diameter. Suppose the distance to be exactly 1/20th part of the diameter, and let the diagram represent the Moon’s orb, of which C A F is a great circle, E its centre, and C F a diameter, which consequently bears to the diameter of the Earth the ratio 2:7; and since the diameter of the Earth, according to the most exact observations, contains 7000 Italian miles, C F will be 2000, and C E 1000, and the 1/20th part of the whole, C F, 100 miles. Also let C F be a diameter of the great circle which divides the bright part of the Moon from the dark part (for, owing to the very great distance of the Sun from the Moon this circle does not differ sensibly from a great one), and let the distance of A from the point C be 1/20th part of that diameter; let the radius E A be drawn, and let it be produced to cut the tangent line G C D, which represents the ray that illumines the summit, in the point D. Then the arc C A or the straight line C D will be 100 of such units, as C E contains 1000. The sum of the squares of D C, C E is therefore 1,010,000, and the square of D E is equal to this; therefore the whole E D will be more than 1004; and A D will be more than 4 of such units, as C E contained 1000. Therefore the height of A D in the Moon, which represents a summit reaching up to the Sun’s ray, G C D, and separated from the extremity C by the distance C D, is more than 4 Italian miles; but in the Earth there are no mountains which reach to the perpendicular height even of one mile. We are therefore left to conclude that it is clear that the prominences of the Moon are loftier than those of the Earth.
The faint illumination of the Moon’s disc about new-moon explained to be due to earth-light. I wish in this place to assign the cause of another lunar phenomenon well worthy of notice, and although this phenomenon was observed by me not lately, but many years ago, and has been pointed out to some of my intimate friends and pupils, explained, and assigned to its true cause, yet as the observation of it is rendered easier and more vivid by the help of a telescope, I have considered that it would not be unsuitably introduced in this place, but I wish to introduce it chiefly in order that the connection and resemblance between the Moon and the Earth may appear more plainly.
When the Moon, both before and after conjunction, is found not far from the Sun, not only does its orb show itself to our sight on the side where it is furnished with shining horns, but a slight and faint circumference is also seen to mark out the circle of the dark part, that part, namely, which is turned away from the Sun, and to separate it from the darker background of the sky. But if we examine the matter more closely, we shall see that not only is the extreme edge of the part in shadow shining with a faint brightness, but that the entire face of the Moon, that side, that is, which does not feel the Sun’s glare, is illuminated with a pale light of considerable brightness. At the first glance only a fine circumference appears shining, on account of the darker part of the sky adjacent to it; whereas, on the contrary, the rest of the surface appears dark, on account of the contiguity of the shining horns, which destroys the clearness of our sight. But if any one chooses such a position for himself, that by the interposition of a roof, or a chimney, or some other object between his sight and the Moon, but at a considerable distance from his eye, the shining horns are hidden, and the rest of the Moon’s orb is left exposed to his view, then he will find that this tract of the Moon also, although deprived of sunlight, gleams with considerable light, and particularly so if the gloom of the night has already deepened through the absence of the Sun; for with a darker background the same light appears brighter. Moreover, it is found that this secondary brightness of the Moon, as I may call it, is greater in proportion as the Moon is less distant from the Sun; for it abates more and more in proportion to the Moon’s distance from that body, so much so that after the first quarter, and before the end of the second, it is found to be weak and very faint, although it be observed in a darker sky; whereas, at an angular distance of 60° or less, even during twilight, it is wonderfully bright, so bright indeed that, with the help of a good telescope, the great spots may be distinguished in it.
This strange brightness has afforded no small perplexity to philosophical minds; and some have published one thing, some another, as the cause to be alleged for it. Some have said that it is the inherent and natural brightness of the Moon; some that it is imparted to that body by the planet Venus; or, as others maintain, by all the stars; while some have said that it comes from the Sun, whose rays, they say, find a way through the solid mass of the Moon. But statements of this kind are disproved without much difficulty, and convincingly demonstrated to be false. For if this kind of light were the Moon’s own, or were contributed by the stars, the Moon would retain it, particularly in eclipses, and would show it then, when left in an unusually dark sky, but this is contrary to experience. For the brightness which is seen on the Moon in eclipses is far less intense, being somewhat reddish, and almost copper-coloured, whereas this is brighter and whiter; besides, the brightness seen during an eclipse is changeable and shifting, for it wanders over the face of the Moon, so that that part which is near the circumference of the circle of shadow thrown by the Earth is bright, but the rest of the Moon is always seen to be dark. From which circumstance we understand without hesitation that this brightness is due to the proximity of the Sun’s rays coming into contact with some denser region which surrounds the Moon as an envelope; owing to which contact a sort of dawn-light is diffused over the neighbouring regions of the Moon, just as the twilight spreads in the morning and evening on the Earth:[11] but I will treat more fully of this matter in my book upon the System of the Universe.[12]
Again, to assert that this sort of light is imparted to the Moon by the planet Venus is so childish as to be undeserving of an answer; for who is so ignorant as not to understand that at conjunction and within an angular distance of 60° it is quite impossible for the part of the Moon turned away from the Sun to be seen by the planet Venus?
But that this light is derived from the Sun penetrating with its light the solid mass of the Moon, and rendering it luminous, is equally untenable. For then this light would never lessen, since the hemisphere of the Moon is always illumined by the Sun, except at the moment of a lunar eclipse, yet really it quickly decreases while the Moon is drawing near to the end of her first quarter, and when she has passed her first quarter it becomes quite dull. Since, therefore, this kind of secondary brightness is not inherent and the Moon’s own, nor borrowed from any of the stars, nor from the Sun, and since there now remains in the whole universe no other body whatever except the Earth, what, pray, must we conclude? What must we assert? Shall we assert that the body of the Moon, or some other dark and sunless orb, receives light from the Earth? Why should it not be the Moon? And most certainly it is. The Earth, with fair and grateful exchange, pays back to the Moon an illumination like that which it receives from the Moon nearly the whole time during the darkest gloom of night. Let me explain the matter more clearly. At conjunction, when the Moon occupies a position between the Sun and the Earth, the Moon is illuminated by the Sun’s rays on her half towards the Sun which is turned away from the Earth, and the other half, with which she regards the Earth, is covered with darkness, and so in no degree illumines the Earth’s surface. When the Moon has slightly separated from the Sun, straightway she is partly illumined on the half directed towards us; she turns towards us a slender silvery crescent, and slightly illumines the Earth; the Sun’s illumination increases upon the Moon as she approaches her first quarter, and the reflexion of that light increases on the Earth; the brightness in the Moon next extends beyond the semicircle, and our nights grow brighter; at length the entire face of the Moon looking towards the Earth is irradiated with the most intense brightness by the Sun, which happens when the Sun and Moon are on opposite sides of the Earth; then far and wide the surface of the Earth shines with the flood of moonlight; after this the Moon, now waning, sends out less powerful beams, and the Earth is illumined less powerfully; at length the Moon draws near her first position of conjunction with the Sun, and forthwith black night invades the Earth. In such a cycle the moonlight gives us each month alternations of brighter and fainter illumination. But the benefit of her light to the Earth is balanced and repaid by the benefit of the light of the Earth to her; for while the Moon is found near the Sun about the time of conjunction, she has in front of her the entire surface of that hemisphere of the Earth which is exposed to the Sun, and vividly illumined with his beams, and so receives light reflected from the Earth. Owing to such reflexion, the hemisphere of the Moon nearer to us, though deprived of sunlight, appears of considerable brightness. Again, when removed from the Sun through a quadrant, the Moon sees only one-half of the Earth’s hemisphere illuminated, namely the western half, for the other, the eastern, is covered with the shades of night; the Moon is, therefore, less brightly enlightened by the Earth, and accordingly that secondary light appears fainter to us. But if you imagine the Moon to be set on the opposite side of the Earth to the Sun, she will see the hemisphere of the Earth, now between the Moon and the Sun, quite dark, and steeped in the gloom of night; if, therefore, an eclipse should accompany such a position of the Moon, she will receive no light at all, being deprived of the illumination of the Sun and Earth together. In any other position, with regard to the Earth and the Sun, the Moon receives more or less light by reflexion from the Earth, according as she sees a greater or smaller portion of the hemisphere of the Earth illuminated by the Sun; for such a law is observed between these two orbs, that at whatever times the Earth is most brightly enlightened by the Moon, at those times, on the contrary, the Moon is least enlightened by the Earth; and contrariwise. Let these few words on this subject suffice in this place; for I will consider it more fully in my System of the Universe, where, by very many arguments and experimental proofs, there is shown to be a very strong reflexion of the Sun’s light from the Earth, for the benefit of those who urge that the Earth must be separated from the starry host, chiefly for the reason that it has neither motion nor light, for I will prove that the Earth has motion, and surpasses the Moon in brightness, and is not the place where the dull refuse of the universe has settled down; and I will support my demonstration by a thousand arguments taken from natural phenomena.
Stars. Their appearance in the telescope. Hitherto I have spoken of the observations which I have made concerning the Moon’s body; now I will briefly announce the phenomena which have been, as yet, seen by me with reference to the Fixed Stars. And first of all the following fact is worthy of consideration:—The stars, fixed as well as erratic, when seen with a telescope, by no means appear to be increased in magnitude in the same proportion as other objects, and the Moon herself, gain increase of size; but in the case of the stars such increase appears much less, so that you may consider that a telescope, which (for the sake of illustration) is powerful enough to magnify other objects a hundred times, will scarcely render the stars magnified four or five times. But the reason of this is as follows:—When stars are viewed with our natural eyesight they do not present themselves to us of their bare, real size, but beaming with a certain vividness, and fringed with sparkling rays, especially when the night is far advanced; and from this circumstance they appear much larger than they would if they were stripped of those adventitious fringes, for the angle which they subtend at the eye is determined not by the primary disc of the star, but by the brightness which so widely surrounds it. Perhaps you will understand this most clearly from the well-known circumstance that when stars rise just at sunset, in the beginning of twilight, they appear very small, although they may be stars of the first magnitude; and even the planet Venus itself, on any occasion when it may present itself to view in broad daylight, is so small to see that it scarcely seems to equal a star of the last magnitude. It is different in the case of other objects, and even of the Moon, which, whether viewed in the light of midday or in the depth of night, always appears of the same size. We conclude therefore that the stars are seen at midnight in uncurtailed glory, but their fringes are of such a nature that the daylight can cut them off, and not only daylight, but any slight cloud which may be interposed between a star and the eye of the observer. A dark veil or coloured glass has the same effect, for, upon placing them before the eye between it and the stars, all the blaze that surrounds them leaves them at once. A telescope also accomplishes the same result, for it removes from the stars their adventitious and accidental splendours before it enlarges their true discs (if indeed they are of that shape), and so they seem less magnified than other objects, for a star of the fifth or sixth magnitude seen through a telescope is shown as of the first magnitude only.
The difference between the appearance of the planets and the fixed stars seems also deserving of notice. The planets present their discs perfectly round, just as if described with a pair of compasses, and appear as so many little moons, completely illuminated and of a globular shape; but the fixed stars do not look to the naked eye bounded by a circular circumference, but rather like blazes of light, shooting out beams on all sides and very sparkling, and with a telescope they appear of the same shape as when they are viewed by simply looking at them, but so much larger that a star of the fifth or sixth magnitude seems to equal Sirius, the largest of all the fixed stars.[13]
