PROBLEM XII.

To survey a county, or large tract of land.

1. Choose two, three, or four eminent places, for stations; such as the tops of high hills or mountains, towers, or church steeples, which may be seen from one another; from which most of the towns and other places of note may also be seen; and so as to be as far distant from one another as possible. Upon these places raise beacons, or long poles, with flags of different colours flying at them, so as to be visible from all the other stations.

2. At all the places, which you would set down in the map, plant long poles with flags at them, of several colours, to distinguish the places from one another; fixing them on the tops of church steeples, or the tops of houses, or in the centres of lesser towns.

These marks being then set up at a convenient number of places, and such as may be seen from both stations; go to one of these stations, and, with an instrument to take angles, standing at that station, take all the angles between the other station and each of these marks. Then go to the other station, and take all the angles between the first station and each of the former marks, setting them down with the others, each against his fellow with the same colour. You may, if you can, also take the angles at some third station, which may serve to prove the work, if the three lines intersect in that point where any mark stands. The marks must stand till the observations are finished at both stations; and then they must be taken down, and set up at fresh places. The same operations must be performed, at both stations, for these fresh places; and the like for others. The instrument for taking angles must be an exceeding good one, made on purpose with telescopic sights; and of a good length of radius. A circumferentor is reckoned a good instrument for this purpose.

3. And though it be not absolutely necessary to measure any distance, because a stationary line being laid down from any scale, all the other lines will be proportional to it; yet it is better to measure some of the lines, to ascertain the distances of places in miles, and to know how many geometrical miles there are in any length; as also from thence to make a scale to measure any distance in miles. In measuring any distance, it will not be exact enough to go along the high roads; by reason of their turnings and windings, hardly ever lying in a right line between the stations, which must cause infinite reductions, and create endless trouble to make it a right line; for which reason it can never be exact. But a better way is to measure in a right line with a chain, between station and station, over hills and dales or level fields, and all obstacles. Only in case of water, woods, towns, rocks, banks, &c., where one cannot pass, such parts of the lines must be measured by the methods of inaccessible distances; and besides, allowing for ascents and descents, when they are met with. A good compass that shows the bearing of the two stations, will always direct you to go straight, when you do not see the two stations; and in the progress, if you can go straight, offsets may be taken to any remarkable places, likewise noting the intersection of the station line with all roads, rivers, &c.

4. From all the stations, and in the whole progress, be very particular in observing sea-coasts, river mouths, towns, castles, houses, churches, mills, trees, rocks, sands, roads, bridges, fords, ferries, woods, hills, mountains, rills, brooks, parks, beacons, sluices, floodgates, locks, &c., and in general every thing that is remarkable.