For details of the efforts towards determining the longitude, see History of longitude.
Other positions included Vice-President of the Society for the Encouragement of Fine Arts, Trustee for the British Museum and a Commissioner on the Board of Longitude.
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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).