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84 | “scientia„ |

compound of curiously interrelated atoms. In the fragmentary system of only two particles, their identical position (which may be equally in our notation denoted by the symbols (*x*, η), (ξ, *y*), (*x*, *y*) would be varied under the influence of forces tending to maximum advantage up to a limit investigated by Jevons, in his «Theory of Exchange», and now commonly known as the *Contract-Curve*^{1}. When there are one, two or more dealers on each side of the Market, a like condition of contract must still be fulfilled. Thus in the case above put of two dealers on each side, either of the Xs, say X_{1}, will continue to deal with one of the Ys, say Y_{1}, up to a point beyond which it is impossible to advance a single step with benefit to both parties. The like is true of X_{1}, with respect to Y_{2}, and of X_{2} with respect to either of the Ys.

Moreover, in addition to this purely *contractual* condition the circumstance of *competition* introduced by the duality of the dealers on each side imports a new condition. There cannot be equilibrium unless the slope of the final step taken by any X in conjunction with (parallel to) any Y is the same as the slope of the final step taken by (that or) any other X with any other (or that) Y. For if it be possible let figure I correspond to a state of equilibrium in which X_{1} gives to Y_{2} a final increment of x, say (Δ*x*_{1})_{2}, in return for the final increment of y (Δ*y*_{2})_{1}; while X_{2} gives to Y_{1}, the final increment (Δ*x*_{2})_{1} and receives the final increment (Δ*y*_{1})_{2}; this arrangement cannot stand if the slope designated by the respective pairs of corresponding increments are different. For in that case it would in general be to the advantage of some one of the Xs and one of the Ys to desert their respective partners and take one step at least, and probably several, with each other.

Yet another condition is imposed by competition when we advance to the typical case of indefinitely numerous dealers on each side of the market — a crowd of competitors all of the same order in respect of the possible magnitude of their transactions^{2}. Suppose that, in accordance with the

- ↑ See the writer’s «Mathematical Psychics», pag. 21 et seq.
- ↑ Or more generally of such relative magnitude that the power of any one competitor to influence the market is very small. This condition may be illustrated by its analogy with the condition which must in general be fulfilled by the relative magnitudes of independent statistical quantities, in order that their aggregate may fluctuate in accordance with the normal law of error.