9. We have now to explain the meaning of the Negative Sign in the Theory of Credit, or Debt.

Two Algebraists of the highest eminence have attempted to explain the application of the Negative Sign to the subject of Debts, or Credit, but they have fallen into exactly the same error as Thornton and Cernuschi.

Euler says - "The manner in which we generally calculate a person's property is an apt illustration of what has just been said. We denote what a man really possesses by positive numbers, using or understanding the sign +, whereas his debts are represented by negative numbers, or by using the sign -. Thus when it is said of any one that he has 100 crowns but owes 50, this means that his real possessions amount to 100 - 50, that is to say 50.

"As negative numbers may be considered as debts, because positive numbers represent real possessions we may say that negative numbers are less than nothing. Thus when a man has nothing in the world, and even owes 50 crowns, it is certain that he has 50 crowns less than nothing: for if any one were to make him a present of 50 crowns to pay his debts, he would still be only at the point nothing, though really richer than before."

It is quite evident that Euler has, in this passage, fallen into exactly the same error as Thornton and Cernuschi: namely that of considering a Debt to be money pledged to the Creditor: and so affected with the Negative sign. But as we have distinctly shewn that a Debt is a Personal Duty, it is quite evident that a Personal Duty cannot be subtracted from a sum of money.

It is quite easy to shew that the first paragraph is not a suitable mode of stating the question in Economics. For suppose that a man has 100 crowns, and that he is bound to pay 50 crowns one year hence: it would be quite inaccurate to say that his property is only 50 crowns, or (100 - 50). For he has the 100 crowns to trade with in the meanwhile, as his absolute property: and all that he is bound to do is to have on a certain day at the end of the year 50 crowns to discharge his debt. But the owner of the Debt may put it into circulation, and it may produce all the effects of money till it is paid. So that there may be the 100 crowns and the debt of 50 crowns as well, circulating simultaneously in commerce. And yet his property might be correctly stated (100 - 50) crowns. Here it is quite clear that the 50 crowns are not to be subtracted from his present property. Now by the Law of Continuity, the same must be true if we dimmish the period of payment gradually from one year by small gradations of a day at a time, till we reduce it to 0, or make the debt payable on demand. The fact is that the expression is to be read this way - he possesses 100 crowns as his property, but coupled with the Duty of paying 50 crowns at some given time.

So in the second paragraph, when he possesses no crowns, and owes 50 crowns, he is said to have less than nothing. This clearly means that he is under the Duty, or Obligation, to pay 50 crowns, and has nothing to pay them with. Now let us suppose that being in this position, as Euler says, some one makes him a present of 50 crowns to pay his debt, he is clearly 50 crowns richer than before, and yet his property is now only = 0. This is an example of + x + giving +. Thus Euler is right so far as he goes : but he has manifestly stated only one half of the case. Because there is another combination of algebraical symbols which gives +, namely - x - : and there is another method in commerce of arriving at the same practical result. Suppose his Creditor Releases him from his debt, his property would then also = 0 : and as in the former case, he would be 50 crowns better off than before.

Thus Releasing a debtor from the Duty to pay money, is exactly equivalent to making him a present of money. This shews that the Release ( -) of a Debt ( -) is the same thins as an Increase ( + ) of Wealth ( + ), or that - x - = + x + ; a principle of the most momentous consequence in modern commerce.

Peacock has fallen into exactly the same error; for he con-eiders a Debt as Money or Property owed; which is exactly the error which the Digest, Pothier, and other Civilians have so carefully pointed out. Peacock considers that the subtraction of a debt is the change of the character or affection of money owed to money possessed: in which he is quite mistaken, for the subtraction of a debt is not changing the Right in the money from the Creditor (which does not exist) to the Debtor, but simply extinguishing the Debtor's Duty to pay it.

10. The perplexities of the Theory of Credit can only be unravelled by the great modern Algebraical doctrine of the Separation of the Signs of Affection or Position and Operation.

Writers who are not versed in Natural Philosophy have no conception of the signs + and - meaning anything but addition and subtraction, whereas the symbols +, 0, and - have an immense variety of meanings in Natural Philosophy, according to the particular circumstances under which they occur: and it is wholly impossible to determine their meaning, until we know the particular state of circumstances out of which they arise.

Every great science is founded on some single idea, or conception, or quality, which must be of the most general nature, and every Quantity whatever in which that quality is found is an element in that science no matter what other qualities are found in it. Quantities therefore utterly dissimilar in every other respect are elements in that science, so long as the single fundamental quality is found in them.

Now as Economics is the science of Exchanges, or Values, it necessarily follows that every Quantity whatever, which is capable of being exchanged or valued, must be an Economic Quantity, no matter what its nature is, enduring or evanescent, corporeal or incorporeal.

But these Quantities in the various sciences may be endowed with opposite qualities, and when they are so, it is universally the custom in Natural Philosophy to distinguish them by the signs + and -.