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coincidence that the centre of the Nile this principle would have presented delta lies at the centre of the land-surface many difficulties to the architects of the of the earth ; in other words, the shore- pyramid. The sun not being a point of line along which lie the mouths of the light, but a globe, the shadow of a pointed Nile has been designedly curved so as to rod does not end in a well-defined point. have its centre so placed. And so of The moment of true noon, which is not the other relations. The very fact that the same as ordinary or civil noon, never the four conditions can be fulfilled simul- does agree exactly with the time of the taneously is evidence that a coincidence vernal or autumnal equinox, and may of the sort may result from mere acci- be removed from it by any interval of dent.* Indeed the peculiarity of geo- time between zero and twelve hours. graphical position which really seems to And there are many other circumstances have been in the thoughts of the pyra- which would lead astronomers, like those mid architects, introduces yet a fifth con- who doubtless presided over the sciendition which by accident could be ful- tific preparations for building the great filled along with the four others. pyramid, to prefer a means of determin

It would seem that the builders of the ing the latitude depending on another pyramid were anxious to place it in lati- principle. The stellar heavens would tude 30°, as closely as their means of afford practically unchanging indications observation permitted. Let us consider for their purpose. The stars being all carwhat result they achieved, and the evi- ried round the pole of the heavens, as if dence thus aftorded respecting their skill they were fixed points in the interior of and scientific attainments. In our own a hollow revolving sphere, it becomes time, of course, the astronomer has no possible to determine the position of the difficulty in determining with great exact- pole of the star-sphere, even though no ness the position of any given latitude- bright conspicuous star actually occupies parallel. But at the time when the great that point. Any bright star close by the pyramid was built it must have been a mat- pole is seen to revolve in a very small ter of very serious difficulty to determine circle whose centre is the pole itself. the position of any required latitude-par- Such a star is our present so-called poleallel with a great degree of exactitude. star; and, though in the days when the The most obvious way of dealing with great pyramid was built, that star was the difficulty would have been by obsery- not near the pole, another, and probably ing the length of shadows thrown by a brighter, star lay near enough to the upright posts at noon in spring and pole * to serve as a pole-star, and to indiautumn. In latitude 30° north, the sun at noon in spring (or, to speak precisely, on the day of the vernal equinox) is just

* This star, called Thuban from the Arabian twice as far from the horizon as he is al. Thúban, the Dragon, is now not very bright, from the point vertically overhead; and being rated at barely above the fourth magif a pointed post were set exactly up- nitude, but it was formerly the brightest star right at true noon (supposed to occur at Bayer also assigned to it the first letter of the

of the constellation, as its name indicates. the moment of the vernal or autumnal Greek alphabet ; though this is not absolutely equinox), the shadow of the post wouid decisive evidence that so late as his day it rebe exactly half as long as a line drawn tained its superiority over the second magni. from the top of the pole to the end of tude stars to which Bayer assigned the seccate by its circling motion the position celestial bodies, they only made instruof the actual pole of the heavens. This mental observations upon them when was at that time, and for many subse- these bodies were high in the heavens, quent centuries, the leading star of the and so remained ignorant of the reíracgreat constellation called the Dragon. tive powers of the air.* Now, if they

ond and third Greek letters. In the year 2790 the shadow. But observations based on

B.C., or thereabouts, the star was at its near.

est to the true north pole of the heavens, the * Of course it may be argued that nothing diameter of the little circle in which it then in the world is the result of mere accident, moved being considerably less than oneand some may assert that even matters which fourth the apparent diameter of the moon. are commonly regarded as entirely casual At that time the star must have seemed to all have been specially designed. It would not ordinary observation an absolutely fixed be easy to draw the precise line dividing centre, 'round which all the other stars reevents which all men would regard as to all volved. At the time when the pyramid was intents and purposes accidental from those built this star was about sixty times farther which some men would regard as results of removed from the true pole, revolving in a special providence, But

circle whose apparent diameter was about draws a sufficient distinction, at least for our seven times as great as the moon's. Yet it present purpose.

would still be regarded as a very useful pole



The pole of the heavens, we know, had determined the position of the thirvaries in position according to the lati- tieth parallel of latitude by observations tude of the observer. At the north pole of the noonday sun (in spring or autumn), it is exactly overhead; at the equator then since, owing to refraction, they the poles of the heavens are both on the would have judged the sun to be higher horizon; and, as the observer travels than he really was, it follows that they from the equator towards the north or would have supposed the latitude of any south pole of the earth, the correspond- station from which they observed to be ing pole of the heavens rises higher and lower than it really was. For the lower higher above the horizon. In latitude the latitude the higher is the noonday 30° north, or one-third of the way from sun at any given season. Thus, when the equator to the pole, the pole of the really in latitude 30° they would have heavens is raised one-third of the way supposed themselves in a latitude lower from the horizon to the point vertically than 30°, and would have travelled a overhead; and when this is the case, the little farther north to find the proper observer knows that he is in latitude 30°. place, as they would have supposed, for The builders of the great pyramid, with erecting the great pyramid. On the the almost constantly clear skies of other hand, if they determined the place Egypt, may reasonably be supposed to from observations of the movements of have adopted this means of determining stars near the pole of the heavens, they the true position of that thirtieth parallel would make an error of a precisely oppoon which they appear to have designed site nature. For the higher the latitude to place the great building they were the higher is the pole of the heavens ; about to erect.

and refraction, therefore, which appaIt so happens that we have the means rently raises the pole of the heavens, gives of forming an opinion on the question to a station the appearance of being in a whether they used one method or the higher latitude than it really is, so that other; whether they employed the sun the observer would consider he was in or the stars to guide them to the geo- latitude 30° north when in reality somegraphical position they required. In what south of that latitude. We have fact, were it not for this circumstance, I only then to enquire whether the great should have thought it worth while to pyramid was set north or south of latitude discuss the qualities of either method. 30°, to ascertain whether the pyramid It will presently be seen that the discus- architects observed the noonday sun or sion bears importantly on the opinion we circumpolar stars to determine their latiare to form of the skill and attainments tude; always assuming (as we reasonably of the pyramid architects. Every celes- may), that those architects did propose tial object is apparently raised somewhat to set the pyramid in that particular latabove its true position by the refractive itude, and that they were able to make powers of our atmosphere, being most very accurate observations of the apparaised when nearest the horizon, and least rent positions of the celestial bodies, but when nearest the point vertically over that they were not acquainted with the head. This effect is, indeed, so marked refractive effects of the atmosphere. The on bodies close to the horizon that if the answer comes in no doubtful terms. astronomers of the pyramid times had The centre of the great pyramid's base observed the sun, moon,

and stars atten- lies about one mile and a third south of tively when so placed, they could not the thirtieth parallel of latitude; and have failed to discover the peculiarity. Probably, however, though they noted the time of rising and setting of the

* Even that skilful astronomer Hipparchus, who may be justly called the father of obser

vational astronomy, overlooked this peculiarstar, especially as there are very few conspic- ity, which Ptolemy would seem to have been uous stars in the neighborhood.

the first to recognise.

from this position the pole of the heavens, problem was not so simple as might be as raised by refraction, would appea, supposed by those who are not acto be very near indeed to the required quainted with the way in which the carposition. In fact, if the pyramid had dinal points are correctly determined. been set about half a mile still farther By solar observations, or rather by south the pole would have seemed just the observations of shadows cast by right.

vertical shafts before and after noon, Of course, such an explanation as I the direction of the meridian, or north have here suggested appears altogether and south line, can theoretically be heretical to the pyramidalists. Accord- ascertained. But probably in this case, ing to them the pyramid architects knew as in determining the latitude, the perfectly well where the true thirtieth builders took the stars for their guide. parallel lay, and knew also all that modern The pole of the heavens would mark the science has discovered about refraction; true north ; and equally the pole-star, but set the pyramid south of the true when below or above the pole, would give parallel and north of the position where the true north, but, of course, most conrefraction would just have made the ap- veniently when below the pole. Nor is parent elevation of the pole correct, sim- it difficult to see how the builders would ply in order that the pyramid might cor- make use of the pole-star for this purrespond as nearly as possible to each of pose. From the middle of the northern two conditions, whereof both could not side of the intended base they would bore be fulfilled at once. The pyramid would a slant passage tending always from the indeed, they say, have been set even position of the pole-star at its lower more closely midway between the true and meridional passage, that star at each sucthe apparent parallels of 30° north, but cessive return to that position serving to that the Jeezeh hill on which it is set direct their progress; while its small does not afford a rock foundation any range, east and west of the pole, would farther north. 'So very close,' says Pro- enable them most accurately to determine fessor Smyth, 'was the great pyramid the star's true mid-point below the pole; placed to the northern brink of its hill, that is, the true north. When they had that the edges of the cliff might have thus obtained a slant tunnel pointing broken off under the terrible pressure truly to the meridian, and had carried it had not the builders banked up there down to a point nearly below the middle most firmly the immense mounds of rub- of the proposed square base, they could, bish which came from their work, and from the middle of the base, bore vertiwhich Strabo looked so particularly for cally downwards, until by rough calcula1,800 years ago, but could not find. tion they were near the lower end of the Here they were, however, and still are, slant tunnel; or buth tunnels could be utilised in enabling the great pyramid to made at the same time. Then a subterstand on the very utmost verge of its ranean chamber would be opened out commanding hill, within the limits of the from the slant tunnel. The vertical bortwo required latitudes, as well as over the ing, which need not be wider than necescentre of the land's physical and radial sary to allow a plumb-line to be suspended formation, and at the same time on the down it, would enable the architects to sure and proverbially wise foundation of determine the point vertically below the rock.'

point of suspension. The slant tunnel The next circumstance to be noted would give the direction of the true north, in the position of the great pyramid (as either from that point or from a point at of all the pyramids) is that the sides are some known small distance east or west carefully oriented. This, like the ap- of that point.* Thus, a line from some proximation to a particular latitude, must be regarded as an astronomical

* It would only be by a lucky accident, of

course, that the direction of the slant tunnel's rather than a geographical relation. The axis and that of the vertical from the selected accuracy with which the orientation has central point would lie in the same vertical been effected will serve to show how far plane. The object of the tunnelling would, the builders had mastered the methods vertical planes through these points

lay, and

in fact, be to determine how far apart the of astronomical observation by which

the odds would be great against the result orientation was to be secured. The proving to be zero.

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ascertained point near the mouth of the corresponded with one of the epochs vertical boring to the mouth of the slant wher the star Alpha Draconis was distunnel would lie due north and south, tant 3° 42' from the pole of the heavens. and serve as the required guide for the In other words, there is a slant tunnel orientation of the pyramid's base. If directed northwards and upwards from this base extended beyond the opening of a point deep down below the middle of the slant tunnel, then, by continuing this the pyramid's base, and inclined 26° 17' tunnelling through the base tiers of the to the horizon, the elevation of Alpha pyramid, the means would be obtained Draconis at its lower culmination when of correcting the orientation.

3° 42' from the pole. The last epoch This, I say, would be the course natu- when the star was thus placed was rally suggested to astronomical architects circiter 2160 B.C.; the epoch next before who had determined the latitude in the that was 3440 B.C.; and between these two manner described above. It may even we should have to choose on the hypothbe described as the only very accurate esis that the slant tunnel was really dimethod available before the telescope had rected to that star when the foundations been invented. So that if the accuracy of the pyramid were laid. For the next of the orientation appears to be greater epoch before the earlier of the two named than could be obtained by the shadow was about 28000 B.C., and the pyramid's method, the natural inference, even in date cannot have been more remote than the absence of corroborative evidence, 4000 B.C. would be that the stellar method, and The slant tunnel, while admirably no other, had been employed. Now, in fulfilling the requirements suggested, 1779, Nouet, by refined observations, seems altogether unsuited for any other. found the error of orientation measured Its transverse height (that is, its width in by less than 20 minutes of arc, corre a direction perpendicular to its upper sponding roughly to a displacement of and lower faces) did not amount to quite the corners by about 371 inches from four feet; its breadth was not quite three their true position, as supposed to be de- feet and a half. It was, therefore, not termined from the centre; or to a dis- well fitted for an entrance passage to the placement of a southern corner by 53 subterranean chamber immediately uninches on an east and west line from a der the apex of the pyramid (with which point due south of the corresponding chamber it communicates in the manner northern corner. This error, for a base suggested by the above theory). It length of 9,140 inches, would not be could not have been intended to be used serious, being only one inch in about for observing meridian transits of the five yards (when estimated in the sec- stars in order to determine sidereal time; ond way). Yet the result is not quite for close circumpolar stars, by reason of worthy of the praise given to it by Pro- their slow motion, are the least suited of fessor Smyth. He himself, however, by all for such a purpose. As Professor much more exact observations, with an Smyth says, in arguing against this sugexcellent altazimuth, reduced the alleged gested use of the star, no observer in error from 20 minutes to only 41, or to his senses, in any existing observatory, 9-40ths of its formerly supposed value. when seeking to obtain the time, would This made the total displacement of a observe the transit of a circumpolar star southern corner from the true meridian for anything else than to get the direction through the corresponding northern cor- of the meridian to adjust his instrument by.' ner, almost exactly one foot, or one inch (The italics are his.) It is precisely such in about twenty-one yards-a degree of a purpose (the adjustment, however, not accuracy rendering it practically certain of an instrument, but of the entire structhat some stellar method was used in ture of the pyramid itself), that I have orienting the base.

suggested for this remarkable passageNow there is a slanting tunnel occu- this cream-white, stone-lined, long tube,' pying precisely the position of the tun- where it traverses the masonry of the nel which should, according to this view, pyramid, and below that dug through have been formed in order accurately to the solid rock to a distance of more than orient the pyramid's base, assuming that 350 feet. the time of the building of 'the pyramid Let us next consider the dimensions


of the square base thus carefully placed ously estimated, the largest measure in latitude 30° north, to the best of the being 9,168 inches, and the lowest 9,110 builders' power, with sides carefully inches. The fundamental theory of the oriented.

pyramidalists, that the sacred cubit was It seems highly probable that whatever exactly one 20,000,00oth part of the special purpose the pyramid was intended earth's polar diameter, and that the side to fulfil, a subordinate idea of the build- of the base contained as many cubits and ers would have been to represent sym- parts of a cubit as there are days and bolically in the proportions of the build- parts of a day in the tropical year (or ing such mathematical and astronomical year of seasons), requires that the length relations as they were acquainted with. of the side should be 9,140 inches, lying From what we know by tradition of the between the limits indicated, but still so men of the remote time when the pyramid widely removed from either that it would was built, and what we can infer from appear very unsafe to base a theory on the ideas of those who inherited, how- the supposition that the exact length is ever remotely, the modes of thought of or was 9,140 inches. If the measures the earliest astronomers and mathemati- 9,168 inches and 9,110 inches were incians, we can well believe that they would ferior, and several excellent measures look with superstitious reverence on made by practised observers ranged special figures, proportions, numbers, around the length 9,140 inches, the case and so forth. Apart from this, they may would be different. But the best recent have had a quasi-scientific desire to make measures gave respectively 9,110 and a lasting record of their discoveries, and 9,130 inches; and

and Smyth exclaims of the collected knowledge of their time. against the unfairness of Sir H. James

It seems altogether probable, then, in taking 9,120 as 'therefore the (probthat the smaller unit of measurement used able) true length of the side of the great by the builders of the great pyramid was pyramid when perfect,' calling this a intended, as Professor Smyth thinks, to dishonorable shelving of the honorable be equal to the 500,000,000th part of the older observers with their larger results.' earth's diameter, determined from their The only other measures, besides these geodetical observations. It was perfectly two, are two by Colonel Howard-Vyse, within the power of mechanicians and and by the French savants, giving remathematicians so experienced as they spectively 9,168 and 9,163 44 inches. undoubtedly were the pyramid attests The pyramidalists consider 9,140 inches so much-to measure with considerable a fair mean value from these four. The accuracy the length of a degree of lati- natural inference, however, is, that the tude. They could not possibly (always pyramid base is not now in a condition setting aside the theory of divine inspira- to be satisfactorily measured; and tion) have known anything about the assuredly no such reliance can be placed compression of the earth's globe, and on the mean value 9,140 inches that, on therefore could not have intended, as the strength of it, we should believe what Professor Smyth supposes, to have had otherwise would be utterly incredible, viz. the 500,000,oooth part of the earth's polar that the builders of the great pyramid axis, as distinguished from any other, for knew 'both the size and shape of the their unit of length. But if they made earth exactly.' 'Humanly, or by human observations in or near latitude 30° science, finding it out in that age was, of north, on the supposition that the earth course, utterly impossible,' says Professor is a globe, their probable error would Smyth. But he is so confident of the exceed the difference even between the average value derived from widely conearth's polar and equatorial diameters. ficting base measures as to assume that Both differences are largely exceeded by this value, not being humanly discoverthe range of difference among the esti- able, was of necessity "attributable to mates of the actual length of the sacred God and to his Divine inspiration. We cubit, supposed to have contained may agree, in fine, with Smyth, that the twenty-five of these smaller units. And, builders of the pyramid knew the earth again, the length of the pyramid base- to be a globe; that they took for their side, on which Smyth bases his own esti- measure of length the sacred cubit, which, mate of the sacred cubit, has been vari- by their earth measures, they made very

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