In 1772, William and his brother were at 7 New King Street and their sister Caroline Herschel came to study singing. By 1776, she was performing and in 1778, she was soloist in the Messiah. She later become William's assistant and a notable astronomer in her own right. William began studying astronomy seriously in 1773, building his own telescopes because he could not afford to buy them--his brother was a good mechanic and helped build the telescopes. On 4 Mar 1774 he had a good 5 foot Newtonian telescope working. In the summer, the Herschels moved to a house in Rivers Street. In 1776, William resigned from the Octagon Chapel. In 1779, he composed his most popular piece, 'Favourite Echo Catch', and the next year published his first astronomical papers. In Mar 1781, the Herschels moved to 19 New King Street and on the evening of 13 Mar 1781, he discovered Uranus with a 7 foot telescope magnifying 227 times, though he initially thought it was a comet. Sadly, Caroline was not present -- she was still packing up at the previous house. William was appointed Royal Astronomer to George III in 1782, at a salary of 200 per year. He and Caroline gave a farewell performance at St. Margaret's Chapel on Whit Sunday, 19 May 1782, and then they moved to Datchet, near Windsor, in late July 1782. There is a Herschel House and Museum at 19 New King Street, Bath. In 1884, there was a proposal to erect a memorial window in the Octagon Chapel, but I don't know if it was ever done.
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Thomas Robert Malthus (1766-1834) is buried in the porch of the Abbey Church, Bath.
A descendent of John Napier, General Sir Charles James Napier (1782-1853), the conqueror of Sind, lived at 9 Henrietta Street.
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Frank Morley taught at Bath College for three years in the early 1880s before emigrating to the USA.
To see an Ordnance Survey map click at THIS LINK
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An extract from The Mathematical Gazetteer of the British Isles created by David Singmaster
The original site is at THIS LINK