will produce the greatest effect, must be made against that part of the country where the greatest number of the enemy’s forces are collected together; and the greater the mass of our own forces which we use for this blow, so much the surer shall we be of this success. This natural sequence of ideas leads us to an illustration by which we shall see this truth more clearly; it is the nature and effect of the centre of gravity in mechanics.
As the centre of gravity is always situated where the greatest mass of matter is collected, and as a shock against the centre of gravity of a body always produces the greatest effect, and further, as the most effective blow is struck with the centre of gravity of the power used, so it is also in war. The armed forces of every belligerent, whether of a single state or of an alliance of states, have a certain unity, and in that way, connection; but where connection is there come in analogies of the centre of gravity. There are, therefore, in these armed forces certain centres of gravity, the movement and direction of which decide upon other points, and these centres of gravity are situated where the greatest bodies of troops are assembled. But just as, in the world of inert matter, the action against the centre of gravity has its measure and limits in the connection of the parts, so it is in war, and here as well as there the force exerted may easily be greater than the resistance requires, and then there is a blow in the air, a waste of force.
What a difference there is between the solidity of an army under one standard, led into battle under the personal command of one general, and that of an allied army extended over 50 or 100 miles, or it may be even based upon quite different sides (of the theatre of war). There we see coherence in the strongest degree, unity most complete; here unity in a very remote degree often only existing in the political view held in common, and in that also in a miserable and insufficient degree, the cohesion of parts mostly very weak, often quite an illusion.