English, c. 1820, signed "D. Thomson Invt" and "Bate London, N° 209." Boxwood, 37" long with brass fittings and cursor. Both sides of rule and slider marked with numerous scales, including on the Lunar side "App Alt.," "App. Dist.," "Hor. Par.," "Corr." and "Comp. Corr.," and on the Time side, "Half Sun," "Lat.," "Diff.," "Time P.M.," and "Time A.M.." Brass cursor engraved with Declination scale.

Invented by Captain David Thomson (1789-1834) and made and sold by Robert Bate in 1816, this extremely rare device was used for calculating the longitude at sea, and was described as a "Longitudinal Scale" or "Lunar Corrector" for reducing lunar distance observations in determining the longitude. It was endorsed by many, including Edward Troughton as giving apparent distances within a few arcseconds.

We also have the accompagning booklet explaning the use of this scale:
David Thomson’s : Lunar and Horary Tables: For new and concise methods of performing the calculations necessary for ascertaining the Longitude by Lunar Observations, or ... for acquiring a knowledge of the principal fixed stars. 1836
but not yet :David Thomson, Description & Use of the Longitude Scale or Lunar Corrector, for readily clearing Apparent Lunar Distances from effects of parallax & refraction, etc., London, 1816