[21] It is, however, almost impossible to mark any limits to what may be regarded as evidence of design by a coincidence-hunter. I quote the following from the late Professor De Morgan's Budget of Paradoxes. Having mentioned that 7 occurs less frequently than any other digit in the number expressing the ratio of circumference to diameter of a circle, he proceeds: 'A correspondent of my friend Piazzi Smyth notices that 3 is the number of most frequency, and that 3-1⁄7 is the nearest approximation to it in simple digits. Professor Smyth, whose work on Egypt is paradox of a very high order, backed by a great quantity of useful labour, the results of which will be made available by those who do not receive the paradoxes, is inclined to see confirmation for some of his theory in these phenomena.' In passing, I may mention as the most singular of these accidental digit relations which I have yet noticed, that in the first 110 digits of the square root of 2, the number 7 occurs more than twice as often as either 5 or 9, which each occur eight times, 1 and 2 occurring each nine times, and 7 occurring no less than eighteen times.
[22] I have substituted this value in the article 'Astronomy,' of the British Encyclopædia, for the estimate formerly used, viz. 95,233,055 miles. But there is good reason for believing that the actual distance is nearly 92,000,000 miles.
[23] It may be matched by other coincidences as remarkable and as little the result of the operation of any natural law. For instance, the following strange relation, introducing the dimensions of the sun himself, nowhere, so far as I have yet seen, introduced among pyramid relations, even by pyramidalists: 'If the plane of the ecliptic were a true surface, and the sun were to commence rolling along that surface towards the part of the earth's orbit where she is at her mean distance, while the earth commenced rolling upon the sun (round one of his great circles), each globe turning round in the same time,—then, by the time the earth had rolled its way once round the sun, the sun would have almost exactly reached the earth's orbit. This is only another way of saying that the sun's diameter exceeds the earth's in almost exactly the same degree that the sun's distance exceeds the sun's diameter.'
[24] It has been remarked that, though Hipparchus had the enormous advantage of being able to compare his own observations with those recorded by the Chaldæans, he estimated the length of the year less correctly than the Chaldæans. It has been thought by some that the Chaldæans were acquainted with the true system of the universe, but I do not know that there are sufficient grounds for this supposition. Diodorus Siculus and Apollonius Myndius mention, however, that they were able to predict the return of comets, and this implies that their observations had been continued for many centuries with great care and exactness.
[25] The language of the modern Zadkiels and Raphaëls, though meaningless and absurd in itself, yet, as assuredly derived from the astrology of the oldest times, may here be quoted. (It certainly was not invented to give support to the theory I am at present advocating.) Thus runs the jargon of the tribe: 'In order to illustrate plainly to the reader what astrologers mean by the "houses of heaven," it is proper for him to bear in mind the four cardinal points. The eastern, facing the rising sun, has at its centre the first grand angle or first house, termed the Horoscope or ascendant. The northern, opposite the region where the sun is at midnight, or the cusp of the lower heaven or nadir, is the Imum Cœli, and has at its centre the fourth house. The western, facing the setting sun, has at its centre the third grand angle or seventh house or descendant. And lastly, the southern, facing the noonday sun, has at its centre the astrologer's tenth house, or Mid-heaven, the most powerful angle or house of honour.' 'And although,' proceeds the modern astrologer, 'we cannot in the ethereal blue discern these lines or terminating divisions, both reason and experience assure us that they certainly exist; therefore the astrologer has certain grounds for the choice of his four angular houses' (out of twelve in all) 'which, resembling the palpable demonstration they afford, are in the astral science esteemed the most powerful of the whole. '—Raphaël's Manual of Astrology.
[26] Arabian writers give the following account of Egyptian progress in astrology and the mystical arts: Nacrawasch, the progenitor of Misraim, was the first Egyptian prince, and the first of the magicians who excelled in astrology and enchantment. Retiring into Egypt with his family of eighty persons, he built Essous, the most ancient city of Egypt, and commenced the first dynasty of Misraimitish princes, who excelled as cabalists, diviners, and in the mystic arts generally. The most celebrated of the race were Naerasch, who first represented by images the twelve signs of the zodiac; Gharnak, who openly described the arts before kept secret; Hersall, who first worshipped idols; Sehlouk, who worshipped the sun; Saurid (King Saurid of Ibn Abd Alkohm's account), who erected the first pyramids and invented the magic mirror; and Pharaoh, the last king of the dynasty, whose name was afterwards taken as a kingly title, as Cæsar later became a general imperial title.
[27] It is noteworthy how Swedenborg here anticipates a saying of Laplace, the greatest mathematician the world has known, save Newton alone. Newton's remark that he seemed but as a child who had gathered a few shells on the shores of ocean, is well known. Laplace's words, 'Ce que nous connaissons est peu de chose; ce que nous ignorons est immense,' were not, as is commonly stated, his last. De Morgan gives the following account of Laplace's last moments, on the authority of Laplace's friend and pupil, the well-known mathematician Poisson: 'After the publication (in 1825) of the fifth volume of the Mécanique Céleste, Laplace became gradually weaker, and with it musing and abstracted. He thought much on the great problems of existence, and often muttered to himself, "Qu'est-ce que c'est que tout cela!" After many alternations he appeared at last so permanently prostrated that his family applied to his favourite pupil, M. Poisson, to try to get a word from him. Poisson paid a visit, and after a few words of salutation, said, "J'ai une bonne nouvelle à vous annoncer: on a reçu au Bureau des Longitudes une lettre d'Allemagne annonçant que M. Bessel a vérifié par l'observation vos découvertes théoriques sur les satellites de Jupiter." Laplace opened his eyes and answered with deep gravity. "L'homme ne poursuit que des chimères." He never spoke again. His death took place March 5, 1827.'
[28] The reason assigned by Swedenborg is fanciful enough. 'In the spiritual sense,' he says, 'a horse signifies the intellectual principle formed from scientifics, and as they are afraid of cultivating the intellectual faculties by worldly sciences, from this comes an influx of fear. They care nothing for scientifics which are of human erudition.'
[29] Similar reasoning applies to the moons of Jupiter, and it so chances that the result in their case comes out exactly the same as in the case of Saturn; all the Jovian moons, if full together, would reflect only the sixteenth part of the light which we receive from the full moon. It is strange that scientific men of considerable mathematical power have used the argument from design apparently supplied by the satellites, without being at the pains to test its validity by the simple mathematical calculations necessary to determine the quantity of light which these bodies can reflect to the planets round which they travel. Brewster and Whewell, though they took opposite sides in the controversy about other inhabited worlds, agreed in this. Brewster, of course, holding the theory that all the planets are inhabited, very naturally accepted the argument from design in this case. Whewell, in opposing that theory, did not dwell at all upon the subjects of the satellites. But in his 'Bridgewater Treatise on Astronomy and General Physics,' he says, 'Taking only the ascertained cases of Venus, the Earth, Jupiter, and Saturn, we conceive that a person of common understanding will be strongly impressed with the persuasion that the satellites are placed in the system with a view to compensate for the diminished light of the sun at greater distances. Mars is an exception; some persons might conjecture from this case that the arrangement itself, like other useful arrangements, has been brought about by some wider law which we have not yet detected. But whether or not we entertain such a guess (it can be nothing more), we see in other parts of creation so many examples of apparent exceptions to rules, which are afterwards found to be capable of explanation, or to be provided for by particular contrivances, that no one familiar with such contemplations will, by one anomaly, be driven from the persuasion that the end which the arrangements of the satellites seem suited to answer is really one of the ends of their creation.'
[30] The reader who cares enough about such subjects to take the necessary trouble, can easily make a little model of Saturn and his ring system, which will very prettily illustrate the effect of the rings both in reflecting light to the planet's darkened hemisphere and in cutting off light from the planet's illuminated hemisphere. Take a ball, say an ordinary hand-ball, and pierce it through the centre with a fine knitting-needle. Cut out a flat ring of card, proportioned to the ball as the ring system of Saturn to his ball. (If the ball is two inches in diameter, strike out on a sheet of cardboard two concentric circles, one of them with a radius of a little more than an inch and a half, the other with a radius of about two inches and three-eights, and cut out the ring between these two circles.) Thrust the knitting-needle through this ring in such a way that the ball shall lie in the middle of the ring, as the globe of Saturn hangs (without knitting-needle connections) in the middle of his ring system. Thrust another knitting-needle centrally through the ball square to the plane of the ring, and use this second needle, which we may call the polar one, as a handle. Now take the ball and ring into sunlight, or the light of a lamp or candle, holding them so that the shadow of the ring is as thin as possible. This represents the position of the shadow at the time of Saturnian spring or autumn. Cause the shadow slowly to shift until it surrounds the part of the ball through which the polar needle passes on one side. This will represent the position of the shadow at the time of midwinter for the hemisphere corresponding to that side of the ball. Notice that while the shadow is traversing this half of the ball, the side of the ring which lies towards that half is in shadow, so that a fly or other small insect on that half of the ball would see the darkened side of the ring. A Saturnian correspondingly placed would get no reflected sunlight from the ring system. Move the ball and ring so that the shadow slowly returns to its first position. You will then have illustrated the changes taking place during one half of a Saturnian year. Continue the motion so that the shadow passes to the other half of the ball, and finally surrounds the other point through which the polar needle passes. The polar point which the shadow before surrounded will now be seen to be in the light, and this half of the ball will illustrate the hemisphere of Saturn where it is midsummer. It will also be seen that the side of the ring towards this half of the ball is now in the light, so that a small insect on this half of the ball would see the bright side of the ring. A Saturnian correspondingly placed would get reflected sunlight from the ring system both by day and by night. Moving the ball and ring so that the shadow returns to its first position, an entire Saturnian year will have been illustrated. These changes can be still better shown with a Saturnian orrery (see plate viii. of my Saturn), which can be very easily constructed.