14. But moreover Inverse or Opposite Operations may be performed on these Quantities which are already affected with these opposite signs. And these Inverse or Opposite Operations are also denoted by the same signs 4- and -. And the combination of these opposite signs of opposite operations with the signs of opposite qualities affecting these Quantities, that is the combination of the signs of Affection and Operation give rise to the well-known Algebraical rules -

+ x + gives +

+ x - „ -

- x - „ +

- x + „ -

These laws, which are universally applicable in Natural Philosophy, are equally applicable to Economics, and are alone capable of giving the solution of the Theory of Credit, which has hitherto been the opprobrium of the science.

It will be found that there are Economic Quantities of Inverse or Opposite properties, and therefore, following the strictest analogy with Physical Science, we shall denote them by opposite signs: and also opposite Operations may be performed on these Opposite Quantities bringing into play the well known Algebraical rules, which will lead to consequences which may surprise some of our readers.

Hence Algebra in general, and Commercial Algebra with which we are at present concerned deals with Quantities and Operations. And whenever any of these Quantities, whatever their nature be, possess any Qualities whatever, or are affected by any relations of an opposite nature, they are distinguished by the opposite signs + and -.

Thus Time Past and Time Future; and therefore Products which have been produced in Time Past, and Products which are to be produced in Time Future: and consequently the Rights to these Products respectively: Active and Passive: Rights and Duties: may all be distinguished by the signs + and -.

So among Operations: Adding and Subtracting: Creating and Destroying: Receiving and Paying: may be denoted by the same signs + and -.

Hence if the Right to Demand £100 be denoted by + £100: the Duty to Pay £100 will be denoted by -£100: without any reference to any specific £100.

15. The use of the terms Positive and Negative to denote opposition is very commonly used by Jurists as well as by mathematicians.

Thus Ortolan uses the terms Positive and Negative Rights to denote Rights to acts and Rights to forbearances.

In its relation to a Right a Duty is Negative. But Duties themselves are termed Positive and Negative: as there is the Duty to do something and the Duty to abstain from doing something. Hence we may say that in this case we have a Negative sign within a Negative sign, as we shall presently find will be the case in Economics.

Arguing from these analogies in Mathematics and Law, we are quite at liberty in Economics to apply the terms Positive and Negative to Quantities and Operations of opposite qualities.

16. We shall now shew the application of these principles to Economics.

We have shewn that Property is a Right residing in the person. Now a man may have a Right to some specific actually existing thing, the produce of the past; and he may also have the Right to receive things which will only come into his possession at a future time, and some of which may not even come into existence till some future time. But each of these Rights is Property, and they may each be bought and sold: and therefore they are each Wealth. Consequently the totality of a man's Wealth is the Sum of the two kinds of Property. Now following the ordinary analogy of Natural Philosophy, if we denote the accumulated products of his industry already realised by the sign + > and call them Positive, we may call the products which will only come into his possession at a future time by the sign -, and call them Negative.

If we have some quantity like land which produces a series of products: and if we take the present time as the given era, which we denote by 0: then all the products which the land has produced in time past may be called Positive: and all the products it will produce in time future will be Negative.

But although these products will only come into existence at a future time, yet the Property or Right, to receive them when they do come into existence is Present. Hence the total amount of Property in land comprehends the Right to the produce of the past, together with the Right to the produce of the future: and as the Property in the produce of the past is Inverse, or Opposite, to the Property in the produce of the future, if we call the former Positive, the latter will be Negative, strictly in accordance with the principles of Natural Philosophy.

Now suppose that we purchase an estate in land for £100,000: where is the Value of our money? Does it consist in things which have a present existence? The veriest tyro would answer - certainly not. Where then is the equivalent for the purchase money ?

When we purchase an Estate in land we purchase the Right to the actually existing produce of land and labour, such as the houses, the timber trees, the crops on the ground, together with the Right to receive its annual produce for ever: a series of products which will only come into existence at definite intervals of time for ever. Thus Property in land consists of two perfectly distinct parts: Property in the products of the past, and Property in a series of products of the future, say £3,000 a year for ever, which may be represented thus -

Existing produce of land ( + ) together with -£3,000, -£3,000-£3,000, etc. for ever.

Where the Negative Sign means that the products will only come into existence at future definite intervals of time.

But though the yearly produce of the land will only come into existence at future intervals of time, the Property, or Right, to receive them when they do come into existence is present, and may be bought and sold like a horse or a table. That is to say, each of these annual profits for ever has a Present Value: and the purchase money of the land is simply the sum of the Present Values of this series of future payments for ever.