=Levels of Triangulation Points.=—The altitudes above sea-level of all triangulation points were determined by vertical angular measurements carried out at the occupied stations, an actual sea-level datum being obtained by including rocks awash in the sea among the triangulated points. To secure constancy of atmospheric refraction as far as possible, vertical angles were always read in the middle of the day, where the change of refraction is slowest. For the occupied stations, refraction and curvature were eliminated by reciprocal observations. For intersected points the formula _h_ = _d_ _tan_ θ + (1 − _k_)/2_r_ _d_² was used, the value of _d_ tan θ being first found by five-figure logarithms and then that of the curvature and refraction correction (1 − _k_)/2_r_ _d_² by means of the very convenient “Universal” slide rule of Nessler.[71] The value of _k_ found from a discussion of the first few reciprocal observations was found to be very nearly 0·13, corresponding with the mean of European determinations, and this value for the coefficient was employed throughout the work for intersected points.[72] For obtaining the correction (1 − _k_)/2_r_ _d_² by the slide rule, a mark _R_ was scratched at 1210[73] on the lower scale of the slide; by bringing this mark _R_ opposite to the distance (in kilometres) on the lower scale (or, where the logarithm of the distance was more convenient, by bringing the mark vertically under that logarithm on the log scale of the rule by means of the cursor) the correction could be read off directly on the lowest fixed scale opposite the end-graduation of the slide. Usually four or five values for the altitude of a single point were obtained from a corresponding number of stations, and the mean taken; the various values generally agreed within two metres. The constant combination of vertical angular measurements with horizontal ones was of great service from another point of view from that of providing altitude data for the maps. It frequently happened that a peak observed at one station could not be identified among a number of similar peaks visible at another station. When this trouble arose, the vertical angles offered a way out of the difficulty. Vertical and horizontal angles were read off to a number of likely-looking peaks; on working out the triangles to the nearest minute of the observed angles, the distance of each peak was obtained on the assumption that it was the one required. Then to find which of the several peaks was the correct one, the elevations were worked out, assuming the distances correct; in only one case would the level agree from the two stations, and this obviously discriminated the peak required. The working out of the triangles for this purpose could be done with sufficient accuracy in a very few minutes by means of the slide rule, and many points were thus saved from rejection consequent on misidentification.