to transform—geographical science. He carried out both Hipparchus's plan of determining latitude and longitude by astronomical observations, and that of representing the earth by the modern method of projection—with the "curved meridians and parallels" which Strabo had despised. We can see from the errors which he makes that he did not fully understand Hipparchus's ideas, but he did measurably; and he had the energy to stamp his knowledge upon the world, and thereby became the master of geography.
To examine now the work of the two greatest geographers of antiquity, Eratosthenes the father, and Ptolemy the master.
We have seen Eratosthenes in the library of Alexandria, surrounded by every existing appliance of learning. Besides the data to which we have referred, he had before him what Hipparchus calls the "Ancient Map," possibly that of Anaximander, which Hipparchus prefers in some respects to the map of Eratosthenes. But, with all these appliances, he had not the one great essential to their accurate combination into a system of the world, viz., the length of the earth's circumference. He had, however, made certain astronomical observations that were to help him. By observing the difference of the shadows at the summer and winter solstices, he had calculated the angle of the ecliptic. He had also learned that the city of Syene, in Upper Egypt, was directly under the northern tropic, since there, at the summer solstice, the rays of the sun illumined the bottom of a deep well. Ascertaining by the gnomon, or by the armillary spheres, which he invented, the latitude north of the tropic of Alexandria, which he considered to be on the same meridian with Syene, he found the arc between Syene and Alexandria to be one fiftieth part of the earth's circle. Learning then from the itineraries that the distance between the cities was 5,000 stadia, he multiplied this by fifty and had his circumference, 250,000 stadia; or, as he divided the circle into 360°, each of 700 stadia, he called the circumference 252,000 stadia. Not knowing the precise length of the stadium, we can not tell how exact this measurement was; but to have measured the earth at all was surely a brilliant beginning of Eratosthenes's geographical work. His method, it may be said, is the same that is followed to-day in measuring the earth. Having, then, a basis upon which he can convert degrees into stadia and stadia into degrees, he proceeds to construct his map. He makes no recognition of the lines so prominent in all our maps of the world, the equator and the tropic, and polar circles; but simply establishes a few parallels at irregular distances, viz., of the limits of the inhabitable earth—Meroe, Syene, Alexandria, Rhodes, the Hellespont, Byzantium, the mouth of the Borysthenes, and Thule. Some of the distances between these parallels were determined by itinerary measurements, some by astronomical observations. For example, the distance from Alexandria to Rhodes was determined by estimating the arc between the cities at the rate of 700 stadia to the degree. Again, the latitude of the Borys-
