The method almost universally employed by ancient geographers for determining locations was the compilation of itineraries; the position of a place was found, not by accurate surveys, but by reference to other places at so many stades or so many days’ journey in such and such a direction. Whatever maps the Romans may have had (for example the great representation of the Empire set up by Agrippa in the Porticus Octaviae in Rome) were probably compiled entirely from route traverses. The greater part of the information which even the most accurate and scientific of the Greek geographers, Eratosthenes, Marinus of Tyre, and Ptolemy, possessed, was drawn from such itineraries and from estimates of sea voyages. The figures for the latitude and the longitude of the large number of places given in Ptolemy’s _Geography_ are for the most part not the result of astronomical observations, and the tables cannot be regarded as analogous to modern tables of latitudes and longitudes but must be considered rather as guides for the construction of maps.[156] Other methods besides these simple reckonings of locations were well known, none the less. ASTRONOMICAL DETERMINATION OF LATITUDE The determination of latitude has always been a comparatively easy astronomical problem. No complicated instruments are needed to measure either the vertical elevation of the sun on the meridian or of the north celestial pole, and from both of these the latitude of the observer can be calculated with extreme accuracy. The instrument commonly used by the Greeks for measuring the angle of the sun[157] consisted of an hemispherical bowl (_scaphe_) with a vertical rod (_gnomon_) for a radius. The shadow of the rod on the concave interior of the bowl gives the elevation of the sun (with an error of 16′[158]) and thereby the latitude. Eratosthenes, Hipparchus, and Ptolemy were all familiar with the latitudes of several places that had thus been determined. ASTRONOMICAL DETERMINATION OF LONGITUDE To find longitude by astronomical means is a more difficult matter for people who have neither chronometers nor telegraphs. Eratosthenes, Hipparchus, Pliny, and Ptolemy all understood that it may be found by observing the time of eclipses in different localities.[159] Hipparchus believed that an extensive series of observations should be carried out in order to ascertain, by mathematical and astronomical means alone, latitudes and longitudes of a large number of places.[160] To facilitate such a survey he prepared tables of lunar eclipses and tables to aid in the determination of latitudes, but the practical difficulties of the undertaking were too great and the work was never completed. In fact, throughout antiquity the total number of places whose position had thus been accurately determined probably does not exceed half a dozen, if it is as many.