When we have decided that we can go on to the next point, which is: how does the Road, once formed, react upon its environment; what physical and (much more important) political results flow from its existence? The answer to the first question, “How did that human institution, the Road, come into existence, and why?” is simple, and will be given in much the same terms by anyone to whom it is addressed. The Road is an instrument to facilitate the movement of man between two points upon the earth’s surface. If the surface of the earth were uniform in quality and in gradient--that is, if it were of the same stuff everywhere, of the same degree of moisture everywhere, and everywhere level--the Road between any two points would clearly be a straight line (to be accurate, the arc of a great circle) joining those two points. For when we say that the Road exists “in order to facilitate” travel over the surface of the earth from one point to another the word “facilitate” includes, of course, rapidity in progression, and the straight line is the shortest line between any two points. But the surface of the earth is highly diversified in quality as in gradient. Therefore the _trajectory_ or _course_ of the Road is not in practice, and should not be in theory, a straight line from point to point. That straight line has to be modified if we are to give to the Road an ultimate form such that it shall best serve its end; and when we come to look into the problem we shall see that it is one of very great complexity indeed. That is where the study of the theory even in its most elementary form becomes of such value to the execution in practice. We discover by studying the theory of the Road how many and how varied are the elements of the formula we have to establish. We become prepared in that study for the discovery, in each new particular problem, of any number of novel modifications not present in problems previously attacked. So true is this that the whole history of progress in road-making is a history of discovering methods for dealing with obstacles either novel in character or only appreciated after lengthy use. Let us begin at the beginning, with the very elements of the affair. The first element in the theory of the Road may be put thus: _To find a formula of minimum expense in energy for communication between two given geographical points under given conditions of travel and carriage._ The diversity of geographical circumstance moulds the formula into its final shape through balanced modifications of the direct line.