The geography and geology of south-eastern Egypt

by John Ball

51·5 − 0·801 dφ + 0·546 dT − h₀ = 0 (3)

By solving these equations for dφ, we find

dφ = + 6″·5

whence the latitude is found to be

24° 20′ 56″·5

It may be remarked that the above process was considerably shortened when it was possible to get a pair of observations on the same south star both east and west of the meridian, instead of on two separate south stars. In that case the watch error was found at once from the difference between the star’s R.A. and the mean of the two observed times, and the latitude could be found from two equations instead of three. The condition for this modification of the method was that a nautical almanac star could be found culminating at an altitude slightly greater than that of Polaris at a time convenient for the observation. It is not advisable to select a star which would give too long an interval between the equal east and west altitudes. The best results are obtainable when the interval between the two observations of the south star is about an hour, and when Polaris is near its transit. Under such circumstances the watch correction is obtained quite nearly enough for a good latitude; for, as Gauss[67] pointed out, “the essential condition is not so much that the precise instant when the star reaches a supposed place should be noted, as that at the time which is noted the star should not be sensibly distant from that place.”

The following table shows the latitudes found by observation and triangulation at the various points. It may be remarked that the method used for latitude determination was liable to observational errors of 2″ or so, as well as to errors of possibly more than double that amount due to plumb-line deflection among the mountains,[68] so that the observed latitudes were only taken as checks to prevent any gross error in triangulation being overlooked, and not for any determination of the figure of the earth, for which latter purpose more elaborate observations would have been necessary.

Point.	Lat. observed.	Lat. computed from Triangulation.	Difference computed-observed.
West Peg, Muelih Base	24° 53′ 40″·3	24° 53′ 36″·7	− 3″·6
Beacon on Gebel Um Heshenib	24° 20′ 56″·5	24° 20′ 49″·2	− 7″·3
„ „ Hill near Gebel Selaia	23° 55′ 33″·2	23° 55′ 30″·6	− 2″·6
„ „ Berenice Temple	23° 54′ 39″·5	23° 54′ 40″·3	− 0″·8
„ „ Gimeida Hill	22° 46′ 33″·2	22° 46′ 29″·4	− 3″·8

Azimuths were determined in the usual manner[69] by elongations of close circumpolar stars, Polaris or 51 Cephei being usually selected. The azimuth mark used was an ordinary Egyptian shamadan (candlestick with spring feed) with a glass globe, placed at a distance of one to two kilometres, with its foot firmly bedded in sand and stones to prevent any motion. The azimuths observed at the different stations are shown in the following table:—

Station of Observation.	Point to which Azimuth is given.	Azimuth observed.
Peg at West end of Muelih Base	Peg east end of base	33° 30′ 6″ E. of N.
Beacon on Gebel Um Heshenib	Beacon on Gebel Hamata	45° 15′ 34″ E. of S.
„ „ Hill near Gebel Selaia	„ „ Abu Gurdi	25° 30′ 35″ N. of E.
„ „ Berenice Temple	„ „ Kalalat	61° 10′ 31″ W. of S.
„ „ Gimeida Hill	„ „ Hamra Dom	6° 14′ 46″ E. of S.
Centre of Halaib Fort	„ „ Elba	83° 25′ 0″ W. of S.