The fission theory is reformulated so as to be independent of the action of viscosity. It is found that this results in evolution not along the Jacobi series, but along a similar series of ellipsoids, the lower seff-adjoint series of Riemann. The evolution takes place on the contri'ction timescale t , even in the neighborhood of points where a dynamical instability sets in. This circumstance frees the present formulation from the objection, frequently raised against the classical formulation, connected with the occurrence of a dynamical, or ordinary, instability of the ellipsoidal series under disturbances belonging to the third ellipsoidal harmonics. Certain other objections that have been raised against the fission theory are also reconsidered.