  For a compact manifold, which has a part isometric to a cylinder of finite
length, we consider an adiabatic limit procedure, in which the length of the
cylinder tends to infinity. We study the asymptotic of the spectrum of
Hodge-Laplacian and the asymptotic of the $L^2$-metric on de Rham cohomology.
As an application, we give a pure analytic proof of the gluing formula for
analytic torsion.
