[Footnote 66: The signs of the coefficients follow from those of the trigonometrical functions; but it is useful to remember that the coefficient of _d_φ 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.] [Footnote 67: CHAUVENET, _Astronomy_, Vol. I, p. 283.] [Footnote 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.] [Footnote 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.] [Footnote 70: The Sudan Survey’s positions are all south-east of those which I obtained for the same points.] [Footnote 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.] [Footnote 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.] [Footnote 73: This number 1210 represents the significant figures of √{106·84}, 6·84 metres being the correction given by (1 − _k_)/2_r_ _d_² for a distance of ten kilometres.] [Footnote 74: _Berichte der Commission für Oceanographische Forschungen_, Sechste Reihe, Wien, 1898, pp. 13, 14.]