1424 ROBERT H. MILLER 
surface at A and B. The dashed lines represent surfaces of equal density, 
the figures referring to the percentage changes. It is thus evident that 
the mass within the bed is redistributed into six zones, occurring in pairs. 
The zones of each pair are of opposite nature and in the same vertical 
line. It is evident that the distribution of gravity at the surface caused 
by these zones depends on their magnitude and position relative to one 
another, which is a direct function of the fold, and their position as a 
group relative to the surface of the ground, which is a function of subse- 
quent erosion, deposition, or earth movement. On the assumption that 
the normal density of the sand bed in Figure 2 is 1.8, and that subsequent 
to folding it has been buried to its crest under material of the same dens- 
ity, it is seen that the distribution of gravity would be represented by the 
calculated gradient profile curve BB’ (Fig. 3). If erosion then took 
place to the plane PP (Fig. 2), the position of the base of the sand for- 
mation now coinciding with the blue shale contact of this particular field, 
the calculated distribution of gravity would be represented by the 
gradient profile curve CC (Fig. 3). The close similarity of this curve 
and the observed gradient profile curve in this field (curve AA, Fig. 3) 
is sufficient proof that the compaction and rarefaction of the surface 
formations resulting from folding is the direct cause of the observed 
distribution of gravity. 
The practical value of this theory as a means of interpreting torsion- 
balance results in terms of subsurface structure can be illustrated best 
by considering an actual example. Curve HK (Fig. 4) is the actual 
gradient profile bed across an area in the Los Angeles basin drawn to 
the scales shown. This curve is complex and is obviously the composite 
of several simpler curves. On analysis the curve is found to be composed 
of three simpler curves, LM, NQ, and SV; that is to say, the ordinate 
of any point on curve HK is the algebraic sum of the ordinates of the 
corresponding point on curves LM, NQ, and SV. It is evident from 
what has been said before that curve LM represents the distribu- 
tion of gravity set up by the zone of compression below the crest of an 
anticline, and curve NQ represents the distribution set up by the 
remnant of a zone of extension above the crest of the anticline. Curve 
SV represents the distribution of gravity set up by the zones on the 
flank of the anticline, the upper zone of compression masking the lower 
zone of extension. As there is no disturbance on the other side of the 
anticline corresponding with SV, there is clearly a fault on that side 
against which the beds were folded. Referring to Figure 2, it is seen 
that, in the zone of compression at the axis of the anticline, the surfaces 
134 
