When I speak of my background, I am speaking of something that is as dead as the Dodo,"" says Mrs. Homans at the outset of her engaging memoir. The great granddaughter of John Quincy Adams, she grew up in Quincy, where the garden of the ""Old House"" on Adams Street still boasted the York rose Abigail the first (""the best of the lot"" according to her father) brought home from Europe. The author lost her charming, civilized father when she was still young. She came under the varying benevolences of her urbane Uncle Henry and her brusque, shy Uncle Brooks. Uncle Henry showed her about Washington and included her in his distinctive and distinguished social life at home and abroad. Uncle Brooks took her in hand and to Paris, where in accordance with his belief in convent-bred women, he entrusted her to the Sacre Coeur while he returned home to fight the Spanish American War in his own way. After a memorable summer with Uncle Henry and the Hays at ""Surrenden Dering,"" in Kent, it was time to return to America for a Boston debut which ""at the turn of the century was a pretty momentous affair."" Her fondness for Uncle Brooks was not catching--her husband dutifully repeated to himself ""Remember to like Mr. Adams"" -- but it and the era and a unique American family come across in this modest recall which has style but not side. A stich in the Adams sampler.