  We identify the scaling limits for the sizes of the largest components at
criticality for inhomogeneous random graphs when the degree exponent $\tau$
satisfies $\tau>4$. We see that the sizes of the (rescaled) components converge
to the excursion lengths of an inhomogeneous Brownian motion, extending results
of \cite{Aldo97}. We rely heavily on martingale convergence techniques, and
concentration properties of (super)martingales. This paper is part of a
programme to study the critical behavior in inhomogeneous random graphs of
so-called rank-1 initiated in \cite{Hofs09a}.
