In the first place it is evident that numbers only begin to tell when other things are fairly equal. Quite a few men armed with rifles will be a match for multitudes deprived of firearms, and the history of war is full of smaller forces defeating larger forces from Marathon to Ligny. But when war follows upon a long period of peace and takes place between nations of one civilization all closely communicating one with another, and when war has been the principal study of those nations during the period of peace, then all elements except those of numbers do become fairly equal. And that is exactly the condition of the present campaigns. The enemy have certain advantages in material, or had at the beginning of the struggle, notably in the matter of heavy artillery, but much more in the accurate forecast they had made of the way in which modern fighting would turn. All sorts of their tactical theories turned out to be just. The Allied forces had advantages--the English in personal equipment, medical and commissariat service; the French, Russians, and Serbians, in the type of field gun. The French in particular in their theory of strategy, which has proved sound. But there was no conspicuous difference such as would make a smaller number able to defeat a much larger one, and the historical observer at a distance of time that will make him impartial, will certainly regard the war as one fought between forces of nearly the same weaponing and training. The one great differentiating point will be numbers. Now how is it that these numbers tell? There are two aspects of the thing which I will call (1) The Effect of _Absolute_ Numbers and (2) The Effect of _Proportionate_ Numbers. (1) _Absolute Numbers_. I mean by the effect of absolute numbers the fact that a certain minimum is required for any particular operation. For instance, if you were holding a wall a mile long which an enemy upon the other side desired to surmount, it is evident that you could not hold such a wall with one man even though the enemy on the other side consisted only in one man. The opportunities for the success of the enemy would be too great. You could not hold it with ten men against ten. You could hardly hold it with 100 men against 100. But supposing that you have 3000 men to hold it with, and they are using no weapons save their hands, then 3000 men could hold the wall not only against 3000 others, but against any number of thousands of others; for every man would have as his task the pushing of a ladder off no more than a very small section of the wall with which his own hands could deal. There we see what is meant by the necessity of absolute numbers or a minimum.