GailWhite on Family Tree Circles

My ancestor, William White, b. 1788-d. 1886, was said to have been a direct descendant of Peregrine White. I have not been able to make that link. My William was born in Dutchess County (his obit said Pennsylvania - I think it was NY). He was married twice - first to Lydia Tucker, second to Mary Ann (Margie) Grant. He died in Felix, Grundy County, Illinois.

Does anyone have additional information about William's parents, ancestors? HELP!