The Cornells were apparently travelling in the same circles in Portsmouth and then on to New Jersey as well!
http://members.cox.net/mountgen/cornell.html
"(1) Thomas CORNELL [Sr.], b. about 1594 probably in Essex, England, d. about 1657 in Portsmouth, RI; m., unknown in England, to Rebecca BRIGGS? (b. about 1600, d. 8 Feb 1673); they resided first in Boston, MA, then in Portsmouth, RI, then in Cornell's Neck, New Amsterdam (now Westchester Co., NY), then back in Portsmouth, RI; their children:
i. Sarah, b. about Mar 1623, d. 1703, m. 1st Thomas WILLETT,
2nd Charles BRIDGES, 3rd John LAWRENCE Jr.;
ii. William, b. about Apr 1625, d. Jan 1628;
iii. Richard, b. about 1626, d. Nov 1694, m. Elizabeth JESSUP;
[#2] iv. Thomas [Jr.], b. about Oct 1627, d. 23 May 1673, m. 1st
Elizabeth ____, 2nd Sarah EARLE;
v. Rebecca, b. about Jan 1630, d. about 4 Feb 1713, m. George WOOLSEY;
vi. Elizabeth, b. about May 1631, d. before 1637;
vii. Kelame, b. about 1631-32, d. Oct 1632;
viii. William, b. about Dec 1632;
ix. John, b. about Jun 1634, d. about 1704, m. Mary RUSSELL;
x. Ann, b. about Aug 1635, m. Thomas KENT;
xi. Elizabeth, b. about Jan 1637, d. 1708, m. Christopher ALMY;
xii. Samuel, b. about 1642, d. Feb 1715, m. Grissell?;
xiii. Joshua, b. unknown;
xiv. Mary, b. unknown.
Thomas [Sr.] was a constable for Portsmouth in 1641 and an ensign in the Portsmouth Militia 1642-44.
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(2) Thomas CORNELL [Jr.], b. about Oct 1627 probably in Essex, England, d. 23 May 1673 in Newport, RI; m. 1st to Elizabeth ____; they resided in Portsmouth, RI; their children:
i. Stephen, b. about 1656, d. before 1723, m. Hannah MOSHER / HARDING;
ii. Thomas [III], b. about 1657, d. 14 Oct 1714, m. Susannah LAWTON;
[#3] iii. John [Sr.], b. about 1660, d. unknown, m. Hannah SMITH;
iv. Edward, b. unknown, d. 1708, m. Mary ____.
Thomas CORNELL [Jr]. m. 2nd Sarah EARLE (b. unknown; daughter of Ralph EARLE & Joan AUSTIN); their children:
v. Sarah, b. about 1668, d. 25 Jun 1748, m. 1st John COLE,
2nd Zaccheus BUTTS;
vi. (daughter), b. unknown;
vii. Innocent, b. about 1673, m. Richard BORDEN.
Thomas Jr. was a Deputy to the General Assembly of RI and held other government posts...........
Thomas' siblings..........
"(4) William CORNELL [Sr.], b. about 1693 probably in Hempstead, Queens Co., NY, d. 30 Mar 1749 in Hopewell Twsp., Hunterdon Co., NJ; m. to wife unknown (possibly Elizabeth SMITH, daughter of Jeremiah & Anne SMITH); he resided in Hopewell Twsp., Hunterdon Co. [now Mercer Co.], NJ; his children:
i. Smith, b. 1718, d. 1772, m. Phebe ____;
ii. William [Jr.], b. about 1720, d. 1791, m. Mary ____;
iii. Hannah, b. about 1722, m. Edward? HUNT?;
iv. Elizabeth, b. about 1723, m. Francis BLACKWELL;
v. Mary, b. about 1724, d. 15 Aug 1813, m. William MERRELL;
[#5] vi. John, b. about 1725, d. after 1749;
vii. Benjamin, b. about 1726, d. Jan 1787;
viii. Sarah, b. about 1728;
ix. Charity, b. about 1730, m. Edward HUNT;
x. Martha, b. about 1735;
xi. Edward, b. 22 Feb 1737, d. 30 Apr 1784, m. Sarah BURT.
William [Sr.] was a justice for Hunterdon Co. in 1728.
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(5) ?John CORNELL, b. about 1725, d. after 1749; m. to wife unknown; he resided in Hopewell Twsp., Hunterdon Co. [now Mercer Co.], NJ; his children:
[#6] i. Martha, b. about 1750, d. 14 Mar 1841, m. David BALDWIN;
ii. William, b. unknown;
iii. Abraham, b. unknown;
iv. Benjamin, b. unknown;
v. Jonathan, b. unknown.
Benjamin CORNELL (#4-vii above) mentions in his will his "niece Martha CORNELL, wife of David BALDWIN". Thus, it appears that Martha is a granddaughter of William CORNELL [Sr.] I believe I have narrowed down the possibilities for her father to either John (#5 above) or an unknown son not mentioned in William [Sr.]'s will.
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(6) Martha CORNELL, b. about 1750 probably in Hopewell Twsp., Hunterdon Co., NJ, d. 14 Mar 1841 in Hopewell Twsp., Mercer Co., NJ; m., 30 May 1775 in Hopewell Twsp., Hunterdon Co., NJ, to David BALDWIN (b. 16 Feb 1742, d. 18 Jan 1834). "
So there is supportive evidence for Cornell as well. In one place I saw Wardele mentioned as alias for Cornell!
However, Mother's notes have Innocent Wardell as daughter of William. I have no idea where she got that information and that is a problem with mother's notes sometimes. I guess we need to check to see if William actually had a daughter Innocent of the correct age.