  For each $n$ let $Y^n_t$ be a continuous time symmetric Markov chain with
state space $n^{-1} \Z^d$. A condition in terms of the conductances is given
for the convergence of the $Y^n_t$ to a symmetric Markov process $Y_t$ on
$\R^d$. We have weak convergence of $\{Y^n_t: t\leq t_0\}$ for every $t_0$ and
every starting point. The limit process $Y$ has a continuous part and may also
have jumps.
