TORSION-BALANCE RESULTS IN CALIFORNIA 1427 
of equal density present approximately concentric cylindrical surfaces 
in the immediate vicinity of the axis and that the center of curvature 
of these parts of these surfaces is approximately equidistant from the 
horizontal line tangent to the neutral axis and to the normals through 
the points of inflection @ and b. Therefore, close to the axis, the distribu- 
tion of gravity caused by the disturbing mass in this zone is approximate- 
ly the same as if the mass were concentrated at this point, namely, the 
center of the circle touching the normals through the points of inflection 
and the ground surface, to approximate still further. Thus, in curve 
LM (Fig. 4) the two maxima are the distance ac apart, so that if OX 
represents the surface of the ground, the point would be located at P, 
a distance ac below the surface. The point of symmetry of curve 
NOQ, representing the distribution of gravity caused by the remnant of a 
zone of extension at the axis of the anticline, is offset toward the left 
from that of curve LM, indicating that the beds have been dragged 
down by the fault at the time the anticline was formed, and that the 
sine curve which is the figure of the anticline must be referred to the new 
axes X’O’Y’ instead of the horizontal and vertical axes XOY. The con- 
struction is evident from the figure. On account of the rotation of the 
axes, the period of the sine curve representing the anticline is slightly 
greater than OB, because at the point F, vertically below the center of 
the zones represented by the profile curve SV, the beds are horizontal, 
and not parallel with the new axis O’X’. The period of the sine curve is 
estimated to be O’D, and C is the point of inflection of the sine curve 
referred to the axes X’O’Y’ (shown by the dashed line). The tangent 
CT to the circle O’T, with P as center, gives the inclination y of the nor- 
mal through the point of inflection. Now the equation of this sine curve is 
Uy 
7 Tv 
x 
y =o]: ~ cos %5] 
where a is a constant representing the half-amplitude of the sine curve 
and O’D is the half-period, equal to 6,000 feet, and 
dy’ an (1) 
By measurement the angle TCE (y) is 39.5° and the tangent is 0.83, and 
x equals O’C and is 3,000 feet. Substituting these values in equation 
(x), a is found to be 1,600 feet, approximately. The section of the anti- 
