The object of the present article is to bring the evidence of coins to bear upon a type of Greek state which has received comparatively slight attention at the hands of historians, the federal union of cities or tribes.A preliminary survey of Greek federal money was made some fifty years ago by the Hon. J. B. L. Warren. More recently important additions to our knowledge of the coin-systems of individual leagues have been made by several expert writers on numismatics. But certain aspects of federal coinage have hardly yet been considered.In particular, no systematic attempt has yet been made to use their evidence to illustrate one crucial problem of federal politics, the relation of the federal government to the confederate states. In the following pages an endeavour will be made to throw light upon this problem by means of a survey of the various federal coinage systems.

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The scope of the present article is restricted to a few disconnected points concerning the Great Persian War, and its edges have been carefully left untrimmed. Recent publication on the same subject has been so voluminous as to impose conciseness upon future writers; and the success with which many outstanding problems have latterly been discussed, notably by English scholars, leaves a comparatively narrow field for future research. Yet it may be of interest to revert to particular topics which invite renewed consideration, and to reaffirm certain conclusions which appear to be falling into undeserved disrepute.

Form finding is used to optimize the shape of a semi-finished product, i.e. the material configuration in a forming process. The geometry of the semi-finished product is adapted so that the computed spatial configuration corresponds to a prescribed target spatial configuration. Differences between these two configurations are iteratively minimized. The algorithm works non-invasively, thus there is a strict separation between the form update and the finite element (FE) forming simulation. This separation allows the use of arbitrary commercial FE-solvers. In particular, there is no need for a modification of the FE forming simulation, only the material configuration is iteratively updated. A new method is introduced to calculate the difference between the target and the computed spatial configuration. Thereby the target mesh is separated from the mesh for the FE forming simulation, which enables a more accurate and independent representation of the target configuration. In addition, the possibility of taking into account manufacturing constraints in the optimization process is presented. The procedure is illustrated for the example of the first stage of a novel two-stage sheet-bulk metal forming process.