In 1795 it was published in an updated version, produced by Mechain and Lalande, with new constellations and many more nebulae.
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Finally, the changes in the positions of stars (the original observations were made in the 1690s), led to an update made in the 1770s by the French engineer Jean Nicolas Fortin, supervised by the astronomers Le Monnier and Messier, from the Royal Academy of Sciences in Paris.
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The above correspondence between Flamsteed and Bayer designations is the modern one, which is based on the Atlas Coelestis Novus published by Eduard Heis in 1872.