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. =Survey of the Coast-line.= In the earlier portion of the work, _i.e._, north of latitude 24°, the work on the coast-line was confined to the fixation of prominent points such as spurs and tips of islands. Some of these were fixed as intersected points during the triangulation, while others were determined by observing the depression angle and azimuth to them from trigonometrical stations of known altitude. In this latter method, taking the mean coefficient of refraction as 0·13, the formula[78] employed was _d_ = 35·497 (θ − √{θ² − 11621 _h_}) where _d_ = distance in metres, θ = depression angle in seconds, and _h_ = altitude of station in metres. This formula is rather tedious to work out, though the work is relatively not so great if a number of points are to be calculated from observations at the same station. Prominent points having been fixed in this way, the coast-line north of 24° was sketched in from the Admiralty Chart, adjusting the longitude to fit the points fixed. It was sometimes a little difficult, however, to identify the fixed points on the existing charts, and hence I tried to find some process of surveying the entire remaining coast-line _de novo_ in detail. Traversing along the coast was placed out of question by the great expenditure of time and money which it would have entailed. Eventually I was led to devise a new method, by which long stretches of coast-line could be mapped by polar co-ordinates from mountain stations with great speed and accuracy. The directions of a series of points sufficiently close together along the coast were taken by theodolite, and the depression angles simultaneously observed with the vertical circle. Then, instead of computing the distances to the points, they were plotted by a special scale graduated directly in angles of dip; by thus doing away with all calculation at the station, it was possible to lay down the points on the chart as fast as the observations could be taken, usually at the rate of four or five points a minute, and it was frequently possible to map thirty kilometres or more of coast-line in an hour with great accuracy. As I have given a full account of this new method in a separate publication,[79] I shall not go into it further here, but would refer those interested to the publication just mentioned.