The switching time T
srequired for the circumferential component of magnetization of a ferrite memory toroid to reverse upon application of a circumferential step magnetizing field

can be reduced by the application of a static magnetizing field

orthogonal to

- This fact has been experimentally observed and reported by several investigators. Various analyses of flux reversal in toroids without an orthogonal field and in thin films (and equivalent geometries such as thin-walled ferrite tubes) with an orthogonal field have been given in the literature; no analyses have been given, however, for the more complicated case of a cross-magnetized "thick" toroid. [Cross-magnetization of a ferromagnetic body is defined to occur whenever two or more independent nonparallel (crossed) magnetizing fields are applied simultaneously to the body.] In this paper, the latter problem is analyzed theoretically for the case of incoherent (or nonuniform) rotation of the magnetization vector

and an expression is obtained relating T
sto

, and the core geometry. The results are corroborated experimentally.