1 50 Cincinnati Society of Natural Histoiy. 



As to the plate it is said by the authors: " The map here given is 

 from an original and very careful and minute survey made in 1836, 

 by Charles VVHiittlesey, Esq., Topographical Engineer of the 

 State of Ohio, corrected and verified by careful re-surveys and 

 admeasurements by the authors. It may be relied upon as strictly 

 correct." The chief object of giving this work is to show that the 

 numbers of measures, viz., 24 feet, heretofore used on right lines, 

 are transferred to designate the circumference of a circle. In 

 the Hopeton Works we have a parallel way 2400 feet in length, 

 connected with the great circle whose diameter is 1050 feet, and 

 with the great rectangle whose side s 1080x10 inches. The 

 especial feature of the Newark Works is the great circle of 24x120 

 =2880 feet in circumference, and the great ellipse whose conju- 

 gate diameters are, respectively, 1250 and 11 50 feet in length. It 

 will be seen that the sum of these diameters is 2400 feet, 12 

 times which is 10 times 2880, the circumference of the great circle, 

 while their difference is 100 feet, or 1200 inches; so that the ellipse 

 is made to be related to the circle by the length of the sum of its 

 conjugate diameters. The circle, as is seen. Figure VIII, has a 

 circumference of 2880 feet. Of it the authors say: "Unlike the 

 other circular work, this is a true circle, two thousand eight hun- 

 dred and eighty feet, or upAvards of half a mile in circumfere"nce." 

 It is connected with the octagon by a passage way 300 feet long 

 by 60 feet wide. Recess to "Crown Works" 100 feet, about. 

 Length of mound across crown work 170 feet. Within the octa- 

 gon there are 8 mounds, rectangular truncated pyramids, each 100 

 feet long by 80 feet wide at base, and 5 feet high. Here at once, 

 the relation of these works within the octagon to the cirumference of 

 the circle becomes manifest, 100 feet is 1200 inches, 80 feet is 960 

 inches, and 5 feet is 60 inches, 960X120=115200, the ^^ of which 

 is 2880 inches, the number, in feet of the circumference of this 

 circle. So, also, the the octagon is a shape of 8 sides, and 2880X 

 8=23040 which is 1 1520, or the area of the base of one of the 

 mounds in the octagon, multiplied by 2. Moreover, this relation is 

 also extended to the conjugate diameters of the ellipse. The sum 

 and difference of 1250 and 1150 are, respectively, 2400 and 100 

 feet, or 28800 and 1200 inches, and the suiji of the sum and dif- 

 ference of these is 57600, two-tenths of which is 11520, and the 

 2'oth of which is 2880. 



The ellipse is especially remarkable for the so called "bird 



