I have authored a book using images that I have fund on line.?

It doesn't matter whether you are selling your book or giving it away. You cannot use someone else's copyrighted works without their permission. Making a due diligent effort to contact them isn't good enough. Even if they aren't tagged as being copyrighted, that doesn't mean they're in the public domain. Just because the original copyright holder has passed away doesn't mean their no longer copyrighted. Copyrights are inheritable and are just as enforceable after they've been transferred.

If someone does have a registers copyright on one of the images you use, your legal expenses could easily be in the six figure range.

It's really not worth it. You're better off seeking pictures that you know are in the public domain or find pictures where the copyright holder is contactable (e.g. a stock photo company).

Sorry if I'm sounding all downer, but this is one mess you really don't want to get yourself into.

All original works of authorship are automatically copyright protected at the moment of creation. Even if not all works you found had copyright "noted," they almost certainly are all protected. There is no requirement that copyright be "noted" for there to be protection.

You must obtain the permission of all the copyright holders, or else you cannot legally use the material. The damages for even a single instance can be enormous. If you publish a book with an unauthorized image, you can permanently damage a creator's ability to use it elsewhere. You can even cause very significant damage to their reputation.

Once you start putting infringing material out there, you don't ever get it back. It is highly unlikely you can set aside enough funds to cover the financial damages you can do. And if you do start selling such a thing, your infringement can even rise to a criminal level.

Do NOT do anything further with what you've done. Get permission for the images, or else remove every single one. You can replace them with images for which you've received proper permission.

Try to look for photos like you see on Wikipedia, that are GNU or Public License. Many web sites use photos, but those are often used illegally. Copyright infringement is no joke. Always get permission.

The other answers here have been abusive, I understand, but look up copyright law. Wikipedia has a nice article, making it understandable. Realize that anything you create (and a photographer creates) only expires 70 years after their death.

So, don't chance it.

Well that is stupid.

You can't just take other people's art and pretend that because you tried to find them you have a right to it.

The first guy who files a suit will take very dime you have. When you use something that isn't yours, you don't get to set a price, they and the court does.

So you might as well spend it as it comes in, because you're going to end up broke anyways.

You characterize it as having your hands tied. In fact, your hands are trying to steal something that does not belong to you, and you have no complaint if you are unable to acquire these images legally. You're not supposed to be able to. If you own something, others are not allowed to use it without your permission either.

Set aside a portion? Are you kidding? You're aware you could be sued in court for thousands of dollars, right?