Drift surfaces of guiding centers in the Bumpy Torus static magnetic field have been located and analyzed for various torus parameters by making use of the transverse adiabatic invariant &mgr; =p⊥2/Band the longitudinal adiabatic invariantJ= ∮p∥dl.In addition, the drift equations (for which &mgr; is an invariant) have been solved numerically to investigate limitations on the application of the invariance ofJ. In general,Jis an invariant for the drift equations under adiabatic conditions; however, some special guiding‐center trajectories are presented for which the drift per longitudinal period is sufficiently large that the assumption of the invariance ofJis not valid. Closed surfaces of constantU= ∮B−1dlhave been found. These are also surfaces of constant plasma pressure under static equilibrium conditions at low &bgr; for a hydromagnetic model. The stability of the equilibrium is discussed.