We present a solution for the relative drift velocity between the neutral and ionized matter in a cylindrically symmetric, magnetic cloud, which contracted gravitationally to an equilibrium state from an initially uniform state. The cloud is bounded by a hot and tenuous external medium. The characteristic time (tau/sub D/) for ambipolar diffusion is calculated as a function of position inside the cloud and is compared with the only other known solution, which refers to a uniform density. It becomes necessary to define a second characteristic time, tau/sub B/, which is correct locally and which is the aapropriate one for deciding at which position, if anywhere, in the cloud ambipolar diffusion can resolve ''the magnetic flux problem'' during star formation. The two time scales differ by many orders of magnitude.It is likely that, while ambipolar diffusion is in progress in a cloud, the total magnetic energy of the cloud will not decrease. In such a case, gravitational energy is converted into heat directly through ion-neutral collisions, rather than through dissipation of stored magnetic energy.