e of one country, say the rth country, appreciates in proportion to its balance of payments surplus according to the law
while all other exchange rates adjust instantaneously to equilibrium. The solution of the differential system (6) is
and Deltarr is the cofactor (principal minor) of the element in its rth row and rth column.
For the dynamic process implied in (7) to be stable it is necessary and sufficient that Delta / Deltarr < 0. But this condition is precisely (for the analogous problem in the Walrasian system) the Hicksian condition of imperfect stability for the rth currency; and when the method is applied to each currency (in succession, not simultaneously), we have the complete Hicksian conditions of imperfect stability:
A similar analysis can help to show the usefulness of the Hicks conditions of perfect stability. Suppose that one exchange rate, say pi, is held constant (relative to the numéraire). This amounts to dropping the ith row and column from Delta, so that if the original experiment were repeated, this time with the ith exchange rate constant, we would get, instead of (7),
and the stability condition Deltaii / Deltaii,rr< 0, which is one of the Hicksian conditions of perfect stability. Proceeding along these lines, holding one or another set of prices constant, we get the complete Hicks conditions of perfect stability.
But does this dynamic process have any economic plausibility ? Are we not, as Samuelson argued, allowing "arbitrary modification of the dynamical equations of motion"? The answer is, in a sense, yes. But this can be the exact method needed in the theory of policy, where our purpose is to design stable dynamic systems.
As an example, we might be interested in examining aspects of the stability of an exchange-rate system such as that recently advocated by sixteen distinguished academic economists  -a sliding parity system (with widened exchange-rate margins).9 Is it not precisely a set of conditions such as the Hicks conditions that would be involved? We might ask, first, what wo