This is taken from the book "Campbell Chronicles & Family Sketches" by Ruth Early. Take it all with a grain of salt because this old book is very flawed.
"William Irvine married Polly Anthony and died in 1767, when his only child,
William, Jr., was very small. His widow-married Robert Cowan, who was supposed
to be related to William Cowan, opposing lawyer to Patrick Henry in the case of
Hook against Venable. Wm. Irvine, Sr., built his home, Otter, near Otter river
about seven miles from New London, and was one of Bedford's justices. Wm.
Irvine, Jr., married Martha, the daughter of Jesse Burton, who helped to lay out
Lynchburg; their children were:-Edmund, attorney-at-law, moved to Rocky Mount,
Va.;—Judge Robert, moved to West Virginia;—James, remained in Campbell
county;—Jesse married Clementina, daughter of Col. Wm. and Anne
Carrington-Cabell, of Union Hill, Nelson county. Children of Jesse and
Clementina Irvine were:—Wm. C., m. Mary A., dau. of Meriwether Lewis, of Milton,
N. C.;-Ann C., m. David Flournoy;—Edward C., m., 1st, Jane, dau. of Meriwether
Lewis; m., 2nd, Mrs. Merrett. Edw. C. Irvine served in the 2nd Va. Cav., C. S.
A., was severely wounded in a battle in 1863, and represented Campbell in the
House of Delegates, 1873-74;—Sarah C., m. Judge Asa Dickinson of Prince Edward
county;—Mary E., m. Philip D. Christian of Lynchburg;—Jesse, m. Margaret, dau.
of Dr. Paul C. Venable; he was captain of a cavalry company in Col. Winston
Radford's Regiment, C. S. A., and lost a limb in a charge of his company;—Juliet
M., m. Rev. David W. Shanks (his 2nd wife); Margaret F., m. Thomas Rosser,
relative of Gen. Rosser, of Campbell county.—Alexander, m. Lockie T., dau. of
Capt. Henry Brown, a Revolutionary soldier, and their children were:—John B., of
Kvington, member of llth Va. Cav. under Gens. J. K. B. Stewart and Jubal A.
Early;—Wm. Henry m. Anna, dau. of Col. Jas. Sinkler (of Upper St. Johns,
Berkeley Parish, S. C., and his wife, Anna, dau. of Col. John Huger, of
Charleston, S. C.,) and had sons, Alexander and Guilford Huger of West Virginia
and Dr. James Sinkler Irvine of Otter., who married Evie, dau. of Maj. Fleming
Saunders and his wife, Mary Gwaphmey of Flat Creek." end quote.
I have not studied the later generations of this family and I doubt if they are my kin. The William Irvine Jr. who married Martha Burton, had a sister who married a Bradfute. William Irvine Jr had a son Jesse who married Clementina Cabell. They had several children and probably many grandchildren. Your Addison may be a grandchild of Jesse Irvine or one of his brothers. I am making a wild, speculative guess about this based solely on the similarity of the names. I have studied all the Irvines, Irvins, and Irwins of Bedford/Campbell county, Virginia, but mostly in the Colonial era prior to the Rev. War. Your Addison seems to "fit in" with this line. But, again, I am strictly making an educated guess. Regardless, If you know of a modern day male Irvine from this family, I would love to see his DNA profile if he would get tested. Edwin Dean Irvin