### I.

If *u* be the proportional profit at one point and *u*′ that at another where *u* is less than *u*′, then motion will take place from *u* to *u*′, because every one tries to make the greatest profit he can. Further, the greater the difference between *u* and *u′* the greater the velocity of adjustment. Therefore, if there be *n* proportional profits at *n* different points, there will be a tendency to motion which will cease when all the profits are equal. Therefore, if V, V′, V″, V-‴, V″″, &c., be the amounts invested at different points, the condition that there should be equilibrium is that—

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1/V.dV/dt= 1/V′.dV′/dt=1/V″.dV′/dt=&c.

From this we may deduce a relation between property-values and rate of interest (*r*).

Let V = property-value.

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r = 1/C.dC/dt;

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but 1/V.dV/dt = 1/C.dC/dt = r.

Integrating, we get—

V = V_{o}e^{rt},

and C = C_{o}e^{rt}.

This assumes that *r* is constant, and that all the rent is devoted to buying more land and the interest to increasing capital. Neither of these assumptions is true, for evidently a man who is both a landowner and a capitalist may be most erratic in his investments; but it seems evident that, since the area of land in use is limited, more rent will find its way to capital than interest to land, so that capital will increase more quickly than given above and land-values more slowly. We may, however, deduce a formula free from both these objections by replacing *d*V/*dt* by R; then V, R, and *r* are simultaneous values at any time, and therefore true for all time.

R/V = *r*.

Since R is always greater than O, we see that when *r* = O V = ∞, and *vice versâ*. There is one case in which R = O: that is at and below the margin of cultivation; the formula then gives V = O. True, but of no importance.