Homogeneous superconductors have reversible magnetic properties. We distinguish two types of superconductors, type I and type II. The type I superconductor (most pure superconducting elements are of this type) has a particularly simple magnetic behavior.1 In a macroscopic specimen, the flux density is zero for fields less than the critical field, Hc, that marks the limit of the superconducting state. Above this field the specimen has all the properties of a normal metal including the property that the flux density is essentially equal to the applied field. So, in summary, the type I superconductor is either completely superconducting or completely normal. (This statement is strictly true only for a long thin specimen in a field that is parallel to the axis of the specimen. In other geometries one finds a gross mixture of superconducting and normal regions called the intermediate state that is created by the field concentrations associated with specimen shape.) In recent years it has been appreciated that there is another class of superconductor—usually an alloy or compound—in which the flux in a bulk specimen is completely excluded for fields less than Hc1, but above this field flux penetration is partial and increases with applied field until flux penetration is complete at an upper critical field, Hc2. Since this field is generally larger than the equivalent Hc of type I superconductor, these type II superconductors are known as high-field superconductors. The region between Hc1 and Hc2 is known as the mixed state which is not to be confused with the shape-dependent intermediate state mentioned earlier. The present conception of the mixed state2 pictures the flux as entering in the form of quantized current vortices. The total flux contained in each vortex is 2×10−7 G-cm2. In equilibrium these vortices repel one another to form a lattice that compresses as the field is increased from Hc1 to Hc2 and finally all flux variation smoothly disappears at Hc2. Experimental magnetization curves on homogeneous alloys show good agreement with this theory.3 If the type II is inhomogeneous, there may be impediments to the motion of these flux lines. In this event there will be a gradient of flux as the flux is driven into the specimen.4 This gradient of flux lines is equivalent to a macroscopic current density by Ampere's law, curl H=4πJ/10.4 This behavior allows one to calculate the magnetic behavior of these superconductors in terms of only one parameter, the critical current density, Jc(H)5—the same critical current density that is measured in current transport measurements. The magnetic behavior includes size-dependent magnetization and a hysteresis loop that is the precise diamagnetic equivalent of the Rayleigh hysteresis loop for ferromagnets.