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There is hardly any factor in connection with the theory of the road which needs more material modification as civilization changes than this factor of gradient. The sharpest contrast in the whole of history is that which I have just mentioned: that of the railroads. Men suddenly found themselves possessed of a new instrument which enormously multiplied their power on the flat and yet was quite incapable of anything like the old gradients. Going level or on very slight gradients it could give them travel far more rapid and inexpensive than any that had been known before, but one in fifty bothered it badly, one in thirty was wholly unnatural, and the existing gradients of one in ten, eight, six, were out of the question. Further, the least inclination increased all difficulties, and the addition of inclination produced these difficulties in more than a geometrical progression. The result was the revolution whose effects we see about us everywhere: the tunnel, the cutting, the embankment.
To-day, a couple of generations after that revolution, there comes the new problem of the internal-combustion engine, where the gradient again appears in a new light.
The motor takes gradients far steeper than the rail. Its difficulties are not increased in the same ratio. But it cannot always deal with the horse road. Lynton and Lynmouth and their Devonshire valley form perhaps the best example of this in Great Britain. You have here terrible gradients which were just possible for the horse vehicle and are hardly possible for the motor vehicle, and you have the new road round by Watersmeet attempting partially, but not entirely, to solve the problem.
A special case in this general category of gradients, and one much more complex than appears at first sight, is the case of the pass, or gap. Men have always naturally made for any notch in a line of hills to save themselves the effort of higher climbing. It began with foot travel, and has continued right on throughout the history of the Road. In high mountains provided with low passes the use of a saddle in the range was obvious and often necessary; but there were disadvantages even in that apparently unexceptionable rule. One was the question just dealt with of the double slope: the consideration of the other side—the most obvious pass from the one side did not necessarily lead to the best descent upon the other.
Another was the conformation of many ranges, which is such that the approach to the ridge is much steeper at the summit of a “col” or pass than it is by tracks to one side.
This is a paradox which people living in easy hill-lands have difficulty in appreciating. The Alps especially show roads which puzzle us (who are of a gentler landscape) when we follow them: yet the principle is simple and dependent upon the geological formation of most new mountain ranges, which present a hard core, forming their central ridge. The softer ground wears away on either side of the valley: the ridge remains. The effect is that a direct approach to the notch in the range would give impossible gradients in the last few hundred yards, and therefore the road must gradually curve round by a side of the valley.
A third exceptional case is that of trajectories where the minimum of effort is only to be found by going right over the very summit of the highest hill in your neighbourhood. Lastly, there is the curious case of a pass where it is to the advantage of the road to avoid the lowest passage of the range and to take a line to one side above it.
As examples of these last two paradoxical points I may quote the pass of Sallent in the Pyrenees and the exceedingly important road [from the valley of the Moselle to the valley of Belfort in the Vosges].
In the case of the pass of Sallent there was an obvious notch in the range, which was used from the very earliest times till just the other day. It was through this that the armies of the Moors poured in the eighth century for their attempted conquest of Europe, when they invaded France and nearly reached the Loire. So late as within living memory it was the regular track from the valley of the Gallego to that of Gabas. Now, the modern road, after careful survey, has been constructed to cross the mountain summit somewhat to the west, and a good three hundred feet higher than the old pass. Why was this? It was because the notch of Sallent had a very steep approach in the last few hundred yards upon either side, and the minimum of effort, at any rate for wheeled vehicles of the modern type, was found in taking a lesser gradient to one side, although it involved a much higher climb. The case of the road from the Moselle valley to Belfort in the Vosges is even more remarkable, for one would have said at first asking that no such case could exist: one would have said that a minimum of effort could never be reached by going over the very highest summit in your neighbourhood, but it is so when you deal with what I will call a “star” mountain, as will be seen at once from the following elements.
Sketch IV
Here the contours are such that had the road deflected to the west or the east in order to avoid the highest summit, it would have been compelled either to a very long detour (involving in any case nearly as high a climb) or to a series of steep and profound ups and downs over the spurs of the mountain. The line taken from the Moselle to Belfort on the other side goes within a few feet of the highest point on the hill, and is yet the line of least effort from one point to the other. It is an excellent example of the way in which the formula of minimum effort, when it is thought out, may be quite different from what mere habit would have produced.
CHAPTER IV
THE OBSTACLE OF VEGETATION
The Special Expenditure due to Forest: Roads which Skirt Woodlands: Roads which have been Deflected by Forest: Proximity of Material as a Final Main Cause Modifying the Trajectory of a Road: Cost of Transporting Material and its Effects in Ancient and Modern Times.