The subject of this report is the acceleration of a cylindrical layer of plasma by an azimuthal magnetic field, a process similar to the ordinary BφIz pinch. The magnetic field is generated by a current drawn from a condenser. The system can be represented by an L, C circuit in which the value of the inductance is changing owing to the movement of the plasma conductor. A simple but approximate description of the acceleration of the plasma can then be derived using the adiabatic theorem for oscillators together with the law of conservation of energy. The resulting approximate solutions are compared with numerical solutions of the appropriate differential equations. The approximate solutions are also applied to a rail-type of plasma gun previously reported by Artsimovich, et al. [Zhur. Eksptl' i Teoret. Fiz.33 (1957) 3].