Radliff, thank you so much! If I read it right, one of Frederic's siblings was named after paternal grandmother, yes?
So, I tried to figure out if the 'James' who witnessed William's wedding was one of 'my' Jameses. Can't tell. But when I add all the kids of the direct line, I have:
James, b. 1713, Entwistle and Ann Sneddon
Children:Ellis Greenhalgh 27 Nov 1739 b.in Entwistle, Bolton.
James Greenhalgh b. 04 Feb 1747 in Entwistle, Lancashire.
Hannah Greenhalgh b. 1751 in Entwistle, Lancashire.
Thomas Greenhalgh b. 1753 in Entwistle, Lancashire.
Ellis, b. 1739, Entwistle and Mary Marsh
Children:James Greenhalgh was born in Jul 1765 in Turton, Lancashire.
Thomas Greenhalgh b. 22 Feb 1767 in Turton.
Ann Greenhalgh[6] was born about 23 Oct 1768 in Turton.
Robert Greenhalgh b. 26 Aug 1770 in Turton.
William Greenhalgh b. 13 Dec 1772 in Turton.
James, b. 1765, Turton and Sally Crompton
Children:Mary Greenhalgh b. 19 Apr 1786 in Turton
James Greenhalgh b. 10 Mar 1788 in Entwistle, Lancashire.
Thomas Greenhalgh b. May 1790 in Entwistle, Lancashire.
SallySarah Greenhalgh b. 11 Jan 1792 in Entwistle, Lancashire.
William Greenhalgh b. 26 May 1794 in Entwistle, Lancashire.
John Greenhalgh b. 29 Aug 1796 in Entwistle, Lancashire
Ann(e) Greenhalgh b. 19 Aug 1798 in Entwistle, Lancashire.
Robert Greenhalgh b. 08 Jul 1800 in Entwistle, Lancashire.
Matty Greenhalgh b. 27 May 1802 in Entwistle, Lancashire
Thomas Greenhalgh b. 15 Oct 1804 in Edgworth, Lancashire.
Jane Greenhalgh b. 13 Jan 1807 in Turton, Lancashire
Nancy Greenhalgh b. 06 Dec 1808 in Entwistle, Lancashire
Susan Greenhalgh b. 1811 in Turton, Lancashire.
Jonathan Greenhalgh b. 09 Oct 1812 in Turton, Lancashire
James, b. 1788, Entwistle and Ann Ellison
Children:Ann Greenhalgh b. Nov 1814 in Turton, Lancashire.
James Greenhalgh b. Mar 1816 in Turton, Lancashire.
Henry Greenhalgh b. May 1818 in Turton, Lancashire
Ellis Greenhalgh b. Nov 1819 in Turnton, Lancashire
Simeon Greenhalgh b. Oct 1821 in Turton, Lancashire
John Greenhalgh b. ca.1825 in Turton, Lancashire.
Jane Greenhalgh b. ca.1837 in Turton, Lancashire.
Ellen Greenhalgh b. ca.1837 in Turton, Lancashire.
Ellis b. 1819, Turton, England and Martha Lang (Ellis emigrated to US, don't know when)
Child: James Greenhalgh.
So... there are a lot of Jameses, there's no telling if one of them was related.