adits (modified in certain details by anomalous conditions of chronologic reference, as we shall see presently ; and which, while taking their proof from the geometric basis, are yet distinctly set in contrast with it). This element brings us back to the choice of the particular site on which it was necessary to locate the Pyramid. If we apply to a section of the structure, taken through the chambers and adits, a square whose area is equal to that of the meridian section, wo find that certain divisions and intersections of this “square of equal area” form a perfect geometrical scheme by which the whole of the actual dimensions (the codex of which is contained in the 13th vol. Royal Observatory, Edinburgh, and “pub. lished by order of Her Majesty's Government") are explained, and brought into minutely accurate adjustment with the base and with the axis of the structure; demonstrating at the same time the marvellous accuracy of the measures which have been taken. Until the solution of the geometrical scheme, the framework, so to say, of the internal featares, though fixed and rigid in itself, was loose and on the shift in its vertical and lateral relation to the triangular outline of the Pyramid, as may be seen on comparing any two published drawings of the interior. Now, the singular property of this “ square of equal area " is, that half its side is the sine, with the Pyramid height as radius, of the angle 26° 18. But this angle is the angle of inclination of the great Gallery. But, also, it was the angle of elevation of the then pole.star, a Draconis, at its lower culmination, in the latitude 30° of the Pyramid, at the epoch (as already explained) 2170 B.C., when Pleiades on the meridian above, and the equinoctial point also on the meridian, formed a threefold combination which cannot again occur until the lapse, from that time, of a whole cycle of the precession of the equinoxes. The combination, therefore, marked a zero of the precessional cycle. The Pyramid is the record of that initial combination. It records the event by virtue of its location in the precise latitude where, only, at that moment, the angle of the pole-star (to which also the entrance-adit of the Pyramid pointed) was the particular angle which is in specific relation between a pyramid of the specific proportions of this one and its “square of equal area.” All the astronomical text-books vary in the duration they assign to the period of the precession. This is confessedly one of the important quantities which modern science has not been able to determine minutely. In round numbers, the period is reckoned at 25,800 and some years, more or less. Now, the sum of the diagonals of the base of the Pyramid is, in geodesic inches, 25826-526; which is about a mean of the various values assigned by astronomers. * I beg you to bear in mind that here an inch of length represents a year of time. • In the last edition, dated “September, 1877," of an authoritative text-book on the Pyramid, and repeated in a tract lately published, it is stated that the precessional quantity, 25,826.526, is repeated in the perimeter of the Pyramid at the level of the floor of the Coffer-chamber. This is not true. That perimeter is only 25,734.635, giving a difference of 92 inches, nearly. Also the level of Cofferchamber is not 1702 inches, but 1717.215. There is the less excuse for the continued repetition of these worn-out inaccuracies, seeing that the solution of the Geometrical Scheme, which reconciled the apparently discrepant hypsometric measures, was published in January, 1877 ; and in May, 1877, I published the actual figures of the true length of Pyramid side at Coffer-chamber level, and of the height of that level. K a I have elsewhere shown* that the theory of the precession, based on the assumed cyclical rotation of the Earth's polar axis, ceases to be acceptable since we know that the Sun moves, with its whole system, through space; and that the motion of the axis is more likely the “ apparent motion resulting from the “real motion ” of the whole solar system. It would follow that the period of the precession is really the period of the Sun's revolution in an orbit. The distance traversed in space by the Sun during a year is a problem of such difficulty and complexity that, confessedly, in the present state of our knowledge, a rough approxi. mation only to the quantity can be attained. It is variously stated as about 150 to 190 millions of miles. The quantity specifically indicated by the Pyramid is again about a mean between these extremes, and is 170,460,276 miles. (The proof is a little intricate, and demands for its full comprehension an acquaintance with complex details. As it is already published I need not repeat it here.) For a long time, one of the most inexplicable features of the structure was that the entrance, and the whole of the internal chambers and adits, are not—as we should naturally expect-on the central line of the Pyramid, but some distance to the east. It was evident that so extraordinary a departure from natural order indicated specific intention to express some other very important kosmic or geodesic quantity. When the precise displacement (300·2418 geodesic inches) was identified (by a simple process which enables us to identify minutely any fundamental dimension of the structure), it was found at once to be the sine of the angle (23° 57' 57'.87) of the inclination of the Earth's polar axis at the epoch of the building of the Pyramid. This was another corroboration by the way of the date of the building. Now, it is easy to measure the present inclination of the axis of rotation; but there is a minute secular decrement which is exceedingly difficult, if not impossible, to determine with precision. Nevertheless, when we compute the angle for 2170 B.C. by the astronomical data, the difference from that indicated by the Pyramid is so small as to be in the proportion, for example, of only 163 minutes of time to a whole year. In the course of a brief exposition, it is impossible to give the detailed demonstration of results which have accumulated from the research of many investigators, during many years ; results which involve immense labour of intricate mathematical process. It is impossible to do more than set out, as briefly and intelligibly as may be, the results themselves. The actual measures, and the process of analysis and interpretation of the measures, have been published to the world, and are opeu to any who care to examine them. But, though I know of a great many who are prompt with ignorant ridicule, I have not yet heard of one who has had the grace, or the patience, or the courage, or the honesty, to face a discussion in detail of the mathematical demonstration of the results. The building is utterly ruinous and dilapidated, they say; and, therefore, it is an offence to common sense to expect reasonable men to discuss the pretension of exact measures, still less of refined expression * See the monthly numbers of “Life from the Dead" during the year 1877. of abstract quantities of any kind, on the basis of a thing in that condition. The answer to this is, however, very simple. It is true that the exterior is ruinous, and that some portions of the interior are dilapidated. But the cardinal features, both of the exterior and interior, are neither the one nor the other. For the exterior, the finely-cut sockets in the rock still remain (covered by débris) to attest the original exact size of the base. Innumerable pieces, some of considerable size, of the original fine, hard limestone facing-stones, are in evidence to attest the angle of slope of the flanks ; the angle which proves that the original height was to half the perimeter of the base as 7. The ruin and dilapidation of the exterior, in the end of the days," were foreseen; and the proof that they were foreseen is in the fact that the cardinal portions of the interior were lined with the hardest granite, which the climate of Egypt-hitherto the driest in the world—has preserved intact, even since they were thrown open to the curiosity of the world by the forcible entry of Al Mamûn, in the beginning of the ninth century A.D. The further proof, not only of this, but of the whole matter, is in the demonstrated facts that 1. The cardinal internal features are still capable of minute admeasurement, by anybody who is skilled in measurement, which few are. 2. They have actually been measured with extraordinarily minute accuracy. The measures have been open to the challenge of the world for fourteen years. 3. The accuracy of the measures is such, that mathematicians have been able to deduce from them the abstract synthetic method which explains all their relations, proximate and remote, and the geometric scheme by which they were brought into systematic and harmonious presentment. 4. The palpable, unquestionable result of the mathematical synthesis is to demonstrate, with the full certainty of a proposition in Euclid, that the precise dimensions of the now-ruinous exterior, together with their mathematical relations proximate and remote, in every imaginable varied form of expression, are recorded in the interior with a minuteness that renders necessary, for their discussion in mathematical process, the amplification from the first or second decimal of an inch to an indefinite number of decimal places. Let us examine briefly crucial case which is, of itself, at once sufficient proof that these statements are not exaggerated, and an illustration of the nature of the evidence. The mean of the best authenticated measures of the length of the square base is 9131 geodesic inches, within a fraction. Let us increase this by the minute fraction of to of an inch, and we have 9131.05. Consequently, four times this is the whole perimeter of the base, 36524.2 The angle of slope, deduced from the best measures it is possible to obtain in the actual condition of the exterior, and verified by the finelycat facing-stones, is 51° 51'. This angle is that of a pyramid whose height is to half the perimeter of its square base as 7. It is, thus, easy to compute the height which the structure must necessarily have originally been intended to have. That height then, must be 5813:01 These two dimensions, if they can be verified, absolutely determine the external size and form of the structure. Let us go to what is called the “ Antechamber," and see how they are verified. The mean of six measures of the length of the chamber is 116.25 inches. By synthetic process it can be shown that this measure differs only do of an inch from the pure theoretic quantity, 116.26 But the diameter of a circle whose perimeter equals the perimeter of the square base of the Pyramid (36524.2 as given above) is 11626:02 But, also, the height of the Pyramid is to the whole perimeter of the square base as radius to circumference of a circle, and the radius of the circle just given is 5813.01 Again, this chamber is on the 50th course, and we find that 50 is the factor of its quantities. So again we have the height of the structure by multiplying the length, 116.26, by 50. 5813.01 And, also conversely, 116-26 by a gives the expression of the perimeter of base, 365-242 But this chamber has two lengths. The floor near the entrance is of limestone, the remainder is of granite. The length of the granite floor is 103.03 The diameter of a circle whose area is equal to that of the base of a pyramid whose side is 9131.05 (or perimeter 36524:2) is 10303-3 Lastly, in the Coffer-chamber, the whole matter is repeated in variant forms, and amplified. The width of this chamber is twice, and the length four times, the length of the granite floor of antechamber. That was an easy matter, to build a chamber of a given length and width. Anybody could do it. But it is not so easy to build it so that its cubic diagonal (that is, an imaginary line from one corner of the ceiling to the diagonally opposite corner of the floor) shall be a severely defined length ; which length shall also be the expression of singularly refined abstract mathematical relation, in a complex system of quantities. The cubic diagonal of the chamber is, however, 515.165 But the side of a square whose area is equal to the meridian area of a pyramid, whose base is 9131.05 and height 5813:01, is 5151.65 It would be waste of words to discuss whether all this could be conceivably the result of what is called "accident." The evidence of intention, the evidence of perfect mastery of abstruse mathematical relations, the evidence of extraordinary skill and capacity to embody the expression of those relations in a material form, recoverable after 4,000 years, is too manifest, too overwhelming, too far above the reach of question. In the second part of the exposition, we shall have to consider the close correspondence between the standard measures set forth in the Pyramid, and the British standards; and, finally, the mathematical proof afforded by the Pyramid of the truth of the Holy Scripture. THE FALL OF JERICHO. HOPE FOR THE FUTURE. " By faith the walls of Jericho fell down, after they were compassed about seven days."—HEB. xi. 30. SUCH is Paul's account of this wonderful siege; the sixth chapter of Joshua, with all its marchings and music and marvels, compressed into a single verse; that we, in the hurry of modern times, may the better understand the story, and read its lessons. For it is a story ever fruitful in instruction to the Christian man; and especially is it an illustration of the method and plan of the divine procedure, rich and profitable to hearts wearily contending against the world's sin and sorrow, and sighing for the promised coming of the world's Deliverer. I. So regarding it, we stand at once face to face with the familiar lesson God is ever teaching, and we are ever failing to learn, the need and the power of faith. · By faith the walls of Jericho fell down.” We are apt severely to condemn the distrust so repeatedly manifested by the children of Israel, and sometimes in our self-confidence wish we could journey through the wilderness and conquer Canaan in order to leave the world a better example ; but our strongest faith in its strongest moments would shrink from the test which they here successfully experienced. They were asked to believe that a strong city would be given into their hands, as the result of marching round it to the music of rams' horns ; they believed, and the result justified their faith. Their unbelief has been left in the wilderness, buried with the excluded generation of their fathers; and in their faith they have the weapon which can take a city and conquer kingdoms. All things are possible to God, and therefore all things are possible to faith. To the greatest danger faith saith, "Go,” and it goeth ; to the choicest blessing faith saith “ Come,” and it cometh. The man dwelling on Mount Marvel, who “tumbles the hills about with words,” is the man of faith ; who “laughs at impossibilities, And cries, It shall be done.” Jericho, imgregnable to mere earthly weapons, crumbles into dust at the touch of Israel's faith. As soldiers in the army of God's Anointed, we too have laid siege to the greater Jericho of worldly sin and wrong ; but our efforts have been as the blowing of ram's horns. For eighteen weary centuries the Church has been grappling with its giant foes, and we have but touched the oatermost fringe of the world's darkness. Lands once illuminated have been lost again ; the Church itself has been corrupted and well nigh destroyed. At our very doors Satan mocks our efforts and sin triumphs. The governments of the world are still but manifestations of the rule of the prince of darkness; their “feet are swift to shed blood, the way of peace have they not known, and there is no fear of God before their eyes.” The high places of the earth are full of the habitations of cruelty. The great fortress of iniquity still frowns defiantly in grim majesty before us, manned by giant spirits beside whose powers the fabled strength of the sons of Anak is utter weakness, and enchaining within its iron grasp the myriads of humanity. The Gospel trumpets sound around; but the walls stand unshaken. To all human calculation the dream of a |