  We present a new proof, as well as a ${\bf C/Q}$ extension, of the
Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The
main techniques used are the computations of the adiabatic limits of
$\eta$-invariants associated to the so-called sub-signature operators. We
further show that the Bismut-Lott analytic torsion form can be derived
naturally from the transgression of the $\eta$-forms appearing in the adiabatic
limit computations.
