@Steve - there are places such as the UK where authors receive royalty payments when their books are distributed via Library Loan. In the UK they are known as the Public Lending Rights payments.
Such as in this article
http://www.guardian.co.uk/books/2010...t-payments-cut
Libraries in the US have no such program. Libraries buy their books and authors receive their royalty from that sale, but nothing further in regards to each time the book is then loaned.