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This typeface, named Eastman
appeared in the 1896 ATF specimen book. It didn't make it into the 1897 one, or any later ones, apparently.
While it wouldn't be mistaken for any of those faces, it seems to anticipate some of the features of both Times Roman and Perpetua.
I had been thinking about this because I thought I had seen an image of William Starling Burgess' original sketches on the Internet somewhere, but I couldn't find them again; I wanted to compare them, rather than the face Starling, to Times Roman.