676 PROF. C. p. SMYTH ON THE REPUTED METROLOGICAL SYSTEM 



For the height, then, we take 116-5 metrons, or 5825 primal inches; for the 

 base-breadth, 183 metrons, or 9150 primal inches; or 762*5 feet, i.e., primal or 

 Pyramid feet ; and for the polar axis of the Earth, 5(30,000,000 of the same inches. 



Then, the first of Mr Taylor's two analogies is, in the form chosen by Sir John 

 Herschel, " a band encircling the earth, of the breadth of the base of the Great 

 Pyramid, contains one hundred thousand million square feet." 



Adapting this statement to our primal Pyramid feet, and to a form of 

 expression suitable to bringing out the diameter of the earth, and in inches, we 

 have 



100,000,000,000 



«|i, 3-14159 



1 ^ 



— 500,946,700 Primal or Pyramid inches. 



This resulting quantity, so much greater than the Polar diameter, may be referred, 

 from the encircling-band manner of its derivation, to a mean latitude of 45'. 



The second of the analogies is, that " the height of the Great Pyramid is 

 TTuiWo^h of the earth's circumference." 



Why, however, that particular fraction ? Had it been yduWo or ^^jy^xi^ or 

 even T.ow.ooiy* «-^5 anything easily made up of fives and times of five, there would 

 have been a rude sort of " Pyramid reason" in it : but for 270,000 I could find 

 no reason. Considering, however, the act of standing by the Pyramid on its base, 

 in this inquiry where its height is to be measured against the earth which it is 

 standing upon, —and finding that the area of its base in hundredths of feet has, 

 when thrown into a circular shape, a circumference equal to 270,299, — I presumed 

 that that might be accepted, if not as a reason, at least as an apology, for trying 

 the case with that number. Arranging the expression accordingly so as to brin^ 

 out the axis in inches, there appears, 



270 299 

 Pyramid height in inches x o^r^y^ = ^ \ 



or 5825- x 86038-901 = 501,176,400 Primal or Pyramid inches. 



This diameter of the earth, obtained so directly from the height and act of 

 standing of the Pyramid on its own base, must, if any one result could do so 

 more than another, refer to the diameter in the Pyramid's own latitude : and the 

 Pyramid's position is stated in the French maps, and most of their memoirs, to be, 

 29° 59' 6" ; but maybe assumed in such an approximate case as this, to be 30°. 



Computing next, from a theoretical polar diameter of 500,000,000, the values 

 for latitudes 45° and 30"", with a compression of ^-q, we have the following to 

 compare with the Pyramid deductions : — 



Computed Eartli Diameters. Pyramid Analogies. 



Polar, . 500,000.000. Polar. = 500,000,000. 



Lat. 45° . 500,840,000. 45° ' = 500,946,700. 



Lat. 30° . 501,257,000. 30° = 501,176,400. 



Simple inspection of these numbers will show at once, that by far the greater 

 portion of the whole difference from the Pyramid-base deduction, assumed polar, 



