If these sources of supply and refitment are abundant, that is, if the tracts of territory are wide and rich, if the stores are collected in great depôts to be more speedily brought into use, if these depôts are covered in a military sense in one way or another, if they are in close proximity to the army and accessible by good roads, if they extend along a considerable width in the rear of the army or surround it in part as well—then follows a greater vitality for the army, as well as a greater freedom in its movements. Attempts have been made to sum up all the advantages which an army derives from being so situated in one single conception, that is, the extent of the base of operations. By the relation which this base bears to the object of the undertakings, by the angle which its extremities make with this object (supposed as a point), it has been attempted to express the whole sum of the advantages and disadvantages which accrue to an army from the position and nature of its sources of supply and equipment; but it is plain this elegant piece of geometrical refinement is merely a play of fancy, as it is founded on a series of substitutions which must all be made at the expense of truth. As we have seen, the base of an army is a triple formation in connection with the situation in which an army is placed: the resources of the country adjacent to the position of the army, the depôts of stores which have been made at particular points, and the _province_ from which these stores are derived or collected. These three things are separated in space, and cannot be collected into one whole, and least of all can we substitute for them a line which is to represent the width of the base, a line which is generally imagined in a manner perfectly arbitrary, either from one fortress to another or from one capital of a province to another, or along a political boundary of a country. Neither can we determine precisely the mutual relation of these three steps in the formation of a base, for in reality they blend themselves with each other always more or less. In one case the surrounding country affords largely the means of refitting an army with things which otherwise could only be obtained from a long distance; in another case we are obliged to get even food from a long distance. Sometimes the nearest fortresses are great arsenals, ports, or commercial cities, which contain all the military resources of a whole state, sometimes they are nothing but old, feeble ramparts, hardly sufficient for their own defence. The consequence is that all deductions from the length of the base of operations and its angles, and the whole theory of war founded on these data, as far as its geometrical phase, have never met with any attention in real war, and in theory they have only caused wrong tendencies. But as the basis of this chain of reasoning is a truth, and only the conclusions drawn are false, this same view will easily and frequently thrust itself forward again.