I’m almost certain that both volumes of Astoria are an octavo binding. There are a number of reasons for this; the chain line orientation, period of printing, and the size of the book.
First, the chain lines. I’ve attached an image, but I wasn’t really able to capture the chain lines and take a picture at the same time, as I was using my phone as a light-source to illuminate them. You can see, very faintly, one chain line beginning between my third and fourth fingers, moving vertically across the page. Given that this book is likely not a Folio (it’s quite small, about the size of a contemporary hardcover novel), the vertical chain lines indicate that the book is an Octavo.
The book was also printed in 1832, a period during which Octavo binding was quite popular for books of this style. In addition, it’s about the size of a leaf from an Octavo gathering if one imagines a sheet of about an armspan.
In terms of format, however, what I found most interesting was less the binding and more that the book was published across two volumes for this printing – was this an economic choice? Were the two volumes sold together? None of the paratextual materials suggest that the two were published or printed at separate dates, nor does the catalog in the end of the second volume suggest that either was sold separately. Why, then, two volumes? And why, as I noted in my previous post, is the map only included in the second? The map does seem to suggest that the two were sold as a set; why would a (likely wealthy) buyer purchase only one copy, knowing that they would not then have access to a map which would complement their reading?
Even the content of the books does not necessarily lend itself to this division – it occurs in a somewhat arbitrary point in the narrative. My suspicion, given the method of including the map, the size of the text on the page, and the style of binding, is that this particular printing was possibly a “deluxe” version of the book, one that might look particularly dashing on the bookshelf in a buyer’s foyer, not unlike the practice popular later in the century of purchasing multi-volume encyclopedias for the home; it is doubtful that these served as anything more than a status symbol for their owner, or an adornment/ornament in the living space. It seems to me that a 2-part version of a historical/travel narrative, by so well-known an author as Washington Irving, and referencing so well-known a man as John Jacob Astor, would be an excellent addition to any ornamental library, and if you might just sign on the dotted line here, Sir or Madam, I can ship it to you for the low price of $19,99 (+ shipping and handling)
The sorts of books mentioned in the rear catalog also seem to confirm this theory: geographies and world maps in large form, with many detailed illustrations, are advertised to readers for purchase by mail order.