"Any one who has ever used a dash churn will have no difficulty in recognizing the rhythmic activity which gave the impulse to this rhyme, which, no doubt, originally was accompanied with song..." -Katharine Elizabeth Dopp

Notes

Quote at top from Katharine Elizabeth Dopp, The Place of Industries in Elementary Education
(1902)

Percy B. Green called this an "Essex Charm for a Churn, 1650 A.D." in his book "A History of Nursery Rhymes" (published in 1899).

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Here's another version of this rhyme from Cole's Funny Picture Book No. 1, written and compiled by Edward William Cole (1st Published in 1879 in Melbourne, Australia):

Churn, Butter, Churn!

Churn, butter, churn! come, butter, come!
Peter stands at the gate,
Waiting for a butter cake;
Come, butter, come!