  We investigate the slow passage through a pitchfork bifurcation in a
spatially extended system, when the onset of instability is slowly varying in
space. We focus here on the critical parameter scaling, when the instability
locus propagates with speed $c\sim \varepsilon^{1/3}$, where $\varepsilon$ is a
small parameter that measures the gradient of the parameter ramp. Our results
establish how the instability is mediated by a front traveling with the speed
of the parameter ramp, and demonstrate scalings for a delay or advance of the
instability relative to the bifurcation locus depending on the sign of $c$,
that is on the direction of propagation of the parameter ramp through the
pitchfork bifurcation. The results also include a generalization of the
classical Hastings-McLeod solution of the Painlev\'e-II equation to
Painlev\'e-II equations with a drift term.
