Pagina:Scientia - Vol. VII.djvu/90

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82 “scientia„

of the terms of contract is represented by the movement of the point in the plane. The parties cannot move separately. They are in the same boat. They both have hold of the rudder, but the directions in which they respectively prefer to move are not the same. The magnetic pole towards which X would steer lies to the South East, supposing that the axis of y points to North. The centre of attraction for Y lies to the North West. Motion is possible only as long as both parties are winning towards their respective goals1.

Next let there be two individuals on each side, say X1 and X2 dealing with Y1 and Y2. (The motives or dispositions of X1 may at first be supposed identical with those of X2; the psychic forces acting on Y1 and Y2 being also identical). X1 is free to move in any direction to any distance, provided that either Y1 or Y2 accompany, or at least move parallel to him; and the like is true of X2 with regard to the Ys, and of each of the Ys with regard to the Xs. The conditions are expressed by Figure 1, in which the point (x1, η1) represents the amount of commodity x which the individual X1 gives and the amount of commodity y which he receives (partly, it may be, from Y1, partly from Y2). The point (ξ1, y1) denotes the amount of commodity y which Y1 gives and the amount of commodity x which he receives (in general, partly from X1 and partly from X2). The points (x2, η2), (ξ2, y2) are similarly interpreted. The two points (x1, η1) and (x2, η2) may be considered as moving along a rod which passes through the point (x, y); subject to the condition that those two points are equi-distant from the point (x, y). The points (ξ1, y1) and (ξ2, y2) are similarly related to the point (x, y); which may thus be described as the centre of gravity of the system. The system moves towards a position of equilibrium — a position of maximum energy, as it may be considered — under the influence of forces acting on the constituent particles;

  1. See the construction in the writer’s Mathematical Psychics. Part II, p. 20 et seg., and compare Pareto, Manuel d’Économie Politique, ch. III, S. 58. et passim.