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35. [p. 55] Having, then, fixed the original position of the doorway of the Pyramid, we may state that it was at 668.2 ± .1 above the pavement of the Pyramid; 524.1 ± .3 horizontally inside (or S. of) the N. edge of the Pyramid casing; and its middle 287.0 ± .8 E. of the centre1 of the Pyramid; or 3723.6 from E. side, and 4297.6 from W. side, at its level; the probable error being that of fixing the length of the sides. Thus we have the following positions in the entrance passage, reducing all to the true beginning of the floor:—
The above measures were taken by rods from 124.2 to 285.29 (the rods jointing together with butt ends), by steel tape from 276.63 to 1177.14, and by rods from 1163.6 to the rock; all duly corrected for temperature. On comparing them with Professor Smyth's measures, it will be found that his measures make the passage length about an inch shorter on an average; this is fairly accounted for (1) by his being all piece–meal measures added together, (2) by the rude method of making scratches with a screw-driver to mark the lengths of [p. 57] rod on the stone (L. and W. ii., 46), and (3) by there being "always a certain amount of risk as to the measuring rod slipping on the inclined floor" (L and W. ii., 35). All these errors would make the reading of the length shorter than it should be; and all were avoided by the use of a steel tape lying on the side of the floor. Nevertheless, I tested again, by rod measure, some of the points where the difference of Professor Smyth's measures were greatest from the steel tape, and they come out thus:—
These will practically show what errors may creep in, by not using a continuous measure like a steel tape. The object of measuring the joints, as well as the total length, by steel tape, is sufficiently illustrated by this comparison. One source of error may arise from following the coarsely scratched prolongations of the anciently drawn lines, and of the ascending passage floor and roof. These have been made by modern measurers; and they were always rejected, and a more accurate method employed. The measures from the steel tape onwards, by rods, down to the end of the built passage, where it rests on the rock, are not of the same accuracy as the others; the broken parts of the passage sides, and the awkwardness of measuring over the large block of granite, without any flat surface even to hold the rods against, prevented my taking more care over a point where accuracy is probably not of importance. For the total length of the entrance passage, down to the subterranean rock-cut part, only a rough measurement by the 140-inch poles was made, owing to the encumbered condition of it. The poles were laid on the rubbish over the floor, and where any great difference of position was required, the ends were plumbed one over the other, and the result is probably only true within two or three inches. The points noted down the course of the passage, reckoning from the original entrance (i.e., the beginning of the rock on the E. side of the roof being 1350.7), are the following:—
36. [p. 58] The azimuth and straightness of the passage were carefully measured. The azimuth down the built part was taken by reference to the triangulation, which in its turn was fixed by six observations of Polaris at elongation, from a favourable station (G). The azimuth to the bottom of the rock-cut passage was observed independently, by five observations of Polaris at elongation. The observations of the straightness throughout gives a check by combining these two methods, and they are thus found to agree within 19", or just the sum of their probable errors, equal to only .09 inch lineally on the azimuth of the built part. The results are:—
The observations of the straightness of the walls, floor, and roof of the passage, when all reduced to offsets from its mean axis of the whole length stand thus:—
But the passage in the built part, and indeed for some 40 feet below that, is far straighter in azimuth than the lower part; taking this upper 2/5ths of it alone, it has a mean axis of – 5' 49" ± 7" In azimuth, and varies thus:—
[p. 59] These offsets only being read to 1/20th inch (the 1/100ths merely resulting from computation) it is remarkable that the errors of the mid–line of the passage are so minute; and it shows that in this particular we have not yet gone within the builder's accuracy; readings to 1/100th inch or to 1" on the longer distances, are now required. The absolute position, then, of the middle of the S. end of the entrance passage floor will be, in level, 668.2 – (4140 X sin. 26º 31' 23") – .8 difference of floor offsets = – 1181 ± 1 ?; in distance from N. base of pyramid 524.1 + 3704.3 = 4228 ± 2? or 306 N. from mid-plane; and in distance E. from the mid–plane 287.0 – [ sin. (3' 55" – 3' 44") x 3704 ] – .4 difference of offsets = 286.4 ± 1.0.
37. The Subterranean chambers and passages are all cut roughly in the rock. The entrance passage has a flat end, square with its axis (within at least 1º), and out of this end a smaller horizontal passage proceeds, leaving a margin of the flat end along the top and two sides. This margin is 4.5 wide at E., 3.2 at W., and 5.4 to 6.0 from E. to W. along the top. The dimensions and distances are as follow, from the S. end of the floor of the entrance passage (as deduced from the roof, which is better preserved); and the axial positions and levels are by theodolite observations:—
The large chamber walls are therefore distant from the Pyramid central axis, 302.9 E. at N. wall; 299.6 E. at S. wall; 250.6 W. at N. wall; 254.5 W. at S. wall; 40 S. and 366 S. The central axis thus not passing through the chamber, but 40 inches inside the rock of the N. side. [p. 60] The side chamber is an enlargement of the passage, westward and upward, as are all the chambers of the Pyramid; it is very rough and uneven, and encumbered now with large blocks of stone. The large chamber is most clearly unfinished, both in the dressing of the walls, and more especially in the excavation for the floor. The walls have an average irregularity estimated at ±.7 and projecting lumps of rock are left untouched in some parts. The roof is more irregular, estimated average variation ±3. The floor is most irregular, at the W. end it rises at the highest to only 10 inches from the roof; and over all the western half of the chamber it is irregularly trenched with the cuttings made by workmen to dislodge blocks of the rock. It is, in fact, an interesting specimen of quarrying, but unfortunately now completely choked up, by Perring having stowed away there all the pieces of limestone taken out of his shaft in the floor. After dislodging several blocks, I crawled in over the knobs and ridges of rock, until jammed tight from chest to hack in one place; and thence I pushed about one 140–inch rod, by means of the other, so as to measure the length up to the Western end. To measure along the W. side is impossible, without clearing away a large quantity of stones; and as there is no place to stack them safely without their going down the shaft, I could only measure the width at 100 from the W. end, perhaps somewhat askew. The lower — eastern — part of the floor, 140 below the roof, which is comparatively flat, is, nevertheless, very irregular and roughly trenched, quite unfinished. The best worked floor surface is just around the square shaft, 198 below the roof, and about 40 below the main part of the floor, which is 155 below roof on a knob of rock beside the shaft. The square shaft is not parallel to the chamber, but is placed nearly diagonally.5 Its distances to the walls are, N.W. corner 135 to N. wall; N.E. corner 60 to E. wall; S.E. corner 90 to S. wall. Its sides are, N.E. 68 to 75? S.E. 82½ ; S.W. 80; N.W. 70 above, 79 below (the N. corner being rounded above); N. to S. diagonal 100. The S.E. and S.W. sides stop at 67 deep, or 265 below roof, or 1,321 under pavement; leaving a ledge about 20 inches wide, a second or deeper part of the shaft goes downwards, the N.E. and N.W. sides being continuous with those of the upper part; it is, in fact, a smaller shaft descending out of the N. corner of the larger. The sides of the smaller shaft are, N.E. 57? S.E. 53? S.W. 60, N.W. 56. The original depth of the smaller shaft I could not see, it was apparently about 40 inches according to Vyse, when Perring sunk his round shaft down in the bottom of the ancient square shaft. This hole in the dimly–lighted chamber, about 30 feet deep (with water in it after heavy rains have rushed down the entrance passage), and with a very irregular and wide opening, makes measurement about here somewhat unpleasant. I avoided filling the shaft with the earth removed from the passage, or with the stones which Perring excavated from it, in case anyone should afterwards wish [p. 61] to excavate farther at the bottom. The southern passage is very rough, apparently merely a first drift–way, only just large enough to work in, intended to be afterwards enlarged, and smoothed; its sides wind 6 or 8 inches in and out.
38. The Ascending passage from the entrance passage is somewhat troublesome to measure, owing to the large plugs of granite that fill some 15 feet of its lower part; and also to the irregular way in which much of its floor is broken up. For connecting it with the entrance passage, we must first settle the most probable value of its angle, in order to carry on the projection of its floor; and to complete it over the plugging and breakage, which prevent direct measurement. The angle of the whole passage will be discussed further on; it will suffice to say here that the mean angle is 26º 2' 30"; and there is therefore a presumption that the plugged part is about the same angle, and not the 26½ º of the entrance passage. This is confirmed by direct plumb-line measure of the angle of the plug-blocks at their lower end, giving 26º 7' (± 2'?); and noting that the end is square with the portion of passage beyond it to within 5'. Also the actual angle of the plug-blocks may be computed from Prof. Smyth's sloping measures, combined with my levelling between the floors of the passages, and plumbing up to the lower end of the plugs.6 This gives 26º 12½' for the angle of the lower 300 inches of the passage; and 5' of variation would require a difference of .4 inch vertical on .9 sloping. Hence the other data confirm this so far, that it had better be adopted as the angle through the plugged part; until some one shall improve on Prof. Smyth's sloping measure, or on my levelling. The junction of the passages was not projected over the broken part uncertainly, as had been done before; but a plumb-line was hung from the W. side of the Ascending passage roof, in front of the plug-blocks; and measures vertical, perpendicular, and sloping, were taken to the plugs, the fragments of the ascending, and the top and bottom of the entrance passage. Thus the whole was knit together to a true vertical line, the place of which was fixed on the entrance floor. From the mean of these measures, and 26º 12½ ' as the ascending angle, with 26º 21' as the descending angle at that spot (by Prof Smyth), the Ascending passage roof starts vertically over 1110.90 on the sloping floor of the [p. 62] entrance, reckoning from the casing face; and the floor cuts the entrance floor at 1110.64 from the same, both probably ± .1. Further, the lower end of the plug-block is 74.19 from the intersection of the floors; and the upper end 50.76 from the intersection of the roofs. Having thus fixed the beginning of the Ascending passage, by the point where its floor produced onwards intersects the floor of the entrance passage, we can proceed up the Ascending passage from this as a starting point. The distance past the plug-blocks being determined as above described, and that from the plug-blocks to the S. end of the passage, by steel tape measure on the E. side of the floor; then, the tape being corrected for temperature and tension, the results are thus, on the sloping floor:—
On comparing these measures with Prof. Smyth's, it will be seen that he makes the passage about 3 inches shorter; and that this difference mainly occurs in the lower part, where the floor is much broken. Several lengths were therefore measured as tests, just as in the entrance passage, and the results are:—
The close agreement of these two series of measures, particularly in those parts twice measured by tape, will show (as in the entrance passage) that the error is certainly in the rod measures, and due to the same causes as the error in the entrance passage, i.e., slipping, irregular placing on broken floor, and the marking off of each length. The result therefore is that from the intersections of entrance and ascending passage floors, to the floor joint at the E. side of the grand gallery doorway, is 1546.8 on the slope.7 The granite plugs are kept back from slipping down by the narrowing of the lower end of the passage, to which contraction they fit. Thus at the lower, or N. end, the plug is but 38.2 wide in place of 41.6 at the upper end: the height, however, is unaltered, being at lower end 47.30 E., 47.15 mid, 47.26 W.; and at upper, or S. end 47.3. In the trial passages the breadth is contracted [p. 64] from 41.6 to 38.0 and 37.5 like this, but the height is also contracted there from 47.3 to 42.3. These plug-blocks are cut out of boulder stones of red granite, and have not the faces cut sufficiently to remove the rounded outer surfaces at the corners: also the faces next each other are never very flat, being wavy about ± .3. These particulars I was able to see, by putting my head in between the rounded edges of the 2nd and 3rd blocks from the top, which are not in contact; the 2nd having jammed tight 4 inches above the 3rd. The present top one is not the original end; it is roughly broken, and there is a bit of granite still cemented to the floor some way farther South of it. From appearances there I estimated that originally the plug was 24 inches beyond its present end. It has been a favourite idea with some, that two horizontal joints in the passage roof just south of the plugs, were the beginning of a concealed passage: I therefore carefully examined them. They are 60.5 (or 60.1 second measure) apart vertically, and therefore quite different to the passages of the Pyramid, which are 47 perpendicularly or 52 vertically. Further, there is no possibility of the blocking up of a passage existing there; as the stone of the roof is continuous, all in one with the sides; the three roof-blocks between the two horizontal joints are all girdle-blocks, either wholly round the passage, or partially so; and the block N. of these is a long one, over 125 inches from E. to W., and continuous into both walls. These vertical girdle-blocks are a most curious feature of this passage (first observed and measured by Mr. Waynman Dixon, C.E.), and occur at intervals of 10 cubits (206.3 to 208.9 inches) in the passage measuring along the slope. All the stones that can be examined round the plugs are partial girdle-blocks, evidently to prevent the plugs forcing the masonry apart, by being wedged into the contracted passage. Many of the stones about the blocks in Mamun's Hole are over 10 or 11 feet long; the ends are invisible, but probably they are about 15 feet over all.
39. For the angle of the passage, and its straightness, it will be well to consider it all in one with the gallery floor, as they were gauged together all in one length. The angle of slope I did not observe, as I considered that that had been settled by Prof Smyth; but the azimuth was observed, by a chain of three theodolites, round from the entrance passage. The straightness was observed by offsets to floor and side all along it, read from a telescope at the upper end of the plug-blocks. When I came to plot the results, I found that there were no measures taken at the point where Prof. Smyth's theodolite was set up. The sloping floor is nowhere, having been entirely cut away at the beginning of the gallery; and the top of the ramp (to which the theodolite had been referred) was not offsetted by me, nor was its slope measured by Prof Smyth's clinometer for 300 inches from the place. Hence we cannot say exactly what direct relation the theodolite bore to the passage; but we can obtain the angle of slope very satisfactorily, by taking the angles observed to signal at bottom of ascending [p. 65] passage, and to signal at top of gallery, and then (knowing the distances of these signals) calculate the angle of slope from signal to signal. This, when corrected for lower signal being 3 too high, gives 26º 12' 50" for mean angle of both passage and gallery together. Hence, from my offsets to the places of these signals, the absolute angle, and the variations from it, can be obtained for either part independently. Thus we have the form and direction of the ascending passage, reckoning from the beginning of its floor on the entrance passage floor, with its variations, as follows:—
The surfaces are so much decayed and exfoliated, that it is only just at the ends that two original faces can be found opposite to one another; hence the width and height cannot be measured, and the offsets can only be stated to one surface. From this altitude, the sloping length of the passage being 1546.8, the horizontal length will be 1389.5, and the vertical height 679.7, both being corrected for difference in the offsets of the ends. The determination of the azimuth has, unhappily, a large probable error, ± 3' (owing to bad foundation for the theodolite in Mamun's Hole); and its direction, – 4', is so close to that of the Pyramid side, that it may be assumed parallel to that ± 3'. This, on the passage length, = 1.2 inches for the probable error of the place of the upper end of the passage, in E. to W. direction in the Pyramid. These, added to previous amounts, give for the absolute place of the floor end at the latitude of the E. wall of the gallery (172.9 + 679.7) = 852.6 ± 3 level above pavement; (1517.8 + 1389.5) = 2907.3 ± .6 horizontally from N. edge of Pyramid, or 1626.8 ± .8 northwards from centre; and 287 ± 1.5 for middle of passage eastward from centre of Pyramid.
40. The horizontal passage leading to the Queen's Chamber is the next part to be considered. This was measured with steel tape all along, and the levels of it taken with theodolite. The results for its length and levels are thus, reckoning from the mean door of the gallery at 1546.8 from beginning of ascending passage:— [p. 66]
The azimuth of this passage was not measured, but the beginning of it is 287 ± 1.5 E. of the middle of the Pyramid; then for the axis of it at the end we may say the same, or 287 ± 3, since the gallery above it only differs about two inches from that quantity. In the above measures of length there is a steadily accumulating difference of about 1 in 300 between Prof. Smyth's measures and these, for which it seems difficult to account; but as in the other passages, I have always found on retesting the measures, that such differences are due to errors in the cumulative single rod measures, and not in my steel tape (which was always verified at the starting point after measuring), it seems unlikely that the steel tape should be in error here. Hence I should adopt these measures without alteration.
41. In the Queen's Chamber it seems, from the foregoing statement, that the ridge of the roof is exactly in the mid-place of the Pyramid, equidistant from N. and S. sides; it only varies from this plane by a less amount than the probable error of the determination. The size of the chamber (after allowing suitably in each part for the incrustation of salt) is on an average 205.85 wide, and 226.47 long, 184.47 high on N. and S. walls, and 245.1 high to the top of the roof ridge on E. and W. walls. The variations of the horizontal quantities in detail are as follows, from the mean dimensions. [p. 67]
For example, to take the first entries, at 180 inches over the floor, on the E. wall, the N. wall is (102.92 + .16) = 103.08 from a vertical line below the apex of the roof; and the S. wall is (102.76 – .17) = 102.59 from the same apex line : the sum of these quantities, or the total width, being 205.67. Thus the mean distances of the N. and S. walls from the apex on the E. and W. walls is given at the top of each column; and beneath that the small variations from those mean vertical wall faces. In the last division are given the distances of the E. and W. walls apart, below their apices; both the mean dimension, the variations from it, and the total at each point. It will be observed that the E. and W. walls have both a uniform tilt inwards; if we allow 14' for this as an average, the mean from a straight line inclined that amount is .057 on E. and .025 on W.; a remarkably small amount of error, comparable to the extremely fine work and close joints of the stones themselves. Also the ridge of the roof is not exactly over the middle of the chamber at either end. Beside the above resulting length of the middle of the chamber on the floor, separate measures were taken on the two walls; these give N. 227.41, middle (from above) 227.47, S. 227.61; mean of all 227.50 for floor length.
42. In the matter of height, the courses vary a good deal; and far more care was spent on the closeness, than on the regularity of the joints. For a starting point in measurement, the general floor is hopelessly irregular, consisting plainly of rough core masonry; and furthermore, it has been built over with similar rough masonry, which was afterwards stripped down to insert the chamber walls. This is proved by there being no fewer than eight edges of sunken spaces upon it, made (according to the universal habit of pyramid builders) to let in the inequalities of the upper course into the surface of the course below it. These sunken edges are well seen in other parts of the core masonry, and their [p. 68] meaning here is unequivocal. But all round the chamber, and the lower part of the passage leading to it, is a footing of fine stone, at the rough floor level; this projects 1 to 4 inches from the base of the walls, apparently as if intended as a support for flooring blocks, which have never been introduced. It is to this footing or ledge that we must refer as the starting point; though what floor was ever intended to have been inserted (like the floor of the King's Chamber, which is inserted between its walls) we cannot now say. Certainly, a floor at the level of the higher part of the passage, would not reconcile everything; as that higher floor is also not a finished surface, but has sundry large round holes in it, like those in the chamber floor and elsewhere; intended, apparently, for use in process of building. Starting, however, from this footing at the base of the walls, the mean elevation of each course above the floor is as follows, with the variation + or – from the mean scale, at eleven points around the chamber:—
[ *** This area labeled encumbered in original] The mean course thicknesses, and their mean differences being — from the base upwards — thus:— 34.13 m.d. .19, 33.31 m.d. .18, 31.69 m.d. .14, 28.00 m.d. .21, 28.94 m.d. .27, 28.40 m.d. .48 to top of N. and S. walls. In the first column above, 245.1 is the apex of the E. and W. walls, where the sloping roof stones end at their junction; and the differences entered here, N. and S., are due to the N. and S. slabs not ending at the same level, one having fallen a little below the other in building; the highest shows, therefore, probably the intended point, and this is 1080.1 above the pavement. 214.35, in the first column, refers to the topmost joint on the E. and W. walls. 184.47 is the top of the N. and S. walls, and a joint on the E. and W. walls. 179.09 is a joint that occurs at each side of the E. and W. walls, but which does not run far, being soon shifted upward to the 184 level. 156.07, 127.13, 99.13, are all joint levels around the chamber. 67.44 is a joint level, signalized by the top of the doorway and of the channel mouths in N. and S. walls. 34.13 is a course around the [p. 69] chamber. And 0 is the fine stone footing of the walls, which is about the level of the variable and rough floor of the chamber. It must be remembered that the above figures only give differences from a mean scale, and do not profess to be levels; the columns, in fact, being only rigidly connected at the two sides of any one corner, which hence have no dividing line between them in the table. Assuming, however, that the above series of heights of E. and W. walls are pretty closely adjusted to the heights in the corners next to each, we have for the sloping roof block, the following figures, calculating from the above quantities:–
These roof blocks are seen — where Howard Vyse excavated beneath one at the N.W. corner — to go back 121.6 on slope, behind the wall face; this, coupled with the thickness of these blocks (which is certain, by similar examples elsewhere, to be considerable) throws the centre of gravity of each of the slabs well behind the wall face,8 so that they could be placed in position without pressing one on another. Hence there is never any arch thrust so long as the blocks are intact; they act solely as cantilevers, with the capability of yielding arched support in case they should be broken. The projection on the western side of the doorway, mentioned by Professor Smyth, is really a surplus left on both sides of the corner; in order to protect the stone in transit and in course of building. This undressed part in the chamber, is cut away down to the true surface at the top and at the middle joint, in order to show the workman exactly to where it needed to be dressed in finishing it off; The excess in the chamber begins 1.3 below joint at top of doorway, and thence projects 1.4, with a width of 5.5; it is dressed away for 1.05 at the middle joint, and then continues sloping away rather thinner down to the floor. The projection into the passage is 1.5 maximum at base, usually .8; and it is 5.5 maximum width, or usually 4.5.
43. The niche in the eastern wall of this chamber, from its supposed connection with a standard of measure, was very closely examined. Its original depth back was certainly only 41 inches at every part from the bottom upwards. The surface that might be supposed to belong to the side of a deeper part, is only that of a joint of masonry, one stone of which has been broken up and removed; this is evident as there is mortar sticking to it, and as it is pick-dressed, quite different to the fine surfaces of the niche sides; beside this, it is not flush with the side, or any of the overlappings of the niche; and moreover, all down the niche sides are the traces of the edge of the back, at 41 from the front, where it has been broken away. [p. 70] The general form of the niche was a recess 41 inches (2 cubits) deep back; 62 inches (3 cubits) wide at base, and diminishing its width by four successive overlappings of the sides (at each wall course), each of ¼ cubit wide, until at 156 high it was only 20 (1cubit) wide, and was finally roofed across at 184 high. Thus, of the 3 cubits width of the base, one cubit was absorbed on each side by the overlappings, leaving one cubit width at the top. This cubit is the regular cubit of 20.6 inches, and there is no evidence of a cubit of 25 inches here. The exact dimensions of every part are as follow, giving the mean dimensions, and the variations of each part, + or –, from the mean. All corrected for the salt exudation on the two lower laps, as estimated at each point; there is no salt on the upper three laps:—
44. The channels leading from this chamber were measured by the goniometer already described (h, section 10); they are exactly like the air channels in the King's Chamber in their appearance, but were covered over the mouth by a plate of stone, left not cut through in the chamber wall; no outer end has yet been found for either of them, though searched for by Mr. Waynman Dixon, C.E., who first discovered them, and also by myself on the N. face of the Pyramid. The N. channel is 8.6 high, and about 8 wide in the chamber wall, running horizontally for 76 inches, and then turning upwards. The S. channel is 8.8 high, and runs 80.0 to its turn upwards. The mean angles, measured between the horizontal part and the ascending slope of the channels, are thus:– [p. 71]
each statement being the mean of two observations, which never differed more than 6'. Hence, if these channels were continued to the outside of the Pyramid, their floors would end on the Pyramid faces at 2641.3 above the base, and 2460.8 from the centre of the Pyramid on the N. face; and at 2679.1 above the base, and 2431.2 from the centre on the S. face. I observed something like the mouth of a hole in the 85th course on the S. face, scanning it with a telescope from below; but I was hindered from examining it closely.
45. Returning now to the gallery from which we diverged to the Queen's Chamber, the length of the gallery was measured like the other passages, with the steel tape, but not many joints were measured, and those were on the E. ramp, on which the tape was laid at 6 inches from the edge. The offsets to the floor and E. ramp were also read, in continuation of the series of the ascending passage, as explained before (section 39). The results are as follow, starting from the N. wall of the gallery, at 1546.8 from beginning of ascending passage.
In the variations in altitude, the height of the axis above the ramp top is stated, as well as its height over the floor. The axis, though different in azimuth and altitude from that of the ascending passage, is reckoned to start from the end of it; hence the offsets are a continuous series, though measured from a line [p. 72] which is bent on passing from the passage to the gallery. The first-stated floor offset here (in brackets) is not what the continuation of the floor of the ascending passage actually is at the point; but it is the virtual floor of the gallery, i.e., where it would come if the trend of the rest of the gallery was continued, and also (judging by the altitude observations of Prof Smyth) where it would come if continued parallel to the ramp top. By successive rod measures, Prof. Smyth made the gallery .8 shorter than it appears by this continuous measure; but the continuous measure is certainly better in principle and also in practice, as we have seen in the other passages. The steel tape of 1200 inches required to be shifted in order to measure from one end to the other of the gallery, and three points were common to both tape lengths; the distances between these points were 305.5 by first, 305.6 by second measure, and 480.2 by both first and second measures, showing the same accuracy in this as in the taping of the other passages. The difference between Prof. Smyth's measures and the taping occurs almost entirely from the N. wall to the cut out in the floor, and is probably due to want of straightness and squareness in one or other of those surfaces. Hence the floor of the gallery intersects the S. wall at 1689.0 ± .5 above the pavement; at 61.7 ± .8 S. of the Pyramid centre; and its middle is 284.4 ± 2.8 E. of the Pyramid centre; reckoning the measures of length and angle continuously through from the plug-blocks upwards, so as to avoid all uncertainties of connection at the beginning of the gallery, and duly correcting for difference in offsets.
46. The holes cut in the ramps or benches, along the sides of the gallery (see section of them in Pl. ix.), the blocks inserted in the wall over each, and the rough chopping out of a groove across each block— all these features are as yet inexplicable. One remarkable point is that the holes are alternately long and short, on both sides of the gallery; the mean of the long holes is 23.32, with an average variation of .73, and the mean of the short holes is 20.51, with average variation .40. Thus the horizontal length of a long hole is equal to the sloping length of a short hole, both being one cubit. This relation is true within less than half their average variations. The roof of the gallery and its walls are not well known, owing to the difficulty of reaching them. By means of ladders, that I made jointing together, I was able to thoroughly examine both ends and parts of the sides of the gallery. The roof stones are set each at a steeper slope than the passage, in order that the lower edge of each stone should hitch like a paul into a ratchet-cut in the top of the walls; hence no stone can press on the one below it, so as to cause a cumulative pressure all down the roof; and each stone is separately upheld by the side walls across which it lies. The depth of two of these ratchet-cuts, at the S. end, I measured as 1.0 and 1.9 to 2.0; and the angles of the two [p. 73] slabs there 28º 0' to 28º 18', and 27º 56' to 28º 30', mean 28º 11'; which on a mean slab 52.2 from N. to S., would differ 1.74 inches from the passage slope. The edge of the southernmost slab is 14.5 from the S. wall; the next slab is 47.4 from N. to S. The verticality of the ends of the gallery was measured from a plumb-line; and bottom of each of the laps of stone and the horizontal distances of the top from the ends of the roof are thus:—
The letters h and s in the column of the N. end show the under edge of the lap of stone to be either horizontal or sloping; on the S. end it is always horizontal. The width of the top of the gallery is 40.9 at N., and 41.3 at S. end. The remarkable groove in the lower part of the third lap, along the whole length of the sides, was measured thus, perpendicularly:—
At the S.W. it is cut to a depth of .8 inch, at the S.E. to .6 (?); the upper edge of it is often ill-defined and sloping. According to Prof. Smyth the mean [p. 74] height of this lap above the gallery floor is 166.2 ± .8 vertically; hence the groove is at 172.1 to 179.0 vertically over the floor, and its lower edge is therefore at half the height of the gallery, that varying from 167 to 172. The pickmarks in the groove on the S. end of the W. side are horizontal, and not along the groove, showing that it was cut out after the walls were built, which agrees with its rough appearance. It belongs to the same curious class of rough alterations as the blocks inserted in the sides of the gallery and the rude grooves cut away across them. At the top of the N. end is a large forced hole, cut by Vyse in 1837, and still quite fresh-looking. The whole of the top lap of stone is so entirely cut away there that I could not decide to where it had come, and only suppose it to project 3 inches, like the others. From this the length of the roof of the gallery is 1688.9 – 40.45 = 1648.4 horizontal, or 1838.6 sloping. By plumb-line measure at the S. end, the roof on the E side is inside the floor edge (or overhangs) 20.50, and on the W. side 20.40. On the S. end (eliminating the lean) the projection is 20.9, and on N. 20.4; mean of all, 20.55, for the sum of the seven projections of the laps, or one cubit, the laps being then one palm each in breadth. Thus the laps overhang the ramps along the gallery sides, and the space between the ramps (2 cubits), is equal to the space between the walls at the top. The remarkable shaft, or "well", that leads away from the lower end of the gallery down to the subterranean passage, was fully measured about its mouth but it appears to be so rough and so evidently utilitarian (for the exit of workmen) that it is not worth while to publish more complete measures than those of Prof. Smyth. As, however, the position of its mouth has been supposed to have a meaning, it should be stated that the opening is from 21.8 to 49.0 horizontally from N. wall of gallery on floor, 21.8 to 48.7 near its top, and 21.9 to 48.9 by the sloping distance reduced. Thus the middle of it is at 35.40, 35.25, or 35.37 by different methods. The part of the shaft that passes through a rock fissure filled with gravel (often called the "grotto") has been steined with 10 courses of small stones, varying from 7¼ to 8 inches in height. At the upper end of the gallery, we have already stated the S. wall to be 61.7 ± .8 of the Pyramid centre; and hence the face of the great step at the head of the gallery (which descends behind both floor and ramps) is (61.7 – 61.3) = .4 ± .8 S. of the Pyramid centre. It may, therefore, be taken as intended that the face of this step, and the transition from sloping to horizontal surfaces, signalizes the transit from the Northern to the Southern half of the Pyramid. This same midplane of the Pyramid being also signalized by the midplane of the Queen's Chamber, which is measured as .3 ± .8 N. of the Pyramid centre. [p. 75] The ramps along the sides, where they join this great step, are very irregular. Their top surfaces slope away downwards toward the side walls; thus the E. ramp top varies from 13.20 to 12.18 below the step from E. to W., and the W. ramp top from 12.82 to 12.2 (?) from W. to E. At present, moreover, the ends of the ramps are parted away from the face of the step by .30 on E. and .44 on W., an amount which has been duly subtracted from my length measures of the gallery. Beside this, the top of the step itself, though, straight, is far from level, the W. side being about 1.0 higher than the E. side. And the sloping floor seems to be also out of level by an equal amount in the opposite direction; since on the half width of the step (i.e., between the ramps) the height of the step face is 34.92 or 35.0 on E., and 35.80 or 35.85 on W. The length of the step from N. to S. is on E. side 61.0, and on W. 61.5. All these measurements are very carefully taken with elimination of wear, fractures, and shifting of the stones at the joints. Hence, at the line along which I measured, 6 inches from the edge of the ramp, the step will be 61.1 long; and this at the angle 26º 12' 50" (by which the end of the gallery was calculated from the plug-blocks) will be 30.08 vertically, for the virtual9 above the actual floor end. Then the top of the step will (by above measures) be here 34.88 above actual floor end, and the step dips about .64 to the S. wall at this part; so the top of the step at the S. wall is 34.88 – .64 – 30.08 = 4.16 (say ± .2) above the virtual floor end at the line of taping. And as the virtual floor end is at 1689.0 ± .5, the step surface at the E. side of the S. doorway is 1693.2 ± .6 over the pavement.
47. The Antechamber and its passages were measured both by steel tape and rods, in one length, from the step to the King's Chamber; and the joints and floor levels are as follow:—
[p. 76]
These measures vary somewhat from those of Professor Smyth in 1865; and, comparing the greatest differences, they stand thus:—
So here, as elsewhere, the measures in 1880 – 2 by steel tape and rods, entirely independent of each other, agree fairly together, and suggest that the 1865 rod measures were somewhat in error. This is due generally to the latter starting from different points on different occasions, and to their different series being insufficiently locked together. Hence I adopt the steel tape measures as the most satisfactory.
48. Taking the Antechamber alone, we may say that its dimensions above the granite wainscot of the sides, are as follow:—
The height was measured as follows:—
[p. 77] The mean length is thus 116.30 (by the two series from top to base), breadth 65.00, and height 149.35; or the ceiling over the virtual end of the gallery floor, 152.85 ± .2, and 1841.8 ± .6 over the pavement.
49. Coming now to details of the walls, the rough and course workmanship is astonishing, in comparison with the exquisite masonry of the casing and entrance of the Pyramid; and the main object in giving the following details is to show how badly pyramid masons could work. The great variation in the foregoing measures illustrates this. The N. wall is all rough picked work, with .2 variation commonly; there is a great irregular flaw, and a piece broken out of the stone about the level of the top of the leaf, as much as 1 inch deep. The E. wall has the granite by the side of the leaf wavy and winding, and bulbous at the base, projecting 1.4. On the wainscot block at the S. end of this wall, which is all in one with the S. end of the chamber, are two conjoined deep scores or scrapes nearly vertical, much like the beginning of a regular groove; their distance from the S. wall is 3.6 to 7.2 at 90, and 2.6 to 6.4 at 52 from floor, where they end; they are .48 deep at maximum. The S. wall has all up the E. side of it, over the wainscot, a projection, just equal in width to the wainscot, and varying in thickness from .31 at top to 1.7 halfway down, and thence fading off down to the top of the wainscot. On the W. side of the S. wall the granite has been daubed over for 2 to 6 inches in breadth, with a thin coat of cement; this, at 1 inch from the side is .35 thick; also at 13 from the W. side is a slight sinking of the granite, from .34 to .60 in depth, all quite ill-defined. The W. wall has the top of the granite wainscot uneven, rising toward the front, and there sinking suddenly .35 at 1.4 from the front edge. The southern of the three semicircular hollows on the top of this wainscot (see Pl. xii.)10 has the granite defective at the back of it, and is backed with rough limestone there. The southernmost stone over the wainscot is dressed very flat and true, but rough, + or – .03. The next block has a raised edge to it on the S. side (figured by Prof. Smyth), and along the base of it, which consists of granite left rough, not dressed away in finishing; about 4 inches wide, and .4 projection along the lower edge of the block; and 2 wide and 1.2 maximum projection at the side. The other edges of this block were marked out by saw-cuts in the granite, about .2 deep, to guide the workmen in dressing the face. The various courses and stones of the chamber were measured, but,the only points of interest are the following. The south wall has four vertical grooves all up it, which have been hitherto supposed to have extended down to the top of the passage to the King's Chamber. This was not the case, however; for, though much broken away, it is still clear that they became shallower as they neared the bottom, and probably [p. 78] ended leaving an unbroken flat surface over the doorway. Their depths (as well as the forms of their sides) show this, as follows:—
50. The granite leaf which stretches across the chamber, resting in grooves cut in the granite wainscots, must be somewhat less in width than the breadth between the grooves, i.e., 48.46 to 48.76. Its other dimensions were carefully ascertained, as much theoretic importance had been attached to them; though to anyone looking at the object itself, the roughness and irregularity of it would put any accuracy of workmanship out of the question. The thickness of the two stones that form it was gauged by means of plumb–lines at 33 points; it varies from 15.16 to 16.20, but the details are scarcely worth printing. This leaf is not simply a flat slab of granite, but on both its upper and lower parts it has a projection on its N. side, about 1 inch thick, where it is included in the side grooves. The edge of this projection down the W. side has been marked out by a saw cut; and the whole of the granite on the inner side of this cut has been dressed away all over the face of the leaf, leaving only one patch or boss of the original surface of the block. This boss, of which so much has been made by theorists, is merely a very rough projection, like innumerable others that may be seen; left originally for the purpose of lifting the blocks. When a building was finished these bosses were knocked away (I picked up a loose one among waste heaps at Gizeh) and the part was dressed down and polished like the rest of the stone. It is only in unimportant parts that they are left entire. This boss on the leaf is very ill–defined, being anything between 4.7 and 5.2 wide, and between 3.3 and 3.5 high on its outer face; at its junction with the block it is still less defined, and might be reckoned anything between 7.2 and 8.2 wide, and 5.6 to 6.6 high. It projects .94 to 1.10 from the block, according to the irregularities of the rough hammer–dressing. Anything more absurdly unsuited for a standard of measure it would be difficult to conceive. I write these remarks with a sharp plaster cast of it before me that I took in 1881. Traces of another boss remain on the W. wall of the Antechamber, above the wainscot; here there has been a boss 12 inches wide and 9 high, which has been knocked away, and the surface rough dressed, though the rest of the face of the stone is ground down elsewhere. The block has been turned in building, so that the flat under–edge of the boss is toward the N. Remains of another boss may be seen on a block in the passage to the King's Chamber; remains of 15 or 16 others in the King's Chamber; 5 others complete in the spaces above that; and many on the casing of the Third Pyramid and elsewhere (see Pl. xii.). The E. to W. breadth of the leaf [p. 79] between its side ledges in the grooves, varies from 40.6 to 41.2 at different heights up the middles of the ledges; but furthermore, the edges are not square, and we may say that 40 to 42 will about represent its irregularity. Yet this was another so–called "standard of measure" of the theorists. The top of the upper block of the leaf is a mere natural surface of the granite boulder out of which it was cut, utterly rough and irregular; and not materially broken away as it dips down deeply into the grooves, and is there plastered over. It varies from 51.24 to 59.0, and perhaps more, below the ceiling. Yet the cubic volume of this block was eagerly worked out by the theorists.
51. The King's Chamber was more completely measured than any other part of the Pyramid; the distances of the walls apart, their verticality in each corner, the course heights, and the levels were completely observed; and the results are given in Plate xiii., in which all variations from the mean amounts are shown on their actual size. The principle of concentrated errors enables the eye to grasp at once the character of the variations in workmanship, in a way that no table of figures could show it. For example, the N. wall is on an average 412.59 inches long (see bottom of Pl. xiii.); but the "face of West end" (see left hand of plate) is at the top .18 outside the mean vertical line, and the "face of East end" is .42 inside the mean vertical; hence at the top the length is actually (.42–.18) shorter than the mean, i.e., it is 412.35. The line of the ceiling on the W. edge of the N. wall will be seen to be .18 over the mean level of the course, marked "5" at each side of the sheet; and the ceiling line at the E. edge is as much as 1.00 over the same mean level; hence the ceiling slopes .82 on its length along the N. side. Referring now to the floor or to the 1st course, where the mean levels are marked by continuous straight lines all across the diagram, it will be seen how far the variable lines of the "Actual First course" or "Actual Floor" fluctuate up and down, in relation to their mean level; the first course, beginning at the N.W., is at .23 over its mean level (marked 1 at the edge), and runs upward until it is 1.03 over its mean level at the N.E., then down to below mean level at the S.E., then still further down along the S. wall, turning a little up to the S.W. corner, and then rapidly rising to above its mean level again at the N.W. corner, whence we started. Only the first course and floor were directly levelled all round; the upper courses were connected by vertical measures in each corner, hence their fluctuations along the sides were not measured, and they are only marked by broken lines. On looking down, say, the "Face of the West–end" from joint 5 to 4, it is seen that the line bends out, showing the stone to be slightly hollowed;11 but on the average it is about square with the course line; and any error seen in squareness of angle in the diagram, represents only 1/50 of [p. 80] the actual angular error, or 5º equals 6'. Then, below that, it is seen that the line from joint 4 to 3 begins very slightly outside the line from joint 5 to 4; showing that the stone of the 4th course is set back by that amount, owing to error in placing it. Similarly the squareness of faces, and truth of setting of the stones, is shown for all the other courses in each corner. In fact, a paper model, showing all the errors on the actual scale, might be made by cutting out four sides, following the outlines of the faces of the walls as here marked, and bending each side to make it fit to the irregular edge of its adjacent side. This diagram will represent with quite sufficient accuracy, without numerical tables, the small errors of this chamber; especially as it must be remembered that this shows its actual state, and not precisely its original form. On every side the joints of the stones have separated, and the whole chamber is shaken larger. By examining the joints all round the 2nd course, the sum of the estimated openings is, 3 joints opened on N. side, total = .19; 1 joint on E. = .14; 5 joints on S=.41; 2 joints on W. = .38. And these quantities must be deducted from the measures, in order to get the true original lengths of the chamber. I also observed, in measuring the top near the W., that the width from N. to S. is lengthened .3 by a crack at the S. side. These openings or cracks are but the milder signs of the great injury that the whole chamber has sustained, probably by an earthquake, when every roof beam was broken across near the South side; and since which the whole of the granite ceiling (weighing some 400 tons), is upheld solely by sticking and thrusting. Not only has this wreck overtaken the chamber itself, but in every one of the spaces above it are the massive roof–beams either cracked across or torn out of the wall, more or less, at the South side; and the great Eastern and Western walls of limestone, between, and independent of which, the whole of these construction chambers are built, have sunk bodily. All these motions are yet but small–only a matter of an inch or two–but enough to wreck the theoretical strength and stability of these chambers, and to make their downfall a mere question of time and earthquakes.
52. Applying, then, these corrections of the opened joints to the lengths of the lower course –and also, as being the most likely correction, to the upper parts as well–we have the following values for the original lengths of the chamber, and for the error of squareness of the present corner angles.
Now it will be observed that though the lengths can be corrected by the sum of the openings, the angles cannot be so corrected, as we do not know [p. 81] which angle the change of length has affected. Hence the present angles are entered above, with the reservation that the sides having altered about 1 in 1,000 of their length, the original angles may have easily been 3' or 4' different; and, therefore, all that we can say about the angles is, that the builders were probably not 5' in error, and very possibly less than that; also that the errors change sign from base to top, so that each course must be a true right angle at some level up it. Probably the base of the chamber was the part most carefully adjusted and set out; and hence the original value of the cubit used can be most accurately recovered from that part. The four sides there yield a mean value of 20.632 ± .004, and this is certainly the best determination of the cubit that we can hope for from the Great Pyramid. The top course of both the E. and W. walls consists of a single stone; on the N. and S. walls the joints of it were measured thus :– N. wall, E. end 0, joints 62.1, 248.8; S. wall, E. end 0, joint 189.2. The average variation of the thickness of the courses from their mean is .051, the mean being 47.045 between similar joints, or including the top course, which was necessarily measured in a different way, 47.040 ± .013.
53. The roof of the chamber is formed of nine granite beams, of the following breadths, the two side beams partly resting on the ends of the chamber:–
[p. 82] The column of "skew" shows the difference in the position of the joints on the opposite sides of the chamber; and the "difference of end widths" the variation between the two ends of the same beam. From this table it seems probable that the roofing in of the chamber was begun at the W end, as the skew of the beams increases up to the E. end; and also as the largest beams, which would be most likely to be first used, are at the W. end. The numbering of the slabs in the top space above the King's Chamber also begins at the W. end. Vyse, however, states that these "chambers of construction" were begun at the E. end. These roofing–beams are not of "polished granite", as they have been described; on the contrary, they have rough–dressed surfaces, very fair and true so far as they go, but without any pretence to polish. Round the S.E. corner, for about five feet on each side, the joint is all daubed up with cement laid on by fingers. The crack across the Eastern roof–beam has been also daubed with cement, looking, therefore, as if it had cracked before the chamber was finished. At the S.W corner, plaster is freely spread over the granite, covering about a square foot altogether.
54. The floor of the chamber, as is well known, is quite disconnected from the walls, and stands somewhat above the base of the lowest course. It is very irregular in its level, not only absolutely, but even in relation to the courses; its depth below the first course joint varying 2.29, from 42.94 to 40.65. This variation has been attributed to the sinking caused by excavation beneath it, but this is not the case; it has been only undermined at the W. end beneath the coffer,12 and yet the floor over this undermined part is 1½ inches higher in relation to the first course, than it is at the SE. corner; and along the S. side where it has not been mined it varies 1½ inches in relation to the first course. In these cases I refer to the first course line, as that was the builder's conception of level in the chamber, to which they would certainly refer; but if we refer instead to absolute level, the anomalies are as great and the argument is unaffected. It appears, then, that the floor never was plane or regular; and that, in this respect, it shared the character of the very variable floor of the passage that led to the chamber, no two stones of which are on the same level. The passage floor, even out to the great step in the gallery, is also inserted between the walls, like the floor of the chamber.
55. Among peculiarities of work still remaining, are the traces of 15 bosses or lugs on the faces of the granite blocks , all on the lower course. Those best seen are two on the fourth block of the N. wall, counting from the door; they have been about 12 inches wide and the same high, 14 inches apart, and their flat bottom edges 3 inches from the base of the block (see Pl. xii.). They may be very plainly seen by holding a candle close to the wall below them; this [p. 83] shows up the grinding around them, and the slight projection and very much less perfect grinding of the sites of the bosses. There is a remarkable diagonal drafted line across the immense block of granite over the doorway; it appears not to run quite to the lower corner on the E. side; but this is doubtless due to the amount by which the block is built into the E. wall, thus cutting off the end of the diagonal line. This sunken band across the stone appears to have been a true drafted straight line cut in process of working, in order to avoid any twist or wind in the dressing of the face; this method being needful as the block was too large to test by the true planes otherwise used (see section 135). The position of the King's Chamber in the Pyramid is defined thus: N. wall at base 330.6 ± .8 S. of centre of Pyramid; S. wall 537.0 ± .8 from centre; E. wall (284.4 ± 20.7) = 305.1 ± 3.0 E. of centre; W. wall 107.7 ± 3.0 W. of centre. Base of walls 1686.3 to 1688.5 ± .6 above pavement; actual floor 1691.4 to 1693.7 ± .6 above pavement; ceiling 1921.6 to 1923.7 ± .6 above pavement.
56. The air channels leading from this chamber have been already mentioned (see section 24) and reference has been made to Pl. xi. for the positions of their outer ends. The angles of them had not yet been accurately measured, and therefore I carefully observed them by a sliding signal and a theodolite. The angles on the floors of them at different distances from the theodolite station at the present outer ends are thus :–
For example, on the floor of the N. channel, the angle on the part from 180 to 300 inches from the mouth averages 31º 37' 15"; this is, of course, quite apart from whatever the dip may be from the passage mouth to those points; and it is reduced from the actually observed quantities. The above list of angles are just equivalent to observations by a clinometer, sliding to different parts of the passage. It is striking that the slope of both passages continuously increases up to the outside (except just at the mouth of the S. channel); hence these quantities, which only extend over a part of either passage, cannot give the true mean slope; probably on the whole length the means would not be greater angles than 31º and 44½º respectively. The N. channel has been forced open as a working passage for some way [p. 84] inwards, only leaving the floor and W. side perfect. The channel is now blocked, just below the end of the enlarged part, and on working a rod 4½ feet into the sand, it ran against limestone. The sand in the hole has blown in during gales, which sweep up sand like mist. The remains of the original channel show it to have varied from 8.9 to 9.2 (mean 9.0) in width, and to have been 8.72 and 8.74 in height. The S. channel is blocked by sand at 76 feet down. It is not straight in the clear length, curving more than its own width to the east; and the sides often shift a few tenths of an inch in passing from one stone to another. These details were seen by examining it with a telescope on Feb. 8, and by photographing it on Nov 2, 1881; these being the days on which the sun shines down it at noon. Its width at the top is 8.35 and 8.65, and its height 8.7 to 8.9.
57. The coffer in the King's Chamber is of the usual form of the earliest Egyptian sarcophagi, an approximately flat–sided box of red granite. It has the usual under–cut groove to hold the edge of a lid along the inside of the N., E., and S. sides; the W. side being cut away as low as the groove for the lid to slide over it; and having three pin–holes cut in it for the pins to fall into out of similar holes in the lid, when the lid was put on. It is not finely wrought, and cannot in this respect rival the coffer in the Second Pyramid. On the outer sides the lines of sawing may be plainly seen: horizontal on the N., a small patch horizontal on the E., vertical on the S., and nearly horizontal on the W.; showing that the masons did not hesitate at cutting a slice of granite 90 inches long, and that the jewelled bronze saw must have been probably about 9 feet long. On the N. end is a place, near the W. side, where the saw was run too deep into the granite, and was backed out again by the masons; but this fresh start they made was still too deep, and two inches lower they backed out a second time, having altogether cut out more than 1/10 inch deeper than they intended. On the E. inside is a portion of a tube drill hole remaining, where they tilted the drill over into the side by not working it vertically. They tried hard to polish away all that part, and took off about 1/10 inch thickness all round it; but still they had to leave the. side of the hole 1/10 deep, 3 long, and 1.3 wide; the bottom of it is 8 or 9 below the original top of the coffer. They made a similar error on the N. inside, but of a much less extent. There are traces of horizontal grinding lines on the W. inside. Reference should be made to section 129 for the subject of stone-working in general.
58. The coffer was very thoroughly measured, offsets being taken to 388 points on the outside, to 281 points inside, or 669 in all; besides taking 281 caliper measures. Before raising it from the floor to measure the bottom, its place as it stood on the chamber floor, tilted up at the S. end by a large pebble under it, was observed thus :– [p. 85]
S.E. to S. wall in brackets, was taken at 10 below top, owing to breakage above that. On raising the coffer no trace of lines was to be found to mark its place on the floor, nor any lines on the floor or bottom of the coffer. The flint pebble that had been put under the coffer is important If any person wished at present to prop the coffer up, there are multitudes of stone chips in the Pyramid ready to hand. Therefore fetching a pebble from the outside seems to show that the coffer was first lifted at a time when no breakages had been made in the Pyramid, and there were no chips lying about. This suggests that there was some means of access to the upper chambers, which was always available by removing loose blocks without any forcing. If the stones at the top of the shaft leading from the subterranean part to the gallery had been cemented in place, they must have been smashed to break through them, or if there were granite portcullises in the Antechamber, they must also have been destroyed; and it is not likely that any person would take the trouble to fetch a large flint pebble into the innermost part of the Pyramid, if there were stone chips lying in his path.
59. The measurements of the coffer surfaces by means of offsets from arbitrary lines, have all been reduced in both tilt and skew, and are stated as offsets or variations + and – (i.e., in excess or deficiency of stone) from a set of mean planes. These mean planes, then, are supposed to lie half in and half out of the stone, being in the mean position and direction of the face. The mean planes adopted for the E. and W. sides, both in and out, are all parallel; hence variations from these planes represent errors of flatness of the surfaces, and also errors of parallelism of the quasi–parallel surfaces. The mean planes adopted for the N. and S. ends, both in and out, are similarly all parallel. The mean planes adopted for the bottom, both in and out, and the top, are also parallel These mean planes of the E. and W. sides, and of the N. and S. ends, are all square with the planes adopted for the bottom and top. There is no exception from parallelism in the system of comparison planes; and but one exception from squareness, in that the N. and S. planes are not adopted square with the E. and W. planes. There was such difference from squareness in the work, that to make the planes square with each other, would have altered the offsets so much as to disguise the small curvatures of the faces; and adopting the planes slightly out of square, makes no difference in taking out quantities of length, surface, or bulk, from the tables of offsets. The mean planes to which the coffer surfaces are referred here, and from [p. 86] which the actual surfaces differ by an equal amount + and – , yield the following dimensions : –
The vertical planes all square with the horizontal; but N. and S. planes cut E. and W. planes at 89º 47' at N.E. and SW. corners, and at 90º 13' at N.W. and S.E. corners. For convenience of reference the whole coffer was divided by imaginary lines or planes, 6 inches apart in each direction, and represented by rows of chalk spots during the actual measurements. Thus at the S. end the first vertical plane across the coffer from E. to W. is A, through the midst of that end; the second plane is B, which passes 3 inches clear of the end; then C; and so on to 0, which is 3 inches clear of the N. end; and P the last line, through the midst of the N. end. Then at the W. side the first plane is α, the second β, an inch clear of the side, then γ, δ, ε, ζ, an inch clear of the E. side, and η through the E. side. Then vertically the plane b is 4 inches above the inside bottom, and c, d, e, f are at six–inch intervals; occasionally, in the most perfect parts, another line, g , could be measured on the outside, just at the top. The inside plane, a , was taken at only 3 inches below b , or 1 inch over the bottom; but the outside plane, a , was taken the full six inches below b , i.e., 4 or 5 inches above the outside bottom. In taking means in the inside the offsets to a are only allowed half weight, as they belong to a much shorter space than the others; they ought, theoretically, to have even less weight, but as the inner planes gather in rapidly, just at the bottom below a , this half weight probably gives the truest results. Having, then, adopted the above mean planes for the sides, and divided them for reference at every six inches, we can state all the variations of the actual surfaces as being either + (i.e., an excess of stone beyond the plane) or – (i.e., a deficiency of stone), either inside or outside the coffer. These variations are as follow, stated in hundredths of an inch:–
[p. 87]
[p. 88]
[Text superimposed upon table in original:] Offsets in brackets are from points on the cut out ledge, raised 1.70 inches, which is the mean level of the ledge below adjacent points of the remaining top; thus restoring the top as nearly as may be from the ledge. The actual top only remains at six points. If; for example, the length of the E. side of the coffer is wanted, from the foregoing tables, at the level of d, half way up; on referring to "North outside" and "South outside" it will be seen that at d on East side the coffer is in excess of the mean length by + .02 on N. and + .37 on S.; adding these to the mean length (89.62 + .02 + .37) = 90.01 is the result for the E. outside of the coffer half way up. Similarly at 8 inches under the top on the same side, at f it is (89.62 + .18 + .34) = 90.14 in length; or at 4 inches above the bottom (which is about the lowest point uninjured) it is at a (89.62 + .13 + .54) = 90.29 in length. Or if the inside width is wanted, half way up the N. end, at d; referring to "West inside" and "East inside," at North end, d level, it is seen to be the mean inner width, 26.81, –12 on W., +.02 on E. = 26.71; the signs being, of course, reversed in adding internal offsets together. Similarly at the middle of the length of the coffer (H, d ) the internal width is 26.81 + .06 + .05 = 26.92 [p. 89] If the thickness of the middle of the bottom is wanted, referring to "Bottom outside" and "Bottom inside," at H, d it is seen that the mean thickness 6.89 is changed by – .04 and +.02, and it is therefore 6.87 thick at that point Or if the thickness of the middle of the N. end is wanted at d and d referring to "North outside" and "North inside," it is seen to be (5.67 – .21 + 0) = 5.46 or the middle of the N. end at the top is (5.67 + .21 + .01) = 5.89 Thus the dimensions internal or external, or the thickness of any part, can be easily extracted from the tables by merely adding the corresponding offsets to the mean dimension.
60. The thicknesses of the sides, however, are involved in the measurement of the cubic bulk of the coffer , and therefore need to be very accurately known, in order to test the theories on the subject. And by the above method the thickness is dependent on the combination of many separate measures, and is, therefore, subject to an accumulation of small errors. To avoid this uncertainty, the sides were independently calipered; observing at every six inches, on the same spots on which the offsets were read. And it is to these caliperings which follow that I would mainly trust for determining the solid bulk of the coffer. The thickness is stated in hundredths of an inch.
[p. 90] From these caliperings the mean thickness of each of the sides, as compared with the results of the offsets, are thus:–
Hence there appears to be a constant error of –.01 on an average, making the result of the thickness by the offsets to be less than the truth. This may be due to a tendency to read the offsets too large, or else possibly to a slight skewing of the calipers, as 3º skew would make this difference on 6 inches. To compare in detail the results by calipers and offsets, over a small space, let us take the thickness of the N. end, along the lines C and d, which are near the mid height:–
Thus the mean difference between the thicknesses as ascertained by the two methods is .022, with a constant difference in one direction of .012 on an average. The spots observed on in the two methods were not always exactly identical; and so some difference may be due to waves of short length in the surface of the stone. In stating the offsets on the top, the mean plane adopted is not the simple mean of all the offsets, but the mean of diagonally opposite pairs of offsets, so far as they can be taken. This is necessary in order to obtain a true result, as otherwise (the top being broken away all at one corner) any great tilt that it may have had, in relation to the base planes, would vitiate the result.
61. From the foregoing data the cubic quantities may be calculated of a simple rectilineal box, omitting all notice of the attachments for the lid, employing the mean planes :– Contents– 72,030; solid bulk = 70,500; volume over all, 142,530 cubic inches. Or by the caliper results, instead of the mean planes, the bulk is 1/580 more, and the contents probably about 1/1000 less; hence the quantities would be :– Contents = 71,960; solid bulk = 70,630; volume over all, 142,590. These quantities have a probable error of only about 60 cubic inches on contents and volume, and 100 inches on the bulk. The bulk of the bottom is = 23,830; and hence one side and end is on an average = 23,335. Bulk of bottom x 3 is then = 71,490; and 3/2 x bulk of sides and ends = 70,000, subject to about 100 cubic inches probable error.
62. [p. 91] The spaces, or "chambers of construction," as they have been called, which lie one over the other above the King's Chamber, are entered from a small passage which starts in the E. wall of the gallery, close under the roof. This is apparently an original passage, and leads into the lower chamber; the other four spaces above that can only be entered by the forced ascent cut by Col. Howard Vyse. This latter passage is not so easy to go up as it might be, as it is nearly all in one continuous height, so that a slip at the top chamber means a fall of thirty feet; and as there are no foot–holes, and the shaft is wide, and narrows upwards, an Arab guide of Dr. Grant's refused to venture up it, alleging that he had a wife and family to think of. Ah Gabri, however, was quite equal to the business, and held a rope ladder to help me, which he and I together held for Dr. Grant. The mouth of the passage out of the top of the gallery is 26.3 wide horizontally at top, 26.2 at base, the S. side of it being formed by the topmost lap of the S. end of the gallery. The top and base of the mouth follow the slope of the gallery, the top being the top of the gallery, and the base the bottom of the topmost overlapping; thus the mouth is 29.4 high, square with the gallery. The rough passage is 28½ wide, 32 inches high, and over 20 feet long. All these chambers over the King's Chamber are floored with horizontal beams of granite, rough dressed on the under sides which form the ceilings, but wholly unwrought above. These successive floors are blocked apart along the N. and S. sides, by blocks of granite in the lower, and of limestone in the upper chambers, the blocks being two or three feet high, and forming the N. and S. sides of the chambers. On the E. and W. are two immense limestone walls wholly outside of; and independent of; all the granite floors and supporting blocks. Between these great walls all the chambers stand, unbonded, and capable of yielding freely to settlement. This is exactly the construction of the Pyramid of Pepi at Sakkara, where the end walls E. and W. of the sepulchral chamber are wholly clear of the sides, and also clear of the sloping roof–beams, which are laid three layers thick; thus these end walls extend with smooth surfaces far beyond the chamber, and even beyond all the walls and roofing of it, into the general masonry of the Pyramid. The actual dimensions of these chambers are as follow :–
[p. 92] But these dimensions are merely of the rough masonry; and some lengths could not be measured owing to the encumbrance of blocks of stone and rubbish left in the chambers from Vyse's excavations.
63. In the first chamber the S. wall has fallen outwards, dragging past some of the roof–beams, and breaking other beams at the S.E. corner. The E. and W. end walls have sunk, carrying down with them the plaster which had been daubed into the top angle, and which cracked freely off the granite roofing. On the E. end one block is dressed flat, but all the others are rough quarried. In the second chamber are some bosses on the N. and S. wall stones; and several of the stones of the N. wall are smoothed, and one polished like those in the King's Chamber, seeming as if some spare blocks had been used up here. The S.E. corner shows cracks in the roof .52 wide. The masons' lines, drawn in red and black, are very remarkable in this and the upper chambers, as they show, to some extent, the methods of working. Some of the lines in this chamber, drawn in red on the S. wall blocks of granite, are over some of the plastering, but under other parts of the plaster. These lines, therefore, were drawn during the building, and while the plaster was being laid on, and slopped like whitewash into the joints. The red lines are always ill–defined and broad, about ¼ to 1½ inch; but, to give better definition, finer black lines were often used, either over the red or alone, about 1/10 inch wide. On the S. wall, starting from a drafted edge on the W. wall, 4 inches wide, there is a vertical mason's– line at 22.3, a very bad joint at 51.5, another line at 70.5, another at 435.8, and the E. wall at 471.8. Thus the two end lines are 413.5 apart, evidently intended for the length of the King's Chamber below them, and define the required limits of this upper space. On the E. wall is a vertical mid–line drawn, with a cross line and some signs; from this mid–line to a line at the S. end is 101.8, and to a line at the N. end of the wall is 102.85; total, 204.65, intended for King's Chamber width. There is a large cartouche of Khnumu–Khufu, nearly all broken away by Vyse's forced entrance; but this and other hieroglyphs need not be noticed here, as they have been already published, while the details of the masons' marks and lines of measurement have been neglected. In the third chamber, the N. and S. sides are of granite as before; but they rest on pieces of limestone, put in to fill up hollows, and bring them up to level: this showing, apparently, that the stock of granite supporting blocks had begun to run short at this stage of the building, and that any sort of pieces were used up, being eked out by limestone, which in the upper chambers supplied their places altogether. The flooring beams are very unequal in depth. and hence the sides of many of them are exposed, and show us the masons' marks. On the 1st beam from the E. end is a mid–line on the W. face at 98 from the S. On the 4th beam is a mid–line on the E. face, 102.8 to N., and 101 to S. [p. 93] On the 6th beam is a mid–line on W. face, 100 to N. and 101.5 to S.; these N. and S. ends being merely the rough sides of the chamber. There are two bosses on the S. side of the chamber. The chamber sides are much slopped over with liquid plaster. On the N. side is a vertical line on the western granite block, over the edge of a limestone block beneath it, apparently to show the builders where to place it. From the W. end of the chamber this line is at 10 inches, joints at 210 and 246, a red line at 260, chamber end at 479 (?), and end of granite blocks at 503. In the fourth chamber the supporting blocks along the N. and S. sides are all of limestone, and are much cracked and flaked up by top pressure. The great end walls, between which all these chambers stand, have here sunk as much as 3 inches in relation to the floors and sides; as is shown by the ledges of plaster sticking to them, which have originally fitted into the edges of the ceiling. The roof–beam by the forced entrance has been plastered over, then coloured red, and after that accidentally splashed with some thin plastering. Along the N. wall, from the E. end of the floor as 0, there is a line at 37.8, another at 58.5 another at 450.6, and the W. end at 481 thus the extreme lines are 412.8 apart, with a supplemental line at 20.7 from one of them. This last was probably put on in case the end line should be effaced in building, so that the workmen would not need to remeasure the whole length. One stone, 65 inches long, has a mark on it of "3 cubits." On the S. wall, from the E. end = 0, there is a line at 32.6, another at 384.7, another at 446.5, and the W. end at 467; here the extreme lines are 413.9 apart, with a supplemental line 61.8 (or 3 X 20.6) from one end. Along both sides of the chamber is a red line all the way, varying from 20.6 to 20.2 below the ceiling; with the vertical lines just described crossing it near each end. Remembering the Egyptian habit of building limestone courses in the rough, and marking a line to show to where they were to be trimmed down level, this line seems to have been put on to regulate the trimming down of these lime– stone sides; either as a supplemental line, like those one cubit from the true marks on the granite beams, or else placed a cubit lower than the trimming level, in order that it should not be effaced in the cutting. On the E. floor–beam is a line 98.6 from the S. end. On the third beam is a line 100 to N. and 96.2 to S. end. On the 4th beam a line 98.3 to N., and 100.6 to S. end. On the sixth beam a horizontal line running all along it, with a mid–line 98.0 to N. and 98.1 to S. end; and a supplemental line at 20.3 to 20.6 from S. end. On the other side of the beam a line is at 98.1 to N. and 96 to S. end. The rough tops of the floor–beams of this chamber show most interestingly the method of quarrying them; exactly as may be seen on the rough tops of the granite roofing inside the Third Pyramid. On the top of each stone is a hollow or sinking running along one edge; and branching from this, at right angles across the stone, are grooves 20 to 25 inches apart, about 4 [p. 94] wide, and 1½ deep. These seem to show that in cutting out a block of granite, a long groove was cut in the quarry to determine the trend or strike of the cleavage; and then, from this, holes were roughly jumped about 4 inches diameter and 2 feet apart, to determine the dip of the cleavage plane. This method avoids any danger of skew fractures, and it has the true solidity and certainty of old Egyptian work. In the fifth or top chamber, the width is quite undefined; and we can only say that between the points where the sloping roof–slabs appear is 247 inches. The roof–slabs have separated at the apex 1.55 at E. end, and I.0 at W. end. The end walls are very rough, being merely the masonry of the core. On the second floor–beam are two horizontal lines 20.6 to 20.7 apart, with three vertical lines across them, 103.1 and 103.5 apart. They have triangles drawn in black on both the vertical and horizontal lines, the triangle on the horizontal being 12.5 from the end vertical line, and therefore not apparently at any exact distance along it. On the fourth beam from the E. is a horizontal line on its W. side, with four vertical lines: these are a mid–line, others at 102.6 and 102.6 from it, and a supplemental line 20.0 from one of these. On the E. side of the same is a horizontal and three vertical lines; the two end ones 206.3 apart, and a supplemental line 2I.0 from one end. Both of these horizontal lines have a small black triangle, with one side on the line. The third beam from the E. has four verticals, with a triangle beyond the last. These are 103.3 and 103.25 from a mid–line, with a supplemental line 20.95 from one end. The E. beam has five verticals, 103.0 and 102.7 from the mid–line, with supplemental lines at 20.7 and 19.4 from the ends; it has also a horizontal line, with a large red triangle on the lower side of it, and a smaller black triangle inside the red. On the S. side is a line 29.3 from the W. end, apparently one terminal of the 412 –inch length. The roofing–beams are all numbered, beginning at the W. end of the N. side, going along to the E., turning to the S. side, and so back to the W. end. The numbers visible on the under–sides of the beams are 4, 18, 21, and 23; probably the numbers of the others are on the sides now covered. From all these details of the lines, it seems that the roofing–blocks had usually a mid–line and two end lines marked on their sides as a guide in placing them; and, in case of obliteration, extra lines were provided, generally a cubit (20.6) from each end, but sometimes at other points. The horizontal lines were probably to guide the workman in cutting the straight under–sides of the beams; and it would be desirable to measure through some cracks to find their distances from the ceiling side. The flooring of the top chamber has large holes worked in it, evidently to hold the butt ends of beams which supported the sloping roof–blocks during the building.
64. [p. 95] General summary of the positions inside the Great Pyramid:–
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W.Wall 69½ to 70½ N.Wall 70.3; S.Wall 72.3
59.8
