Physics of the Earth - II The Figure of the Earth Bulletin of the National Research Council (1931) / Chapter Skim
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Chapter XI. Gravity Measurements with the Eotvos Torsion Balance
Chapter XI. Gravity Measurements with the Eotvos Torsion Balance
Pages 167-190
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From page 167... ...
S TORSION BALANCE ~ DONALD C BARTON Consulting Geologist and Geophysicist, Howslon, Texas The essential working system of an Eotvos torsion balance consists of' a vertical torsion wile suspended by its upper end and carrying a horizontal aluminum bar susper~(lecl from its lower end.
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From page 168... ...
Normally, within the system of the Eotvos torsion balance the level surfaces near each weight are not horizontal with respect to the center of gravity of the balance, and as the only movement that is possible for the weight is horizontal rotation, it tends to fall horizontally through the inclined level surfaces. The distortion of the level surfaces caused by the introduction of a heavy mass such as that of Figure 2 into a gravitational held in which the level surfaces are parallel surfaces, plane or spherical, is twofold.
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From page 169... ...
a, b tic = level surfaces, V1, A, V, V`< = lines of the ~ ertica1 TB\V~Y, = Eotvos balance, TV1 = upper weight, W = lower weight. tional field ire which the level surfaces within the held of' the balance deviate in either or both of' these ways f:'rom parallel and plane or spherical surfaces, the level surfaces in the vicinity of each weight will not be horizontal, and the weights will tend to i'a11 horizontally through the level suri:'aces and therefore to rotate, until the weights are in the lowest level surl'ace touchecl.
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From page 170... ...
3. Blocl: cliagram of space around an Eotvos or Coulomb b;llance ~epre sentin~gr, curvature of the level surfaces.
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From page 171... ...
ALFt and SCOW represent ~spectively, vertic~1 pleaded of m~xT~um divergence RD] of parallelism of the level sUrI~ces; a; t, c; d; e, represent the traces of level surfaces; We level surface c Coincides with the borizont~1 plane thfongh the center of grain of go torsion Balance system; the upper Feint LW ~D]
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From page 172... ...
That portion of the horizontal component of gravity which is a function of the differential warping of the level surfaces can be shown to be a function f(,a`J of the a%imut,h a of the point and of gravity, times the
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From page 173... ...
But within the very small area of an Eotvos or Coulomb balance, the level surfaces approximate closely to surfaces all of whose vertical profiles parallel to the planes of maximum and minimum curvature are small portions of very large circles of either positive or negative curvature. Such surfaces may be small portions of synclastic surfaces, which are small portions of very large ellipsoidal, paraboloidal, hyperboloidal or similar s.ynclastic surfaces; or saddle-shaped, anticlastic surfaces.
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From page 174... ...
~4 FI G URE OF THE EAR TH From the relation of the vertical to a level surface g1 and go are perpendicular to h and k, respectively, and therefore are no longer perpendicular B I've / 1 ~.
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From page 175... ...
aW and bW then will be the components of S and T respect.ively, acting perpendicularly to the balan.ce beam ancl their difference multiplied b~ the distance I and the mass will be the torque F
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From page 176... ...
The terms a U , a U a U and U U often shortened to Ups Ups DxAz ayaz Obey' By- Ox~ ' US and US-UXX or Ups, are the shorthand symbols of calculus for these and two other quantities, to be discussed shortly, U being the Newtonian gravitational potential.
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From page 177... ...
The magnitude and azimuth of the Eotvos curvature value can then be calculated from those quantities by the I'ormul~e of equation ( 8 ~ . The Eotvos torsion balance is a special type of the Coulomb balance if' the assumption is made that within the very small area of the working system of' the Lotvos torsion balance the curvature of' all level surfaces is identical.
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From page 179... ...
As g cos a = :Y,q? ~ q ~ ~ the torsion balance is able to measure the gravity gradient.
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From page 180... ...
=~/U~.~+U'J,,,2' U.~z tan a = U CALCULATION OF THE CURVATURE AND GRADIENT (13) The balance beam of the Mottos torsion balance through its weights is under the influence of the two turning moments, one the horizontal directive force, and the other the horizontal component of gravity varying as the gradient.
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From page 181... ...
In field work with the Eotvos torsion balance, levels are run out to 20, 50, or 100 meters from the instrument, the distance depending on the irregularity and relief of the topography, and the effects on the gradient and differential curvature are calculated by simple tabular forms. In rugged country the ejects of the more distant topography have to be calculated with the help of topographic maps.
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From page 182... ...
For most practical purposes, the ~eciproeal of' the numerical value of' the gradient ill Eotvos units is a, sufficiently close a,pproxin~ation to the radius of curvature of' the vertical in terms of units of ~ x 10i'' em.. and can be obta;.necl without l |
From page 183... ...
The i' orm of' the e quip otent.i al surface ancl the do fleets on of' the verti cat can be calculated, however, i'or all stations of' a torsion balance survey, ii' astronomic-geoclet,ic, measurements of' the deviation of' the vertical have been made for two points with the accompanying determination of' the n~ean curvature of' the level surface between the two points, if' the torsion balance stations are closely spac,ecl, and if the terrain is nearly level. These calculations were worked out by Ec~tvcis~ for his survey with the torsion balance near Aracl in the Hungarian plain in an area now just within the Roun~anian border but are not usually Treacle in connection with torsion balance survey s.
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From page 184... ...
Empirically, the values of' Use, Use, Up, U$y observed in work with the torsion balance ra.n~,e most commonly from ~ to DOxiO-9 dynes per gram per centimeter with a mean maximum value of 15O x 10-9 Jvno~ rear .ornm nor o~ntim~t~r An +h~ All;+ 1 v in-g -- ~-~~~ A -- I -- - rid ~ em ^~ an dynes per '~ram per centi~net.er, was the one used by Baron Eotvos and is the one in common use in torsion balance world today, Schweydar * has suggested that it be called an " Eotvos,'' abbreviated to " E." Although the significance of the R values lies in their indication of the cliffere~:~ce in the curvature of' the level surfaces in the two principal ' W
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From page 185... ...
But as the range of the actual value of the reciprocal of the value of gravity where torsion balance surveys are likely to be made is less than five-tenths of one per cent, as the value of the reciprocal is about 1.02 x 10-3, and as the value of R as observed in the field rarely is significant to within five per cent., the numerical value of R in terms of Eotvos units is the same for most practical purposes as the numerical value of the differential curvature in terms of ~XiO-~0 I
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From page 186... ...
The deviations from a still, homogeneous sphere of' the form and distrihution of mass in the earth that appreciably affect the gradient and curvature values and gravity at the surface May be class;.fiecl in the i'ollowirlg orders of' magnitude: first order, the planetary or " normal " deviation clue to the rotation and the consequent oblate spheroidal i'orm of' the earth; second order, the continental irregularities.; third order, the irregularities due to large mountain systems, such as the Alps or Rocl:.~ Mountains; fourth order, the irregularities due to small mountain masses, such as the Panhanclle graIlit.e ridge of' Texas; fifth order, the irregula-rities clue to salt comes, volcanic necks, ancl such moclerate-sized teleologic structures; sixth order, irregularities due to very local structures such as blurted stream channels, small faults; seventh order, survival irregularities ifs the soil and subsoil; and eighth or: filer, the topographic i rregula.rities.. The to~'ogral~hie irregularities are ~ orrecterl for, atoll the surficial ;r regularities are avoided by judicious ch.o;ce of' station sites, if possible or t}leir ell'ects are minilll;%e(l.
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From page 187... ...
Positive rock masses, whether the upthrow side of' a fault, hoists, or anticlines, tend in `~eneral.to be denser than the normal rocks at the same level. NYhere thick salt masses form the core of' anticlines or of' salt domes, I'ormations older than late Tertiary, the opposite holds true and the positive mass as a whole may tend to be lighter than normal rocl~s at the same level.
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From page 188... ...
. Bestimmung der Gradienten der Schwerkraft und ihrer Niveauflachen mit Hulfe der Drehwage, Verh.
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From page 189... ...
The Eotvos torsion balance method of mapping geologic structure.
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From page 190... ...
Die Genauigkeit der mit der Eotvos'schen Drehwage durchgefuhrten relativen Schwerkraftsmessungen. Geodatische Arbeiten d.
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