Thanks Malcolm for that online link to Eckenstein's Comparative Studies in Nursery Rhymes book.
I like reading books and articles about comparative folklore and rhymes. And with regard to some of Eckenstein's conclusions, l still believe. So call me credulous :o)
Also, I think that Lina Eckenstein was one heck of a woman for her day and time.
I haven't read this book yet, but here's a link to the book that seems to be most often cited that Eckenstein wrote: