“King William” was a very popular play-party song. Below is the full text of the song, as well as two different versions of the game.
King William was King James’s son,
All the royal races run;
Upon his breast he wore a star
Pointing to the Russian war.
Choose to the east, and choose to the west,
Choose the one that you love best;
If she’s not here to take her part,
Choose another with all your heart.
Down on the carpet you shall kneel,
While the grass grows in yon field,
Salute your bride and kiss her sweet,
Rise again upon your feet.
A young man stood with a broad-brimmed hat in his hand, and, as the singing proceeded, presented himself to one of the girls, placing the hat on her head. The pair then marched arm-in-arm until the girl, in her turn, put the hat on the head of another young man; and so the play continued until everyone had been crowned with the hat, and the whole company...marched round,’singing with a will the words over and over.’ Iona and Peter Opie, The Singing Game. New York: Oxford University Press, 1985, 123.
...all the couples join hands and form a big circle, with one odd boy in the center. Those in the circle dance about as the first stanza is sung, but halt to sing the second, while the boy in the middle walks around scrutinizing each girl in turn. At the beginning of the third stanza he kneels before one of the girls, bows his head and kisses her hand. This done, he rises and steps into the line beside her, and the man whose place her takes must go in the center and be the next one to represent King William. Vance Randolph, “The Ozark Play-party,” The Journal of American Folklore 42 (165): 227