‘Precisely,’ said Sylla, ‘for as all reflexion takes place at equal angles, there is some reason in saying that when the moon is in mid-heaven at half-moon, the light is not carried from her on to the earth, but glances off beyond it; for the sun, being [Sidenote: 930] on the horizon, touches the moon with his rays, which will therefore, being reflected at equal angles, fall on the further side and beyond us, and will not send the light here; or else there will be a great distortion and variation in the angle, which is impossible.’ ‘I assure you’, said Lucius, ‘that point was mentioned also;’ and here he glanced at Menelaus the mathematician, as he went on: ‘I am ashamed, dear Menelaus,’ he said, ‘in your presence to upset a mathematical assumption which is laid down as fundamental in all the Optics of Mirrors. But I feel obliged to say’, he continued, ‘that the law which requires reflexion in all cases to be at equal angles is neither self-evident [Sidenote: B] nor admitted. It is impugned in the instance of convex mirrors, when magnified images are reflected to the one point of sight. It is impugned also in that of double mirrors, when they are inclined towards one another so that there is an angle between them, and each surface returns a double image from one face, four images in all, two on the right, two on the left, two from the outer parts of the surfaces, two dimmer ones deep within the mirrors.[333] Plato[334] gives the cause why this takes place. He has told [Sidenote: C] us that if the mirrors be raised on either side, there is a gradual shifting of the visual reflexion as it passes from one side to the other. If then some images proceed directly to us, while others glance to the opposite side of the mirrors, and are returned thence to us, it is impossible that reflexion in all cases takes place at equal angles. They observe[335] that these images meet in one point, and further claim that the law of equal angles is disproved by the streams of light which actually proceed from the moon to the earth, holding the fact to be [Sidenote: D] far more convincing than the law. However, if we are so far to indulge the beloved geometry as to make her a present of this law, in the first place it may be expected to hold of mirrors which have been made accurately smooth. But the moon has many irregularities and rough parts, so that the rays proceeding from a large body, when they fall on considerable eminences, are exposed to counter-illuminations and reciprocal dispersion; the cross-light is reflected, involved, and accumulated as though it reached us from a number of mirrors. In the next place, even if we allow that the reflexions are produced at equal [Sidenote: E] angles upon the actual surface of the moon, yet, when the distance is so great, it is not impossible that the rays may be broken in their passage, or glance around, so that the light reaches us in one composite stream. Some go further, and show by a figure that many lights