Graphical Terrane Correction for Gravity Gradient Page: 9
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DIFFERENTIAL CURVATURE CHART
otherwise affecting the charts. According to the law of similar
bodies similarly placed in projection of one another, the gradient
effect at the point xp, y, units from the origin produced by a body
whose dimensions are Xm to x,, yo to yq, and z, to z, units of linear
distance, is the same whether the unit of measurement is inches, feet,
yards, centimeters, meters, or kilometers. The charts, therefore, can
be used to supplement the Lancaster Jones-Shaw gradient terrane
correction formulae by taking the measurements in feet instead of
meters and by erasing the word "meter" in the charts and sub-
stituting for it " feet."
7. The distance to which the gradient correction should be taken
and the degree of accuracy necessary in leveling and in measuring
the distances can be determined by inspection of the charts, Figures 2
and 3. The effect of the topography should be corrected as far out
as 100 x n meters wherever the elevation at 100 x n meters rises or
falls more than 2.5 x n meters above or below the center of gravity
of the instrument. At a distance of 5 x n meters the levels at eleva-
tions of 0.3 x n to 2 x n. meters should be accurate to 0.05 x n meters.
ADVANTAGES OF METHOD
Various graphical terrane correction charts similar in general type
to the present charts but differing in details of design can be con-
structed and for special situations will have special features of ad-
vantage. For example, where a series of observations are to be taken
down a long linear valley or in front of a long straight scarp there
would be considerable advantage in using a chart or charts based on
infinitely long horizontal rectangular prisms, each of which produced
a constant gradient effect at the origin, ' along the perpen-
dicular from the station to the edge of the valley or of the scarp;
s be and by- would then be determined trigonometrically from
DIFFERENTIAL CURVATURE CHART
For the calculation of the differential curvature correction it is
possible to construct an analogous graphical chart, such as the chart
of Figure 5. There is, however, little practical advantage to such a
chart; the value of the differential curvature effect of a small block or
prism moving vertically is very nearly constant within 15 of the
horizontal plane through the center of gravity of the instrument, and
for all practical purposes the effect of a block n units high is n times
the effect if the block is only one unit high, as long as the block is
wholly within about 150 of the horizontal plane through the center
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Barton, Donald C. Graphical Terrane Correction for Gravity Gradient, report, 1929; [Washington D.C.]. (digital.library.unt.edu/ark:/67531/metadc66454/m1/13/: accessed April 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.