(but not sufficient) for stability to be independent of the speeds of adjustment (Metzler ).6 Morishima proved that they were equivalent for certain classes of complements. They are also sufficient conditions for convergence of any nonoscillating system, since Hicksian (perfect) stability implies the absence of positive real roots. They are, moreover, conditions that, if not satisfied, yield anomalous comparative statics results, and thus seem at least to be necessary conditions for useful applications of the correspondence principle, at least in the context of analysis of the Walrasian system. Thus, even though Hicks' method seems to lack theoretical justification,7 the Hicks stability conditions produced by that method have proved exceedingly useful.
How can a wrong method yield useful results ? Leaving aside coincidence, the answer may lie in the two-way character of the correspondence principle. Samuelson  had observed that
not only can the investigation of the dynamic stability of a system yield fruitful theorems in statical analysis, but also known properties of a (comparative) statical system can be utilized to derive information concerning the dynamic properties of a system.
When Hicks is specifying the signs of changes in excess demands when a given price is put above or below its equilibrium value, various subsets of other prices remaining constant, he is at the same time implying specific comparative statics results. Provided these results correspond to known properties of a statical system the conditions implied should be related to stability conditions if the reciprocal character of the correspondence principle is valid.
Another reason why the Hicks method may appear more reasonable than Samuelson's original criticism of it suggests is that our knowledge of the precise laws governing dynamical systems is scanty. The empirical "output" according to the methodology of the correspondence principle is a set of comparative statics results, while the empirical "input" is (a) the nature of the dynamic proce