Part 24

It may, perhaps, occur to the reader to inquire what diameter of the earth, supposed to be a perfect sphere, would be derived from a degree of latitude measured with absolute accuracy near latitude 30°. A degree of latitude measured in polar regions would indicate a diameter greater even than the equatorial; one measured in equatorial regions would indicate a diameter less even than the polar. Near latitude 30° the measurement of a degree of latitude would indicate a diameter very nearly equal to the true polar diameter of the earth. In fact, if it could be proved that the builders of the pyramid used for their unit of length an exact subdivision of the polar diameter, the inference would be that, while the coincidence itself was merely accidental, their measurement of a degree of latitude in their own country had been singularly accurate. By an approximate calculation I find that, taking the earth's compression at 1-300, the diameter of the earth, estimated from the accurate measurement of a degree of latitude in the neighbourhood of the great pyramid, would have made the sacred cubit--taken at one 20,000,000th of the diameter--equal to 24·98 British inches; a closer approximation than Professor Smyth's to the estimated mean probable value of the sacred cubit.

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.

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.

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.'

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.

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 Coeli, 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.

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.

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.'

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.'

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.'

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.

Not 'of course' because Tycho used it, for, like other able students of science, he made mistakes from time to time. Thus he argued that the earth cannot rotate on her axis, because if she did bodies raised above her surface would be left behind--an argument which even the mechanical knowledge of his own time should have sufficed to invalidate, though it is still used from time to time by paradoxers of our own day.

Chinese chronicles contain other references to new stars. The annals of Ma-touan-lin, which contain the official records of remarkable appearances in the heavens, include some phenomena which manifestly belong to this class. Thus they record that in the year 173 a star appeared between the stars which mark the hind feet of the Centaur. This star remained visible from December in that year until July in the next (about the same time as Tycho Brahe's and Kepler's new stars, presently to be described). Another star, assigned by these annals to the year 1011, seems to be the same as a star referred to by Hepidannus as appearing A.D. 1012. It was of extraordinary brilliancy, and remained visible in the southern part of the heavens during three months. The annals of Ma-touan-lin assign to it a position low down in Sagittarius.

Still a circumstance must be mentioned which tends to show that the star may have been visible a few hours earlier than Dr. Schmidt supposed. Mr. M. Walter, surgeon of the 4th regiment, then stationed in North India, wrote (oddly enough, on May 12, 1867, the first anniversary of Mr. Birmingham's discovery) as follows to Mr. Stone:--'I am certain that this same conflagration was distinctly perceptible here at least six hours earlier. My knowledge of the fact came about in this wise. The night of the 12th of May last year was exceedingly sultry, and about eight o'clock on that evening I got up from the tea-table and rushed into my garden to seek a cooler atmosphere. As my door opens towards the east, the first object that met my view was the Northern Crown. My attention was at once arrested by the sight of a strange star outside the crown' (that is, outside the circlet of stars forming the diadem, not outside the constellation itself). The new star 'was then certainly quite as bright--I rather thought more so--as its neighbour Alphecca,' the chief gem of the crown. 'I was so much struck with its appearance, that I exclaimed to those indoors, "Why, here is a new comet!'" He made a diagram of the constellation, showing the place of the new star correctly. Unfortunately, Mr. Walter does not state why he is so confident, a year after the event, that it was on the 12th of May, and not on the 13th, that he noticed the new star. If he fixed the date only by the star's appearance as a second-magnitude star, his letter proves nothing; for we know that on the 13th it was still shining as brightly as Alphecca, though on the 14th it was perceptibly fainter.

The velocity of three or four miles per second inferred by the elder Struve must now be regarded (as I long since pointed out would prove to be the case) as very far short of the real velocity of our system's motion through stellar space.

M. Cornu's observations are full of interest, and he deserves considerable credit for his energy in availing himself of the few favourable opportunities he had for making them. But he goes beyond his province in adding to his account of them some remarks, intended apparently as a reflection on Mr. Huggins's speculations respecting the star in the Northern Crown. 'I,' says M. Cornu, 'will not try to form any hypothesis about the cause of the outburst. To do so would be unscientific, and such speculations, though interesting, cumber science wofully.' This is sheer nonsense, and comes very ill from an observer whose successes in science have been due entirely to the employment of methods of observation which would have had no existence had others been as unready to think out the meaning of observed facts as he appears to be himself.

The same peculiarity has been noticed since the discovery of the dark ring, the space within that ring being observed by Coolidge and G. Bond at Harvard in 1856 to be apparently darker than the surrounding sky.

I cannot understand why Mr. Webb, in his interesting little work, Celestial Objects for Common Telescopes, says that the satellite theory of the rings certainly seems insufficient to account for the phenomena of the dark ring. It seems, on the contrary, manifest that the dark ring can scarcely be explained in any other way. The observations recently made are altogether inexplicable on any other theory.

A gentleman, whose acquaintance I made in returning from America last spring, assured me that he had found demonstrative evidence showing that a total eclipse of the moon then occurred; for he could prove that Abraham's vision occurred at the time of full moon, so that it could not otherwise have been dark when the sun went down (v. 17). But the horror of great darkness occurred when the sun was going down, and total eclipses of the moon do not behave that way--at least, in our time.

It is not easy to understand what else it could have been. The notion that a conjunction of three planets, which took place shortly before the time of Christ's birth, gave rise to the tradition of the star in the east, though propounded by a former president of the Astronomical Society, could hardly be entertained by an astronomer, unless he entirely rejected Matthew's account, which the author of this theory, being a clergyman, can scarcely have done.

As, for instance, when he makes Homer say of the moon that

Around her throne the vivid planets roll, And stars unnumbered gild the glowing pole.

It is difficult, indeed, to understand how so thorough an astronomer as the late Admiral Smyth could have called the passage in which these lines occur one of the finest bursts of poetry in our language, except on the principle cleverly cited by Waller when Charles II. upbraided him for the warmth of his panegyric on Cromwell, that 'poets succeed better with fiction than with truth.' Macaulay, though not an astronomer, speaks more justly of the passage in saying that this single passage contains more inaccuracies than can be found in all Wordsworth's 'Excursion.'

It may be necessary to throw in here a few words of explanation, lest the non-astronomical reader should run away with the idea that the so-called exact science is a very inexact science indeed, so far as comets are concerned. The comet of 1680 was one of those which travel on a very eccentric orbit. Coming, indeed, from out depths many times more remote than the path even of the remotest planet, Neptune, this comet approached nearer to the sun than any which astronomers have ever seen, except only the comet of 1843. When at its nearest its nucleus was only a sixth part of the sun's diameter from his surface. Thus the part of the comet's orbit along which astronomers traced its motion was only a small part at one end of an enormously long oval, and very slight errors of observation were sufficient to produce very large errors in the determination of the nature of the comet's orbit. Encke admitted that the period might, so far as the comparatively imperfect observations made in 1680 were concerned, be any whatever, from 805 years to many millions of years, or even to infinity--that is, the comet might have a path not re-entering into itself, but carrying the comet for ever away from the sun after its one visit to our system.

For a portion of the passages which I have quoted in this essay I am indebted to Guillemin's 'Treatise on Comets,' a useful contribution to the literature of the subject, though somewhat inadequate so far as exposition is concerned.

Something very similar happened only a few years ago, so that we cannot afford to laugh too freely at the terrors of France in 1773. It was reported during the winter of 1871-1872, that Plantamour, the Swiss astronomer, had predicted the earth's destruction by a comet on August 12, 1872. Yet there was no other foundation for this rumour than the fact that Plantamour, in a lecture upon comets and meteors, had stated that the meteors seen on August 10, 11, and 12 are bodies following in the track of a comet whose orbit passes very near to the earth's. It was very certainly known to astronomers that there could be no present danger of a collision with this comet, for the comet has a period of at least 150 years, and had last passed close to the earth's orbit (not to the earth herself, be it understood) in 1862. But it was useless to point this out. Many people insisted on believing that on August 12, 1872, the earth would come into collision, possibly disastrous, with a mighty comet, which Plantamour was said to have detected and to have shown by a profound calculation to be rushing directly upon our unfortunate earth.

A rather amusing mistake was made by the stenographers of a New York paper in reporting the above sentence, which I happened to quote in a lecture upon Comets and Meteors. Instead of Paradise they wrote Paris. Those acquainted with Pitman's system of short-hand, the one most commonly employed by reporters, will easily understand how the mistake was made, the marks made to represent the consonants p, r, d, and s differing little from those made to represent the consonants p, r, and s (the 'd' or 't' sound is represented, or may be represented, by simply shortening the length of the sign for the preceding consonant). The mistake led naturally to my remarking in my next lecture that I had not before known how thoroughly synonymous the words are in America, though I had heard it said that 'Good Americans, when they die, go to Paris.'

On the occasion of my first visit to America, in 1873, I for the first time succeeded in obtaining a copy of this curious pamphlet. It had been mentioned to me (by Emerson, I think) as an amusing piece of trickery played off by a scientific man on his brethren; and Dr. Wendell Holmes, who was present, remarked that he had a copy in his possession. This he was good enough to lend me. Soon after, a valued friend in New York presented me with a copy.