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From William Dunbar to Thomas Jefferson in 1804 (Library of Congress web site):

  "I mentioned in my last that one very simple method had occured to me of ascertaining in certain Circumstances the Longitude of places, which is much better calculated for travellers by land than Voyagers by Sea; the method is such that a Single observer with a good altitude instrument, altho' deprived of the use of a time keeper, may still make useful observations for the advancement of geographical Knowledge. I shall now just mention the principles & shall hereafter Send you some examples of the Calculation. The excellence of the usual lunar method of determining the Longitude depends (supposing her theory to be perfect) upon her quick change of place from west to east; but it cannot be denied that it requires great dexterity to make good observations, which is evident from the disproportion of the times to the distances in the hands of the best Observers, and this arises from the slow progress of the moon which Causes the Contact to appear to be continued for many seconds of time; were this observation similar to a meridian altitude, it might certainly be taken to any desireable accuracy, that is, were the motion of the moon from North to South in place of from West to east, the moon's altitude when brought upon the meridian by the rotation of the earth would furnish an easy & very Correct mode of ascertaining the Longitude: Now altho' the proper motion of the moon is from West to East, yet her orbit makes so considerable an angle with the equinoctical circle, that there are two portions of each lunation when the moon's change of declination is very rapid, exceeding 6 in 24 hours, that is 5" of a degree in one minute of time; if therefore under favorable Circumstances we take the moon's greatest altitude near the meridian, we shall thence be enabled to ascertain the moon's declination at the moment of her passing our meridian; we must then find the time at Greenwich when the moon had that declination and also the time when the moon passed the meridian of Greenwich, from which data the Longitude is easily found: this method will require the use of some interpolations and an equation for the Correction of the Moon's altitude on the Meridian, because her greatest altitude will not be on the meridian, but to the East or West according as She is increasing or diminishing her North polar distance. I have communicated this method to my Worthy friend Mr. Briggs who is pleased with the idea & intends giving it consideration. "

 

There's lots more including detailed calculations on the LOC web site: http://lcweb2.loc.gov/cgi-bin/query then search on "lunar Dunbar".