People often are recorded in old newspapers with a nickname instead of their given name. There are countless examples; often used are Bill for William, Jack for John, Liz for Elizabeth, etc. Make sure that you not only search for "William Jones", but also with a given name, such as Bill, Will, or Willie. You will get lots more results. Here is a list of common ones.
Give it a try. You will be surprised how many more search results that you get!