If you look at a detailed map of the Roman road system in Gaul or Britain you will see how the moment it comes to a broken district the straight lines are replaced by a waving trace such as you would have in a modern English road. For instance, beyond the Fosse in Dorsetshire and Devon the Roman coast road is as winding as any modern road can be. The same is true of the crossings of the Apennines, and, of course, of the crossings of the Alps and the Pyrenees. It seems to be equally true of the Ardennes gorges, but the trace here is often so much obliterated that it is difficult to say exactly how the Romans dealt with that mixed problem of wood and ravine. The third modification was that of gradient. The Roman Road would take a very steep gradient indeed; but there was a limit, and when the slope was too steep the road diverged or zig-zagged, or took a combe in a great curve, or swept round the base of a hill. We have examples of all these points upon the map of England, the best of which, I think, are the great sweep of the Stane Street on Bignor Hill in Sussex and the great loop round Down Barn, north of Andover, on the road from Winchester to Glo’ster. The greatest ingenuity was shown by the planners of the Roman roads in the choice of trace. Granted that you were to make a trajectory of many days’ march in large straight limbs, each limb had to be thought out very carefully, straight though it was, to yield something like a minimum of effort. You had to make your turning-points, or hinges, in the system at places where the straight lines joining them would cross water or hilly country to the best advantage, and it is astonishing with what skill these terminal points of the straight limbs were chosen. For instance, that one road of them all which has been most certainly of purely military use and designed to join Chichester with London (all of which I have worked out some years ago and on which I have written a monograph),[2] has its first bend from Chichester, just after the end of the first day’s march at the crossing of the Arun on Burgh Hill. The angle of the bend is one of seventeen degrees, the direction is north by twenty-two degrees east. Now, this direction of the two limbs which join at Burgh Hill exactly secures two things essential to the minimum of effort. One plain straight from Chichester to Leith Hill would have involved heavy effort in gradients and water. This plan of two limbs meeting at the Arun crossing gives every advantage: (1) It makes the road cross the intervening range of the downs just where, by a slight curve, a reasonable gradient can be used; (2) It makes it cross water and marsh at the narrowest point between Hardham and Pulborough, and at the same time just avoids the double water crossing of the Arun and the Rother. It is true that there is here something of a coincidence, but it was plan and survey which discovered that coincidence. iii