Pagina:Scientia - Vol. VII.djvu/91

on the use of the differential calculus etc. 83

subject to the constraints which have been indicated. Among those conditions is one very unusual in Physics, very difficult to represent mechanically, that no part of the system does work against another. For instance, the point (x1, η1) cannot suffer a change by the subtraction of Δx1 from x1, the addition of Δη1 to η1, if such that a step in the direction defined by the ratio Δη1x1 is one in which the individual is averse to move. The conception may be extended to any number of Xs, on one side, and any number of Ys on the other. The forces actuating the different members of one group need not be identical; they need to act, not in exactly the same direction, but in what may be called the same sense.

As to the variation of the forces acting on a particle with the variation of its position — the change in the motives of an individual, e. g., Xr (or Yr) with the amount of x (or y) that he retains, and the amount of y, (or x) that he has obtained — the natural and usual supposition is that the forces are a fonction only of the position defined by those amounts, viz xr and yr. This state of things is here designated by the term «independent dealing», the symbol A. But we shall also have to entertain the supposition, not very usual in physics, that the forces acting on any particle at the point (x, y) depend not only on the co-ordinates which define that position, but also on the position of the system — upon the coordinates of its centre of gravity, as we may say, when the number of particles on each side is equal. The supposition will be more fully explained in the sequel, under the head of «interdependent dealing», labelled B.

I do not attempt here to cultivate the fields which have been indicated; but as I pass in the course of a rapid survey, I may sometimes root up a weed which has proved noxious, or drop a seed which may germinate.


A) Independent Dealing.

Simple Exchange. — This heading is meant to designate the simplest form of market, the conception of which has been attained in the introductory description of two groups of Xs and Ys, dealing respectively in two commodities x and y. This is the economic molecule; itself, as we have seen, a