OF THE GREAT PYRAMID. ' 677 



is explained by the compression hypothesis, combined with the latitudes 45° and 

 30°. The amount of difference left outstanding, is indeed much smaller than the 

 limits of errors of observation in the best modern measures of the earth's polar 

 diameter : so that perhaps we ought therewith to be content. But of course the 

 question will be asked, in which way do the residual differences point, i.e., for 

 more, or less, polar compression than that favourite quantity of 3-^ ? 



And then comes the answer ; that they indicate the average quantity of 3^ 

 to be exceedingly close to the truth ; but accompanied by an irregularity, tending 

 to produce a protrusion near Lat. 45°, at the expense probably of the neighbouring 

 parts ; and inclining to give the earth, in meridian section, something of that 

 squarish look, which Sir William Herschel thought that he had detected tele- 

 scopically in the planet Saturn. Mr Main's Greenwich observations of Saturn 

 are, indeed, considered in some quarters to have annihilated the Herschelian idea ; 

 and they have proved that there is no very large quantity of such squareness ; 

 but such a moderate amount as what is indicated by the Pyramid analogies, is 

 far beyond the powers of astronomical micrometer observation, in our bad ob- 

 serving atmosphere and even in the present day, to hope to reveal. 



(4.) Latitude Markings. 



The grounds on which we have hitherto considered that the latitudes 45° and 

 30° were intended to be alluded to in the Pyramid, are certainly of a hypothetical 

 character ; and therefore, though the hypotheses be ever so sound, they will be 

 improved and strengthened in the opinion of many persons, if proofs of a prac- 

 tical character can be found to support them. 



Proofs too, of this order, do really appear to exist in the building still ; 

 though we must begin with something of hypothesis to arrive at them. 



In figure 3 (Plate XXIII.), therefore, is a carefully drawn theoretical meridian 

 section of the Pyramid, as in fig. 1, (p. 668) ; but in place of the large square 

 of the base, there is now a small square, symmetrically placed with it. The size 

 of this small square is 103"246 metrons in the side, and is obtained by computa- 

 tion as being equal to the area of the Pyramid's meridian section. 



This small square, in itself, and by some very simple divisions, shown by the 

 dotted lines in fig. 3, enables us to arrive quickly at the placiugs of all the few 

 chambers and passages in the Pyramid. 



To prove this important relation, fig. 4 (Plate XXIV.) contains a careful 

 copy of Colonel Howard Vyse's large meridian section of the Pyramid, in the 

 1st volume of his great work ;* and to facilitate the comparison, I have added to 

 it the chief lines of the hypothetical Plate XXIII. fig. 3, in rows of dots. 



* This section, like most meridian sections published, since the time of Professor Grea.ves in 

 1637, agrees to overlook the small distance by which the passages of the Pyramid, though truly in 

 the plane of the meridian, are slightly to the east of the true central meridian section of the 

 Pyramid. See fig. 7, Plate XXVII. 



