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Melanie, here are a few bits which might be useful...

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From IOM wills index:

HARPER William 1795- Bra E d 106404

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link to images:

www.familysearch.org/ark:/61903/3:1:3Q9M-CSNH-Q9SH-3?cat=234410

images 681 to 690

Administration papers (he died intestate)

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From Frances’s Manx Note Book will summaries---( but it’s unlikely that these two are connected to your William Harpur, though):
1772-3 E d HARPER Ann BERKLEY d 18 jul 1772;only surv ch ann harper;inv
1772-3 E d HARPER Thomas d mar 1772 coast guinea on board Patsey liverpool capt peterson;due goods gmo ann 1770;only sis ann

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Ann Harper and Thomas Harper images:

www.familysearch.org/ark:/61903/3:1:3Q9M-CSND-RJBM?i=990&cat=234410

images 991 to 993

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Have you come across this baptism for an illegitimate child ? (copied from familysearch):

Name: Caroline Anne Harper • Edit
Event Type: Christening
Event Date: 18 Apr 1788 • Edit
Event Place: St George's, Douglas, Isle of Man • Edit
Gender: Female
Father's Name: Willm Harper • Edit
Mother's Name: Anne Willson Kelly

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I’ll attach a copy of the entry.

Caroline was buried 31 March 1789.

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Then there’s this burial of a widow who possibly could have been William’s mother ?

Name:Catherine Harpur • Edit
Event Type:Burial
Event Date:04 Feb 1777 • Edit
Event Place:Braddan, Isle of Man • Edit
Gender:Female

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Does anyone have access to 1788 presentments to see if there are any details for the William Harper who was the father of baby Caroline ?

Jean C