*This seems to be referring to the Clyde River in western Scotland.
The mouth of a river is the lower point of the river where it drains into an ocean, sea, other body of water.

This rhyme can not be found in one of the most comprehensive collections of nursery rhymes called The Oxford Dictionary of Nursery Rhymes (1951). However, it can be found in The Annotated Mother Goose (1962), in the section entitled "Modern Mother Goose". I believe it was new to the early 20th century. I found it in The Little Mother Goose (1912).

If anyone knows anything else about the origin of this rhyme, or if you recall hearing it growing up, please email me and let me know. -Mama Lisa

Thanks and Acknowledgements

This rhyme can be found in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, and printed in the USA.