A French writer remarks that "it is not by chance that the Egyptian foot equals 360,000 to a degree." He considers that "it is thus certain that these measures have been drawn from the dimensions of the earth, and that they are derived from them, following the sexagesimal progression." Dufeu sees "in the vertical height of the Great Pyramid the standard of two of the great itinerary measures of the earth."

16. THE TRUE SHAPE OF THE EARTH.

We moderns are aware that this home of ours is not a regular globe, seeing that it is an oblate spheroid, with a bulging out at the equator, or flattening at the poles.

Hekekyan Bey, who is so full of the wonders of the pyramid. as to say, "This Siriadic monument masonifies information which would fill volumes," has seen how it can express this polarity difference.

"The square root," he writes, "of the three-fifths of the difference between the length of the side of the rock platform, and twice the measure deducted from it to obtain the length of a side of the first course of masonry on the platform, gives the measure of the proportion of the polar compression to the equatorial diameter."

These he finds to be 302.2 to 301.2. In this way he gets the equatorial axis 8,752,847,053-3 noctas, and the polar 8,723,890,885.9.

Dufeu, in his system of calculation, obtains for the imaginary height of the pyramid 692 0937. This, says he, is one-hundredth part of the flattening of the earth at the pole, or one two-hundredth of the difference of the diameter at the equator and the

axis of rotation. Though Laplace declares for 68,671.123, yet the mean of modern measures for this flattening is 69,209 8708. But it will be seen that the pyramid measure very nearly approaches the last as 100 × 692-0987 produces 69,209.87.

This height is thus obtained. He does not believe the pyramid ever higher than the present platform of 202 steps, or 450 feet 10 inches. He supposes a cippe, pole, or column of 6.827 metres to represent the imaginary apex. Thus he concludes the elevation above the lowest level of the Red Sea to be 692.1785 feet. M. Jomard originally suggested the cippe top. The platform base is now about 150 feet above the level of the desert.

17. THE DENSITY OF THE EARTH.

Citing a passage in Isaiah, upon "weighing the mountains in scales," Mr. Piazzi Smyth thinks he detects the mean density of the earth "to have been introduced into the capacity and weight measures of the pyramid at a time when it was an utter impossibility to men;" that is, he supposes it pleased the Most High to reveal what astronomers have only recently discovered by science.

He finds the coffer contents to be 70,970-2 inches, and the coffer weight of water at 68° to be 17,905 500 gallons. Thence he gets by a division of these two quantities the approximate density of 5.672.

Mr. William Petrie has ascertained that the mass of the pyramid is to the earth as 1 to 10 5X3. He estimates the weight of the pyramid at 5,273,834 pyramid tons, and that of the earth 5,271,900,000,000,000,000,000. Reckoning the mean density of the earth at 5-7 times water, he regards the earth as exactly a thousand billions times the weight of the pyramid.

Mr. St. John Day, after noting that the exterior dimensions

of the sarcophagus or coffer are twice those of the interior, proceeds to demonstrate that, taking the internal cubical measurement at 71,250 inches, if we divide 71,250 by the recognised mean density of the earth, 5·7, we obtain in the result, 12,500, the weight of the coffer of water at the temperature of 68°. He realises the coffer contents, 71,250, by multiplying the cube of 50 pyramid inches by the density, 5'7, and dividing the whole by 10. The weight of the pyramid is declared to be 165 × 3 of the weight of the globe.

Sir Edmund Beckett ridicules the attempt to make the pyramid tell this density tale, especially as its advocates have "the figures wrong, according to all the received measures, from Newton's to the present day."

18. THE DISTANCE OF THE SUN.

It is

A very simple law has been found for this calculation. to multiply the height of the pyramid by the ninth power of the number 10.

The steps of the building establish the relation of ten and nine; so much so, that it was thought two poles, of 10 and 9 feet respectively, were set up at right angles, for guidance to the workmen.

As the height bears a definite relation to the base, the one as radius, the other as circumference, the accurate measurement of the base will give the proper ideal height. Mr. Piazzi Smyth makes the latter 5819 inches of our own times. But Mr. Wm. Petrie estimates 5835 as nearer the truth.

The distance of the sun, by the ninth power of 10 multiplied by 5819, will be about 91,840,000 miles; but by 5835 inch

height, 92,093,000. Currently, the distance has been reckoned 95,000,000. More recent calculations have placed it some three millions less. The pyramid measurement, therefore, is more correct according to modern data.

The sun's distance is estimated at one thousand million times the height of the pyramid.

19. THE DAYS IN A YEAR.

Some curious calculations are brought out by Prof. Smyth, Captain Tracey, Mr. Petrie, Mr. Yeates, and others, upon the number of days in the year.

Mr. Thomas Yeates, in 1833, started the view, "whether or not the Great Pyramid of Ghizeeh was designed as a monument of the discovery of the Egyptian year." Again, he says, "The measure of the pyramid will be found to agree with the number of days in the solar year. Moreover, admitting my exposition of the ark of Israel to be correct, then will its measures of length and breadth be found to correspond in cubits with the number of days in the lunar year, viz., 354."

As mentioned elsewhere, Mr. Yeates identified the pyramid with Noah's ark. "The form of the ark," he said, "was quadrangular, and consisted of four equal sides, or parallelograms, of which the measure of one is given in three numbers-300, 50, and 30 cubits." Again, "The four sides include four rectangular parts of one dimension in length and breadth; and the whole equal a square of 350 cubits, inside measure, and four more for the outside, making in all 354 cubits, or about 7371⁄2 feet (25 inches to a cubit). Compare this with the measure of the Great Pyramid."

Mr. Wm. Petrie shows that the side of the pyramid will equal 365 3 multiplied by the cubit of 25-025 British inches. Assuming the ancient vertical height as 5813 inches, he would multiply that sum by the ninth power of 10, to realise the radius vector. He finds the number of days to go a round number of times into the circumference of the earth's orbit. The latter is taken at 36,525,430,000,000; and the former, 365-25636. But that circumference is associated with the perpendicular 5813; being thus produced-5813 × 109 × twice 3.1416 36,528,430,000,000.

=

Prof. Hamilton L. Smith of New York, according to Mr. Piazza Smyth, taking "one length and two breadths of the King's Chamber for radius in a trigonometrical computation with the peculiar passage angle 26° 18' 10", the resulting sine, or length of the vertical side of the triangle, where the above radius is hypotheneuse, brings out exactly the year-day number, 365 242, &c." He also shows that the height of the niche in the Queen's Chamber, taken as 182 62, multiplied by 2 will give 365 24 solar days. He finds this height of the niche, if taken as 185 multiplied by 3-1416, and then by 10, will bring 5812, the height of the pyramid; but taken as 182-62, multiplied by 10 and divided by 2, the base, 9131, is obtained.

Capt. Tracey, R. N., has some pretty mathematical results from the Ante chamber to the King's Chamber. The length of 116-26 inches he notes to be partly of granite, partly of limestone. The granite portion is 103-033 in pyramid inches, which are about a thousandth part larger than the British. Taking 103 for the side of a square, he gets the area of a circle whose