Arcelaus Adams was the son of John Adams and Elizabeth Woodman. My information: Archelaus, son of Lieutenant John Adams, was born in 1674, at Ipswich, Massachusetts, died at Salisbury. He settled in Newbury, Massachusetts. He married (first) March 10, 1698, Sarah March, widow, who died March 4, 1718, aged forty-five years. He married (second) March 4, 1719, Sarah Greene, who died September 5, 1740. He married (third) August 26, 1741, Mrs. Dorothy Clement, who died October 7, 1741, aged thirty-two years. Children by first wife, born at Newbury: Sarah, born January 25, 1699; Mary, October 29, 1701; John, mentioned below; Elizabeth, May 29, 1707; Samuel, April 29, 1710; Stephen, March 14, 1712; Archelaus, November 21, 1714, married Mrs. Mary Pierson; Nathaniel, June 29, 1717, died September 1, 1717.
source: New England Families Genealogical and Memorial: Third Series, Volume III. Cutter, William Richard. 1915. Reprint, Baltimore: Genealogical Publishing Co., Inc., 1996. International Standard Book Number: 0-8063-4612-4
(Note: John was not a lieutenant. Archelaus was attached to the wrong grandparents at this source.)
By the way, he is the grandson of Robert and Eleanor Adams and there is alot of information about their line!!