  Partially overlapping two parallel armchair nanotubes are investigated
theoretically with the $\pi$ orbital tight bonding model. Considering the
interlayer Hamiltonian as perturbation, we obtain approximate analytical
formulas of the interlayer transmission rates $T_{\sigma',\sigma}$ from channel
$\sigma$ to $\sigma'$ for all the four combinations
$(\sigma',\sigma)=(\pm,\pm)$ and $(\pm,\mp)$, where suffixes $+$ and $-$
represent symmetric and anti-symmetric channels, respectively, with respect to
the mirror plane of each tube. Landauer's formula conductance is equal to the
sum of them in units of $2e^2/h$. According to the perturbation calculation,
the interlayer Hamiltonian is transformed into the parameter
$w_{\sigma',\sigma}$ that determines the analytical formula of
$T_{\sigma',\sigma}$. By comparison with the exact numerical results, the
effective range of the analytical formulas is discussed. In the telescoped
coaxial contact, the off-diagonal part $T_{-,+}+T_{+,-}$ is very small compared
to the diagonal part $T_{+,+}+T_{-,-}$. In the side contact, on the other hand,
the off-diagonal part is more significant than the diagonal part in the zero
energy peak of the conductance.
