  We explore the connection between Hilbertian metrics and positive definite
kernels on the real line. In particular, we look at a well-known
characterization of translation invariant Hilbertian metrics on the real line
by von Neumann and Schoenberg (1941). Using this result we are able to give an
alternate proof of Bochner's theorem for translation invariant positive
definite kernels on the real line (Rudin, 1962).
