Castlereagh's Balance of Power is what I believe mathematicians call a multiple balance. It was not like a pair of scales, in which you have only two weights or forces balanced one against the other. It was rather like a chandelier, in which you have five or six different weights co-operating to produce a general stability or equilibrium. In Castlereagh's scheme it would not much matter if one of the weights were a little heavier than the others, because there would be four or five of these others to counterbalance it; and his assumption was that these other Powers would naturally combine for the purpose of redressing the balance and preserving the peace. But a simple balance between two opposing forces is a very different thing. If there are only two, you have no combination on which you can rely to counteract the increasing power of either, and the slightest disturbance suffices to upset the balance. Castlereagh's whole scheme therefore presupposed the continued and permanent existence of some five or six great Powers always preserving their independence in foreign policy and war, and automatically acting as a check upon the might and ambition of any single State. THE CHANGE SINCE CASTLEREAGH Now, it was this condition, essential to the maintenance of Castlereagh's Balance of Power, which completely broke down during the course of the nineteenth century. Like most of the vital processes in history, the change was gradual and unobtrusive, and its significance escaped the notice of politicians, journalists, and even historians. Men went on repeating Castlereagh's phrases about the Balance of Power without perceiving that the circumstances, which alone had given it reality, had entirely altered. The individual independence and automatic action of the Great Powers in checking the growing ambitions and strength of particular States were impaired, if not destroyed, by separate Alliances, which formed units into groups for the purposes of war and foreign policy, and broke up the unity of the European system, just as a similar tendency threatens to break up the League of Nations. There was a good deal of shifting about in temporary alliances which there is no need to recount; but the ultimate upshot was the severance of Europe into the two great groups with which we are all familiar, the Triple Alliance of Germany, Austria, and Italy on one side, and the Triple Entente between Russia, France, and Great Britain on the other. The multiple Balance of Power was thus changed into a simple balance between two vast aggregations of force, and nothing remained outside to hold the balance, except the United States, which had apparently forsworn by the Monroe Doctrine the function of keeping it even.