The author studies the backward limit and the circumference at spatial infinity of Type II ancient solutions to the Ricci flow on noncompact two-dimensional surfaces. In particular, he proves that the circumference at spatial infinity of such a solution is finite and independent of time and that \(\lim_{t \to -\infty}R_{\max} R(t) >0\) where \(R_{\max}= \sup R(\cdot,t)\).