Interesting - could you please share the link that shows Carter Bays wrote "Encyclopedia of Antique Sewing Machines"
Every link I've found so far lists his book (all editions) as "Encyclopedia of Early American Sewing Machines"
I'm not trying to be snippy - I've found a lot of misinformation, and sometimes there is a less common book out there and it gets real hard to wade through all the other information out there.
looks like an actual book (the second title) can run a lot of money - if you find one. Probably not any reason to get an early edition unless you collect books along with sewing machines. I collect cooking books, so often I'll pay more for a 1st edition over a later one. But I'm not buying them as reference books. I also like to collect early sewing instruction books - those are fun to read and see how things have changed, even terminology - and for sure the writing style.