Dunthorne also contributed a method for clearing nautical lunar observations of the effects of refraction and parallax, for the purpose of finding the longitude at sea, and Maskelyne included this in his 'Tables requisite to be used with the Nautical Ephemeris', an accessory volume published to accompany the Nautical Almanac. It is also reported that Dunthorne in 1772 received from the Board of Longitude a reward of £50 for this contribution towards shortening the tedious calculations involved in "clearing the lunar distance" (at the same time as a similar reward was given to the contributor of an alternative method for the same purpose, Israel Lyons, 1739–1775). Improvements were added and "Dunthorne's improved method" was included in an edition of 1802.