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 in horology, a device for equalizing the relaxing of a watch or clock spring (see ); the “balancing of engines,” the art of minimizing the total vibrations of engines when running, and consisting generally in the introduction of masses which induce vibrations opposed to the vibrations of the essential parts of the engine. BALANCE OF POWER, a phrase in international law for such a “just equilibrium” between the members of the family of nations as should prevent any one of them from becoming sufficiently strong to enforce its will upon the rest. The principle involved in this, as Hume pointed out in his Essay on the Balance of Power, is as old as history, and was perfectly familiar to the ancients both as political theorists and as practical statesmen. In its essence it is no more than a precept of commonsense born of experience and the instinct of self-preservation; for, as Polybius very clearly puts it (lib. i. cap. 83): “Nor is such a principle to be despised, nor should so great a power be allowed to any one as to make it impossible for you afterwards to dispute with him on equal terms concerning your manifest rights.” It was not, however, till the beginning of the 17th century, when the science of international law took shape at the hands of Grotius and his successors, that the theory of the balance of power was formulated as a fundamental principle of diplomacy. According to this the European states formed a sort of federal community, the fundamental condition of which was the preservation of the balance of power, i.e. such a disposition of things that no one state or potentate should be able absolutely to predominate and prescribe laws to the rest; and, since all were equally interested in this settlement, it was held to be the interest, the right and the duty of every power to interfere, even by force of arms, when any of the conditions of this settlement were infringed or assailed by any other member of the community. This principle, once formulated, became an axiom of political science. It was impressed as such by Fénelon, in his Instructions, on the young duke of Burgundy; it was proclaimed to the world by Frederick the Great in his Anti-Machiavel; it was re-stated with admirable clearness in 1806 by Friedrich von Gentz in his Fragments on the Balance of Power. It formed the basis of the coalitions against Louis XIV. and Napoleon, and the occasion, or the excuse, for most of the wars which desolated Europe between the congress of Münster in 1648 and that of Vienna in 1814. During the greater part of the 19th century it was obscured by the series of national upheavals which have remodelled the map of Europe; yet it underlay all the efforts of diplomacy to stay or to direct the elemental forces let loose by the Revolution, and with the restoration of comparative calm it has once more emerged as the motive for the various political alliances of which the ostensible object is the preservation of peace (see : History).

An equilibrium between the various powers which form the family of nations is, in fact,—as Professor L. Oppenheim (Internat. Law, i. 73) justly points out—essential to the very existence of any international law. In the absence of any central authority, the only sanction behind the code of rules established by custom or defined in treaties, known as “international law,” is the capacity of the powers to hold each other in check. Were this to fail, nothing could prevent any state sufficiently powerful from ignoring the law and acting solely according to its convenience and its interests.

BALANCE OF TRADE, a term in economics belonging originally to the period when the “mercantile theory” prevailed, but still in use, though not quite perhaps in the same way as at its origin. The “balance of trade” was then identified with the sum of the precious metals which a country received in the course of its trading with other countries or with particular countries. There was no doubt an idea that somehow or other the amount of the precious metals received represented profit on the trading, and each country desired as much profit as possible. Princes and sovereigns, however, with political aims in view, were not close students of mercantile profits, and would probably have urged the acquisition of the precious metals as an object of trade even if they had realized that the country as a whole was exporting “money’s worth” in order to buy the precious metals which were desired for political objects. The “mercantile theory” was exploded by Adam Smith’s demonstration that gold and silver were only commodities like others with no special virtue in them, and that they would come into a country when there was a demand for them, according to the amount, in proportion to other demands, which the country could afford to pay; but the ideas in which the theory itself has originated have not died out, and the idea especially of a “balance of trade” to which the rulers of a country should give attention is to be found in popular discussions of business topics and in politics, the general notion being that a nation is prosperous when its statistics show a “trade balance” in its favour and unprosperous when the reverse is shown. In modern times the excess of imports over exports or of exports over imports, shown in the statistics of foreign trade, has also come to be identified in popular speech with the “balance of trade,” and many minds are no doubt imbued with the ideas (1) that an excess of imports over exports is bad, and (2) an excess of exports over imports is the reverse, because the former indicates an “unfavourable” and the latter a “favourable” trade balance. In the former case it is urged that a nation so circumstanced is living on its capital. Exact remedies are not suggested, although the idea of preventing or hampering foreign imports as a means of developing home trade and of thus altering the supposed disastrous trade balance is obviously the logical inference from the arguments. A consideration of these ideas and of recent discussions about imports and exports, appears accordingly to be needed, although the “mercantile theory” is itself exploded.

The phrase “balance of trade,” then, appears to be an application of a trader’s language in his own business to the larger affairs of nations or rather of the aggregate of individuals in a nation engaged in foreign trade. A trader in his own books sets his sales against his purchases, and the amount by which the former exceed the latter is his trade balance or profit. What is true of the individual, it is assumed, must be true of a nation or of the aggregate of individual traders in a nation engaged in the foreign trade. If their collective sales amount to more than their collective purchases the trade balance will be in their favour, and they will have money to receive. Contrariwise, if their purchases amount to more than their sales, they will have to pay money, and they will presumably be living on their capital. The argument fails, however, in many ways. Even as regards the experience of the individual trader, it is to be observed that he may or may not receive his profit, if any, in money. As a rule he does not do so. As the profit accrues he may invest it either by employing labour to add to his machinery or warehouses, or by increasing his stock-in-trade, or by adding to his book debts, or by a purchase of stocks or shares outside his regular business. At the end of a given period he may or may not have an increased cash balance to show as the result of his profitable trading. Even if he has an increased cash balance, according to the modern system of business, this might be a balance at his bankers’, and they in turn may have invested the amount so that there is no stock of the precious metals, of “hard money,” anywhere to represent it. And the argument fails still further when applied to the transactions between nations, or rather, to use the phrase already employed, between the aggregate of individuals in nations engaged in the foreign trade. It is quite clear that if a nation, or the individuals of a nation, do make profit in their foreign trading, the amount may be invested as it accrues—in machinery, or warehouses, or stock-in-trade, or book debts, or stocks and shares purchased abroad, so that there may be no corresponding “balance of trade” to bring home. There is no doubt also that what may be is in reality what largely happens. A prosperous foreign trade carried on by any country implies a continuous investment by that country either abroad or at home, and there may or may not be a balance receivable in actual gold and silver.