I have the following information from the book "Martin Dial and Related Familes with their Ancestors, Descendants and Connections" published by Hastings Harrison in 1959.
There is a small section within this work on the Abercrombie connection with Martin Dial (pg. 233). I have reproduced it verbatim as it exists in this publication.
---start of Abercrombie section----
Rebecca Abercrombie who m. Hastings Dial, and Chrystie Abercrombie who m. his youngest brother, Martin Dial, were daughters of James Abercrombie, Jr. Some say that their mother was Elizabeth Sherrill of Lord Baltimore's Coloney of Md., their father's second wife. Old records left by Geo. W. Dial, of Detroit, owned by Miss Rebecca Dial, a dau. of the late S.C. U.S. Senator, Nathaniel B. Dial, show their mother's name as Hannah Pickard, and as their father's first wife. Since I have found no conclusive documentation of the maiden name of Chrystie and Rebecca Abercrombie's mother, I prefer to let others debate and resolve the matter.
Veteran students disagree as to who was the father of James Abercrombie, Jr. Some say that his father was Sir James Abercrombie of Scotland, the British Attorney General of the Colony of S.C. from 1732 to 1744. They say that Sir James Abercrombie's wife was Mary Gordon, that both of them were born and died in Scotland. I have no proof of this tradition but I believe it is true. There are some who claim that it has been established that Sir James Abercrombie, the Colonial Attorney General, was a bachelor! I do not believe that he was. It is generally agreed that the father of Chrystie Abercrombie who m. Martin Dial, and Rebecca Abercrombie, who m. Hastings Dial was James Abercrombie, Jr., and that their grandfather was James Abercrombie of the Colony of S.C. Some say that Mary Gordon's father was Sir Arthur Straylock of Scotland.
There are those who give references to support their claim that among "our" ancestral Abercrombie families was the Abercrombie family of Burkenbog in the Shire of Banff, Scotland, including Humphrey de Abercrombie who obtained a charter from King Robert Bruce in 1315. They cite "Burk's Peerage and Barrentage" to show that "our" Sir James Abercrombie was a son of Sir Alexander of Birkenbog. Having not been able to consult the references given or otherwise verify these claims I simply submit them as interesting surmises. It is generally acknowledged that the children of "our" James Abercrombie, Jr., whose Wife or wives I have been unable positively to identify were:
1. Isabel Abercrombie -m. _____ Blackwell of Va. 2. Mary Abercrombie -m. _____ Dial of N.C. 3. Thomas Abercrombie -m. Mrs. Ruckett of N.C. 4. Isaac Abercrombie - granted land in Laurens Dist., S.C. in 1769; returned to N. C. 5. John Abercrombie. 6. James Bercrombie. 7. Alexander Abercrombie. 8. Charles Abercrombie. 9. Colvill Abercrombie. 10. Rebecca Abercrombie -m. Hastings Dial. ll. Chrystie Abercrombie -m. Martin Dial.
George Troy Jones of Rt. 3, Laurens Co., S.C., a descendant of James Abercrombie, Jr., through his son, James, and his granddau., Hannah Abercrombie (Mrs. Elias Brock), whose family settled in Calhoun Co., Ala., has provided me a wealth of data on the S.C., Ga., Ala. and Texas progeny of our ancient ancestor, James Abercrombie, Jr. I deeply regret that they cannot be included in this supplement to "Martin Dial and Related Families." If a second edition is published, perhaps these invaluable data that he has supplied can be included. Troy Jones was b. Dec 16, 1892 in Laurens Co., S.C. He married Mrs. Frances Garrett in 1953. She died in 1954. His parents are Green J. and Emma Josephine (Fowler) Jones.