Yes, if the book was published in 1913, the copyright has expired.
You can freely scan it in and publish it. But note you have NO copyright to the material. You didn't write it. Copyright law gives rights to the AUTHOR of a work. It doesn't matter how much effort you went to scanning it in and formatting it. Nothing in copyright law says that that gives you any rights.
If you add anything creative of your own, you would own the copyright to the new material. Like if you drew new illustrations and added them to the book. Or if you included your own commentary. Or you added explanatory footnotes. That still wouldn't give you rights to the original text, but you would own the new material.
But in the same vein, if the book was originally published in 1913, but the copy you have includes material added by a later editor, that later material might still be protected by copyright.
Just a side thought, it occurs to me that if I was going to republish a public domain book, a good idea would be to add footnotes. If my footnotes appear on almost every page, then no one else could just take my electronic files and sell them himself. He'd have to go through page by page and purge out all the footnotes. Make it hard for someone to "borrow" your work and you might scare them off.