22 GEOMETRICAL EARTHWORKS OF OHIO. 
salis. We were therefore surprised to find after a very careful survey 
the close approximation to a true circle in these cases. 
As it is impossible to show this satisfactorily in a figure on the scale 
given here, the attention of the reader is called to the following facts, 
which he can verify independently by making for himself a plat on a 
larger scale from the notes given above relating to the High Bank circle. 
(1) The chords forming the sides of the inclcsed quadrilateral sub- 
tend equal ares of the surveyed line; that is to say, the distance along 
the wall from @ to d is equal to that from b to ¢, also to that from ¢ to d and 
from d to a; the distance in each case being 830.4 feet, or one-fourth of 
the circumference according to the survey. As these chords are respect- 
ively 744, 746, 743, and 741 feet in length, showing an extreme varia- 
tion of less than 3 feet from a medium and of but 3 feet from a true 
quadrant, we have an evidence of the close approximation to a true 
circle. 
(2) The extreme difference between the various diameters (except at 
the eccentric point at the southeast, between the gate-ways) does not 
exceed 3 feet, or a variation from the medium of 4 feet, and from that of 
the true circle of more than 5 feet. 
(3) A circle with a radius of 526 feet and center at the intersection 
of the two given diameters varies at no point from the surveyed line 
(except at the eccentric point in the southeast) more than 6 feet; or, 
in other words, both would fal] on a wall only 6 feet wide. 
It is evident, therefore, that we have here a very close approximation 
to a true circle. 
OCTAGON OF THE HIGIL BANK WORKS. (See Plate VII.) 
The Octagon at this point differs from that at Newark chiefly in size 
and a closer approximation to a square. The variation from the usual 
form resulting from throwing the gate-way along the wall between the 
angles is readily accounted for by the fact that there is here a some- 
what abrupt depression, which is avoided by the curve given the wall. 
The field-notes of the resurvey are as follows—commencing at station 
1, in the middle of the gate-way leading to the circle: 
Survey of the Octagon of the High Bank works. 
| | 
| 
| Station." Bearing. 
Station. Bearing. 
e) 
8to 9.) N.53 37 
2to3....| §.43 50H || 9to10.| N.42 57 
3 to 4...2/'S. 30.178 2 |) 10to1l.| N.31 27 
AOI CUR Sods elogW oe seen eacee eames | 449 || 11 to 1.| N.43 27 
HOG, Soa|PS, CORSA. wae tema cies see esas 340 || 5tol12.| S. 60 43 
B tosreseel S70) STW ae cc ee ce | 57 
65 || 12 to 10.| N. 42 
HL OsB EA AN: SO LAO RVs ee See Soe | 60 || | 
| 
