=

result. Suppose his creditor releases him from his debt, his property would then be 0, and he would also be 50 crowns better off than before. This clearly shews that the release (—) of a debt (-) is the same thing as an increase (+) of wealth.

19. Hence we see the enormous importance of a very careful attention to the mode of stating the facts in Economics.

A man's property and his obligations being then analogous to opposite quantities, we have manifestly the following laws:If we add (+) to his property (+), his obligations (—) remaining the same, that is an increase (+) of property.

If we take away (-) from his property (+), that is a diminution (-) of his property.

If we add (+) to his obligations (-), that is in effect a diminution (-) of his property.

But if we take away (-) from his obligations (-), that is in effect an increase (+) of his property.

Hence we obtain this doctrine in commerce,-A RELEASE FROM A DEBT IS AN AUGMENTATION OF CAPITAL.

We shall see afterwards that this doctrine leads to consequences of the most momentous nature in commerce, which may possibly surprise some of our readers.

The whole subtlety in the case is in distinguishing between one quantity being equal and opposite to another, and therefore neutralising its effects, and taking it way altogether. The opposition in Parliament do not take away, or subtract, an equal number of ministerialists, they only neutralize their effects. To take away from the opposition does not add to the Government numbers, it only takes away a quantity which neutralized their effects.

20. Another very eminent writer, Peacock, Dean of Ely, after saying that property and debts may be symbolized by + and -, says "if a denoted property possessed, and -a a debt, V=1. a might denote property neither possessed nor owed, such as a mere deposit would be."

Peacock has explained his ideas at greater length at p. 366, Art. 447. of the same volume. He says "There are many cases, however, of quantities which cannot be represented, unless symbolically, by lines, which are susceptible of affections denoted 1 Algebra, 1st Edit., p. 77.

D

by + and, which are appropriate to their specific nature: thus, if a represented property possessed, -a may represent the same property owed; under such circumstances, what is the meaning which may be attached to a V-1 and av-1? If we consider the succession of quantities a, av—1, a(v— 1)2, a( V— 1)3,

or,

-

a, av-i, -a, a v—1,

and if the first represents property possessed, and the third property owed, the second can neither represent property possessed nor owed, under the same circumstances or by the same person, inasmuch as in such a case, it would be symbolically represented by a ora: it may represent, however, property deposited, which admits of similar relations when considered as property possessed and property owed by another person; under such circumstances, the affectation of a denoting property possessed by A by the sign V-1 would convert it into property possessed by B: and the affectation of a v-1 by V-1, would convert property possessed by B into property owed by A: thirdly, the affectation of a by V-1 would convert property owed by A into property owed by B: and fourthly, the affectation of V-1 by i would convert property owed by B into property possessed by A: the repetition of the process of affectation by the sign 1, would reproduce continually the same succession of transfers of property from A to B, and of conversions of property possessed into debt, and of debt into property possessed, which is required to correspond to the succession of the same symbolical results.

- a

"In this case, the interpretation of the sign 1 which we have given, satisfies the symbolical conditions, and also coincides with the interpretation of the meaning of the signs + and -, which is otherwise established: we cannot give it the additional authority of the coincidence of this interpretation with the interpretation of the meanings of the quantities corresponding to a' and a', for those quantities in the case under consideration admit of no interpretation."

21. With all deference to so great a writer, we think this view is not correct. In fact there is no such thing as property owed. As Credit is a personal Right residing in the Creditor,

so Debt is a personal Duty residing in the Debtor. The Credit itself is an article of property, which must have arisen out of some previous exchange, and what is really meant by saying that a man is in debt is, that he must exchange some of his property to buy this Debt or Credit. Now the symbol -1 denotes that operation which being twice repeated, changes + into.

Hence, if this symbol is applicable to Economics at all, it must denote the operation which, being twice repeated, changes property into a debt. But depositing a thing twice with a man does not change property into a debt. Nor does it transfer the property. These are single operations of the will, and, therefore, it appears to us that Economics is a science to which the symbol V-1 is not applicable.

After venturing the criticism contained in the preceding paragraph on the views of Peacock, we have had the great satisfaction of finding that De Morgan has expressed similar sentiments in the article Algebra in the English Cyclopædia. He says "It is impossible that a perfect Algebra can be founded on ideas of time, loss and gain, or any in which only two directions can be imagined. Space, from the affinity of directions which it admits, is as yet the only perfect medium of explanation. Time before and time after a certain epoch may be represented by the positive and negative quantity; but what is there in the idea of time to which the sign 1 can possibly apply? Again, shew us a commercial operation which performed upon a gain, produces a sort of result which can neither be called gain or loss, but which repeated two or more times upon a gain turns it into a loss-and we can immediately see a system of Commercial Algebra in which 1 shall be intelligible."

22. As this point is, in fact, the greatest subtlety in Economics, and involves consequences of the most momentous nature, which we dare say our readers little dream of at present, but which are fully explained afterwards, we shall extract what Peacock has said in the 2nd edition of his Algebra, p. 15. :—

"We conclude our observations upon this subject with the discussion of one more example of a problem of very extensive application.

"A merchant possesses a pounds and owes b pounds; his substance is therefore a - b, where a is greater than b.

b

-

“But since a and b may possess every relation of value, we may replace by ac, or by a + c, according as a is greater or less than b; in the first case we get

(a + c)

If c therefore express his substance or property, when solvent, c will express the amount of his debts when insolvent: and if from the use of and as signs of affection, or quality, in this case, we pass to their use as signs of operation, then inasmuch as

a + (—c) =α c and a

it will follow, that the addition of a debt (c) is equivalent to the subtraction of property c of an equal amount, and the subtraction of a debt (c) is equivalent to the addition of property c of an equal amount, and it consequently appears that the subtraction of a debt, in the language of symbolical algebra, is not its obliteration or removal, but the change of its affection or character, from money or property owed, to money or property possessed."

23. We hope we shall succeed in shewing that the views expressed in this latter paragaph are not correct.

In the first place we must say that there is no such thing as property owed. A debt in commerce is a species of property itself, which was created in exchange for some property. And when a man is in debt it means that he is bound to buy up, or exchange some part of his property for this debt. But there is no particular part of his property which he may be said to owe more than another. His property is absolutely his own, and indeed he may spend it all and leave his debts unpaid.

Now as a debt always arises out of an exchange, and must necessarily do so, an addition of debt also arises out of an additional exchange. It is a new property created in exchange for more property. Hence to add and to subtract a debt, is in fact to create and to destroy property. As we shall shew.

A banker receives £100 in money from his customer, and in

exchange for that, he creates £100 of debt, which is the property of his customer. His property is then stated

£100 £100 = 0.

Now arguing according to the common mode, that means there is no property at all in existence, a conclusion that is manifestly

erroneous.

he

It is perfectly true that, so far as regards the banker himself, may be said to be no richer than he was before, but as far as regards Economics-and it is the master subtlety of the subject -the effects are very different. The banker has now £100 in money, which is his own property, which he may trade with, and make a profit by. And his customer has £100 as well, in the banker's notes, with which he can buy anything he wants, as well as with money. Hence there are two circulating and exchangeable properties instead of one. And though no doubt the banker is always liable to be called on to exchange some of his money for his liabilities, yet the very business of banking is based on the probability that he will not be called upon to do so to any very appreciable amount at any one time.

The banker, then, possesses as his own property £100, coupled with the Duty to pay £100, if required to do so. The customer has the Right to demand £100, in the banker's notes, which pass currently as money. Now suppose that for any reason, the

customer chooses to release the banker from his debt. He does this by presenting him with his own notes. The banker, then, has £100 in money, and besides that he has the Duty to pay. £100 (£100) and the Right to demand £100 (+£100). Now these two latter quantities cancel each other; and the banker has now the £100 in money, freed from any Duty to pay and therefore he is practically £100 richer than before; but so far as regards Economics, there has been a destruction of property. By this operation his assets remain exactly as they were before, but his liability has been destroyed.

:

Hence we see where Peacock's error lies, and it is a very important one, and must be thoroughly explained. Peacock considers a Debt to be money owed, or money affected with the Negative Sign, and the subtraction of a Debt to be the change of the sign of affection of money owed into money possessed. But this is a great error. As Credit is the abstract Right to demand residing in the person of the Creditor, so the Debt is the