  In order to compute the packing dimension of orthogonal projections
  Falconer and Howroyd (1997) introduced a family of packing dimension profiles
${\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently,
Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles
$\hbox{${\rm P}$-$\dim$}_s$ and proved, among many other things, that
$\hbox{${\rm P}$-$\dim$}_s E={\rm Dim}_s E$ for all integers $s>0$ and all
analytic sets $E\subseteq\R^N$. The goal of this article is to prove that
$\hbox{${\rm P}$-$\dim$}_s E={\rm Dim}_s E$ for all real numbers $s>0$ and
analytic sets $E\subseteq\R^N$. This answers a question of Howroyd (2001, p.
159). Our proof hinges on a new property of fractional Brownian motion.
