Annie,
I see an Edward Dargan recorded at Drummeel Townland, Clonbroney Civil Parish, County Longford, Ireland in the Tithe Applotment Books of County Longford in 1826. This is probably John Edward Dargan's father. What a great age John Edward Dargan lived to. The world he left in 1901 was certainly a very different place to the world he was born into in 1799.
I do not see any Dargans recorded at Drummeel Townland in my 1854 Griffith's Primary Valuation index book, by which time your Dargan family had emigrated to the U.S.
Hoping this is of interest.
All the Best,
David Leahy
davidleahy @ eircom.net
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