This note is a sequel to a former one, a knowledge of which will be assumed. We here develop the methods of that note to give a proof of Jordan's Theorem. We write ind C (P) for 1/2π times the absolute value of the change in log (z − P) as z describes the continuous arc C. If C is a Jordan curve, ind C (P) is either 0 or 1. Further, if C is a polygonal line, the index is a continuous function of P. If C is a closed continuous curve, interior to a circle to which P is exterior, then ind C (P) = 0.