Part 6

Not only do the names remain, but some of the observances connected with the old astrological systems remain even to this day. As ceremonies derived from Pagan worship are still continued, though modified in form, and with a different interpretation, in Christian and especially Roman Catholic observances, so among the Jews and among Christians the rites and ceremonies of the old Egyptian and Chaldæan astrology are still continued, though no longer interpreted as of yore. The great Jewish Lawgiver and those who follow him seem, for example, to have recognised the value of regular periods of rest (whether really required by man or become a necessity through long habit), but to have been somewhat in doubt how best to continue the practice without sanctioning the superstitions with which it had been connected. At any rate two different and inconsistent interpretations were given in the earlier and later codes of law. But whether the Jews accepted the Sabbath because they believed that an All-powerful Being, having created the world in six days, required and took rest ('and was refreshed') on the seventh, as stated in Exodus (xx. 11 and xxxi. 17), or whether they did so in remembrance of their departure from Egypt, as stated in Deuteronomy (v. 15), there can be no question that among the Egyptians the Sabbath or Saturn's day was a day of rest because of the malignant nature of the powerful planet-deity who presided over that day. Nor can it be seriously doubted that the Jews descended from the old Chaldæans, among whom (as appears from stone inscriptions recently discovered) the very word Sabbath was in use for a seventh day of rest connected with astrological observances, were familiar with the practice even before their sojourn in Egypt. They had then probably regarded it as a superstitious practice to be eschewed like those idolatrous observances which had caused Terah to remove with Abraham and Lot from Ur of the Chaldees. At any rate, we find no mention of the seventh day of rest as a religious observance until after the Exodus. It was not their only religious observance having in reality an astrological origin. Indeed, if we examine the Jewish sacrificial system as described in Numbers xxviii. and elsewhere, we shall find throughout a tacit reference to the motions or influences of the celestial bodies. There was the morning and evening sacrifice guided by the movements of the sun; the Sabbath offering, determined by the predominance of Saturn; the offering of the new moon, depending on the motions of the moon; and lastly, the Paschal sacrifice, depending on the combined movements of the sun and moon--made, in fact, during the lunation following the sun's ascending passage of the equator at the sign of Aries.

Let us return, however, after this somewhat long digression, to astrological matters.

Horary astrology is manifestly much better fitted than the casting of nativities for filling the pocket of the astrologer himself; because only one nativity can be cast, but any number of horary questions can be asked. It is on account of their skill in horary astrology that the Zadkiels of our own time have occasionally found their way into the twelfth house, or House of Enemies. Even Lilly himself, not devoting, it would seem, five minutes to inquire into the probable success of the affair, was indicted in 1655 by a half-witted young woman, because he had given judgment respecting stolen goods, receiving two shillings and sixpence, contrary to an Act made under and provided by the wise and virtuous King James, First of England and Sixth of Scotland.

State astrology relates to the destinies of kingdoms, thrones, empires, and may be regarded as a branch of horary science relating to subjects (and rulers) of more than ordinary importance.

In former ages all persons likely to occupy an important position in the history of the world had their horoscopes erected; but in these degenerate days neither the casting of nativities nor the art of ruling the planets flourishes as it should do. Our Zadkiels and Raphaëls publish, indeed, the horoscopes of kings and emperors, princes and princesses, and so forth; but their fate is as that of Benedict (according to Beatrice)--men 'wonder they will still be talking, for nobody marks them.' Even those whose horoscopes have been erected show no proper respect for the predictions made in their behalf. Thus the Prince of Wales being born when Sagittarius was in the ascendant should have been, according to Zadkiel, a tall man, with oval face, ruddy complexion, somewhat dusky, and so forth; but I understand he has by no means followed these directions as to his appearance. The sun, being well aspected, prognosticated honours--a most remarkable and unlooked-for circumstance, strangely fulfilled by the event; but then being in Cancer, in sextile with Mars, the Prince of Wales was to be partial to maritime affairs and attain naval glory, whereas as a field-marshal he can only win military glory. (I would not be understood to say that he is not quite as competent to lead our fleets as our battalions into action.) The House of Wealth was occupied by Jupiter, aspected by Saturn, which betokened great wealth through inheritance--a prognostication, says Professor Miller, which is not unlikely to come true. The House of Marriage was unsettled by the conflicting influences of Venus, Mars, and Saturn; but the first predominating, the Prince, after some trouble in his matrimonial speculations, was to marry a Princess of high birth, and one not undeserving of his kindest and most affectionate attention, probably in 1862. As to the date, an almanack informs me that the Prince married a Danish Princess in March 1863, which looks like a most culpable neglect of the predictions of our national astrologer. Again, in May 1870, when Saturn was stationary in the ascending degree, the Prince ought to have been injured by a horse, and also to have received a blow on the left side of the head, near the ear; but reprehensibly omitted both these ceremonies. A predisposition to fever and epileptic attacks was indicated by the condition of the House of Sickness. The newspapers described, a few years since, a serious attack of fever; but as most persons have some experience of the kind, the fulfilment of the prediction can hardly be regarded as very wonderful. Epileptic attacks, which, as less common, might have saved the credit of the astrologers, have not visited 'this royal native.' The position of Saturn in Capricorn betokened loss or disaster in one or other of the places ruled over by Capricorn--which, as we have seen, are India, Macedonia, Thrace, Greece, Mexico, Saxony, Wilna, Mecklenburgh, Brandenburgh, and Oxford. Professor Miller expresses the hope that Oxford was the place indicated, and the disaster nothing more serious than some slight scrape with the authorities of Christchurch. But princes never get into scrapes with college dons. Probably some one or other of the 'hair-breadth 'scapes' chronicled by the reporters of his travels in India was the event indicated by the ominous position of Saturn in Capricorn.

A remarkable list of characteristics were derived by Zadkiel from the positions of the various planets and signs in the twelve houses of the 'royal native.' Some, of course, were indicated in more ways than one, which will explain the parenthetical notes in the following alphabetical table which Professor Miller has been at the pains to draw up from Zadkiel's predictions. The prince was to be 'acute, affectionate, amiable, amorous, austere, avaricious, beneficent, benevolent, brave, brilliant, calculated for government' (a quality which may be understood two ways), 'candid, careful of his person, careless, compassionate, courteous (twice over), delighting in eloquence, discreet, envious, fond of glory, fond of learning, fond of music, fond of poetry, fond of sports, fond of the arts and sciences, frank, full of expedients, generous (three times), gracious, honourable, hostile to crime, impervious, ingenious, inoffensive, joyous, just (twice), laborious, liberal, lofty, magnanimous, modest, noble, not easy to be understood (!), parsimonious, pious (twice), profound in opinion, prone to regret his acts, prudent, rash, religious, reverent, self-confident, sincere, singular in mode of thinking, strong, temperate, unreserved, unsteady, valuable in friendship, variable, versatile, violent, volatile, wily, and worthy.' Zadkiel concludes thus:--'The square of Saturn to the moon will add to the gloomy side of the picture, and give a tinge of melancholy at times to the native's character, and also a disposition to look at the dark side of things, and lead him to despondency; nor will he be at all of a sanguine character, but cool and calculating, though occasionally rash. Yet, all things considered, though firm and sometimes positive in opinion, this royal native, if he live to mount the throne, will sway the sceptre of these realms in moderation and justice, and be a pious and benevolent man, and a merciful sovereign.' Fortunately, the time has long since passed when swaying the sceptre of these realms had any but a figurative meaning, or when Englishmen who obeyed their country's laws depended on the mercy of any man, or when even bad citizens were judged by princes. But we still prefer that princes should be well-mannered gentlemen, and therefore it is sincerely to be hoped that Zadkiel's prediction, so far as it relates to piety and benevolence, may be fulfilled, should this 'royal native' live to mount the throne. As for mercy, it is a goodly quality even in these days and in this country; for if the law no longer tolerates cruelty to men, even on the part of princes, who once had prescribed rights in that direction, there are still some cruel, nay brutal sports in which 'royal natives' might sometimes be tempted to take part. Wherefore let us hope that, even in regard to mercy, the predictions of astrologers respecting this 'royal native' may be fulfilled.

Passing however, from trivialities, let us consider the lessons which the history of astrology teaches us respecting the human mind, its powers and weaknesses. It has been well remarked by Whewell that for many ages 'mysticism in its various forms was a leading character both of the common mind and the speculations of the most intelligent and profound reasoners.' Thus mysticism was the opposite of that habit of thought which science requires, 'namely, clear ideas, distinctly employed to connect well-ascertained facts; inasmuch as the ideas in which it dealt were vague and unstable, and the temper in which they were contemplated was an urgent and aspiring enthusiasm, which could not submit to a calm conference with experience upon even terms.' We have seen what has been the history of one particular form of the mysticism of ancient and mediæval ages. If we had followed the history of alchemy, magic, and other forms of mysticism, we should have seen similar results. True science has gradually dispossessed science falsely so called, until now none but the weaker minds hold by the tenets formerly almost universally adopted. In mere numbers, believers in the ancient superstitions may be by no means insignificant; but they no longer have any influence. It has become a matter of shame to pay any attention to what those few say or do who not merely hold but proclaim the ancient faith in these matters. We can also see why this has been. In old times enthusiasm usurped the place of reason in these cases; but opinions so formed and so retained could not maintain their ground in the presence of reasoning and experience. So soon as intelligent and thoughtful men perceived that facts were against the supposed mysterious influences of the stars, the asserted powers of magicians, the pretended knowledge of alchemists, the false teachings of magic, alchemy, and astrology, were rejected. The lesson thus learned respecting erroneous doctrines which were once widely prevalent has its application in our time, when, though the influence of those teachings has passed away, other doctrines formerly associated with them still hold their ground. Men in old times, influenced by erroneous teachings, wasted their time and energies in idle questionings of the stars, vain efforts to find Arcana of mysterious power, and to acquire magical authority over the elements. Is it altogether clear that in these our times men are not hampered, prevented to some degree from doing all the good they might do in the short life-time allotted to them, by doctrines of another kind? Is there in our day no undue sacrifice of present good in idle questionings? is there no tendency to trust in a vain fetishism to prevent or remove evils which energy could avert or remedy? The time will come, in my belief, when the waste of those energies which in these days are devoted (not merely with the sanction, but the high approval, of some of the best among us) to idle aims, will be deplored as regretfully--but, alas, as idly--as the wasted speculations and labours of those whom Whewell has justly called the most intelligent and profound reasoners of the 'stationary age' of science. The words with which Whewell closes his chapter on the 'Mysticism of the Middle Ages' have their application to the mysticism of the nineteenth century:--'Experience collects her stores in vain, or ceases to collect them, when she can only pour them into the flimsy folds of the lap of Mysticism, who is, in truth, so much absorbed in looking for the treasures which are to fall from the skies, that she heeds little how scantily she obtains, or how loosely she holds, such riches as she might find beside her.'

II.

THE RELIGION OF THE GREAT PYRAMID.

During the last few years a new sect has appeared which, though as yet small in numbers, is full of zeal and fervour. The faith professed by this sect may be called the religion of the Great Pyramid, the chief article of their creed being the doctrine that that remarkable edifice was built for the purpose of revealing--in the fulness of time, now nearly accomplished--certain noteworthy truths to the human race. The founder of the pyramid religion is described by one of the present leaders of the sect as 'the late worthy John Taylor, of Gower Street, London;' but hitherto the chief prophets of the new faith have been in this country Professor Smyth, Astronomer Royal for Scotland, and in France the Abbé Moigno. I propose to examine here some of the facts most confidently urged by pyramidalists in support of their views.

But it will be well first to indicate briefly the doctrines of the new faith. They may be thus presented:

The great pyramid was erected, it would seem, under the instructions of a certain Semitic king, probably no other than Melchizedek. By supernatural means, the architects were instructed to place the pyramid in latitude 30° north; to select for its figure that of a square pyramid, carefully oriented; to employ for their unit of length the sacred cubit corresponding to the 20,000,000th part of the earth's polar axis; and to make the side of the square base equal to just so many of these sacred cubits as there are days and parts of a day in a year. They were further, by supernatural help, enabled to square the circle, and symbolised their victory over this problem by making the pyramid's height bear to the perimeter of the base the ratio which the radius of a circle bears to the circumference. Moreover, the great precessional period, in which the earth's axis gyrates like that of some mighty top around the perpendicular to the ecliptic, was communicated to the builders with a degree of accuracy far exceeding that of the best modern determinations, and they were instructed to symbolise that relation in the dimensions of the pyramid's base. A value of the sun's distance more accurate by far than modern astronomers have obtained (even since the recent transit) was imparted to them, and they embodied that dimension in the height of the pyramid. Other results which modern science has achieved, but which by merely human means the architects of the pyramid could not have obtained, were also supernaturally communicated to them; so that the true mean density of the earth, her true shape, the configuration of land and water, the mean temperature of the earth's surface, and so forth, were either symbolised in the great pyramid's position, or in the shape and dimensions of its exterior and interior. In the pyramid also were preserved the true, because supernaturally communicated, standards of length, area, capacity, weight, density, heat, time, and money. The pyramid also indicated, by certain features of its interior structure, that when it was built the holy influences of the Pleiades were exerted from a most effective position--the meridian, through the points where the ecliptic and equator intersect. And as the pyramid thus significantly refers to the past, so also it indicates the future history of the earth, especially in showing when and where the millennium is to begin. Lastly, the apex or crowning stone of the pyramid was no other than the antitype of that stone of stumbling and rock of offence, rejected by builders who knew not its true use, until it was finally placed as the chief stone of the corner. Whence naturally, 'whosoever shall fall upon it'--that is, upon the pyramid religion--'shall be broken; but on whomsoever it shall fall it will grind him to powder.'

If we examine the relations actually presented by the great pyramid--its geographical position, dimensions, shape, and internal structure--without hampering ourselves with the tenets of the new faith on the one hand, or on the other with any serious anxiety to disprove them, we shall find much to suggest that the builders of the pyramid were ingenious mathematicians, who had made some progress in astronomy, though not so much as they had made in the mastery of mechanical and scientific difficulties.

The first point to be noticed is the geographical position of the great pyramid, so far, at least, as this position affects the aspect of the heavens, viewed from the pyramid as from an observatory. Little importance, I conceive, can be attached to purely geographical relations in considering the pyramid's position. Professor Smyth notes that the pyramid is peculiarly placed with respect to the mouth of the Nile, standing 'at the southern apex of the Delta-land of Egypt.' This region being shaped like a fan, the pyramid, set at the part corresponding to the handle, was, he considers, 'that monument pure and undefiled in its religion through an idolatrous land, alluded to by Isaiah; the monument which was both "an altar to the Lord in the midst of the land of Egypt, and a pillar at the border thereof," and destined withal to become a witness in the latter days, and before the consummation of all things, to the same Lord, and to what He hath purposed upon man kind.' Still more fanciful are some other notes upon the pyramid's geographical position: as (i.) that there is more land along the meridian of the pyramid than on any other all the world round; (ii.) that there is more land in the latitude of the pyramid than in any other; and (iii.) that the pyramid territory of Lower Egypt is at the centre of the dry land habitable by man all the world over.

It does not seem to be noticed by those who call our attention to these points that such coincidences prove too much. It might be regarded as not a mere accident that the great pyramid stands at the centre of the arc of shore-line along which lie the outlets of the Nile; or it might be regarded as not a mere coincidence that the great pyramid stands at the central point of all the habitable land-surface of the globe; or, again, any one of the other relations above mentioned might be regarded as something more than a mere coincidence. But if, instead of taking only one or other of these four relations, we take all four of them, or even any two of them, together, we must regard peculiarities of the earth's configuration as the result of special design which certainly have not hitherto been so regarded by geographers. For instance, if it was by a special design that the pyramid was placed at the centre of the Nile delta, and also by special design that the pyramid was placed at the centre of the land-surface of the earth, if these two relations are each so exactly fulfilled as to render the idea of mere accidental coincidence inadmissible, then it follows, of necessity, that it is through no merely accidental coincidence that the centre of the Nile delta lies at the centre of the land-surface of the earth; in other words, the shore-line along which lie the mouths of the Nile has been designedly curved so as to have its centre so placed. And so of the other relations. The very fact that the four conditions can be fulfilled simultaneously is evidence that a coincidence of the sort may result from mere accident. Indeed, the peculiarity of geographical position which really seems to have been in the thoughts of the pyramid architects, introduces yet a fifth condition which by accident could be fulfilled along with the four others.

It would seem that the builders of the pyramid were anxious to place it in latitude 30°, as closely as their means of observation permitted. Let us consider what result they achieved, and the evidence thus afforded respecting their skill and scientific attainments. In our own time, of course, the astronomer has no difficulty in determining with great exactness the position of any given latitude-parallel. But at the time when the great pyramid was built it must have been a matter of very serious difficulty to determine the position of any required latitude-parallel with a great degree of exactitude. The most obvious way of dealing with the difficulty would have been by observing the length of shadows thrown by upright posts at noon in spring and autumn. In latitude 30° north, the sun at noon in spring (or, to speak precisely, on the day of the vernal equinox) is just twice as far from the horizon as he is from the point vertically overhead; and if a pointed post were set exactly upright at true noon (supposed to occur at the moment of the vernal or autumnal equinox), the shadow of the post would be exactly half as long as a line drawn from the top of the pole to the end of the shadow. But observations based on this principle would have presented many difficulties to the architects of the pyramid. The sun not being a point of light, but a globe, the shadow of a pointed rod does not end in a well-defined point. The moment of true noon, which is not the same as ordinary or civil noon, never does agree exactly with the time of the vernal or autumnal equinox, and may be removed from it by any interval of time not exceeding twelve hours. And there are many other circumstances which would lead astronomers, like those who doubtless presided over the scientific preparations for building the great pyramid, to prefer a means of determining the latitude depending on another principle. The stellar heavens would afford practically unchanging indications for their purpose. The stars being all carried round the pole of the heavens, as if they were fixed points in the interior of a hollow revolving sphere, it becomes possible to determine the position of the pole of the star sphere, even though no bright conspicuous star actually occupies that point. Any bright star close by the pole is seen to revolve in a very small circle, whose centre is the pole itself. Such a star is our present so-called pole-star; and, though in the days when the great pyramid was built, that star was not near the pole, another, and probably a brighter star lay near enough to the pole to serve as a pole-star, and to indicate by its circling motion the position of the actual pole of the heavens. This was at that time, and for many subsequent centuries, the leading star of the great constellation called the Dragon.

The pole of the heavens, we know, varies in position according to the latitude of the observer. At the north pole it is exactly overhead; at the equator the poles of the heavens are both on the horizon; and, as the observer travels from the equator towards the north or south pole of the earth, the corresponding pole of the heavens rises higher and higher above the horizon. In latitude 30° north, or one-third of the way from the equator to the pole, the pole of the heavens is raised one-third of the way from the horizon to the point vertically overhead; and when this is the case the observer knows that he is in latitude 30°. The builders of the great pyramid, with the almost constantly clear skies of Egypt, may reasonably be supposed to have adopted this means of determining the true position of that thirtieth parallel on which they appear to have designed to place the great building they were about to erect.

It so happens that we have the means of forming an opinion on the question whether they used one method or the other; whether they employed the sun or the stars to guide them to the geographical position they required. In fact, were it not for this circumstance, I should not have thought it worth while to discuss the qualities of either method. It will presently be seen that the discussion bears importantly on the opinion we are to form of the skill and attainments of the pyramid architects. Every celestial object is apparently raised somewhat above its true position by the refractive power of our atmosphere, being most raised when nearest the horizon and least when nearest the point vertically overhead. This effect is, indeed, so marked on bodies close to the horizon that if the astronomers of the pyramid times had observed the sun, moon, and stars attentively when so placed, they could not have failed to discover the peculiarity. Probably, however, though they noted the time of rising and setting of the celestial bodies, they only made instrumental observations upon them when these bodies were high in the heavens. Thus they remained ignorant of the refractive powers of the air. Now, if they had determined the position of the thirtieth parallel of latitude by observations of the noonday sun (in spring or autumn), then since, owing to refraction, they would have judged the sun to be higher than he really was, it follows that they would have supposed the latitude of any station from which they observed to be lower than it really was. For the lower the latitude the higher is the noonday sun at any given season. Thus, when really in latitude 30° they would have supposed themselves in a latitude lower than 30°, and would have travelled a little further north to find the proper place, as they would have supposed, for erecting the great pyramid. On the other hand, if they determined the place from observations of the movements of stars near the pole of the heavens, they would make an error of a precisely opposite nature. For the higher the latitude the higher is the pole of the heavens; and refraction, therefore, which apparently raises the pole of the heavens, gives to a station the appearance of being in a higher latitude than it really is, so that the observer would consider he was in latitude 30 north when in reality somewhat south of that latitude. We have only then to inquire whether the great pyramid was set north or south of latitude 30°, to ascertain whether the pyramid architects observed the noonday sun or circumpolar stars to determine their latitude; always assuming (as we reasonably may) that those architects did propose to set the pyramid in that particular latitude, and that they were able to make very accurate observations of the apparent positions of the celestial bodies, but that they were not acquainted with the refractive effects of the atmosphere. The answer comes in no doubtful terms. The centre of the great pyramid's base lies about one mile and a third south of the thirtieth parallel of latitude; and from this position the pole of the heavens, as raised by refraction, would appear to be very near indeed to the required position. In fact, if the pyramid had been set about half a mile still farther south the pole would have seemed just right.

Of course, such an explanation as I have here suggested appears altogether heretical to the pyramidalists. According to them the pyramid architects knew perfectly well where the true thirtieth parallel lay, and knew also all that modern science has discovered about refraction; but set the pyramid south of the true parallel and north of the position where refraction would just have made the apparent elevation of the pole correct, simply in order that the pyramid might correspond as nearly as possible to each of two conditions, whereof both could not be fulfilled at once. The pyramid would indeed, they say, have been set even more closely midway between the true and the apparent parallels of 30° north, but that the Jeezeh hill on which it is set does not afford a rock foundation any farther north. 'So very close,' says Professor Smyth, 'was the great pyramid placed to the northern brink of its hill, that the edges of the cliff might have broken off under the terrible pressure had not the builders banked up there most firmly the immense mounds of rubbish which came from their work, and which Strabo looked so particularly for 1800 years ago, but could not find. Here they were, however, and still are, utilised in enabling the great pyramid to stand on the very utmost verge of its commanding hill, within the limits of the two required latitudes, as well as over the centre of the land's physical and radial formation, and at the same time on the sure and proverbially wise foundation of rock.'

The next circumstance to be noted in the position of the great pyramid (as of all the pyramids) is that the sides are carefully oriented. This, like the approximation to a particular latitude, must be regarded as an astronomical rather than a geographical relation. The accuracy with which the orientation has been effected will serve to show how far the builders had mastered the methods of astronomical observation by which orientation was to be secured. The problem was not so simple as might be supposed by those who are not acquainted with the way in which the cardinal points are correctly determined. By solar observations, or rather by the observations of shadows cast by vertical shafts before and after noon, the direction of the meridian, or north and south line, can theoretically be ascertained. But probably in this case, as in determining the latitude, the builders took the stars for their guide. The pole of the heavens would mark the true north; and equally the pole-star, when below or above the pole, would give the true north, but, of course, most conveniently when below the pole. Nor is it difficult to see how the builders would make use of the pole-star for this purpose. From the middle of the northern side of the intended base they would bore a slant passage tending always from the position of the pole-star at its lower meridional passage, that star at each successive return to that position serving to direct their progress; while its small range, east and west of the pole, would enable them most accurately to determine the star's true mid-point below the pole; that is, the true north. When they had thus obtained a slant tunnel pointing truly to the meridian, and had carried it down to a point nearly below the middle of the proposed square base, they could, from the middle of the base, bore vertically downwards, until by rough calculation they were near the lower end of the slant tunnel; or both tunnels could be made at the same time. Then a subterranean chamber would be opened out from the slant tunnel. The vertical boring, which need not be wider than necessary to allow a plumb-line to be suspended down it, would enable the architects to determine the point vertically below the point of suspension. The slant tunnel would give the direction of the true north, either from that point or from a point at some known small distance east or west of that point. Thus, a line from some ascertained point near the mouth of the vertical boring to the mouth of the slant tunnel would lie due north and south, and serve as the required guide for the orientation of the pyramid's base. If this base extended beyond the opening of the slant tunnel, then, by continuing this tunnelling through the base tiers of the pyramid, the means would be obtained of correcting the orientation.

This, I say, would be the course naturally suggested to astronomical architects who had determined the latitude in the manner described above. It may even be described as the only very accurate method available before the telescope had been invented. So that if the accuracy of the orientation appears to be greater than could be obtained by the shadow method, the natural inference, even in the absence of corroborative evidence, would be that the stellar method, and no other, had been employed. Now, in 1779, Nouet, by refined observations, found the error of orientation measured by less than 20 minutes of arc, corresponding roughly to a displacement of the corners by about 37-1/2 inches from their true position, as supposed to be determined from the centre; or to a displacement of a southern corner by 53 inches on an east and west line from a point due south of the corresponding northern corner. This error, for a base length of 9140 inches, would not be serious, being only one inch in about five yards (when estimated in the second way). Yet the result is not quite worthy of the praise given to it by Professor Smyth. He himself, however, by much more exact observations, with an excellent altazimuth, reduced the alleged error from 20 minutes to only 4-1/2, or to 9-40ths of its formerly supposed value. This made the total displacement of a southern corner from the true meridian through the corresponding northern corner, almost exactly one foot, or one inch in about twenty-one yards--a degree of accuracy rendering it practically certain that some stellar method was used in orienting the base.

Now there is a slanting tunnel occupying precisely the position of the tunnel which should, according to this view, have been formed in order accurately to orient the pyramid's base, assuming that the time of the building of the pyramid corresponded with one of the epochs when the star Alpha Draconis was distant 3° 42' from the pole of the heavens. In other words, there is a slant tunnel directed northwards and upwards from a point deep down below the middle of the pyramid's base, and inclined 26° 17' to the horizon, the elevation of Alpha Draconis at its lower culmination when 3° 42' from the pole. The last epoch when the star was thus placed was circiter 2160 B.C.; the epoch next before that was 3440 B.C. Between these two we should have to choose, on the hypothesis that the slant tunnel was really directed to that star when the foundations of the pyramid were laid. For the next epoch before the earlier of the two named was about 28,000 B.C., and the pyramid's date cannot have been more remote than 4000 B.C.

The slant tunnel, while admirably fulfilling the requirements suggested, seems altogether unsuited for any other. Its transverse height (that is, its width in a direction perpendicular to its upper and lower faces) did not amount to quite four feet; its breadth was not quite three feet and a half. It was, therefore, not well fitted for an entrance passage to the subterranean chamber immediately under the apex of the pyramid (with which chamber it communicates in the manner suggested by the above theory). It could not have been intended to be used for observing meridian transits of the stars in order to determine sidereal time; for close circumpolar stars, by reason of their slow motion, are the least suited of all for such a purpose. As Professor Smyth says, in arguing against this suggested use of the star, 'no observer in his senses, in any existing observatory, when seeking to obtain the time, would observe the transit of a circumpolar star for anything else than to get the direction of the meridian to adjust his instrument by.' (The italics are his.) It is precisely such a purpose (the adjustment, however, not of an instrument, but of the entire structure of the pyramid itself), that I have suggested for this remarkable passage--this 'cream-white, stone-lined, long tube,' where it traverses the masonry of the pyramid, and below that dug through the solid rock to a distance of more than 350 feet.

Let us next consider the dimensions of the square base thus carefully placed in latitude 30° north to the best of the builders' power, with sides carefully oriented.

It seems highly probable that, whatever special purpose the pyramid was intended to fulfil, a subordinate idea of the builders would have been to represent symbolically in the proportions of the building such mathematical and astronomical relations as they were acquainted with. From what we know by tradition of the men of the remote time when the pyramid was built, and what we can infer from the ideas of those who inherited, however remotely, the modes of thought of the earliest astronomers and mathematicians, we can well believe that they would look with superstitious reverence on special figures, proportions, numbers, and so forth. Apart from this, they may have had a quasi-scientific desire to make a lasting record of their discoveries, and of the collected knowledge of their time.

It seems altogether probable, then, that the smaller unit of measurement used by the builders of the great Pyramid was intended, as Professor Smyth thinks, to be equal to the 500,000,000th part of the earth's diameter, determined from their geodetical observations. It was perfectly within the power of mechanicians and mathematicians so experienced as they undoubtedly were--the pyramid attests so much--to measure with considerable accuracy the length of a degree of latitude. They could not possibly (always setting aside the theory of divine inspiration) have known anything about the compression of the earth's globe, and therefore could not have intended, as Professor Smyth supposes, to have had the 500,000,000th part of the earth's polar axis, as distinguished from any other, for their unit of length. But if they made observations in or near latitude 30° north on the supposition that the earth is a globe, their probable error would exceed the difference even between the earth's polar and equatorial diameters. Both differences are largely exceeded by the range of difference among the estimates of the actual length of the sacred cubit, supposed to have contained twenty-five of these smaller units. And, again, the length of the pyramid base-side, on which Smyth bases his own estimate of the sacred cubit, has been variously estimated, the largest measure being 9168 inches, and the lowest 9110 inches. The fundamental theory of the pyramidalists, that the sacred cubit was exactly one 20,000,000th part of the earth's polar diameter, and that the side of the base contained as many cubits and parts of a cubit as there are days and parts of a day in the tropical year (or year of seasons), requires that the length of the side should be 9140 inches, lying between the limits indicated, but still so widely removed from either that it would appear very unsafe to base a theory on the supposition that the exact length is or was 9140 inches. If the measures 9168 inches and 9110 inches were inferior, and several excellent measures made by practised observers ranged around the length 9140 inches, the case would be different. But the best recent measures gave respectively 9110 and 9130 inches; and Smyth exclaims against the unfairness of Sir H. James in taking 9120 as 'therefore the [probable] true length of the side of the great pyramid when perfect,' calling this 'a dishonourable shelving of the honourable older observers with their larger results.' The only other measures, besides these two, are two by Colonel Howard Vyse and by the French savants, giving respectively 9168 and 9163·44 inches. The pyramidalists consider 9140 inches a fair mean value from these four. The natural inference, however, is, that the pyramid base is not now in a condition to be satisfactorily measured; and assuredly no such reliance can be placed on the mean value 9140 inches that, on the strength of it, we should believe what otherwise would be utterly incredible, viz. that the builders of the great pyramid knew 'both the size and shape of the earth exactly.' 'Humanly, or by human science, finding it out in that age was, of course, utterly impossible,' says Professor Smyth. But he is so confident of the average value derived from widely conflicting base measures as to assume that this value, not being humanly discoverable, was of necessity 'attributable to God and to His Divine inspiration.' We may agree, in fine, with Smyth, that the builders of the pyramid knew the earth to be a globe; that they took for their measure of length the sacred cubit, which, by their earth measures, they made very fairly approximate to the 20,000,000th part of the earth's mean diameter; but there seems no reason whatever for supposing (even if the supposition were not antecedently of its very nature inadmissible) that they knew anything about the compression of the earth, or that they had measured a degree of latitude in their own place with very wonderful accuracy.

But here a very singular coincidence may be noticed, or, rather, is forced upon our notice by the pyramidalists, who strangely enough recognise in it fresh evidence of design, while the unbeliever finds in it proof that coincidences are no sure evidence of design. The side of the pyramid containing 365-1/4 times the sacred cubit of 25 pyramid inches, it follows that the diagonal of the base contains 12,912 such inches, and the two diagonals together contain 25,824 pyramid inches, or almost exactly as many inches as there are years in the great precessional period. 'No one whatever amongst men,' says Professor Smyth after recording various estimates of the precessional period, 'from his own or school knowledge, knew anything about such a phenomenon, until Hipparchus, some 1900 years after the great pyramid's foundation, had a glimpse of the fact; and yet it had been ruling the heavens for ages, and was recorded in Jeezeh's ancient structure.' To minds not moved to most energetic forgetfulness by the spirit of faith, it would appear that when a square base had been decided upon, and its dimensions fixed, with reference to the earth's diameter and the year, the diagonals of the square base were determined also; and, if it so chanced that they corresponded with some other perfectly independent relation, the fact was not to be credited to the architects. Moreover it is manifest that the closeness of such a coincidence suggests grave doubts how far other coincidences can be relied upon as evidence of design. It seems, for instance, altogether likely that the architects of the pyramid took the sacred cubit equal to one 20,000,000th part of the earth's diameter for their chief unit of length, and intentionally assigned to the side of the pyramid's square base a length of just so many cubits as there are days in the year; and the closeness of the coincidence between the measured length and that indicated by this theory strengthens the idea that this was the builder's purpose. But when we find that an even closer coincidence immediately presents itself, which manifestly is a coincidence only, the force of the evidence before derived from mere coincidence is pro tanto shaken. For consider what this new coincidence really means. Its nature may be thus indicated: Take the number of days in the year, multiply that number by 50, and increase the result in the same degree that the diagonal of a square exceeds the side--then the resulting number represents very approximately the number of years in the great precessional period. The error, according to the best modern estimates, is about one 575th part of the true period. This is, of course, a merely accidental coincidence, for there is no connection whatever in nature between the earth's period of rotation, the shape of a square, and the earth's period of gyration. Yet this merely accidental coincidence is very much closer than the other supposed to be designed could be proved to be. It is clear, then, that mere coincidence is a very unsafe evidence of design.

Of course the pyramidalists find a ready reply to such reasoning. They argue that, in the first place, it may have been by express design that the period of the earth's rotation was made to bear this particular relation to the period of gyration in the mighty precessional movement: which is much as though one should say that by express design the height of Monte Rosa contains as many feet as there are miles in the 6000th part of the sun's distance. Then, they urge, the architects were not bound to have a square base for the pyramid; they might have had an oblong or a triangular base, and so forth--all which accords very ill with the enthusiastic language in which the selection of a square base had on other accounts been applauded.