  In this paper, we prove that Wright's equation $y'(t) = - \alpha y(t-1) \{1 +
y(t)\}$ has a unique slowly oscillating periodic solution for parameter values
$\alpha \in (\tfrac{\pi}{2}, 1.9]$, up to time translation. This result proves
Jones' Conjecture formulated in 1962, that there is a unique slowly oscillating
periodic orbit for all $ \alpha > \tfrac{\pi}{2}$. Furthermore, there are no
isolas of periodic solutions to Wright's equation; all periodic orbits arise
from Hopf bifurcations.
