that it must have this effect (a) when the prices of other commodities are given, or (b) when other prices are adjusted so as to preserve equilibrium in the other markets?
To resolve the difficulty Hicks introduced his concepts of perfect and imperfect stability. He noted first that it was necessary to distinguish a series of conditions-that a rise in the price of X will make supply greater than demand (1) all other prices being given, (2) allowing for the price of Y being adjusted to maintain equilibrium in the Y market, (3) allowing for the prices of Y and Z being adjusted, and so on, until all prices have been adjusted. He then defined as imperfectly stable a system in which a rise in price of a commodity causes excess supply for the commodity after all repercussions are allowed for, and as perfectly stable a system in which a rise in price causes excess supply regardless of how many other prices are adjusted to attain equilibrium values in their respective markets.4
Samuelson  criticized Hicks' concept of stability on the grounds, as stated above, that "stability conditions are not deduced from a dynamic model, except implicitly." Hicksian stability is not equivalent to "true" dynamic stability, and the Hicks conditions are neither necessary nor sufficient for the convergence of the dynamical system implicit in Hicks' dynamics, that is, the dynamic system Samuelson postulated as the "natural extension" of the Walrasian system. True dynamic stability requires that the roots of the characteristic equation of the dynamic system have negative real parts, and this requirement is not equivalent to the Hicks conditions.5
Samuelson's criticism undermined the logic of Hicks' method. But the conditions of stability produced by that method retained an important place in the literature. Samuelson had already observed that the Hicks conditions were equivalent to the conditions of "true" dynamic stability in the symmetrical case. Metzler showed that they were equivalent in the case of gross substitutes, and also necessary (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