The first postulate in all military problems is that, other things being equal, numbers are the decisive factor in war. This does not mean that absolute superiority of numbers decides a campaign necessarily in favour of the superior power. What it means is that _in any particular field_, if armament and discipline are more or less equal on the two sides, the one that has been able to mass the greater number _in that field_ will have the victory. He will disperse or capture his enemy, or at the least he will pin him and take away his _initiative_--of which word "initiative" more later. Now, this field in which one party has the superior numbers can only be a portion of the whole area of operations. But if it is what is called the decisive portion, then he who has superior numbers _in the decisive time and place_ will win not only there but everywhere. His local victory involves consequent success along the whole of his line. For instance, supposing five men are acting against three. Five is more than three; and if the forces bear upon each other equally, the five will defeat the three. But if the five are so badly handled that they get arranged in groups of two, two, and one, and if the three are so well handled that they strike swiftly at the first isolated two and defeat them, thus bringing up the next isolated two, who are in their turn defeated, the three will, at the end of the struggle, have only one to deal with, and the five will have been beaten by the three because, although five is larger than three, yet _in the decisive time and place_ the three never have more than two against them. It may be broadly laid down that the whole art of strategics consists for the man with superior numbers in bringing all his numbers to bear, and for the man with inferior numbers in attempting by his cunning to compel his larger opponent to fight in separated portions, and to be defeated in detail. As in every art, the developments of these elementary first principles become, with variations of time and place, indefinitely numerous and various. Upon their variety depends all the interest of military history. And there is one method in particular whereby the lesser number may hope to pin and destroy the power of the greater upon which the French tradition relied, and the value of which modern German criticism refused. Before going into that, however, we must appreciate the mental qualities which led to the acceptance of the theory upon the one side and its denial upon the other. The fundamental contrast between the modern German military temper and the age-long traditions of the French service consists in this: That the German theory is based upon a presumption of superiority, moral, material, and numerical. The theory of the French--as their national temperament and their Roman tradition compel them--is based upon an _envisagement_ of inferiority: moral, material, and numerical.