(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 processes, and (b) the assumption of stability. Acceptance of (b) is the essence of the correspondence principle, but how are we to determine (a)?
Consider, for example, the following alternative expressions for dynamical systems:
To each of these systems there will correspond a different set of stability conditions. System (1) is a version of that used by Samuelson to prove that the Hicks conditions are neither necessary nor sufficient for stability. Yet, as he himself noted, more complete generalizations such as (2) and (3) can be developed with different consequences for comparative statics. There is, therefore, an element of arbitrariness in the specification of dynamic systems in the absence of empirical information and there may on these grounds be a pragmatic justification for Hicks' method of developing " stability conditions " that are "timeless." The Samuelson criterion is completely general and is an appropriate methodological approach, but for purposes of yielding practical results generality often implies emptiness.
The purpose of this chapter is to show that the Hicksian stability analysis is a useful contribution to the integration of statical and dynamical theory. First, we shall show that the perfect and imperfect stability conditions do correspond to the dynamic stability conditions of some dynamic processes, irrespective of the pattern of signs of the price-matrix. Second, we shall argue that, despite their usefulness in the form Hicks presented them, the perfect stability conditions are not completely general, since they do not yield the information obtained by extending his method to the commodity "adopted" as the standard commodity. Third, we shall show that generalized conditions can be obtained by interpreting his device of holding subsets of prices constant with respect to the standard commodity as an arbitrary method of forming various composite commodity groupings. Further, we shall show that dynamic systems that fail to satisfy the generalized conditions will be unstable at some speeds of a