Page:Encyclopædia Britannica, Ninth Edition, v. 3.djvu/283

Rh The ordinary Decimal Balance is a combination of levers illustrated by fig. 9. a, c, b, d, e, g, h, f, are all joints or pivots ; a and h rest on the fixed framework of the machine, and consequently indirectly on the ground ; c rests on the lever ab. In the actual machine cd supports the &quot; bridge&quot; which accommodates the load, while at / is suspended a pan for the weight. The pan is so adjusted Fm. 9. Decimal Balance. that it balances the bridga Suppose the load P to be placed so that its centre of gravity is at i, and a portion P c of P will press on the knife-edge at c, the rest P &amp;lt;( will pull at d and, with the same force, at g. Now, P, &#61; P., equivalent to P,. pulling at b or e, equivalent to cd ab The dimensions are so chosen _, ac id eli P . . . pulling at g. J 7 t * O / ab cd gfi that [ math ], hence the effect of P,. at g is equivalent to ab eh _ id a weight P. &#61; . The other portion of P, viz., P d , pulls cd 1C at d, and consequently also at g, with a force P. . cd Hence the effect of the total load is equivalent to P . ( lC u ) &#61; P units suspended at g, and if, for instance, cd / ffh TG fyf, one pound in the pan will counterpoise ten pounds at any point of the bridge.|1}}

5. Torsion Balances.—Of the several instruments bearing this name, the majority are no balances at all, but machines for measuring horizontal forces (electric, magnetic, &c.), by the extent to which they are able to distort an elastic wire vertically suspended and fixed at its upper end. In the torsion balances proper the wire is stretched out horizon tally, and supports a beam so fixed to it that the wire passes through its centre of gravity. Hence the elasticity of the wire here plays the same part as the weight of the beam does in the common balance. An instrument of this sort was invented by Ritchie for the measurement of very small weights, and for this purpose it may offer certain advan tages; but, clearly, if it were ever to be used for measuring larger weights, the beam would have to be supported by knife-edges and bearings, and in regard to such application therefore (i.e., as a means for serious gravimetric work), it has no raison d'être. See and. 6. For Hydrostatic weighing machines see the article.  BALANCE OF POWER. The theory of the Balance of Power may be said to have exercised a preponderating influence over the policy of European statesmen for more than two hundred years, that is, from the Treaty of Westphalia until the middle of the present century; and to have been the principal element in the political combinations, negotiations, and wars which marked that long and eventful period of modern history. It deserves, therefore, the attentive consideration of the historical student, and, indeed, the motive cause of many of the greatest occurrences would be unintelligible without a due estimate of its effects. Even down to our own times it has not been without an important influence ; for the Crimean War of 1854 was undertaken by England and France for no other object than to maintain the balance of power in Eastern Europe, and to prevent the aggrandise ment of Russia by the dismemberment of the Ottoman empire and the conqiiest of Constantinople. Nevertheless there is, perhaps, no principle of political science, long and universally accepted by the wisest statesmen, on which modern opinion has, within the last twenty years, under gone a greater change ; and this change of opinion is not merely speculative, it has regulated and controlled the policy of the most powerful states, and of none more than of Great Britain, in her dealings with the continent of Europe. At the date of the publication of the last edition of this work, the theory of the balance of power was believed to be so firmly established, both by reason and experience, that it was laid down, in the forcible words of Earl Grey, that &quot; the poorest peasant in England is inter ested in the balance of power, and that this country ought to interfere whenever that balance appeared to be really in danger.&quot; At the present time no English statesman would lay down that proposition categorically ; and pro bably no European statesman would be prepared to act upon it. In proportion as the theory of the balance of power has lost much of its former authority, the doctrine of non-intervention has gained strength and influence, and this has been accepted at the present day both by Whig and Tory ministers, so that no strong difference of opinion can at the present time be said to exist in the British nation on the subject. Within the last fifteen years political changes of extraordinary magnitude have been brought about in Europe by force of arms and by revolutions. In former times such changes would certainly have led to a general war, on the principle that it was essential to maintain the relative strength and independence of states, and to support the fabric of European policy. But, under the policy of non-intervention, the effects of these contests have been confined to the states which were directly engaged in them ; and the other powers of Europe have maintained a cautious neutrality, which has probably not lessened their own strength, and which has saved the world from a general conflagration. The theory of the balance of power rested on several assumptions. It was held, more especially from the time of Grotius, in the early part of the 17th century, that the states of Europe formed one grand community or federal league, of which the fundamental principle and condition was the preservation of the balance of power ; that by this balance (in the words of Vattel) was to be understood such a disposition of things, as that no one potentate or state shall be able absolutely to predominate and prescribe laws to the others ; that all were equally interested in maintaining this common settlement, and that it was 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. The principle can hardly be more tersely expressed than in the words of Polybius (lib. i. cap. 83) : &quot; Neque enim ejusmodi principia contemnere oportet, neque tanta cuiquam astruenda est potentia, ut cum eo postea de tuo quamvis manifesto jure disceptare ex aequo non queas.&quot; Or, to borrow the language of Fenelon in his Instructions, drawn up by him for the guidance of the Due de Bourgogne, &quot; This attention to maintain a sort of equality and equipoise between neighbouring nations is the security of the general tranquillity. In this respect all neighbouring nations, trading with each other, form one great body and a sort of community. Thus, Christendom is a kind of universal republic, which has its interests, its fears, and its precautions to be taken. All the members 