  We show that, for a stationary version of Hammersley's process, with Poisson
sources on the positive x-axis and Poisson sinks on the positive y-axis, the
variance of the length of a longest weakly North--East path $L(t,t)$ from
$(0,0)$ to $(t,t)$ is equal to $2\mathbb {E}(t-X(t))_+$, where $X(t)$ is the
location of a second class particle at time $t$. This implies that both
$\mathbb {E}(t-X(t))_+$ and the variance of $L(t,t)$ are of order $t^{2/3}$.
Proofs are based on the relation between the flux and the path of a second
class particle, continuing the approach of Cator and Groeneboom [Ann. Probab.
33 (2005) 879--903].
