It was an Alexandrian astronomer named Aristarchus, who about 270 B.C. first determined the distance of the sun from the earth in comparison with that of the moon. He knew that the moon was a round ball, and that its various shapes or phases were produced by the sun shining upon it at different angles. He carefully watched the growing sickle of the moon from day to day, waiting for the time when the moon should appear to be exactly a half-circle. When this is the case an imaginary line drawn from the eye of the observer to the centre of the moon is at right angles to a similar line drawn from the centre of the moon to the sun, as shown in the picture (Fig. 6). At the instant when the sun’s light was seen to be shining squarely on the moon, that is just before sunset, Aristarchus pointed one leg of an instrument like a pair of compasses to the moon, and the other leg to the sun. The angle between the two directions was found to be not quite a right angle. It measured, in fact, 87 degrees (Fig. 6), whereas a right angle contains 90 degrees. [Illustration: Fig. 6.--Comparing the Distances of the Sun and Moon.] Now, if a triangle be drawn like that in Fig. 6, in which the angle at M is a right angle, and that at E is 87 degrees, this triangle illustrates the results of the observations. The moon’s distance is represented in the triangle by the line EM, and the sun’s distance by SM. It does not matter how large or small the triangle is drawn; for, if the lines are inclined at the proper angles, the line SM will always be the same number of times longer than EM. Aristarchus concluded from his observations that the sun was eighteen or nineteen times farther away than the moon. In reality, it is about four hundred times that distance, but considering that the ancients had very imperfect instruments, and that it is almost impossible to decide the exact instant when the moon is just half-full, it is not remarkable that the result obtained was far too small. As the result of other observations, Aristarchus found that 720 suns, placed edge to edge, would just circle the sky, and this is very close to the truth. Men of science honour him for his ingenious methods of measuring the sun’s distance and size, and for his painstaking observations, though the results were not perfect.