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 on which the values of commodities produced within any “nation” are determined, and then to consider whether any change must be made when we bring in other nations. We are at once met with the difficulty, What is a “nation”? The orthodox answer appears to be that within any nation (for which the term “ economic area ” might perhaps be advantageously substituted) there is effective industrial and commercial competition. This appears to imply no more than is contained in the principle noticed above, that relative values tend to be equal to the normal expenses of production (commercial competition), and that the expenses tend to be proportioned to the real cost (industrial competition). The question then arises, Do these conditions not exist in international trade? The answer appears to be, first, that commercial competition certainly holds good; for as soon as a trade is established the commodities will sell at the same prices in both countries (allowance being made for cost of carriage). It would plainly be absurd to say that the value of Manchester goods is determined by their expenses of production if they are consumed in England, but by something else if they are sent to India. If then there is any difference between domestic and international values, it must arise owing to the absence of effective industrial competition; that is to say, in the same country (or economic area) the real cost determines the expenses of production on account of the supposed perfect mobility of labour and capital, but between different economic areas these agents of production do not pass with sufficient readiness to secure a similar correspondence. It thus follows that a country may import articles which it could produce at less real cost, provided that it pays for these imports with exports which cost even less. A very striking example of this doctrine of comparative cost, as it is termed, was furnished by Victoria after the great gold discoveries. All kinds of produce were imported and paid for with gold, because there was less real cost involved in obtaining the gold to pay for imports than in making the articles. According to this theory every country will devote its labour and capital to its most productive uses; and, if by some new imports a domestic industry is checked or abolished, it is argued that the labour and capital will be devoted to increasing the exports so as to pay for the new imports. It must clearly be assumed as axiomatic that in the absence of loans, tributes, &c., imports can in the long run only be paid for by exports, and also that those articles will be exported which can be produced at the least comparative real cost. This theory then may be held to explain in a satisfactory manner the origin and development of international trade; but the question of values is still undetermined. Consistently with exports paying for imports many different rates of exchange are possible, and the particular rate actually adopted is said to depend entirely on reciprocal demand. And in an extreme case, in which new countries trade solely in articles of which each has a monopoly, this answer would seem to be correct; but, when we consider that under present conditions trading countries have many articles in common, and that a slight margin of profit suffices to expand or diminish an export trade, this answer seems too vague and unreal. In general it is clear that the rate will be determined independently of the foreign trade, or at least that the foreign trade is only one factor to be considered. If the rate of profit falls, a trade which before was impossible becomes possible. The opinion may be hazarded that the best way of explaining the general theory of international values would be to start with the foreign exchanges; but such an investigation is too technical and difficult for this place (see ).

VALVE (Lat. valve, a leaf of a double or folding door, allied to volvere, to roll, as of a door on its hinges), a term applied to many mechanical appliances, devices or natural features, which control, by opening and shutting, the flow of air, liquids, vapour, gas, &c., through a passage, tube, pipe or other vessel.

VALVES, or (Fr. pistons, cylindres; Ger. Ventile; Ital. pistoni), in music, mechanical contrivances applied to wind instruments in order to establish a connexion between the main tubing and certain supplementary lengths required for the purpose of lowering, the pitch. Various devices have been tried from the days of ancient Greece and Rome to produce this effect, the earliest being the additional tubes ( ) inserted into the lateral holes of the aulos and tibia in order to prolong the bore and deepen the pitch of each individual hole; these tubes were stopped by the fingers in the same manner as the holes. This device enabled the performer to change the mode or key in which he was playing, just as did the crooks many centuries later. But the resourcefulness of the ancients did not stop there. The tibiae found at Pompeii (see ) had sliding bands of silver, one covering each lateral hole in the pipe; in the band were holes (sometimes one large and one small, probably for semitone and tone) corresponding with those on the pipe. By turning the band the holes could be closed, as by keys when not required. By fixing the  in the holes of the bands, the bore was lengthened instantly at will, and just as easily shortened again by withdrawing them; this method was more effective than the use of the crooks, and foreshadowed the valves of eighteen centuries later. The crooks, or coils of tubing inserted between the mouthpiece and the main tube in the trumpet and horn, and between the slide and the bell joint in the trombone, formed a step in this direction.

Although the same principle underlies all these methods, i.e. the lengthening of the main column of air by the addition of other lengths of tubing, the valve itself constitutes a radical difference, for, the adjustment of crooks demanding time and the use of both hands, they could only be effective for the purposes of changing the key and of rendering a multiplicity of instruments unnecessary. The action of the valve being as instantaneous as that of the key, the instrument to which it was applied was at once placed on a different basis; it became a chromatic instrument capable of the most delicate modulations from key to key. The slide had already accomplished this desirable result, but as its application was limited to instruments of which the greater part of the bore was cylindrical, i.e. the trumpet and trombone, its influence on concerted musical composition could not be far-reaching. In fact it is doubtful whether the chromatic possibilities of the slide were fully realized until the end of the 18th century, when key mechanism having made some advance, it was being applied successfully to the transverse flute and to the clarinet and oboe families. In 1760 Kölbel, a Bohemian horn-player engaged in the St Petersburg Imperial Orchestra, turned his attention to this method of extending the compass of brass instruments. His experiments, followed up by Anton Weidinger of Vienna at the beginning of the 19th century, produced a trumpet with five keys and a complete chromatic compass. Halliday followed with the keyed bugle in 1810. Halary applied the principle of the keyed bugle to the bass horn in 1817, and produced the ophicleide—an ideal chromatic bass as far as technical possibilities were concerned. The horn had become a chromatic instrument through Hampel’s discovery of bouché sounds, but the defects in intonation and timbre still remained.

Such were the conditions prevailing among the wind instruments of the orchestra when the successful application of the valve to brass wind instruments by Heinrich Stölzel of Silesia caused an instantaneous revolution among makers of wind instruments. Further efforts to perfect the key system as applied to the brass wind were abandoned in favour of valves. The short space of two decades witnessed the rise of the Flügelhorns, the tubas, the saxhorns and the cornet-à-pistons; the trombone, French horn and trumpet having led the van.

Sound is produced on brass wind instruments by overblowing the members of the harmonic series (see ). The harmonic series itself is invariable, whether obtained from a string or a column <-- -->