Assuming James was a miner in Ohio as in Scotland:
OHIO MINES
Ohio’s coal region covers thirty-two counties, and is located to the south and east of a line that would stretch roughly from Portsmouth through Zanesville to Youngstown.
http://www.miningartifacts.org/Ohio-MInes.htmlsee Google maps for locations.
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searching at familysearch.org
last name: Torrance
born: Scotland, 1800 to 1840
residence: Ohio, 1860 to 1870
4 results:
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eliminated: Jennett Torrance, in Cincinnati. no mines in the area, children born 24 years earlier in Indiana
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eliminated: Lilly Dorrance, born 1804, Scotland, living in Jefferson County, Ohio. coal country but husband Samuel Dorrance was born in Pennsylvania, and was a farmer.
https://www.familysearch.org/ark:/61903/1:1:M6VL-3S7-----
maybe: John Torrance, b 20 May 1834, Scotland, parents: Hugh Torrance and Janet Allen, an iron molder, died in New Concord, Muskingum County, 1909.
borderline coal country, but he's not a miner
https://www.familysearch.org/ark:/61903/1:1:X8Z5-PBL-----
maybe: James Torrance, born about 1840, no location. married 1861 in Guernsey County.
rich coal country, but need more information
https://www.familysearch.org/ark:/61903/1:1:XD7Z-XXB=====
same search using Kirkwood
2 results, eliminated both: a lady in Columbus (no coal), a man in Wiliams County (as far from coal as you can get and still be in Ohio.)
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so your best bets, if your James went to Ohio because he knew someone, are:
the James Torrance, b c 1840, who married in Guernsey County.
or
the man who died in Muskingum County. at least you know he was born in Scotland.
Can you trace either of them back to Bothwell Lanark?