ii
Gradients. The obstacle of gradient the “minimum of vertical effort” is the most evident of all the factors which modify the trajectory of a road; yet it is, upon the whole, the most complex. To determine the minimum of effort you have to find a formula consisting of many factors, [some of which I have already enumerated in the opening words of this essay]. In the first place, you have to consider the average nature of the travel to be served. The Road used by men on foot without burdens, by men on foot with burdens, by pack animals, by wheeled vehicles, etc., must conform itself, on the whole, to the least gradient useful to those who travel by it, but that “on the whole” least gradient is a factor by no means easy to determine. It depends not only upon the nature of the instruments of travel, but upon habit, upon vigour, and to some extent upon surface. It depends also on the proportionate use of the Road. You cannot sacrifice ninety-nine travellers to the special weakness of one.
There is also the question of durability. A primitive road, taking a very steep gradient, will be more durable than one taking a lesser gradient round the slopes of a hill and subject to falls from above and to degradation down the slope below; it will need less upkeep, for it is always shorter—and this last consideration explains what would otherwise be inexplicable: the extraordinarily steep gradients which primitive roads and even the roads of a high civilization will take.
One of the best examples of this in England is [the behaviour of the Fosse Way in the neighbourhood of Radstock in Somerset]. Here the original road was presumably a prehistoric track, but we know that it was carefully remodelled by the high Roman civilization. It must have been used for the great mass of travel during four hundred years from the first occupation of the West of England by the Romans about A.D. 50 to the breakdown about 450, and right on into the Dark Ages—that is, for not less than one thousand years. During the first half of this time (and especially during the first third) it had to carry the travel of a very full, well-developed, and complex society to one of the most important centres of its wealth, the town of Bath. Yet the road goes up the most astonishing gradients.
Sketch III
Somehow or other, these gradients were normally used—but it is a puzzle to say how. The modern road has frankly abandoned the effort, and takes a long sweep round both sides of the valley at a gradient of about 1 in 12. Even so, it is quite steep enough for our modern methods of travel.
The question of gradient is complicated, again, by another variable which makes the solution of the problem much more intricate than the discovery of minimum effort upon a particular gradient. You have to consider not only the uphill or downhill upon a given slope, but the type of further uphill and downhill to which your road, once established on that slope, is leading you. It is not enough to determine your best formula under such and such conditions of travel for overcoming one side of the obstacle. You have also to ask yourself whether, having got your best uphill road, you may not have led the traveller to an impossible position on the further side. Extreme cases of this one often sees in the Jura range, where the hills are shaped like waves in a storm: a steep escarpment upon the eastern side, very difficult to go up or down, and an easy slope upon the western. Here you have to balance the advantage of your gradient upon the one side with the advantage of the gradient that you will find upon the other, and, of course, to direct your line principally with a view to travel on the more difficult steeper side. That is why you often find yourself following in the Jura a road which goes up the easy western side by an apparently over-steep trajectory: you wonder why the road does not take some obviously easier line which lies below you. The reason you only discover upon reaching the summit and seeing the precipitous escarpment overhanging the eastern valley—your road has made for some exceptional advantage down this cliff, some cleft, which an easier advance from the west would not have hit. A balance has to be struck between the advantage of gradients on both sides of the hill, save in the rare cases where a range (such as the Vosges) is symmetrical and gives you equal gradients upon either slope.
That balance is always a matter of careful calculation. Where it has been brought to a fine art is, of course, in surveying for a modern railroad, for there the slightest differences of gradient make such a vast difference in the expense of working that the discovery of a true minimum over an obstacle of hill country is of the first importance.