From Rhode Genealogies #1, Genealogies of R.I. Families, Volume I, Cornell Family, page 275:
"In many of the genealogical records of the Cornell Family it has been assumed that Thomas Cornell, son of Thomas of Portsmouth, R.I., married for his first wife Elizabeth Fiscock. Although this statement has several times appeared in print, it might not of itself be a matter of great importance, except that thereupon is based the belief that the family originated in Hertfordshire, where fruitless efforts have been made to trace it.
This belief..is founded on certain entries in the Records of the Reformed Dutch Church of New Amsterdam, where among the Marriages we find: 'Nov. 2, 1642, Thomas Cornelis, j. m. Uyt de Provincie Van Hertfort en Elizabeth Fiscock, j. d. Van Pleymouth in Engelt (N.Y. Gen. Record, VI., 35).
Among the Baptisms in the same church are those of Elizabeth, daughter of Thomas Corenwell, Jan. 12, 1644; Sara, daughter of Thomas Carrnwell, Feb. 21, 1646; Johannes, aged 3 years, and Maria 10 weeks, children of Thomas Carrnwell, Aug. 14, 1650 (Ib. V, 34, 87, 94).
If these records referred to Thomas Cornell of R.I. we should naturally expect to find among the sponsors at some of these baptisms, his sisters Sarah Willett and Rebecca Wolsey, who were married and living in New Amsterdam, and who were present as parents or sponsors at no less than ten baptisms between 1643 and 1650. Instead of these sisters we find among the witnesses to the baptisms Eduart Fiscock, Jan Haes, who married in 1645 Edwart Fiscock's widow, Susanna Breser, probably sister of Henry Bresner, who married a daughter of Smauel Spicer of Gravesend, and Sara Cornelis, who evidently was not the Sarah Cornell who married Thomas Willett, three years before. She apparently belonged to a Dutch Cornelis family then somewhat numerous in New Amsterdam.
...I have found nothing to indicate that Thomas 2nd of R.I. was ever in New Amsterdam. That he was twice married is certain, but he had no children answering to the above (a description of of Elizabeth F's marriage and the children).
No. 9 East 54th Street, New York Charles B. Curtis)"