  According to a formula by Gordon and Litherland, the signature of a knot K
can be computed as the signature of a Goeritz matrix of K minus a suitable
correction term, read off from the diagram of K. In this article, we consider
the family of two bridge knots K(p/q) and compute the signature of their
Goeritz matrices in terms of the coefficients of the continued fraction
expansion of p/q. In many cases we also compute the value of the correction
term. We show that for every two bridge knot K(p/q), there are "even continued
fraction expansions" of p/q, for which the correction term vanishes, thereby
fully computing the signature of K(p/q). We provide an algorithm for finding
even continued fraction expansions.
  This article is the result of an REU study conducted by the first author
under the direction of the second.
