Biographical Information Concerning Henry Sherwin Henry Sherwin's Mathematical Tables achieved some popularity. The first edition was published ~1706 and the fifth and last in 1771. Some editions were more erroneous than others and the error rate was not monotonically decreasing.  The 1873 Royal Society Report says:
"Sherwin's tables are of historical interest as forming part of the main line of descent from BRIGGS; and the different editions cover the greater part of the last century. The chief succcssion (considering only logarithms of numbers) is BRIGGS, VLACQ, ROE, JOHN NEWTON, SHERWIN, GARDINER; and then there are two branches; viz. HUTTON founded on SHERWIN and CALLET on GARDINER, the editions of VEGA forming an offshoot."
Q: What biographical information exists concerning Henry Sherwin?
 A: Next to nothing is known about the life of Henry Sherwin. He is mentioned by some scholars, for instance in the Sudelbücher of G. C. Lichtenberg, and his Tables were not only in public libraries but also in private possession of scholars like Gauss. But his person is not touched. Encyclopedia Britannica, British National Library, the voluminous work of Moritz Cantor, and even Wikipedia have no biographical data.
There are only few letters, for instance that one sent to Abraham Sharp of March 1704 which in full text is reproduced in
William Cudworth: Life and Correspondence of Abraham Sharp London (1889) and a letter from Edmond Halley of February 1704, belonging to the Macclesfiled Collection
The first edition of Sherwin's ordinary seven-figure tables of logarithms of numbers and trigonometrical functions appeared in 1705-6. It was reprinted in 1710, 1717, 1726, 1742, 1761, and 1771. In 1785 Hutton's new edition of Sherwin's Tables took the leading position and maintained it for a century. An overwiew about the editions and libraries holding Sherwin's Tables is given here. The Tables have been reprinted most recently by Ulan Press and by Forgotten Books.
From the preface of the 1726 edition we can obtain, that Henry Sherwin was alive at that time. The third edition in 1742 was edited by William Gardiner, so Sherwin was certainly no longer alive. The fourth and fifth edition, 1761 and 1771 respectively, were edited by Samuel Clark.
OCLC gives the following bibilographical data: born before 1690, died after 1717 and Janus gives born before 1700, died 1740
From the letter to Sharp we can obtain that, at the beginning of the 18th century, Henry Sherwin lived in London.
A: 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: 
1) 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. 
2) 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 entries from ref. 2 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 to Sharp' (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 haven't to date found a transcript of the latter in the public domain (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 or of any other records of his activities there, 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. Most of the footnotes are just short entries noting that Sherwin's Tables are being referred to. A longer footnote 8 on page 286 is querying if the first edition was in two parts.
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
A: Possible leads that arose in Answer 1 (dated Feb. 10th 2013) and 2 (dated Dec. 18th 2013) have been followed up and offered as a separate Answer.  
Sherwin’s relation to Trinity House, London?
Sherwin’s letter to Flamsteed in 'letter 1015b' cited in Answer 2 was sent on   behalf of 'The Brotherhood’ of Trinity House (associated with pilotage,   lighthouses, navigation etc.). The Trinity House Records Manager, Neil Jones,   kindly checked their records and remarked via email:
"I have scoured through the list of Younger Brethren from 1706 back to 1670, and have found no mention of Sherwin. Likewise for the list of Elder Brethren." Sherwin was presumably writing on behalf of Trinity House brotherhood in another role.
The Records Manager notes that the London Metropolitan Archives hold a large amount of Trinity House records. The Court minutes, 1661-date (Ms 30004) was one suggested.
I don't have ready access to them but they may provide some insight into Sherwin's activities with Trinity House and possibly his background.  
Letters: Five letters to or from Sherwin have been reported to date, three have transcripts online in the public domain as mentioned in Answer 1 and 2. My own attempts at transcripts of the other two letters are offered in the Appendix 1 and 2 from hi-res photoscans of the originals. Any comments on insights which the letters may reveal are welcomed.   
Transcript of letter from Edmond Halley to Henry Sherwin dated Feb. 18 1704/5. (See Appendix 1)
Cited in Answer 1. Discusses edits of Halley's chapters 'Of Compound Interest and Annuities' and 'Constructing the Logarithms' in the Tables. The text suggested for the latter closely follows the text in the Tables on p.14. No address for Sherwin included nor any insights into Sherwin's background.   
Transcript of letter from Henry Sherwin to Abraham Sharp dated Nov. 20 1705.  (See Appendix 2)
Cited in Answer 2. Discusses some promise of books by Sherwin to Sharp. The reason stated for Sherwin's planned trip to Jamaica on a postal 'paquet boat' from Plymouth seems ambiguous: "having an invitation to the [best busines] I could either expect or desire" - could mean commercial, scientific, personal? Uncertain whether the mention of being at God's disposal was just a turn of phrase or if suggests a theological background? (No record exists for a Henry Sherwin in the Clergy of the Church of England Database online.)  
'Mr. Yarwell' is likely John Yarwell a noted scientific instrument maker of the time recorded as supplying lenses to Sharp. No lead on the 'Joshua Reyner' to date or 'Mr. Stanfield'. There seems to be extensive published research on the British postal packet boats, possibly to a likely named vessel and captain for a given date, but uncertain if these include records of passengers to confirm if Sherwin did travel, or if reciprocal info' on ship arrivals in Jamaica.  
Speculation: Did Sherwin successfully travel to and arrive in Jamaica, if so, did he later return to UK or die there?
There is an extensive list of Jamaican wills online from 1655-1816 at 
http://www.rootsweb.ancestry.com/~jamwgw/sz.htm and one of these is to a Henry Sherwin 1708-9 (“RGO/SpTw/Liber 12, Folio 5, 1708-1709”). It is the only Sherwin listed in this wide date range perhaps suggesting it was not that common a local surname amongst either Jamaican residents or visitors of a status to leave a will. Admittedly speculative and could well be a coincidence that there’s a will for another Henry Sherwin in Jamaica a few years after the ‘Tables Sherwin’ was planning to go there.   
For it to be this Sherwin, would the Publishers / Printers have instigated the sometimes extensive Errata lists and corrections in the 1705/6, 1717 and 1726 editions/reprints before Gardiner was editing the third edition in 1742? Although comparing the five reprints/editions at www.archive.org and my own of 1726, Sherwin's signed July 1705 dated Dedication / Preface / Content remains unchanged up to and including the 1726 edition. Typically uncommented Errata were inserted up to that date, although one Errata entry in 1717 does have an unsigned comment, which if by Sherwin rather than Publishers would rule out the death in Jamaica. Quote below.  
1717 edition after p.69. "These Tables having been carefully Examined and the Errata Collected into this Page; if therefore the Reader pleased to amend the Faults in the Tables with his pleasure we presume we may recommend them to the World as the most perfect Tables this Kind now Extant."  
If the will was checked, there's no guarantee it has contents that could confirm or rule out the 'Tables Sherwin'. A death record if available may also be worth checking.  
David Walker
Appendix 1
Letter from Edmond Halley, Oxford to Henry Sherwin dated Feb. 18 1704/5
Transcript from library supplied scan with original spelling, puctuation. Text in square brackets uncertain. Halley's underlining to indicate italics in Sherwin's Tables. Final text in curled brackets was written along left edge of single first sheet, not clear what order to be read. 
The Macclesfield Collection. Papers of John Flamsteed.
Letter from Edmond Halley to Henry Sherwin
Dated Feb. 18 1704/5
Classmark: MS Add.9597/13/6/88 
Location: Cambridge University Library  
Oxon Feb 18o 1704[/5]  
Sr
I received yours and will take care to give you
your papers about annuitys as they ought to be.
In the case you proposed tis plain otherwise than
I took it, for by forbearance I meant that the
annuity had been obtained after due, which you sup=
posed, as to the last year, but then due. Which occasions
all the disputes between us. If that be the question
tis rather more easy than the other and I believe
your rules are right. And if I have given trouble
by mistaking you, I will make you amends by the
resolutions of the two affected cases, you want.
In the meantime that your proofs may go on, pleased
to insert in your pag. 14 L.29 instead of the beginning of the
break. This being laid down, it is obvious that insert
"these words". But if instead of supposing the Logarithms
"composed of a number of equall ratiunculae proportionall
"to each ratio, [n]or shall take the ratio of Unity to
"any number to consist always of the same infinite
"number of ratiunculae, their magnitudes in this case
"will be as their number in the former. Wherefore if
"between Unity and any number proposed &C this I believe
 will make it more clear. I shall be in town about [yc]
beginning of march which I suppose may time enough
 {for your Interest paper.  
Either
pray leave out my Captainship
in your title.
I am Sr
Your humble Servt.
E. Halley}  
Or
I am Sr pray leave out my Captainship
in your title.
Your humble Servt.
E. Halley}  
Appendix 2
Letter from Henry Sherwin to Abraham Sharp Dated Nov. 20 1705  
Transcript from library supplied scan with original spelling, puctuation and crossings out. Text in square brackets uncertain. 
Papers of John Flamsteed
Letter from Henry Sherwin to Abraham Sharp
Dated Nov. 20 1705
Classmark: RGO 1/69/C f.111rv
Location: Cambridge University Library  
Mr. Abr. Sharp                                       London Nov. 20. 1705  
Sr. I have now before me your obleidging letter
dated Sept. 18 which I had answerd sooner
but that I was in dayly expectation to
have sent you some books  but as I am
disappointed so I cant helpe you for I [asure]
you I never had but 6 books and I have
given 4 of them away I could tell a long
storie of it but I forbear onely the
Bookseller being poor he has [pawnd] them
all, this is the Case I have [perswaded] him
However [I a] present you with two of them
which I indever shall goe from hence
by ye Carrier to Mr. [Stanfeild] next [Fryday]
I will not promise because he seldome keeps
his word, I will indever to be the bearer of them
myselfe.  
It's time I invited a Correspondence with me
at London and where ever I am in my freindship
shall be the same but since then it has pleased
God (at whose disposall I am) to make it expedient
for me to live some time at Jemeica having
the an invitation to the [best busines] I could
either expect or desire where if I can anyway 
Transcript note: letter continued overleaf 
for I must be their to goe away in the Paquet
boate that carries the letters from London the
last thursday in this months (for their is paquet
goes from Plimo to the west indies [the last  -
?] after the arrivall there of the [last]
Let Thursdays letters from London every
month) and I must set out from London on
Wednesday 28 inst in the morning, I take
my leave at present wishing that hereafter
I may be servicable unto you, in the least
matters, and can never but value my selfe
upon yr freindship. Mr. Joshua Reyner lives
at Long Houghton near Wakefeild Yorkshire
upon the Receipt of your letter I went to Mr.
Yarwell who said he did not know what was
wanting in your last parcell but if you
would write what would be most acceptable
he would send it you, if you write to me
to be in London on Monday next pray
write a letter to him at the bottom I will
deliver it him pray excuse my hast and
give me leave to subscribe my selfe  
Sr. your obleidgd freind
and humble Servt
Hen. Sherwin  
A: I have obtained a copy of the will to a Henry Sherwin dated July 19th 1708, Jamaica mentioned in previous answer to see if its contents suggested it was the author of the tables. Sherwin was known to have planned a trip to Jamaica on a packet boat at the end of November 1705. Since last answer, to date one family of Sherwin has been found recorded at the time from familysearch.org but no mention of a native Henry Sherwin.
Some key points below, parts of the handwriting were hard to interpret and/or text went into ledger gutter. [ ...?...] = undecipherable word or loss in gutter.

*

*will transcribed into ledger, i.e. handwriting comparison to Sherwin's letters not possible


*lived in the parish of Kingston


*'That everyone of our principals and correspondents in England be first remitted [...?...] [a]ccording to their orders as if I also [...?...]'


*residue of estate to 'Beloved Brother [gap] Sherwin of Staples Inn London attorney at Law, and my very good friend Thomas Smith [...?...] in Artillery Row of Buttolph bishopgate in London' ..... 'to pay all my debts in England and the residue to be disposed of, according [...?...] Will I made in London November 1705, remaining in the hands of my said brother'.
Notes on will, comments welcomed:

*

*This Sherwin in Jamaica has well establised links with London, England, i.e. a brother and other contacts - suggesting not native to Jamaica?

*The will left with brother in London November 1705 would fit in well with Sherwin deciding to make a will immediately before his planned potentially hazardous trip to Jamaica at the end of that month.

*Is the London will still in existence, if so, a possible lead. Attempts at online searches have not been fruitful to date.

*Attempts to find packet boat passenger lists at the time to confirm he went to Jamaica unsuccessful to date.

*Is the London will evidence that this may be the Henry Sherwin who compiled the tables, but no firm contents of the Jamaican will to support this.

*My thanks to local Jamaican researcher Ann Marie Lazarus who obtained a facsimile of the will and who provided information on its transcription into a ledger. I don't currently have permission to put the will into the public domain but can email a copy to anyone interested for personal use.

