And so in this matter there are certain test facts which upset the adroitest statistical legerdemain. Though, really, the fallacy which regards an addition of territory as an addition of wealth to the "owning" nation is a very much simpler matter than the fallacies lying behind gambling systems, which are bound up with the laws of chance and the law of averages and much else that philosophers will quarrel about till the end of time. It requires an exceptional mathematical brain to refute those fallacies, whereas the one we are dealing with is due simply to the difficulty experienced by most of us in carrying in our heads two facts at the same time. It is so much easier to seize on one fact and forget the other. Thus we realize that when Germany has conquered Alsace-Lorraine she has "captured" a province worth, "cash value," in my critic's phrase, $330,000,000. What we overlook is that Germany has also captured the people who own the property and who continue to own it. We have multiplied by _x_, it is true, but we have overlooked the fact that we have had to divide by _x_, and that the result is consequently, so far as the individual is concerned, exactly what it was before. My critic remembered the multiplication all right, but he forgot the division. Let us apply the test fact. If a great country benefits every time it annexes a province, and her people are the richer for the widened territory, the small nations ought to be immeasurably poorer than the great, instead of which, by every test which you like to apply--public credit, amounts in savings banks, standard of living, social progress, general well-being--citizens of small States are, other things being equal, as well off as, or better off than, the citizens of great States. The citizens of countries like Holland, Belgium, Denmark, Sweden, Norway are, by every possible test, just as well off as the citizens of countries like Germany, Austria, or Russia. These are the facts which are so much more potent than any theory. If it is true that a country benefits by the acquisition of territory, and widened territory means general well-being, why do the facts so eternally deny it? There is something wrong with the theory.