5. Longitudes
The probability of some watches breaking in the course of seven months’ travel had been foreseen, and from the outset it appeared improbable that any use could be made of the watches in the direct determination of longitude of so long and difficult a journey. We had decided accordingly to depend ultimately on dead-reckoning for longitude, making every effort to obtain an unbroken chain of compass-bearings and estimated distances between Jaghbub and some known place in the Sudan, the bearings to be taken with a good compass with all possible precision, at very frequent intervals, and the estimates of distance to be carefully made each day from the marching time of the baggage-camels, assuming a normal rate of 4 km. per hour over average desert, and making allowance for the variations in speed over ground of varying character. The journey being predominantly north to south, the estimates of distance could mostly be well controlled by the latitudes, while errors of bearing would not be cumulative, and would tend to cancel out over any considerable stretch of route. The primary reason for taking six watches was therefore not to determine longitude, for which at best they could afford only somewhat uncertain values, but to make sure of at least one watch being available throughout the journey for latitude-observations, without which no proper control of the all-important distances could be obtained.
The doubts about the possibility of safely transporting the watches proved justified, for all but one broke down before the end of the journey. But fortunately on the one hand the watch which survived sufficed amply for the determination of latitude (though its rate was insufficiently constant for it to be used uncontrolled in finding longitudes), and on the other hand the program of a continuous chain of very careful bearings and estimation of distances was scrupulously adhered to from the departure of the caravan from Jaghbub, the last known place in Egypt, to Furawia, the first known place in the Sudan—a journey of 2430 kilometers—and from this chain of bearings and estimated distances, combined with the observed latitudes, it was possible to estimate the longitudes of all places on the route with a fairly high probability of accuracy.
For the estimation of the longitude of Jalo (El Erg) a slightly different procedure was followed from that adopted for the other principal camps on the route. It will be noticed from the map that the general direction of the march from Jaghbub to Jalo was predominantly from east to west, instead of from north to south as in the rest of the journey. Consequently the observed latitudes do not afford so good a means of correcting the estimated distances in this stretch as elsewhere. But fortunately the observed latitude at Jalo does enable us to correct the previous estimation by Hassanein Bey (in 1920) of the distance of that place from Jedabia, and this combined with the then observed bearings would lead to one value for the longitude for Jalo, while if we can assume the accuracy of the estimated distances from Jaghbub to Jalo, we may use the observed latitude of the latter place to correct the bearings and thus arrive at another value for its longitude.
From careful consideration of all the available data, the two methods appear likely to be about equal in degree of approximation. The position at present accepted for Jedabia (Lat. 30° 48′ 10″ N., Long. 20° 13′ 30″ E.) is open to a little uncertainty,[2] and the bearings taken by Hassanein Bey on his former expedition are probably a little less accurate than those of the present one. On the other hand, the estimations of the distances from Jaghbub to Jalo, as gaged by the latitude-control of the other portions of the route of the present expedition, are remarkably close to the truth, while a uniform correction to his bearings of less than half a degree would swing his dead-reckoning position for Jalo on to its observed parallel of latitude.
For the longitude of Jalo on the map I have therefore taken the mean of the two longitudes found (1) by assuming Hassanein Bey’s bearings correct from Jedabia and correcting his distances by the latitudes, and (2) by assuming his distances from Jaghbub correct and using the observed latitudes to correct his bearings. The results are:
| ° | ′ | ″ | |
| (1) From Jedabia, long. of Jalo (El Erg) | 21 | 29 | 48 |
| (2) From Jaghbub “ “ “ | 21 | 26 | 19 |
| Adopted mean | 21 | 28 | 3 |
It may be remarked in passing that the result places Jalo almost precisely where it is shown on Rohlfs’s map of 1880.
As regards the longitudes adopted for the other principal camps along the route, the procedure has been as follows. The route was divided into the following nine sections between principal camps where latitudes had been observed: Jalo, El Harrash, Taj, Arkenu, Ouenat, Erdi, Agah, Enebah, Bao, Furawia; and the compass-traverse for each section was plotted on a scale of 1:500,000 from the recorded bearings and estimated distances. A true meridian was then drawn on each section from the mean of the observed compass-variations at its two ends, and the total difference of latitude of each section was scaled off and compared with the difference of latitude given by the latitude-observations. This comparison gave, of course, the average error of estimation of distance along each section, assuming the bearings correct. The results of the comparison for the various sections are tabulated below:
Correction to Estimated Distances
| Section of traverse | Plotted difference of latitude | True difference fromlatitude-observations | True-plotted diff. lat. | Correction to estimated distances |
|---|---|---|---|---|
| km. | km. | km. | % | |
| Jalo-El Harrash | 375.0 | 399.0 | + 24.0 | + 6.4 |
| El Harrash-Taj | 131.5 | 134.2 | + 2.7 | + 2.1 |
| Taj-Arkenu | 217.7 | 223.7 | + 6.0 | + 2.8 |
| Arkenu-Ouenat | 36.0 | 37.0 | + 1.0 | + 2.8 |
| Ouenat-Erdi | 369.0 | 363.2 | − 5.8 | − 1.6 |
| Erdi-Agah | 75.6 | 79.2 | + 3.6 | + 4.8 |
| Agah-Enebah | 57.0 | 57.5 | + 0.5 | + 0.9 |
| Enebah-Bao | 99.0 | 97.7 | − 1.3 | − 1.3 |
| Mean error of estimation of distances,per cent | 2.6 | |||
The average error of distance-estimation in each section of the route having been thus found, the next step was to scale off the various departures from the plotted traverses, correcting for the errors of distance-estimation, and then to convert the departures into differences of longitude. When this was done, the resulting total difference of longitude between Jalo and Furawia was 2° 25′ 55″. But assuming the true longitude of Jalo to be that found above, and the true longitude of Furawia to be as shown on sheet 53 D of the 1:250,000 Sudan survey map of 1921,[3] we have:
| ° | ′ | ″ | |
| Longitude of Jalo | 21 | 28 | 3 |
| Longitude of Furawia | 23 | 38 | 10 |
| Difference | 2 | 10 | 7 |
So that the difference of longitude found by the dead-reckoning requires correction by 15′ 48″. This correction, which implies an average error in the observed compass-bearings of less than a degree, and a negligible correction to the adjusted distances, was distributed along the entire traverse in proportion to the difference of latitude between the principal camps, leading to the finally adopted longitudes shown in the following table:
Concluded Longitudes
| Dead-reckoningcorrected by the latitudes | Furthercorrection | Concluded longitude | ||||||
|---|---|---|---|---|---|---|---|---|
| ° | ′ | ″ | ′ | ″ | ° | ′ | ″ | |
| Jalo | — | — | 21 | 28 | 3 E. | |||
| El Harrash | 22 | 15 | 5 E. | 4 | 10 | 22 | 10 | 55 “ |
| Taj | 23 | 29 | 5 “ | 5 | 34 | 23 | 23 | 41 “ |
| Arkenu | 24 | 52 | 10 “ | 7 | 55 | 24 | 44 | 15 “ |
| Ouenat | 25 | 2 | 34 “ | 8 | 18 | 24 | 54 | 16 “ |
| Erdi | 23 | 22 | 34 “ | 12 | 5 | 23 | 10 | 29 “ |
| Agah | 23 | 28 | 49 “ | 12 | 54 | 23 | 15 | 55 “ |
| Enebah | 23 | 25 | 58 “ | 13 | 30 | 23 | 14 | 28 “ |
| Bao | 23 | 16 | 18 “ | 14 | 31 | 23 | 1 | 47 “ |
| Furawia | 23 | 53 | 58 “ | 15 | 48 | 23 | 38 | 10 “ |
In attempting to estimate the probable degree of accuracy of the concluded longitudes, we are faced with the difficulty that while we may be certain that the average error of the compass-bearings was less than 1°, which average error has been allowed for in the adjustment, we have no proof that in some of the individual sections the errors may not have been considerably greater. But in view of the great number of the observed compass-bearings (339) which make up the directional data of the 1754 kilometers of traverse from Jalo to Furawia (an average of thirty-eight observed bearings for each of the nine sections), and bearing in mind also the remarkable accuracy of the estimations of distance as evidenced by the latitude-observations, it would seem unlikely that any of the above-adopted longitudes for the principal camps can be in error by more than three or four miles. This implies a degree of accuracy which it would have been difficult to insure by transport of even a considerable number of chronometers over a land journey lasting more than three months. It may, I think, be concluded that no better values for the longitudes can be obtained without the aid of wireless time-signals.