  Asymptotically locally conical (ALC) metric of exceptional holonomy has an
asymptotic circle bundle structure that accommodates the M theory circle in
type IIA reduction. Taking Spin(7) metrics of cohomogeneity one as explicit
examples, we investigate deformations of ALC metrics, in particular that change
the asymptotic S^1 radius related to the type IIA string coupling constant.
When the canonical four form of Spin(7) holonomy is taken to be anti-self-dual,
the deformations of Spin(7) metric are related to the harmonic self-dual four
forms, which are given by solutions to a system of first order differential
equations, due to the metric ansatz of cohomogeneity one. We identify the
L^2-normalizable solution that deforms the asymptotic radius of the M theory
circle.
