The most obvious modifications to a direct trajectory arise from the two primary circumstances of surface and gradient. It is easier to go over one kind of soil than another; easier to go over one kind of surface in summer and another in winter; easier to go over one kind of surface in wet, and another in dry weather; easier to go over one kind of surface with a heavy load and another with a light load; over one with sumpter animals, over another on wheels, and so on. Again, it is for all kinds of travel easier to go upon the flat than uphill, and this element of gradient is much more complicated than at first it would appear. Thus travel of one kind--travel on foot, for instance--can take a sharp gradient for the sake of a short trajectory more easily than can traffic with burdens; and traffic with burdens carried by animals can take a sharper gradient with advantage than can wheeled traffic; and wheeled traffic differs according to the character of the vehicle in this respect. Again, a road of diverse use must strike a compromise in its formula between the various needs subserved. If the great bulk of its use is to provide for rapid military advance by marches, you must sacrifice to shortness some of the easier gradients which would be demanded for traffic mainly civilian, yet if of three main users even the least important is incapable of more than a given gradient, your formula can never exceed that gradient, and so forth. So we have even in this simplest and most primary of all analyses of the Road considerable elements of complexity appearing. As the study progresses an indefinite series of further complexities arises, and one soon reaches that _crux_ in the theory of the Road which has led to so much discussion and which some still call unsolved: whether the formula of the Road is best left to the unconscious or half-conscious action of experiment, which in time should lead to an exact minimum of expense in energy, or whether it is best to arrive at it by a fully conscious, exact, and (as we say to-day) “scientific” examination of all the conditions and a deliberate and immediate conclusion upon them. Should the road _grow_ or should it be _planned_? The discussion is not idle. The clash of opinion upon it is at the root of the contrast between national systems, and a right answer will make all the difference between success and failure in our approach to a new road system such as is now upon us. ii