Which famous nursery rhyme mentions a bough?

"Rock a by baby" is a famous nursery rhyme that mothers have sung or quoted to their children for many years. There are many versions of the rhyme that was first printed in Mother goose's Melody. The version of the nursery rhyme that is most frequently quoted is as follows: "Rock a by baby in the tree top. When the wind blows, the cradle will rock. When the bough breaks, the cradle will fall and down will fall baby, cradle and all." I have heard many mothers change these Words to say and "mother will catch you, cradle and all". This later version is more assuring to both the baby and the mother.