[66]The signs of the coefficients follow from those of the trigonometrical functions; but it is useful to remember that the coefficient of dφ is + or − according as the star is north or south, while that of dT is + or − according as the star is east or west of the meridian.
[67]Chauvenet, Astronomy, Vol. I, p. 283.
[68]In this connexion it is interesting to note that as the general level of the country to the south of Gebel Um Heshenib is some 250 metres higher than that to the north of it, the plumb-line will be deflected to the south by local attraction, thus explaining why the observed latitude at that station exceeds by so much the value calculated from the triangulation. Berenice temple, on the other hand, is on a coast-plain remote from mountains, and the observed latitude agrees closely with the calculated one.
[69]The method of observation and reduction was that usually described in text books of field astronomy. See, for instance, Michie and Harlow’s Practical Astronomy, 1902, pp. 161-168, and the tables on pp. 198-201 of the same work.
[70]The Sudan Survey’s positions are all south-east of those which I obtained for the same points.
[71]For calculations of this type and for tacheometric and other reductions in the field, the Nessler “Universal” slide rule, which is specially designed for surveyors, was found to be a most valuable time-saver. See my paper in the Cairo Scientific Journal, “On the Use of the Slide-rule in Surveying,” Dec. 1907.
[72]A careful discussion which I have recently undertaken of the entire series of reciprocal observations made during the three seasons’ work shows that k varies according to the altitude of the lines and according as the lines pass over land or sea. I hope later to publish a separate account of this discussion, which has an important bearing on the vertical distribution of temperature in the air. But I may here state that for overland lines the formula k = 0·1503 + 0·0000164 (h − 830), where h is the mean altitude of the line in metres, gives a good agreement with the observations; while on oversea lines at altitudes above 100 metres k is always very near to 0·135. The errors in the resulting altitudes of intersected points due to the uniform employment of k = 0·13, are very trifling, and will seldom exceed one or two metres; for example, at a distance of thirty kilometres the substitution of k = 0·16 for k = 0·13 will only change the altitude by two metres.
[73]This number 1210 represents the significant figures of √106·84, 6·84 metres being the correction given by 1 − k2rd2 for a distance of ten kilometres.
[74]Berichte der Commission für Oceanographische Forschungen, Sechste Reihe, Wien, 1898, pp. 13, 14.
[75]In particular, the adoption of the above three longitudes as of equal accuracy with Suez will lead to a better longitude for Jidda. The longitude of Jidda is at present fixed only by chronometer transport from Suez, a distance of some 650 miles; but by regarding Halaib as a fixed point the distance of comparison can be reduced to 150 miles. The data for this revision of the longitude of Jidda already exist in the Reports of the “Pola” expedition, and the discussion is certainly worth undertaking before any future surveys are conducted in the central portion of the Red Sea.