Hence one may regard the pyramid as the next astronomical instrument to the horizon. While then it is possible that such culmination observations soon replaced in some measure that class of observations which heretofore had been made on the horizon, another teaching of horizon observations became apparent. By and by travellers observed that as they travelled northwards the stars that were just visible on the southern horizon, when culminating, gradually disappeared below it. These observations were at once seized on, and Anaximander accounted for them by supposing that the earth was a cylinder.[2] The idea of a sphere did not come till later; when it did come then came the circle as an astronomical instrument. For let us consider that a person on the earth stands, say, at the equator; then he will just be able to see along his north and south horizon the stars pointed to by the axis of the globe: if now he is transported northwards, his horizon will change with him; he will no longer be able to see the southern stars, but the northern ones will gradually rise above his horizon till he gets to the north pole, when the north pole star, instead of being on his horizon, as was the case when he was at the equator, will be over his head. So by moving from the equator to the pole (or a quarter of the distance round the earth) the stars have moved from the horizon to the point overhead, or the zenith, that is also a quarter of a circle. So it appears that if an observer moves to such a distance that the stars appear to move over a certain division of a circle with reference to the horizon, he must have moved over an equal division on the earth’s surface. Then, as now, the circle in the Western world was divided into 360°, so that the observer in moving 1° by the stars would have moved over 1/360 of the distance round the earth, on the assumption that the earth is a globe; and if the distance over which the observer has moved be multiplied by 360, the result will be the distance round the earth. [Illustration: FIG. 2.—The Zodiac of Denderah. ] Now let us see how Posidonius a long time afterwards (he was born about 135 years B.C.) applied this conception. He observed that at Rhodes the star Canopus grazed the horizon at culmination, while at Alexandria it rose above it 7½°. Now 7½° is 1/48 of the whole circle; so he found that from the latitude of Rhodes to that of Alexandria was 1/48 of the circumference of the earth. He then estimated the distance, getting 5,000 stadia as the result; and this multiplied by 48 gave him 240,000 stadia, his measure of the circumference of the earth.