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Jan Kalivoda and Frank Reed referred to Thomson's tables.

Just in case it's of interest, here's what Eva Taylor has to say about David 
Thomson, in "Mathematical practitioners of Hanoverian
England, 1714-1840." published 1966.

The numbered references in square brackets are to the entries elsewhere in that volume.

1446. THOMSON, David, Mariner (1789-1834); R.N. Captain.
Thomson invented and described a Longitude Scale or Lunar Corrector in 1816, 
which was made and sold by Bate [1079].

1816. Description & use of the Longitude Scale or Lunar Corrector, for readily 
clearing Apparent Lunar Distances from effects of
parallax & refraction, etc.

1824. He had in the Press a work on the Methods of finding the Longitude at 
Sea by Lunar Observations & Chronometers (Philosophical
magazine).

1824. Lunar & Horary Tables. These were reviewed and praised by George Carey 
[1289] in The Artisan: ' The tedious & complicated
methods of calculation generally given for correcting the Observed Distances, 
and finding the Apparent Time, have frequently been
objected to'. Those who approved Thomson's scale included T. Hurd [733], J. 
Horsbrugh [850], T.S.Evans [[961], Thomas Firminger
[1121], J.N.Campbell [1502], Thomas Lynn [1009], and George Carey [1289]. 
Thomas Firminger said thatresults from the scale never
differed by more than four or five seconds from that by calculation, while its 
use could be taught in half an hour to anyone
familiar with the first four rules of arithmetic. Edward Troughton [778] said 
in 1823: From my knowledge of nautical instruments I
must say that no seaman can with certainty get the Apparent Distance nearer 
than 15", and as far as I have tried your apparatus I
have always come within a fifth of that quantity. I certainly am not an enemy 
to the rigorous computation, and to the few who are
capable of performing it nothing that I say will divert them from its 
employment.@ But Thomson's scale is adapted ' to the
avocations and educations of the many'.

Thomson was accidentally killed in December 1834.

The work mentioned as 'in the Press' in the Philosophical Transactions (1824) 
was in fact the second edition of the book of 1816
'greatly enlarged and improved, containing the Tables required with the 
Nautical Almanac and scale, in finding the Longitude either
by lunar observations, or chronometers'. This was published for the author in 
1823, and a copy is known which was in the possession
of the explorer Charles Sturt.

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There seems to be a bit of confusion, above, between the virtues of Thomson's 
Tables, and those of his "Longitude Scale or Lunar
Corrector", whatever that may be. My own copy of Thomson's Lunar and Horary 
Tables is dated1857, and is the 52nd edition! It must
have sold well. At that date its proprietor was Boulter J Bell. There is no 
mention in that edition of his Longitude Scale.

On page 92, Taylor describes Thomson's Longitude Scale as follows-

Many attempts were made to provide mechanical devices to relieve the 
non-mathematical seaman of the dreaded labour of computation,
and among the most successful was the Longitude Scale and Lunar Corrector 
designed by Captain David Thomson [1446]. It was a rather
complicated brass scale, with movable limbs, and is mentioned with approval by 
a number of navigators and mathematicians who,
although they did not need such an aid themselves, recognised how easy it was 
to make errors in computing a lunar distance. Thomas
Firminger [1121] for example, said that the results achieved with Thomson's 
scale 'never differed by more than for or five seconds
from that by calculation, while its use can be taught in half an hour to 
anyone conversant with the first four rules of arithmetic'.
It was submitted to Edward Troughton too, and even he conceded its usefulness: 
'for no seaman can with certainty get the Apparent
Distance nearer than 15 seconds, and as far as I have tried your apparatus I 
have always come within a fifth part of that quantity'.
All the same, to a man like Troughton even three seconds constituted a 
considerable error, and he added that he would be unwilling
to deter the few, who could take (and work out) an observation with greater precision, from doing so.

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I don't recall seeing Thomson's "Longitude Scale and Lunar Corrector"  in a 
museum, and Taylor doesn't offer a diagram. Can anyone
offer further information about it?

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.

   

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