  We study the backbone connecting two given sites of a two-dimensional lattice
separated by an arbitrary distance $r$ in a system of size $L$. We find a
scaling form for the average backbone mass: $<M_B>\sim L^{d_B}G(r/L)$, where
$G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim
x^{\psi}$ with $\psi=0.37\pm 0.02$. This result implies that $<M_B> \sim
L^{d_B-\psi}r^{\psi}$ for the entire range $0<r<L$. We also propose a scaling
form for the probability distribution $P(M_B)$ of backbone mass for a given
$r$. For $r\approx L, P(M_B)$ is peaked around $L^{d_B}$, whereas for $r\ll L,
P(M_B)$ decreases as a power law, $M_B^{-\tau_B}$, with $\tau_B\simeq 1.20\pm
0.03$. The exponents $\psi$ and $\tau_B$ satisfy the relation
$\psi=d_B(\tau_B-1)$, and $\psi$ is the codimension of the backbone,
$\psi=d-d_B$.
