetic. Just try it
for yourself.

That gave the lunar distance, which really was needed twice, to provide
bracketing values, to interpolate between, to get the Greenwich time.


And still you had to observe the lunar distance, and "clear" it, before you
could compare it with the predicted value.

Once the lunar distance had been precomputed in the Almanac, those steps,
except that last, had been done for you.

When Cook set off on his first circumnavigation in 1768, Nautical Almanacs
hadn't been produced far enough in advance to cover the four years of the
voyage, and his astronomer had to revert to the old method of long
calculation. The astronomer, Green, didn't survive the voyage, and the
celestial observations were written-up many years later by William Wales, in
his "Astronomical observations ... " of 1788, which I don't have easy access
to.

Cook had this to say, quoted in the Beaglehole edition of his Journals, vol
1, page 392.

"   it is only by such means that this method of finding the Longitude at
Sea can be put into universal practice- a method we have generally found can
be depended on to within half a degree; which is a degree of accuracy
sufficient for all Nautical purposes. Would Sea officers once apply
themselves to the makeing and calculating these observations they would not
find them so very difficult as they at first imagine, especially with the
help of the Nautical Almanac and Astronomical Ephemeris, by the help of
which the calculations for finding the Longitude take up little more time
that that of an Azimuth for finding theVariation of the compass; but unless
the Ephemeris is published for some time to come more that either one or two
Years it can never be of general use in long Voyages, and in short Voyages
is not so much wanting; without it the Calculations are laborious and
discouraging to beginners and such as are not well Vers'd in these kind of
caalculations."

Cook was echoing Maskelyne's claim, in his preface to the 1767 Almanac,
which read-

"The Tables of the Moon had been brought by the late Professor Mayer of
Gottingen to a sufficient exactness to determine the Longitude at Sea,
within a Degree, as appeared by the Trials of several Persons who made Use
of them. The Difficulty and Length of the necessary Calculations seemed the
only Obstacle to hinder them from becoming of general Use: To remove which
this Ephemeris was made; the Mariner being hereby relieved from the
Necessity of  calculating the Moon's Place from the Tables, and afterwards
computing the Distance to Seconds by Logarithms, which are the Principal and
very delicate Part of the Calculus; so that the finding the Longitude by the
Help of the Ephemeris is now in a Manner reduced to a Computation of the
Time, an Operation equal to that of an Azimuth, and the Correction of the
Distance on account of Refraction and Parallax, which is also rendered very
easy by either of the Two Methods invented by Mr Lyons and Mr Dunthorne, and
published among the Tables required to be used with the Ephemeris."

In his final point there, Maskelyne drew attention to the two methods of
clearing the lunar distance provided in his "Tables Requisite ...", which
were intended for use with the Almanac, and which became a bast-seller.

In my own view Maskelyne's claims were entirely justified. I can't provide
references to contemporary estimates of the time navigators took over a
Lunar before and after the step-change when the Almanac appeared, but in my
own view, a reduction from "several hours" to twenty minutes or less seems
entirely reasonable.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.



--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@fer3.com
To , send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply