The 'dynamo theory' ascribes the origin of the earth's magnetic field to the dynamo action of motions in the conducting fluid of the earth's core. This paper supports the theory by proving rigorously that it is possible to postulate a pattern of motions in a sphere filled with conducting fluid in such a way that the arrangement acts as a dynamo producing a magnetic field extending outside the conductor. The equations of motion of the fluid are ignored. The proof is given for a model consisting of two eddies in the earth's core, and does no more than demonstrate that motions in a sphere filled with conducting fluid can act as a steady dynamo. It is certainly not suggested that the motions in the earth's core are so simple. There is nothing pathological about the relative orientations of the angular velocity vectors of the two eddies which lead to dynamo action; in fact about half of the possible relative orientations work.