FIG. 6—Sketch map constructed from the list of geographical positions appended to the Paris manuscript of Raymond of Marseilles’ _Marseilles Tables_. The outline of the coast, arbitrarily indicated by a shaded band, is shown merely to give some idea of the type of map that might have been constructed from the data given in the tables. This may be compared with the Henry of Mayence map (see above, p. 124) shown in outline in the inset. The original Henry of Mayence map reveals far greater detail and upon it east (not north, as in this figure) is at the top. This list is based on the observations of the eleventh-century Arabic astronomers Al-Khwārizmī and Az-Zarqalī. Cities and other points have been plotted according to the coördinates of this list. The resulting map of the Mediterranean region and the Near East is remarkable for its comparative accuracy. For a key to the names represented by the numbers on the diagram and for the figures for the latitudes and longitudes, see J. K. Wright, _Knowledge of Latitudes and Longitudes_, 1923, pp. 87–88. ] METHODS OF FINDING LATITUDE AND LONGITUDE That such observations were carried out is entirely possible, for there is absolutely no doubt that methods of finding latitudes and longitudes were well understood in theory and were sometimes put to practical use. Rules are given for finding latitude in Az-Zarqalī’s _Canons_, in Plato of Tivoli’s translation of the _Astronomy_ of Al-Battānī, and in many other astronomical and astrological treatises.[1122] Two principal methods were recommended. You may either measure with the astrolabe the altitude of the sun above the horizon at noon at the spring or autumn equinox and find the latitude by subtracting this angle from 90° or you may measure the altitude of the celestial pole above the horizon, which is the same as the latitude. As to longitude, the fact that there are differences in local time between points east and west of each other was recognized and clearly explained by several writers of our age.[1123] The _Marseilles Tables_ give a rule for finding longitude by the observation of eclipses. Roger of Hereford indicates that he himself, by observing an eclipse in 1178, ascertained the positions of Hereford, Marseilles, and Toledo in relation to Arin, the world center of the Moslems.[1124] Gerard of Cremona describes a method of finding longitude by noting the distance of the moon from a given point in the heavens and thereby dispensing with eclipses,[1125] though it is doubtful whether this method was used until the sixteenth century. The lack of accurate instruments for ascertaining time must have rendered it extremely difficult to calculate longitude under any circumstances. Making allowances for this, it is surprising to find how accurate the few coöordinates that have come down to us seem to be, if our interpretation of them is correct.[1126]