Myths and Marvels of Astronomy Part 3

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 Abbe 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 lat.i.tude 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 circ.u.mference. 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 ant.i.type 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 lat.i.tude 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 sh.o.r.e-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 sh.o.r.e-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.[16] 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 lat.i.tude 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 lat.i.tude-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 lat.i.tude-parallel with a great degree of exact.i.tude. 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 lat.i.tude 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 circ.u.mstances 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 lat.i.tude 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[17] 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 lat.i.tude 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 lat.i.tude 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 lat.i.tude 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 circ.u.mstance, 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.[18] Now, if they had determined the position of the thirtieth parallel of lat.i.tude 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 lat.i.tude of any station from which they observed to be lower than it really was. For the lower the lat.i.tude the higher is the noonday sun at any given season. Thus, when really in lat.i.tude 30 they would have supposed themselves in a lat.i.tude 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 lat.i.tude 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 lat.i.tude than it really is, so that the observer would consider he was in lat.i.tude 30 north when in reality somewhat south of that lat.i.tude. We have only then to inquire whether the great pyramid was set north or south of lat.i.tude 30, to ascertain whether the pyramid architects observed the noonday sun or circ.u.mpolar stars to determine their lat.i.tude; always a.s.suming (as we reasonably may) that those architects did propose to set the pyramid in that particular lat.i.tude, 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 lat.i.tude; 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 lat.i.tudes, 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 circ.u.mstance 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 lat.i.tude, 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 lat.i.tude, 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 pa.s.sage tending always from the position of the pole-star at its lower meridional pa.s.sage, 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.[19] 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 lat.i.tude 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, a.s.suming 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 pa.s.sage 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 circ.u.mpolar 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 circ.u.mpolar 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 pa.s.sage--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 lat.i.tude 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 superst.i.tious 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 lat.i.tude.

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 lat.i.tude 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 916344 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 a.s.suredly 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 a.s.sume that this value, not being humanly discoverable, was of necessity 'attributable to G.o.d 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 lat.i.tude in their own place with very wonderful accuracy.[20]

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 a.s.signed 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.[21] 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.

Next let us consider the height of the pyramid. According to the best modern measurements, it would seem that the height when (if ever) the pyramid terminated above in a pointed apex, must have been about 486 feet. And from the comparison of the best estimates of the base side with the best estimates of the height, it seems very likely indeed that the intention of the builders was to make the height bear to the perimeter of the base the same ratio which the radius of a circle bears to the circ.u.mference. Remembering the range of difference in the base measures it might be supposed that the exactness of the approximation to this ratio could not be determined very satisfactorily. But as certain casing stones have been discovered which indicate with considerable exactness the slope of the original plane-surfaces of the pyramid, the ratio of the height to the side of the base may be regarded as much more satisfactorily determined than the actual value of either dimension. Of course the pyramidalists claim a degree of precision indicating a most accurate knowledge of the ratio between the diameter and the circ.u.mference of a circle; and the angle of the only casing stone measured being diversely estimated at 51 50' and 51 52-1/4', they consider 50 51' 143" the true value, and infer that the builders regarded the ratio as 314159 to 1. The real fact is, that the modern estimates of the dimensions of the casing stones (which, by the way, ought to agree better if these stones are as well made as stated) indicate the values 31439228 and 31396740 for the ratio; and all we can say is, that the ratio really used lay _probably_ between these limits, though it may have been outside either. Now the approximation of either is not remarkably close. It requires no mathematical knowledge at all to determine the circ.u.mference of a circle much more exactly. 'I thought it very strange,' wrote a circle-squarer once to De Morgan (_Budget of Paradoxes_, p. 389), 'that so many great scholars in all ages should have failed in finding the true ratio, and have been determined to try myself.' 'I have been informed,' proceeds De Morgan, 'that this trial makes the diameter to the circ.u.mference as 64 to 201, giving the ratio equal to 31410625 exactly. The result was obtained by the discoverer in three weeks after he first heard of the existence of the difficulty. This quadrator has since published a little slip and entered it at Stationers' Hall. He says he has done it by actual measurement; and I hear from a private source that he uses a disc of twelve inches diameter which he rolls upon a straight rail.' The 'rolling is a very creditable one; it is as much below the mark as Archimedes was above it. Its performer is a joiner who evidently knows well what he is about when he measures; he is not wrong by 1 in 3000.'

Such skilful mechanicians as the builders of the pyramid could have obtained a closer approximation still by mere measurement. Besides, as they were manifestly mathematicians, such an approximation as was obtained by Archimedes must have been well within their power; and that approximation lies well within the limits above indicated. Professor Smyth remarks that the ratio was 'a quant.i.ty which men in general, and all human science too, did not begin to trouble themselves about until long, long ages, languages, and nations had pa.s.sed away after the building of the great pyramid; and after the sealing up, too, of that grand primeval and prehistoric monument of the patriarchal age of the earth according to Scripture.' I do not know where the Scripture records the sealing up of the great pyramid; but it is all but certain that during the very time when the pyramid was being built astronomical observations were in progress which, for their interpretation, involved of necessity a continual reference to the ratio in question. No one who considers the wonderful accuracy with which, nearly two thousand years before the Christian era, the Chaldaeans had determined the famous cycle of the Saros, can doubt that they must have observed the heavenly bodies for several centuries before they could have achieved such a success; and the study of the motions of the celestial bodies compels 'men to trouble themselves' about the famous ratio of the circ.u.mference to the diameter.

We now come upon a new relation (contained in the dimensions of the pyramid as thus determined) which, by a strange coincidence, causes the height of the pyramid to appear to symbolise the distance of the sun.

There were 5813 pyramid inches, or 5819 British inches, in the height of the pyramid according to the relations already indicated. Now, in the sun's distance, according to an estimate recently adopted and freely used,[22] there are 91,400,000 miles or 5791 thousand millions of inches--that is, there are approximately as many thousand millions of inches in the sun's distance as there are inches in the height of the pyramid. If we take the relation as exact we should infer for the sun's distance 5819 thousand millions of inches, or 91,840,000 miles--an immense improvement on the estimate which for so many years occupied a place of honour in our books of astronomy. Besides, there is strong reason for believing that, when the results of recent observations are worked out, the estimated sun distance will be much nearer this pyramid value than even to the value 91,400,000 recently adopted. This result, which one would have thought so damaging to faith in the evidence from coincidence--nay, quite fatal after the other case in which a close coincidence had appeared by merest accident--is regarded by the pyramidalist as a perfect triumph for their faith.

They connect it with another coincidence, viz. that, a.s.suming the height determined in the way already indicated, then it so happens that the height bears to half a diagonal of the base the ratio 9 to 10. Seeing that the perimeter of the base symbolises the annual motion of the earth round the sun, while the height represents the radius of a circle with that perimeter, it follows that the height should symbolise the sun's distance. 'That line, further,' says Professor Smyth (speaking on behalf of Mr. W. Petrie, the discoverer of this relation), 'must represent'

this radius 'in the proportion of 1 to 1,000,000,000' (or _ten_ raised to power _nine_), 'because amongst other reasons 10 to 9 is practically the shape of the great pyramid.' For this building 'has such an angle at the corners, that for every ten units its structure advances inwards on the diagonal of the base, it practically rises upwards, or points to suns.h.i.+ne' (_sic_) 'by _nine_. Nine, too, out of the ten characteristic parts (viz. five angles and five sides) being the number of those parts which the sun s.h.i.+nes on in such a shaped pyramid, in such a lat.i.tude near the equator, out of a high sky, or, as the Peruvians say, when the sun sets on the pyramid with all its rays.' The coincidence itself on which this perverse reasoning rests is a singular one--singular, that is, as showing how close an accidental coincidence may run. It amounts to this, that if the number of days in the year be multiplied by 100, and a circle be drawn with a circ.u.mference containing 100 times as many inches as there are days in the year, the radius of the circle will be very nearly one 1,000,000,000th part of the sun's distance. Remembering that the pyramid inch is a.s.sumed to be one 500,000,000th part of the earth's diameter, we shall not be far from the truth in saying that, as a matter of fact, the earth by her orbital motion traverses each day a distance equal to two hundred times her own diameter. But, of course, this relation is altogether accidental. It has no real cause in nature.[23]

Such relations show that mere numerical coincidences, however close, have little weight as evidence, except where they occur in series. Even then they require to be very cautiously regarded, seeing that the history of science records many instances where the apparent law of a series has been found to be falsified when the theory has been extended.

Of course this reason is not quoted in order to throw doubt on the supposition that the height of the pyramid was intended to symbolise the sun's distance. That supposition is simply inadmissible if the hypothesis, according to which the height was already independently determined in another way, is admitted. Either hypothesis might be admitted were we not certain that the sun's distance could not possibly have been known to the builders of the pyramid; or both hypotheses may be rejected: but to admit both is out of the question.

Considering the mult.i.tude of dimensions of length, surface, capacity, and position, the great number of shapes, and the variety of material existing within the pyramid, and considering, further, the enormous number of relations (presented by modern science) from among which to choose, can it be wondered at if fresh coincidences are being continually recognised? If a dimension will not serve in one way, use can be found for it in another; for instance, if some measure of length does not correspond closely with any known dimension of the earth or of the solar system (an unlikely supposition), then it can be understood to typify an interval of time. If, even after trying all possible changes of that kind, no coincidence shows itself (which is all but impossible), then all that is needed to secure a coincidence is that the dimensions should be manipulated a little.

Let a single instance suffice to show how the pyramidalists (with perfect honesty of purpose) hunt down a coincidence. The slant tunnel already described has a transverse height, once no doubt uniform, now giving various measures from 4714 pyramid inches to 4732 inches, so that the vertical height from the known inclination of the tunnel would be estimated at somewhere between 5264 inches and 5285. Neither dimension corresponds very obviously with any measured distance in the earth or solar system. Nor when we try periods, areas, etc., does any very satisfactory coincidence present itself. But the difficulty is easily turned into a new proof of design. Putting all the observations together (says Professor Smyth), 'I deduced 4724 pyramid inches to be the transverse height of the entrance pa.s.sage; and computing from thence with the observed angle of inclination the vertical height, that came out 5276 of the same inches. But the sum of those two heights, or the height taken up and down, equals 100 inches, which length, as elsewhere shown, is the general pyramid linear representation of a day of twenty-four hours. And the mean of the two heights, or the height taken one way only, and impartially to the middle point between them, equals fifty inches; which quant.i.ty is, therefore, the general pyramid linear representation of only half a day. In which case, let us ask what the entrance pa.s.sage has to do with half rather than a whole day?'

On relations such as these, which, if really intended by the architect, would imply an utterly fatuous habit of concealing elaborately what he desired to symbolise, the pyramidalists base their belief that 'a Mighty Intelligence did both think out the plans for it, and compel unwilling and ignorant idolators, in a primal age of the world, to work mightily both for the future glory of the one true G.o.d of Revelation, and to establish lasting prophetic testimony touching a further development, still to take place, of the absolutely Divine Christian dispensation.'

III.

_THE MYSTERY OF THE PYRAMIDS._

Few subjects of inquiry have proved more perplexing than the question of the purpose for which the pyramids of Egypt were built. Even in the remotest ages of which we have historical record, nothing seems to have been known certainly on this point. For some reason or other, the builders of the pyramids concealed the object of these structures, and this so successfully that not even a tradition has reached us which purports to have been handed down from the epoch of the pyramids'

construction. We find, indeed, some explanations given by the earliest historians; but they were professedly only hypothetical, like those advanced in more recent times. Including ancient and modern theories, we find a wide range of choice. Some have thought that these buildings were a.s.sociated with the religion of the early Egyptians; others have suggested that they were tombs; others, that they combined the purposes of tombs and temples, that they were astronomical observatories, defences against the sands of the Great Desert, granaries like those made under Joseph's direction, places of resort during excessive overflows of the Nile; and many other uses have been suggested for them.

But none of these ideas are found on close examination to be tenable as representing the sole purpose of the pyramids, and few of them have strong claims to be regarded as presenting even a chief object of these remarkable structures. The significant and perplexing history of the three oldest pyramids--the Great Pyramid of Cheops, Shofo, or Suphis, the pyramid of Chephren, and the pyramid of Mycerinus; and the most remarkable of all the facts known respecting the pyramids generally, viz., the circ.u.mstance that one pyramid after another was built as though each had become useless soon after it was finished, are left entirely unexplained by all the theories above mentioned, save one only, the tomb theory, and that does not afford by any means a satisfactory explanation of the circ.u.mstances.

I propose to give here a brief account of some of the most suggestive facts known respecting the pyramids, and, after considering the difficulties which beset the theories heretofore advanced, to indicate a theory (new so far as I know) which seems to me to correspond better with the facts than any heretofore advanced; I suggest it, however, rather for consideration than because I regard it as very convincingly supported by the evidence. In fact, to advance any theory at present with confident a.s.surance of its correctness, would be simply to indicate a very limited acquaintance with the difficulties surrounding the subject.

Let us first consider a few of the more striking facts recorded by history or tradition, noting, as we proceed, whatever ideas they may suggest as to the intended character of these structures.

It is hardly necessary to say, perhaps, that the history of the Great Pyramid is of paramount importance in this inquiry. Whatever purpose pyramids were originally intended to subserve, must have been conceived by the builders of _that_ pyramid. New ideas may have been superadded by the builders of later pyramids, but it is unlikely that the original purpose can have been entirely abandoned. Some great purpose there was, which the rulers of ancient Egypt proposed to fulfil by building very ma.s.sive pyramidal structures on a particular plan. It is by inquiring into the history of the first and most ma.s.sive of these structures, and by examining its construction, that we shall have the best chance of finding out what that great purpose was.

According to Herodotus, the kings who built the pyramids reigned not more than twenty-eight centuries ago; but there can be little doubt that Herodotus misunderstood the Egyptian priests from whom he derived his information, and that the real antiquity of the pyramid-kings was far greater. He tells us that, according to the Egyptian priests, Cheops 'on ascending the throne plunged into all manner of wickedness. He closed the temples, and forbade the Egyptians to offer sacrifice, compelling them instead to labour one and all in his service, viz., in building the Great Pyramid.' Still following his interpretation of the Egyptian account, we learn that one hundred thousand men were employed for twenty years in building the Great Pyramid, and that ten years were occupied in constructing a causeway by which to convey the stones to the place and in conveying them there. 'Cheops reigned fifty years; and was succeeded by his brother Chephren, who imitated the conduct of his predecessor, built a pyramid--but smaller than his brother's--and reigned fifty-six years. Thus during one hundred and six years, the temples were shut and never opened.' Moreover, Herodotus tells us that 'the Egyptians so detested the memory of these kings, that they do not much like even to mention their names. Hence they commonly call the pyramids after Philition, a shepherd who at that time fed his flocks about the place.'

'After Chephren, Mycerinus, son of Cheops, ascended the throne, he reopened the temples, and allowed the people to resume the practice of sacrifice. He, too, left a pyramid, but much inferior in size to his father's. It is built, for half of its height, of the stone of Ethiopia,' or, as Professor Smyth (whose extracts from Rawlinson's translation I have here followed) adds 'expensive red granite.' 'After Mycerinus, Asychis ascended the throne. He built the eastern gateway of the Temple of Vulcan (Phtha); and, being desirous of eclipsing all his predecessors on the throne, left as a monument of his reign a pyramid of brick.'

This account is so suggestive, as will presently be shown, that it may be well to inquire whether it can be relied on. Now, although there can be no doubt that Herodotus misunderstood the Egyptians in some matters, and in particular as to the chronological order of the dynasties, placing the pyramid kings far too late, yet in other respects he seems not only to have understood them correctly, but also to have received a correct account from them. The order of the kings above named corresponds with the sequence given by Manetho, and also found in monumental and hieroglyphic records. Manetho gives the names Suphis I., Suphis II., and Mencheres, instead of Cheops, Chephren, and Mycerinus; while, according to the modern Egyptologists, Herodotus's Cheops was Shofo, Shufu, or Koufou; Chephren was Shafre, while he was also called Nou-Shofo or Noum-Shufu as the brother of Shofo; and Mycerinus was Menhere or Menkerre. But the ident.i.ty of these kings is not questioned.

As to the true dates there is much doubt, and it is probable that the question will long continue open; but the determination of the exact epochs when the several pyramids were built is not very important in connection with our present inquiry. We may, on the whole, fairly take the points quoted above from Herodotus, and proceed to consider the significance of the narrative, with sufficient confidence that in all essential respects it is trustworthy.

There are several very strange features in the account.

In the first place, it is manifest that Cheops (to call the first king by the name most familiar to the general reader) attached great importance to the building of his pyramid. It has been said, and perhaps justly, that it would be more interesting to know the plan of the architect who devised the pyramid than the purpose of the king who built it. But the two things are closely connected. The architect must have satisfied the king that some highly important purpose in which the king himself was interested, would be subserved by the structure. Whether the king was persuaded to undertake the work as a matter of duty, or only to advance his own interests, may not be so clear. But that the king was most thoroughly in earnest about the work is certain. A monarch in those times would a.s.suredly not have devoted an enormous amount of labour and material to such a scheme unless he was thoroughly convinced of its great importance. That the welfare of his people was not considered by Cheops in building the Great Pyramid is almost equally certain. He might, indeed, have had a scheme for their good which either he did not care to explain to them or which they could not understand. But the most natural inference from the narrative is that his purpose had no reference whatever to their welfare. For though one could understand his own subjects hating him while he was all the time working for their good, it is obvious that his memory would not have been hated if some important good had eventually been gained from his scheme. Many a far-seeing ruler has been hated while living on account of the very work for which his memory has been revered. But the memory of Cheops and his successors was held in detestation.

May we, however, suppose that, though Cheops had not the welfare of his own people in his thoughts, his purpose was nevertheless not selfish, but intended in some way to promote the welfare of the human race? I say his purpose, because, whoever originated the scheme, Cheops carried it out; it was by means of his wealth and through his power that the pyramid was built. This is the view adopted by Professor Piazzi Smyth and others, in our own time, and first suggested by John Taylor.

'Whereas other writers,' says Smyth, 'have generally esteemed that the mysterious persons who directed the building of the Great Pyramid (and to whom the Egyptians, in their traditions, and for ages afterwards, gave an immoral and even abominable character) must therefore have been very bad indeed, so that the world at large has always been fond of standing on, kicking, and insulting that dead lion, whom they really knew not; he, Mr. John Taylor, seeing how religiously bad the Egyptians themselves were, was led to conclude, on the contrary, that those _they_ hated (and could never sufficiently abuse) might, perhaps, have been pre-eminently good; or were, at all events, of _different religious faith_ from themselves.' 'Combining this with certain unmistakable historical facts,' Mr. Taylor deduced reasons for believing that the directors of the building designed to record in its proportions, and in its interior features, certain important religious and scientific truths, not for the people then living, but for men who were to come 4000 years or so after.

I have already considered at length (see the preceding Essay) the evidence on which this strange theory rests. But there are certain matters connecting it with the above narrative which must here be noticed. The mention of the shepherd Philition, who fed his flocks about the place where the Great Pyramid was built, is a singular feature of Herodotus's narrative. It reads like some strange misinterpretation of the story related to him by the Egyptian priests. It is obvious that if the word Philition did not represent a people, but a person, this person must have been very eminent and distinguished--a shepherd-king, not a mere shepherd. Rawlinson, in a note on this portion of the narrative of Herodotus, suggests that Philitis was probably a shepherd-prince from Palestine, perhaps of Philistine descent, 'but so powerful and domineering, that it may be traditions of his oppressions in that earlier age which, mixed up afterwards in the minds of later Egyptians with the evils inflicted on their country by the subsequent shepherds of better known dynasties, lent so much fear to their religious hate of Shepherd times and that name.' Smyth, somewhat modifying this view, and considering certain remarks of Manetho respecting an alleged invasion of Egypt by shepherd-kings, 'men of an ign.o.ble race (from the Egyptian point of view) who had the confidence to invade our country, and easily subdued it to their power without a battle,' comes to the conclusion that some Shemite prince, 'a contemporary of, but rather older than, the Patriarch Abraham,' visited Egypt at this time, and obtained such influence over the mind of Cheops as to persuade him to erect the pyramid. According to Smyth, the prince was no other than Melchizedek, king of Salem, and the influence he exerted was supernatural. With such developments of the theory we need not trouble ourselves. It seems tolerably clear that certain shepherd-chiefs who came to Egypt during Cheops' reign were connected in some way with the designing of the Great Pyramid. It is clear also that they were men of a different religion from the Egyptians, and persuaded Cheops to abandon the religion of his people. Taylor, Smyth, and the Pyramidalists generally, consider this sufficient to prove that the pyramid was erected for some purpose connected with religion. 'The pyramid,' in fine, says Smyth, 'was charged by G.o.d's inspired shepherd-prince, in the beginning of human time, to keep a certain message secret and inviolable for 4000 years, and it has done so; and in the next thousand years it was to enunciate that message to all men, with more than traditional force, more than all the authenticity of copied ma.n.u.scripts or reputed history; and that part of the pyramid's usefulness is now beginning.'

There are many very obvious difficulties surrounding this theory; as, for example (i.) the absurd waste of power in setting supernatural machinery at work 4000 years ago with c.u.mbrous devices to record its object, when the same machinery, much more simply employed now, would effect the alleged purpose far more thoroughly; (ii.) the enormous amount of human misery and its attendant hatreds brought about by this alleged divine scheme; and (iii.) the futility of an arrangement by which the pyramid was only to subserve its purpose when it had lost that perfection of shape on which its entire significance depended, according to the theory itself. But, apart from these, there is a difficulty, nowhere noticed by Smyth or his followers, which is fatal, I conceive, to this theory of the pyramid's purpose. The second pyramid, though slightly inferior to the first in size, and probably far inferior in quality of masonry, is still a structure of enormous dimensions, which must have required many years of labour from tens of thousands of workmen. Now, it seems impossible to explain why Chephren built this second pyramid, if we adopt Smyth's theory respecting the first pyramid.

For either Chephren knew the purpose for which the Great Pyramid was built, or he did not know it. If he knew that purpose, and it was that indicated by Smyth, then he also knew that no second pyramid was wanted.

On that hypothesis, all the labour bestowed on the second pyramid was wittingly and wilfully wasted. This, of course is incredible. But, on the other hand, if Chephren did not know what was the purpose for which the Great Pyramid was built, what reason could Chephren have had for building a pyramid at all? The only answer to this question seems to be that Chephren built the second pyramid in hopes of finding out why his brother had built the first, and this answer is simply absurd. It is clear enough that whatever purpose Cheops had in building the first pyramid, Chephren must have had a similar purpose in building the second; and we require a theory which shall at least explain why the first pyramid did not subserve for Chephren the purpose which it subserved or was meant to subserve for Cheops. The same reasoning may be extended to the third pyramid, to the fourth, and in fine to all the pyramids, forty or so in number, included under the general designation of the Pyramids of Ghizeh or Jeezeh. The extension of the principle to pyramids later than the second is especially important as showing that the difference of religion insisted on by Smyth has no direct bearing on the question of the purpose for which the Great Pyramid itself was constructed. For Mycerinus either never left or else returned to the religion of the Egyptians. Yet he also built a pyramid, which, though far inferior in size to the pyramids built by his father and uncle, was still a ma.s.sive structure, and relatively more costly even than theirs, because built of expensive granite. The pyramid built by Asychis, though smaller still, was remarkable as built of brick; in fact, we are expressly told that Asychis desired to eclipse all his predecessors in such labours, and accordingly left this brick pyramid as a monument of his reign.