I have been able to trace Mahlon D. Adams back to Jeremy Adams, born 1604/5 England and immigrated to Cambridge, Mass. 1632.I have also traced his wife, Judith W. (nee Mathis), back to the "Great" John Mathis, born 1690, Wales, immigrated c1700, and moved from Oyster Bay to settle in the Bass River area, Little Egg Harbor, NJ. Both Mahlon and Judith were born in Little Egg Harbor Township.
An excellent source for information on the Mathis family and other early families of the Bass River area (L.E.H.) is the book "History of Little Egg Harbor Township, Burlington Co., NJ" by Leah Blackman, 1963, originally written for the West Jersey Surveyors Assoc, (re-issued by the Great John Mathis Foundation), Trenton Printing, 1963. Mahlon Adams can also be found on pg 21 in the book "Jeremy Adams of Cambridge, MA and Hartford, CT" by A. Adams, republished with corrections 1955.