These observations were carried out by Biot, with the assistance of Mudge and of his son Richard Zachariah Mudge, at Leith Fort on the River Forth, and Biot assisted Mudge in extending the arc to Uist in the Shetland Islands.
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It is to Mudge that William Wordsworth alludes in his poem Written with a Slate Pencil on a Stone, on the Side of the Mountain of Black Comb, on Black Combe, written in 1811-1813; Wordsworth had heard in Bootle from the Rev. James Satterthwaite the story of the surveyor (identified with Mudge) on top of Black Combe, famous for its long-distance views inland and out to sea, who was not able to see even the map in front of him when fog or darkness closed in.
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On the extension of the English arc of the meridian into Scotland, the French Bureau des Longitudes applied for permission for Jean-Baptiste Biot to make observations for them on that line.
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He made two large ones with a magnifying power of two hundred times; one of these he gave to Hans Moritz von Brühl, and it passed to the Gotha Observatory, the other descended to his son William Mudge.