Suppose that you have to construct a straight line from A to B, A and B not being visible one from the other, and the distance between them being considerable. If you have plenty of men with which to work (and the Roman military commanders did not lack these), you will proceed as follows: You send out your men from either end, in two chains as it were, each individual easily in sight of his next neighbour, but not nearer to him than is necessary for the observation of signals. These chains of men are either directed from the two ends of the line, or, if you can work only from one end, you send them out from that end, instructing the head of the chain when he comes in sight of the other end to work towards it and establish himself there. At the end of the process, whether you have been working with two lines approaching each other from either end and joining hands in the middle, or from one end only, you will end up with a line which will certainly not be straight--on the contrary, very irregular--but which will at least join your two goals. Probably, if you had been working from both ends, A and B, you would have something like sketch VI; while if you be working from one end only--A--the head of your column would probably be widely out at the conclusion of your experiment. Your column would have to double back sharply on to its goal when at last it was caught sight of, and you will have some such trace as on sketch V. [Illustration: _Part II_, Sketch V _Part II_, Sketch VI]