In a previous article in this Journal mention was made of an unexamined manuscript by Hariot belonging to the Petworth Collection entitled The Doctrine of Nauticall Triangles Compendious, which promised to be of interest to navigators. When Lord Leconfield, the owner of the Collection, heard of this he very kindly himself brought this manuscript to the British Museum for study there, and meanwhile Dr. Shirley of the United States, who is at work on other aspects of Hariot's life, sent over from America a transcript from a microfilm copy which was in his possession. The contents of the manuscript more than fulfilled expectation, for it appeared that the main theme was the computation of meridional parts for drawing a Mercator chart and, as Mr. Sadler, the Superintendent of H.M. Nautical Almanac Office, shows in the second part of this paper, Hariot was remarkably in advance of his time in his mathematical treatment of this problem, which continued to be a favourite one for discussion until the discovery of the calculus. As is well known, the first table of meridional parts to be published was that compiled (by simple addition of secants) by Edward Wright (1558–1615) of Caius College, Cambridge, a mathematician who had been nautical adviser to the Earl of Cumberland, and on occasion to the Lord High Admiral himself.