Thank you for this valuable summary of the known information on Henry Sherwin and links. My own interest in his biographical details was piqued when I obtained an original 1726 edition of his tables.
Some searches have brought up a few other pieces of information and summarised below in case of interest.
Key points?
Described as a 'mathematician' in a modern bio' entry. (Has not been clear from own readings to date if a mathematician, astronomer, publisher or mix.)
The Sherwin to Flamsteed letter 1015b a good lead perhaps to his 'Court of the Trinity house' connections. (Trinity House was/is concerned with lighthouses, pilotage, navigation etc.)
An intriguing mention of a planned visit to Jamaica in a letter to Sharp.
Details:
Under Newton’s Shadow. Astronomical Practices in the Seventeenth Century by Lesley Murdin, Pub. Adam Hilger Ltd, 1985, page 92, Table 6.1 ‘Flamsteed’s correspondents on astronomical and related subjects'. 50+ correspondents are listed including a ‘Henry Sherwin’. Google Snippet shows list.
The Correspondence of John Flamsteed, The First Astronomer Royal: Volume 3, Eds. Forbes, Murdin, Wilmoth, Pub. Taylor & Francis, 2001. Amazon UK link.
Ref. 1 above prompted a browse through the 3 vol. chronological set. Volume 1 and 2 have no entries for Sherwin in the Index or with Contents search.
Vol. 3 has over 50 index entries either to him, his Tables or to footnotes in text. (The Index entries and most actual entries can be viewed online using Amazon UK’s ‘Look Inside’ and ‘Search Inside’ feature with ‘Sherwin’ as keyword – handy, as don’t have ready access to the £600+ set!)
A summary of these is below.
a) 'Biographical notes' at end, extensive listing for people mentioned. Entry for Sherwin in full as follows:
'Sherwin, Henry (fl. 1705-17), mathematician, editor of Mathematical tables (London, [1705]-1710): in 1705 he was planning a trip to Jamaica (letter to Sharp, RGO 1/69C, f.111r,v). Taylor (II). p.143; Cudworth, pp.171-74.
I have ordered a copy of this letter (RGO was the Royal Greenwich Observatory) and will report back with a transcript, also ordered the letter from Halley to Sherwin in the Macclesfield Collection mentioned in earlier Answer 1 as both at same source (Cambridge Univ. Lib.)
aa) 'Taylor (II)' from a) is The mathematical practitioners of Hanoverian England, 1714-1840, E G R Taylor, Cambridge, 1966. (Taylor I is for '.... of Tudor and Stuart England', 1954.) Google Snippet doesn't reveal how long Sherwin entry is.
b) One letter: Letter 1015b, London 22nd July (1705?) Henry Sherwin to Flamsteed. Signed 'H. Sherwin', no address. This can be read in full via Amazon 'Search Inside' feature on p.189.
In the letter, Sherwin is seeking Flamsteed’s help after a debate at a 'Court of the Trinity house' on the 'more than ordinary change in the variation of the Needle' and its impact on navigation. Would welcome opinions on what this letter may reveal on Sherwin (perhaps implies nautical or navigation as well as maths interests?). The way this letter is phrased suggests he was involved with the work at 'Court of the Trinity house' and was contacting Flamsteed on their behalf.
Entry notes that the court records are at the Guildhall Library, London but not consulted by the Eds for firm letter date. I'm a long way from London to access. If the records include the debate that prompted Sherwin's query, it perhaps provides a lead on his background?
c) Remaining entries are of Sherwin, and/or his tables and/or footnotes in ca. 27 letters between Flamsteed and Sharp approx. 1705 to late 1706, ie when Sherwin's Tables were first being published. From a browse of those viewable in Amazon feature, they are primarily brief mentions in letters on wider topics and typically concerned with correcting copies of the tables and in particular discussion of delays in obtaining copies promised and in later letters, what appears to be increasing frustration in acquiring copies of the tables.
Others have probably tried, but a search of the online Cambridge and Oxford University alumni gave no records for a Henry Sherwin at that time with various spelling variants. His education, if known, may provide some leads.
The increasingly extensive catalogues searchable online of legal, probate etc info' also gave no leads at origins.net and National Archive, UK websites.
Hope these may be of use in eking out further biographical info' on the seemingly elusive Henry Sherwin!
regards David Walker, Huddersfield, UK