1422 ROBERT H. MILLER 
be expressed as a sine function. It will be shown that the distribution 
of gravity observed throughout many California oil fields is mainly the 
result of the folding of the surface formations which behave like a rigid 
surface crust. 
AB (Fig. 2) represents a vertical section of a sand formation through 
one of the Los Angeles basin oil fields drawn to scale. Below this sand 
formation are blue shales. The sine function assumed by this bed may 
be expressed by 
xT 
y = 1,000 E — cos | 
9,000 

where x and y represent, respectively, distance and height in feet from the 
origin O, of points on the lower surface of the bed. The points a and b 
are points of inflection at which there is no bending. Between a and b 
the arch is convex upward so that the part near the upper surface is 
extended, and the part near the lower surface is compressed. Between 
A and a, B and 6, the arch is convex downward and the reverse is true. 
There is, therefore, a part of the bed between the upper and the lower 
surface which is neither extended nor compressed. This part of the bed 
is named the neutral surface, and its vertical section is the neutral axis. 
One of the consequences of bending is that at any point in a normal 
section the strain is proportional to the distance of that point from the 
neutral surface. As the change of density is equal to the strain, the 
terms may be used synonymously. If compression is considered as a 
positive density change and rarefaction as a negative density change, 
and if points above the neutral surface are considered positive and 
points below negative, the distance of a point from the neutral surface 
in a normal section, where the density change is 46, is given by a, where 

p being the radius of curvature of the neutral axis at that section, being 
positive where the axis is concave upward and negative where the axis 
is concave downward. As the radius of curvature of a sine curve passes 
from a minimum at the points A, B, and C, to infinity at the points of 
inflection a and 3, there is a deficiency of mass concentrated above the 
neutral surface at C, and below the neutral surface at A and B, and an 
excess of mass below the neutral surface at C and above the neutral 
132 
