10 GEOMETRICAL EARTHWORKS OF OHIO. 
cireumference into equal parts can be found only by first ascertaining 
the circumference ; in the second place it is not possible, even with the 
utmost care and best instruments, that the angles should be precisely 
the same and the steps exactly equal throughout, where the top of the 
circular wall is from 4 to 6 feet wide. ' 
It was probably the intention of the authors that this should be taken 
as a hypothetical illustration. But why give an imaginary “ Field 
Book” and example when they could have referred to any one of their 
own surveys? Why do they fail to give a single illustration from their 
actual work if they placed the full confidence in it which their words 
imply? Not only is this disappointing to the student of archeology, 
but the illustration of their methods is not calculated to inspire confi- 
dence in the accuracy of their surveys. Itis evident from the language 
of the note and the supplementary plan that the ‘306 feet” refers to the 
chords and not to the ares. As it is not presumable they had a chain or 
measuring line 300 feet long, the chord would have to be measured by 
steps, a task which, as any surveyor or mathematician knows, is far 
more difficult to accomplish than any work our authors were likely to un- 
dertake. It is therefore apparent that they have given an illustration 
which is impracticable and which is not drawn from their own work. 
Moreover, the doubts which these facts raise in our minds are not al- 
layed by a resurvey of the Liberty Township works, in connection with 
which the note and supplementary plan referred to are given. 
LIBERTY TOWNSHIP WORKS. 
Tor example, the smaller of the two prominent circles of the Liberty 
Township group, shown on pl). Xx, to which reference has just been 
made and which they represent as a true circle, with a diameter of 800 
feet (certainly a round number where great accuracy is claimed), is in 
fact an irregular ellipse of the form shown in Fig. 2. The longer di- 
ameter, measuring to the middle of the wall, as ascertained by the sur- 
vey, is 866 feet, and the shorter 748 feet, the difference between the 
two being 118 feet. This survey was made precisely inthe manner sug- 
gested by Messrs. Squier and Davis, save that the chords were 100 
feet each, except a gap of 313 feet where the wall is too nearly obliter- 
ated to be traced satisfactorily: this gap is indicated on the plat (Fig. 
~) by dotted lines. 
The field-notes of this resurvey are given here, that the ¢ritical reader 
may have before him all the facts, so far as it is possible to put them ip 
print, upon which our conclusions are based. 
Beginning at station 1 (see Fig. 2) at the end of the wall on the south 
side of the gateway leading into the large circle, the courses were run 
from station to station westward, northward,,and around to the place 
of beginning.! 
Oo 
1g. 
1Tho - - i : : - ) x a . eat ah 
Phe measurements are always to be understood as to and along the middle of the 
walls unless otherwise noted. 
