of a hundred, simply the element D,- difficulty of attainment. The other element, U, or intrinsic utility, will be perfectly inoperative. Let the thing (measured by its uses) be, for your purposes, worth ten guineas, so that you would rather give ten guineas than lose it; yet, if the difficulty of producing it be only worth one guinea, one guinea is the price which it will bear. But still not the less, though U is inoperative, can u be supposed absent? By no possibility; for, if it had been absent, assuredly you would not have bought the article even at the lowest price: U acts upon you, though it does not act upon the price. On the other hand, in the hundredth case, we will suppose the circumstances reversed. You are on Lake Superior in a steamboat, making your way to an unsettled region 800 miles ahead of civilization, and consciously with no chance at all of purchasing any luxury whatsoever, little luxury or big luxury, for a space of ten years to come: one fellow-passenger, whom you will part with before sunset, has a powerful musical snuff-box; knowing by experience the power of such a toy over your own feelings, the magic with which at times it lulls your agitations of mind, you are vehemently desirous to purchase it. In the hour of leaving London you had forgot to do so here is a final chance. But the owner, aware of your situation not less than yourself, is determined to operate by a strain pushed to the very uttermost upon U, upon the intrinsic worth of the article in your individual estimate for your individual purposes. He will not hear of D as any controlling power or mitigating agency in the case and finally, although at six guineas apiece in London or Paris, you might have loaded a wagon with such boxes, you pay sixty rather than lose it when the last knell of the clock has sounded which summons you to buy now or to forfeit for ever. Here, as before, only one

8

element is operative: before it was D, now it is u. But, after all, D was not absent, though inoperative. The inertness of D allowed u to put forth its total effect. The practical compression of D being withdrawn, u springs up like water in a pump when released from the pressure of air. Yet still that D was present to your thoughts, though the price was otherwise regulated, is evident; both because U and D must coexist in order to found any case of exchange value whatever, and because undeniably you take into very particular consideration this D, the extreme difficulty of attainment, (which here is the greatest possible, viz. an impossibility,) before you consent to have the price racked up to U. The special D has vanished; but it is replaced in your thoughts by an unlimited D. Undoubtedly you have submitted to u in extremity as the regulating force of the price; but it was under the sense of D's latent presence. Yet D is so far from exerting any positive force, that the retirement of D from all agency whatever on the price, this it is which creates, as it were, a perfect vacuum, and through that vacuum u rushes up to its highest and ultimate graduation.

This is the foundation of any true solution applied to the difficulty of subdividing exchange value; and this statement of the case is open to a symbolical expression of its principle; which principle, let the reader not forget, is, — that, under an eternal co-presence of two forces equally indispensable to the possibility of any exchange value at all, one only of those forces (and each alternately, as the ultimate circumstances take effect) governs and becomes operative in the price. Both must concur to raise any motive for purchasing; but one separately it is which rules the price. Let not the reader quarrel beforehand with illustrations by geometrical symbols; the use which will be made of them is not of a kind

to justify any jealousies of a surreptitious logic. It is a logic in applying which we abstract altogether from the qualities of objects, and consider them only in so far as they are liable to the affection of more and less. Simply the most elementary of geometrical ideas will be used; and the object is this, - sometimes to render the student's apprehension of the case more definite, but sometimes, also, to show him that the same difficulty, or one analogous, might arise and be representable in the austere simplicities of geometry; in which case, by parity of argument, the explanation of the difficulty as represented in space will become inversely the explanation for the original difficulty.

U

D

10

Here the line U represents the utility value to the purchaser of any article whatever; that is, the very ultimate value to 20which, by possibility, it could ascend in the case that a screw were made to operate upon the purchaser's secret appreciation of 10its serviceable qualities. But in ordinary circumstances this cannot happen; and under such ordinary circumstances, what will be the price? It will be the price determined by D, difficulty of attainment, and this difficulty is expressed by the line D. But mark how it acts. From the summit of the line D, standing on the same base as U, draw at right angles the dotted line which cuts U; that is to say, D, which is at present the operative force, the true determining force as regards the price, takes up from U precisely as much (and no more at any time) as corresponds to itself. D is, in this case, the true and sole operating force. U, which must indeed be co-present, (because else the purchaser would not be a purchaser, he would have no motive for purchasing, — case epsilon,) yet,

for all that, is inert quoad the price; itself submits to an action of D, but it exerts none, it reflects none the very smallest.

Now, suppose the case reversed: suppose not D, but U, to become suddenly the ruling force, D has become infinite, (as in the case of the musical toy in Canada,) that is, the difficulties in the way of supplying the market by a continued reproduction of the article (in one word, the resistance) must be supposed so vast as to be quite beyond the power of any individual to overcome. Instantly, under these circumstances, U springs up to its utmost height. But what is the utmost? Because D, by ceasing to be finite and measurable, has caused u to come into play,—will u therefore follow D, so as also to become infinite? Not at all: once called into action as the operating principle, u will become the sole principle; D will be practically extinct for any action that it can exert upon the price. The rare holders of the article, as surviving from past times or regions now inaccessibly distant, will fix a strain upon the few purchasers by means of the intrinsic or U value; each of the candidates must submit to see his own outside or extreme esteem for the article made operative against himself as the law of the price. He must ascend to the very maximum of what he will pay, under the known alternative of losing the article for ever if he will not pay it. U is therefore governed by no recollection of the past D, by no consideration of the present unlimited D, but simply thrown back upon its own potential force; i. e. upon each purchaser's appreciation of the article for his own purposes, which can have no connection whatever with the D, or variable resistance to the reproduction of that article in any particular place or time. If you submit to pay £30 of income tax, doubtless the power of the state determines the gen

eral result of your paying at all; but it is not that which determines the how much: this is a mixed result from the Exchequer ratio on the one hand, and the amount of your income on the other.

And that this is really so, that both U and D, under the alternate circumstances, will become passive-latent, nugatory, as regards the price-may be shown ex abundanti; viz. by showing that under any possible changes, either to U or to D, no beginning-no initial moment of action will arise for the one, so long as the other is operative. Figure to yourself, as the object concerned in such a valuation, some powerful drug. Suppose it the Peruvian or Jesuit's bark, and that suddenly, by applying to it the agency of sulphuric acid, some new product (the sulphate of this foreign bark) arises with prodigiously greater powers, not only greater by far, when applied to the common cases open equally to the old medicine and the new, but also, in another respect, greater; viz. that it is applicable to a set of cases from which the old medicine, by its bulk, or by its tendency to febrile symptoms, had found itself excluded; suppose under this enlarged power, for the basis of the medicine, that the line U, expressing its utility value, should run up to triple or decuple of its present altitude, would that change disturb the present appreciation under D? Not by an iota. Nay, to press the principle to an excess, suppose u to become infinite, still, in all the cases where D is at all the regulative force, D will continue even under this change to be the sole force. Nay, suppose that, even concurrently with this increase to U,-D, by some cheaper or briefer process for obtaining the sulphate, should descend; still, even in such a compound case, (vast increase for U, sudden decrease for D,) not the less, U would still continue inert, potentially capable, under the proper cir