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new order whatever of Variable Quantities, they must rigorously conform to the general laws of Variable Quantities. To suppose that a new order of Variable Quantities could depend upon laws fundamentally contrary to the general theory of Variable Quantities would at once shake to its foundations the whole of mathematical science, just in the same manner as if we could imagine a science in which 3×3=11 would destroy the generality of Arithmetic.

Now the fundamental condition of the science of any body of Variable Quantities of either order is this, that there can only be one single and general expression which must be capable of grasping all the phenomena.

In the history of the various physical sciences, such as Astronomy, Optics, &c., different opinions have been held as to which was the true general theory of the subject. But no one ever supposed that there could by any possibility be more than one. No one ever dreamt of breaking up the body of phenomena into a number of distinct classes, and accounting for each by means of a distinct theory, which was contradictory to each of the others. No one ever dreamt of writing a book on Astronomy and explaining one class of phenomena by means of the Ptolemaic theory, another class of phenomena by means of the Copernican theory, and another class by means of the Tychonian theory. No one ever wrote a book upon Optics in which one chapter adopted the Corpuscular theory, and another chapter the Wave theory of Light. In such a way of treating the subject, there could, of course, be no such thing as a general law in the science.

Arguing then from analogy, and by the great doctrine of the Continuity of Science, we may lay it down as a fundamental condition that if we have to discuss any new order of Variable Quantities, it must conform to the general theory of Variable Quantities.

Now, Economic Science treats of a new order of Variable Quantities, and the science regards them in a new variable relation, namely, that of Exchangeability. The object of the science is to ascertain the variations of their exchangeable relations with each other. Arguing then on the above mentioned principles, it may be said that it is a fundamental condition of the science that the exchangeable relations of all

quantities, whatever their nature be, must be brought under the grasp of one single general law, or one single general equation, and no more.

Now, admitting that the Ricardo-Mill system of Economics is widely prevalent in this country, it is well known that it breaks up Economic phenomena into a number of distinct classes of cases, and it assigns a distinct law of Value for each of these classes. Now such a method of investigation is utterly inadmissible. If it be true that Economics is a physical science, such a method of investigation is in direct violation of the fundamental principles of Natural Philosophy.

To permit such a method of investigation would be simply to destroy the generality of the Theory of Variable Quantities, as much as if we could imagine that in any case whatever 3 × 3=11, it would destroy the generality of arithmetic; for it would be as much as to say that there is an order of Variable Quantities which is not subject to the general Theory of Variable Quantities.

It is quite easy to demonstrate that there is, as the principles of Natural Philosophy shew that there must be, one great general equation which comprehends all the phenomena of the exchangeable relations of all quantities, whatever their nature be, and all the distinctions set up by the Ricardo-Mill system may be annihilated by the Law of Continuity, and reduced to this one general law.

And now we see how Economics is a great Physico-Mathematical Science. The Physical part of it, or the facts, can only be known to those who are properly instructed. Many persons suppose that it is very easy to see and describe facts. But that is a great mistake. In all sciences it requires an educated eye to be able to see the facts. Nothing can be more remarkable than the statements of two able men, Senior and Whately, that "the facts on which the general principles of the Science rest may be stated in a very few sentences, and indeed in a very few words." "Political Economy, is indeed a science which is founded on facts, and which has a practical application in reference to facts; but which yet requires for the establishment of its fundamental principles very little information beyond what is almost unconsciously, and indeed unavoidably required by 1 Senior's Treatise on Political Economy, p. 4.

every one." So far from the facts of Economics being capable of being stated in a very few words, and being unconsciously and unavoidably acquired by every one, we may say that it requires a greater variety of knowledge than any other science whatever, even to see the facts. For what are the facts of Economics? It deals with all Property of every description, and with all commerce. Consequently a knowledge of the Law of Property of every description, and a thorough knowledge of the entire mechanism of commerce is absolutely indispensable to enable any one even to see the facts of Economics and to devise a Theory of the Phenomena, which shall be conformable to the principles of Natural Philosophy, of course indispensably requires a knowledge of Physical Science, and the methods of reasoning which have brought the various sciences to their present state.

53. These considerations will be sufficient to satisfy all persons of competent knowledge that Economics is essentially a physical science. But we will now go further and shew from the books that are in constant use that it is already implicitly acknowledged to be a Mathematical Science.

If we take up any book of Algebra, we find it stated among the usual illustrations of the meaning of the Algebraical signs + and, that Money is a positive quantity, and that a Debt is a negative quantity. Now Money and Debts are each of them exchangeable, and therefore Economic Quantities. Hence we see it at once acknowledged that there are Positive Economic Quantities, and Negative Economic Quantities. Now let us ask this question-What can be the meaning of a NEGATIVE Economic Quantity?

Now we know perfectly well that in other great sciences there are positive quantities and negative quantities. Mathematicians have fully explained to us the meaning of the Negative Sign in Algebra, Trigonometry, Analytical Geometry, Mechanics, Optics, Astronomy, Electricity, and so on. We all know the meaning of the negative sign in each of these. But has any Mathematician ever told us what a Negative Economic Quantity is? Or has any Mathematician ever explained the Theory of the Negative Sign in Economics?

Some persons may be ready to give some sort of reply like

1 Whately's Lectures, p. 149.

this: a man's money is positive and his debts negative. Subtract one from the other, and the remainder, if any, is his property.

The slightest reflection will show that this explanation wholly fails. Take any of the sciences already mentioned, in which the negative sign occurs, and are negative quantities subtractions from positive ones? They certainly are not. Every one knows that in all these sciences negative quantities are not subtractions from positive ones, but separate and independent quantities, having as real an existence as positive ones; and that the total science is composed of positive quantities together with negative quantities.

We may already see, then, from the analogy of all other sciences that Negative Economic Quantities cannot be subtractions from Positive Economic Quantities, but that they must be separate and independent ones, and that the complete Science of Economics must comprehend Positive Quantities together with Negative Quantities.

We are told that a Debt, or Credit, is a negative quantity. Now a Debt, or Credit, is the Right to a Future Payment, and is the type of an enormous mass of Property. The Funds are of the same class of Property. They are also Negative Economic Quantities, and what are they to be subtracted from? We have already stated that upwards of £5,000,000,000 of Debts, or Credit, passed through the London Clearing House in one year; these are Negative Quantities, and what are they to be subtracted from? And this stupendous sum is only a small part of the credit employed in the country. Take the accounts of any great public bank-on one side of the account is a sum of a great many millions of credit, entirely Negative Quantities; on the other side is an equal sum consisting of a comparatively small sum in money, or Positive Quantities, together with a much larger sum in credit, Negative Quantities. Now in these great accounts, consisting chiefly of Negative Quantities, what are they to be subtracted from?

Furthermore under this species of Property is included about 32 parts of 33 of the value of Land, Copyrights, Patents, Tolls, Ferries, all Annuities, and that stupendous mass of Property, consisting of Shares in Commercial Companies: in short, the whole of that species of Property known in law by the name of

Incorporeal Property, which in this country includes about 95 per cent. of Economic Quantities, and the greater part of which is entirely omitted from the ordinary books on Political Economy. Now, how are we to subtract 95 per cent. of Economic Quantities from the remaining 5 per cent.: and how is Incorporeal Property to be subtracted from Corporeal Property?

It is manifest that it is a scientific problem of the highest importance to develope the Theory of the Negative Sign in Economics, as under these Negative Quantities, which Algebraists pass over with a simple remark, is contained the whole Theory of Credit, which has exercised such prodigious effects upon nations for good and for evil, which are not in any way inferior to those of the Steam Engine.

54. According to this conception, then, of Economics, which is the one to which the majority of Economists are now gravitating, we see at once that a great new Physical Science is presented to us, which is in all respects fitted to be raised to the rank of an exact science. For we shall find that the same general laws of Exchange hold good among all nations, among the rudest and the most civilized, and in all ages and countries. We find that the same causes are invariably followed by the same effects, which are always measured numerically, and that is why Economics may be raised to the rank of a permanent and universal science of the same rank as the physical ones, because it is based upon principles of human nature which are found to be as universal and permanent as those of physical substances upon which the physical sciences are based.

55. We have shewn that this conception of the nature of the Science exactly represents the ideas of the Physiocrates, only that they restricted it to the exchange of material products. It also correctly represents the idea of Smith, for in B. I., c. 4, he explains the object of the first two Books of his work, which is the constructive part of it: he says they are "to investigate the principles which regulate the exchangeable value of commodities;" and McCulloch in his note to the first of the work, says page "This science might indeed be called the Science of Values." Ricardo's work, however imperfect, is a treatise on Value. And this is so evident from the whole

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