148 . Cincinnati Society of Natural History. 



1 1200 feet, to which, if 100 be added, the sum is 11300 feet, or 10 

 times the length of the long way. The same may be shown in 

 this way : The height of 100 feet taken from 10 times the length of 

 the long way, or 1 1300 feet, is 11 200 feet, twice which, or 22400 feet, 

 ecjuals the area of the rectangular out-work. By this we are led to 

 look to the divisions of the figures, or component parts thereof, by 

 2, and the use of such parts by means of additions and subtractions 

 to show intended interrelations. So also we are taught by all the 

 measures of the groups: (i) that the reverse or inverse reading of 

 key numbers is used to produce as keys, other and controlling 

 and correlating relations, such as, 24 may be used as 42, 528 as 

 825, 21 as 12; (2) that key numbers are divided into other parts 

 to apply to differing geometrical shapes, as for instance, 2400 feet, 

 the length of a long way, is divided into 1250 and 11 50 feet, to 

 show the conjugate diameters of an ellipse, and so on. 



To show the application : Part of r ^ forms, for such purpose, 

 the diameter line of the circle, which is 250 feet long, and this 

 naturally divides into halves of 125 feet each, to form the radii of 

 the circle. By sympathy, 280 feet of the length of the out-work, 

 connected, as seen, with this circle, and with the long way, may 

 be divided into lialves of 140 feet each, so that from these parts 

 we have the numbers 140 and 125 thus desired. We see the 

 number 8 used about the works as the digit of 80 and 800. Di- 

 vide 1 130 by 8, and we have 14125, which ' is the sum of the two 

 numbers, 140 and 125, used as 140+00125=14125. Such rela- 

 tions show a puri)Ose of checking, using and emphasizing the meas- 

 ures and parts of measures of the various parts by means of geo- 

 metrical construction ; but in this case all serve to concentrate 

 upon and point to the number 1130. 



But again take the measures and parts of measures of the out- 

 work, located as a connecting constructive link between the 1130, 

 and the 250 and 125 of the circle. 140 feet is 1680 inches, the 

 eighth part of which is 210 inches, while 80 feet is 960 inches, the 

 eighth part of which is 120 inches. Here we get the 21 and 12, 

 which from the standard of 12 and 9 inches on the elliptical stone 

 produce 1050 and 1080, the key numbers of the works in general; 

 for 21X5 = 105, and 12X9=108. 



What can there be of significance about the combined use of 

 these two numbers, 1050 and 1080, fitting them to the scheme of 

 common measure, adapted interchangeably to differing geometrical 

 shapes, as, for instance, squares and circles ? 



