second thoughts about Michael's wife's maiden name, unless he married twice. I haven't found him in 1900 yet.
He did marry twice.
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There are a couple of deaths at familysearch.org for Bridget Herons in Philadelphia between 1880 and 1884, both married, but the ages are off from the one on the 1880 census, both older than Michael. Still one of them might be her.
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Here is Michael's 2nd marriage, 27 Nov 1884, to Catherine Johnston
https://www.familysearch.org/ark:/61903/1:1:Q2WN-VPF1---
1900 Census, Philadelphia
at 1067 Front Street
unreadable Herron, 46, born Sep 1853, Ireland, married 15 years, horseshoer
Catherine Herron, 39, born Nov 1860, New Jersey, married 15 years, 1 child, 1 alive,
John Herron, son, 12, born April 1888 in Pennsylvania, father born in Ireland, mother in NJ
Mary Herron, 23, boarder, born July 1876, Pennsylvania, both parents born in Ireland, occupation: operator
https://www.familysearch.org/ark:/61903/1:1:M37V-XMGedited to add:
Mary, 23, looks like Michael's daughter by his 1st wife Bridget.
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also:
Michael's daughter Mary's Social Security Application says her parents were Michael Heron and Bridget Heron. There is a date on her record of December 1936, so she lived that long, at least. Her name was still Heron in 1936.
The date of birth on the application is July 6, 1876, same as the Philadelphia birth records have for her.
source: US SS Applications and Claims Index