General Jack Adams of Georgia / SC

A friend of mine was hunting down around Montecello, Georgia and found a gravestone where a General Jack Adams, his two brothers and daughter were all buried. It said that he was Speaker of the House and sometimes president of the House of Representaives. He moved to Georgia from South Carolina shortly after the Revolution. He was 69 at time of death in 1834. If anyone knows anything, please respond. Seems a shame a man of his stature and his grave was all covered up.