Hello Brian
For me, it figures that Philips Barry would use Child numbers because he was Harvard-based or educated. As was Kittredge. As you will know, Sharp knew Kittredge and met him when in the USA. I think I am right here.
Child was president of the society that produced American Journal of Folklore. I learned this from a review of one of the parts of his opus at the back of the first every issue. It says it won't be a eulogy, but plainly is! His position explains, I think, why ballads are mentioned in the opening piece in the journal. The introduction to the first volume I have quoted before as showing the 'racialist' thinking of the early folklorists, as do some of the pieces in it.
Not sure how we got here from Harker, but finding the discussion interesting!