Do you think these books are in the public domain?

I collect old math books, and I have several ranging from 50 to 200 years old. I would like to scan a few of them (none newer than roughly 75 years old) in their entirety and post the images online for people to use and look at. None of the books I want to scan are still in print, and I am fairly certain that all of the authors are deceased. I looked at the copyright office's website, and it said that books copyrighted before 1978 were not in the online database and required the services of the office (at a whopping $75 per hour or fraction of an hour for an informal search, plus an additional $80 per hour for certified results). Is there any law on the books that would spare me the expense of performing such a search (i.e., prove that the books are in the public domain)? Also, if you have experience with these searches, about how many titles do you expect they can find in one hour? I may as well get my money's worth if I have to pay them for a whole hour. Thanks in advance!

That's a good idea Lisa. Some of the publishers do not seem to be around anymore, at least not under the same names. Do you know where I can find out what happened to the companies, or who bought them?

All works published in the United States before 1923 are in the public domain. All other works are copyrighted until 70 years after the copyright holder's death for an individual author or 95 years for corporate authors.

I can't site a law for you, but I do know that many the copyrights for many books are owned by the publisher, not the author. So, even though the author is deceased, you could still get into trouble with the publisher. If it were me, I would contact the publisher.