Let $B$ be a Brownian motion on $R$, $B(0)=0$, and let
$f(t,x)$ be continuous. T.~Salisbury conjectured that if the total variation
of $f(t,B(t))$, $0\leq t\leq 1$, is finite $P$-a.s., then $f$ does not
depend on $x$. Here we prove that this is true if the expected total
variation is finite.