The geography and geology of south-eastern Egypt

by John Ball

In the case of very long sights, even this method failed, because the circle could only be read to half-minutes, which was too coarse a graduation to give a good result, and in these cases the method used was one of repetition. The wire being brought to the base of the staff as before, and a first reading of the vertical circle taken, the wire was brought to the top of the staff by the tangent screw, then to the bottom again by altering the levelling screws slightly, again to the top by the tangent screw, and so on, three or four times, and then a second reading was taken on the vertical circle. The slight alteration of level had no sensible influence on the result, and it is obvious that by automatically summing up, say, four intercepts in this way, a very much more accurate value of the subtense angle was obtained than was possible from a single measurement. In practice I found it was best to carry in the waistcoat pocket a card giving the distance corresponding to any number of minutes of difference of reading after a four-fold repetition, and it was quite practicable to measure up to three kilometres of distance within one hundred metres of the truth; as this only represented a millimetre on the sheet, and as, moreover, errors were not cumulative, owing to the independent fixation of each successive station by re-section, the accuracy was all that could be desired, and the rapidity of measurement was very great. In this long distance type of tacheometry, finely graduated staves were of no use; the form of staff employed was a broad-faced one, fifteen centimetres wide, bearing fifty-centimetre divisions painted alternately black and white right across the whole breadth of the staff.[77]

An average of about six or eight conspicuous points having been telemetrically fixed from a station, the detail was sketched in around them, and other more distant points were at the same time fixed by plane-table intersections from several stations. At the stations the pencil sketching of relief was by form-lines which were subsequently replaced by hachure-rendering when inking up the sheets in camp.

Occasionally, when a high hill-station was employed overlooking a long wadi, time was saved by reading only two distances, both in the same wadi, one very near to the station and the other two or three kilometres away, at the same time observing the depression-angles to these points. The slope of the wadi being found in this way, the depression-angles to intermediate points gave the distances of such points without the necessity of staff reading at the intermediate points at all. Thus, suppose the near point was close under the station, with a distance of 500 metres and a depression-angle of 18°, while the remote point up the wadi had a distance of three kilometres and a depression-angle of 2° 30′. By means of a slide rule or three-figure logarithms, the near point was found to be 163 metres below the station, and the distant one 130 metres. A point in the wadi estimated roughly as half way between the two would be about 146 metres below the station; so that if the observed depression-angle to it was, say, 4° 40′, its distance would be 146tan 4° 40′, or 1·8 kilometres. Any possible error of preliminary estimation of the distance in order to find the level would be without sensible influence on the resulting true distance.

The process of traversing between stations was seldom resorted to, as the method of fixing stations by re-section from triangulation points is much more accurate (the errors not being cumulative) besides being more rapid. But in certain tortuous cañon-like wadis, where great and time-consuming climbs would have had to be undertaken in order to see any triangulation points, the method of traversing with the tacheometer had to be employed.

Levels along the line of march were measured trigonometrically whenever possible; the vertical angles to one or more triangulation points being read with the tacheometer, and the distances scaled off the map, the differences of height, corrected for refraction, were found by the slide rule in the same manner as in the triangulation already described. Heights of passes and camps whence no triangulation points were visible were determined by barometer-comparisons between them and points of precisely determined altitude.

Names of places were written down by the guides in Arabic characters on the spot where they were ascertained, and transliterated on the Egyptian Government system for insertion in the map. Most of the place-names were checked by getting the guides to give them from several different stations.

Detail Surveying at Occupied Triangulation Stations.

It was generally necessary to remain for at least a week on the mountain summits which formed the main triangulation stations, for only on about one day in seven was the air clear enough for sighting the beacons on the longer lines. Occasionally the entire landscape was blotted out for ten or more consecutive days by clouds surrounding the summit, while at other times it was possible to see only for a limited distance round the station owing to haze. Such times were made use of to map all visible detail within a moderate range (say within a radius of twelve kilometres) round the station.

In this work the first stage was to find a small base, one end of which was the station itself. Usually a minor peak of the same range, 500 to 1,000 metres away from the station, was fairly easily accessible, and was chosen for the other end of the base. The six-inch theodolite being at the main station, the five-inch tacheometer was set up at the auxiliary station, and all noteworthy hill tops, as well as a few points along each main line of drainage, were triangulated off this small base. The length of the base was found by including one or two main triangulation points in the round of angles. These minor triangles were conveniently reduced by the slide rule, and the points plotted at once on the plane-table by means of the alidade and the calculated distances. The base being short, it was necessary to observe to fine marks; cracks in the rocks, and the droppings of birds on the peaks, and the centres of selected tree trunks in the wadis, were usually chosen. The levels of these minor points were determined by vertical angulation in the ordinary way. Usually about thirty points were thus fixed round each high station. Once a number of points were fixed in the wadis, the levels of these gave the slope, and the difference of height between any other parts of the wadis and the station could be estimated to within a few metres by means of the knowledge thus obtained. A sketch being now made of the wadis, which appeared spread out almost like a map below the station, a hundred or more points along them were selected, and their depths below the station being very approximately known from the wadi slope, their distances were found by observing depression angles to them and reducing the vertical triangle by means of the slide rule on the spot. In all, therefore, measurements were usually made of the distances of from 100 to 200 conspicuous points in the area round the station, and when these were plotted with the alidade on the plane-table sheet it was not difficult to sketch in all the detail with considerable accuracy. Usually it was not possible to see all round the mountain from the station itself, so that subsidiary plane-table stations near the main one were necessary. In other cases more than one small base was measured in order to get good angles to various points by the minor triangulation.

By the combined use of minor triangulation for peaks, and vertical angulation for points situated along drainage lines, it was found that far more sketching could be done in a few days at a main station than would have been possible in the same time by tacheometric work on the lower ground, and that of greater accuracy. More than half of the entire detail sketching was in fact done at the main stations.