According to The Annotated Mother Goose, "This rhyme would seem to refer to the 'promenade' of marriageable maidens... such a 'promenade' usually took place after church on a Sunday. The 'marriageable maidens' strolled while the young bloods of the town looked them over with an eye to selecting a future wife."

All Around the Green Gravel - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

The Real Mother Goose (1916), illustrated by Blanche Fisher Wright, has this rhyme as follows:

Around the green gravel the grass grows green,
And all the pretty maids are plain to be seen;
Wash them with milk, and clothe them with silk,
And write their names with a pen and ink.

The Annotated Mother Goose (1962), edited by William and Ceil Baring-Gould, has the same version as The Real Mother Goose just above, with the note, "In later versions, the last line reads:

'And the first to go down shall be married.'"

The rhyme makes the most sense putting that all together:

Around the green gravel the grass grows green,
And all the pretty maids are plain to be seen;
Wash them with milk, and clothe them with silk,
And write their names with a pen and ink.
And the first to go down shall be married.

Thanks and Acknowledgements

The illustration comes from Kate Greenaway's Mother Goose or the Old Nursery Rhymes (1881). The 2nd illustration is from Children's Singing Games by Winifred Smith (David Nutt, 1894).

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