How do I know that a melody I have composed isn't already used?

I've just signed on to compose film scores for silent films, and the first one they sent me was a western. This is good, because western themes are easy to compose, but at the same time, it's bad because they are SO easy to compose, that I can never be sure if the theme I have written isn't already out there some where. Is there a way to find out for sure?