Physics of the Earth - II The Figure of the Earth Bulletin of the National Research Council (1931) / Chapter Skim
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Chapter V. Earth Tides
Chapter V. Earth Tides
Pages 68-80
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From page 68... ...
For brevity let us speak of the "solid" earth, meaning thereb:all the rest of the earth except the atmosphere and the hydrosphere, and not thereby denying the possibility that the substance composing the central portions of the earth may in many respects act like a very dense liquid under high pressure.* In addition to the deformation due directly to the action of the tide-producing forces in the " solid '' earth, there are obviously deformations transmitted downward from the surface and caused by the varying, tidal load of the ocean water.
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From page 69... ...
If we disea.rd the simplifying assumption of incompressibility the period is increased by six minutes only for an assumed rigidity equal to that of steel and by a little less for a Breather rigidity. Thus from any point of' view it is clear that the earth has time to adjust itself to the instantaneous field of force of the semidiurnal and diurnal tides and a forttori' to the force-fields of the longperiod tides.
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From page 70... ...
The first premise may be proved mathematically; the second premise seems highly plausible from what we know of materials under stress and at such high t,emperatures as we suppose to prevail within the earth, but it, cannot be asserted as an absolute, demonstrable truth. The mere rotation of the earth would impart an ellipticity equal to 1/~80 to the originally spherical equipotential surfaces surrounding a perfectly rigid sphere of mass equal to that of the earth and having, for the radius of the outer equipotential surface the mean radius of the earth.
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From page 71... ...
It is not intended to imply that it is beyond our mathematical power to dispense with the simplifying assumptions of incompressibility and of uniform density and elasticity; the assumptions underlying the calculation can be brought into closer conformity with the presumed actual conditions prevailing within the earth but only at the expense of an enormous increase ire the mathematical difficulties of the problem, an increase attended by a smaller change in the values of h, and of similar related quantities, than might at first be expected. Herglotz s made computations that allowed for the decrease in density from center to surface; the assumptions of uniform modulus of rigidity and of incompressibility were retained.
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From page 72... ...
W/g from observation and thence we deduce 1+k-h. A determination from the long-period tides was published in Thomson and Tait's Natural Philosophy and in revised form in Sir George Darwin's Collected Scientific Papers.i The observations of lon~-period tides at all available ports gave for 1+7~-h a value a little greater than two-thirds.
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From page 73... ...
This method consists in determining the earth tides by the changes they produce in the direction of the vertical. These changes may be referred to the direction of the earth's axis or to the ground old which the instrument for detecting them rests.
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From page 74... ...
This was interpreted as meaning, that the earth was stiffer in one cl.irectio~n than in another, and various explanations were attempted, all of them more ingenious than satisfying,; Loved showed that the supposed causes of this peculiarity were quantitatively insufficient. The most reasonable explanation is that it is the result of' the secondary effect of the oceanic tides; these latter of course are not in phase with the earth tides nor do they vary with latitude and longitude according, to any simple law.
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From page 75... ...
~ ~s bn~ h~e hundreJ feet lo~g. E~cn vitb this len~T1 tbe line~r displ~cements ~re of conFsc ver~ minute; heing oT tbe order of ~ ver~ Te~ tenthous~ndths of ~n incb.
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From page 76... ...
:~al£ times the theoretical value; at a point in Korea about four times. The opinion has sometimes been expressed that local geological concl.itions may have considerable effect on earth tides; among such conditions are supposed to be the presence of extensive beds of rock near the surface having a modulus of rigidity markedly different from the average and the nearness of faults or volcano vents.
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From page 77... ...
On account of mathematical difficulties and the uncertainty of the data., namely, the ra.~¢,es and lunitida.l intervals in midocean, the calculations were not pushed to a definite numerical conclusion. The value of 1+7e-h is all that observations of earth tides alone will give.
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From page 78... ...
The effect of any change in the direction of the instrument due to a tide in the crust of the earth is removed when the spirit levels of the transit instrument or zenith telescope are read and the proper correction appliecl. However, the smallest angular change that can be detected by an observation for latitude and longitude is much larger than the corresponding quantity in an observation with the horizontal pendulum or the Michelson-Gale apparatus, so that trustworthy conclusions can be derived only from long series of observations.
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From page 79... ...
The photographic observations for the variation of latitude made at Gaithersburg, Maryland, simultaneously with the regular observations of the International Latitude Service have been discussed by Stetson.~5 He finds a lunar effect, that is, an apparent earth tide, much larger than that riven by the visual observations at the same place in the hands of ~ it, ~ ~ ~ 1 ~ · ~ ~ ~ 1 ~1 _ 1~ 1 L:~ Lid ~1 l~rzbyllok. The earth tide iounct by Stetson Is several times that preclicted by theory.
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From page 80... ...
Beobachtungen uber die Deformation des Erdkorpers. Astronomische Nachrichten, 186: 80 (1910)
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