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The Elston Press is noted by one author, at least, as being the most important of New York's private presses.
When I stumbled onto one of their books on Google Books, I immediately noticed the strong resemblance to the books of William Morris:
But on a web page about that press, to which I went in order to find information about the types used by that press, I found that they apparently made do with what they could get from ordinary sources, particularly ATF.
Initially, searching for the source of one typeface with an unfamiliar name led me to Lanston Monotype, but in fact the face originated at Barnhart Brothers & Spindler, and continued its existence at ATF, being licensed, like Century Expanded, to Lanston.
But while the web page referenced above indicates that the sample from an Elston Press publication is likely to be in Caslon Old Roman, and an enlarged image on a web site about Lanston Monotype seemed to confirm that, looking in specimen books for Barnhart
and for Lanston Monotype
instead gave the impression of a dated type not close enough to either the original Jenson or to a modification in the spirit of Morris' Golden Type to produce the attractive kind of private press book that Elston produced.
Of course, there could be more than one typeface under the name of Caslon Old Roman. (It was originally called just Old Roman, but a more condensed face was under that name in the BB&S specimen book I looked at.)
Or it could just be subjectivity distorting my perceptions. The same BB&S book gave extended body copy samples of Fifteenth Century, which looked far less bad than I would have expected (another name for that reprobate, Caslon Antique).