Physics of the Earth - II The Figure of the Earth Bulletin of the National Research Council (1931) / Chapter Skim
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Chapter XVI. The Variation of Latitude
Chapter XVI. The Variation of Latitude
Pages 245-278
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From page 245... ...
J, Yale Observatory, Yale Vniversit? J PRELIMIN A:RY CONSIDERATIONS The astronomical latitude of a place is the angle between the vertical of the place and the plane o:l the equator; or, id: we wish to bring into the definition the earth's axis and its poles, we may say that the colatitude (complement of the latitude or ninety degrees nitrous the latitude)
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From page 246... ...
Nevertheless, this does not imply that continuous and careful observations of latitude might not be useful in detecting or disproving the existence of a suspected crustal creep in regions of seismic activity.! There is another way in which the direction of the vertical may change.
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From page 247... ...
HISTORICAL AND DESCRIPTIVE ACCOUNT Aside from the vague suspicions that beset the early history of every subject of this kind, the first consideration of variations of latitude appeared in 1760 in Euler's mathematical discussion of the problem of ~ A displacement of this sort would change the field of centrifugal force due to the rotation of the earth and hence the direction of the vertical, but if we consider the change in latitude due to a displacement of the axis or of the pole as a small quantity, then the change in latitude for an unyielding earth due to the change in direction of the vertical is at most 1/588 of this small quantity and may generally be neglected. For an elastically yielding earth the effect is only a little greater The term " centrifugal force " is here used, as usual, to denote the force required to balance the l~inetic reaction to rotation, or Muir.
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From page 248... ...
In an absolutely rigid body the positiol1 of the axis of figure is of course fixed in the body, but is not necessarily fixed in space. There is, however, an axis the direction of which, apart from external forces, is fixed in space.
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From page 249... ...
tboorctic~lly continue indchnitcly, since no account is take of friction in this acorn. Aatrono~crs dig not tbink it p~ot~blc Ant them could romain any EUlcrinn nutrition of large amplitude continuing from the ore ~ some c~t~atropbe in geologic~1 Sac and not act Jumpy out t friction~I rcsist~nces, hut they dig think it possible abut cb~nges in the Cam> CTUSt dUC to cs~tb~kea or caste mo~cmcn~ of over BOltS might produce from time to Sac ~n EUlcri~n nutrition not too smog to tic ictcCtc]
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From page 250... ...
This announcement at once awoke the liveliest interest, and the matter was promptly talker up by the International Geodetic Association Observations were set on foot at Berlin, Prague, Stra.ssburg, and Potsdam, and these showed art agreement that left few doubting the reality of latitude variations. There were a few, however.
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From page 251... ...
Abet it does can be Roan Ace Imply Cow the following con~dCr~tioD: Imaging the earn to be ~ bomogeneous Typhoid, entirely covered by an occaD of .tbc same density limb itsclL It is then evident that, if the Bole mass he set in uniform rotation monad ~ axis Whither, the ocean ~1 Bums the form of AD obl~t~elipsoid of revolution, Bose Sadler axis coincides vita that of rot~hon. Back the ages ~ rotation Ed of figure ~1 be in poem coincidence under 3~_.
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From page 252... ...
Hence the angular motion as seen from P is less than that from P' in the ratio of P'R: PR. Belt as R rotates, P' continually changes its position and rotates also, remaining on the straight line PR.
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From page 253... ...
This, bo~evcr, is not ~h~t is ~C~Dt. Ibc yieldisg is to be t~[cn ~s el~stic, th~t i~ proportion~I to tbe force urd not incre~ing ~itb thc ti~c, ~ccpt for thc yieldin)
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From page 254... ...
NYhen Taloott's method is used, this is possible only when the observatories have practically the same latitude. The conference of the International Geodetic Association held at Berlin in 189.~ began the world of or~ani%in, the International Latitude Service.
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From page 255... ...
During the World War they were operated under the auspices of a Reduced Geodetic Association among, Neutral Factions, organized to keep geodesy, as an essentially international science, alive during the conflict, and more particularly for the purpose of operating, the international latitude stations. This organization continued until 1922, when the latitude work betas taken over by the International Astronomica1 IJnion and by the Section of Geodesy of the International Geodetic and Geophysical Union, both organized after the war.
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From page 256... ...
i' tiny circles without attached numerals inclicate positions at intervals of 0.1 year. The whole number of elapsed years may be found by counting, forward or back along, the lull line, which gives the path of the pole of rotation.
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From page 257... ...
Ibe gr~JU~1 increase add decrease of the r~Jius-vector are Mite cb~r~teristic of the pa~ actually observed. If the undisturbed pole of inertia goes not start out in coincidence with the inst~nt~ncous pole of rotations me ~ get instead of CUSPS either open concavities or closed loops; according to the initi~1 condihons as sbov~ in Figure 3.
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From page 258... ...
The loan numerals correspond to twelfths of a year or approximately to elapsed months, the position XII representing, January i, and ~ about February 1. The smaller ellipse inside represents the !
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From page 259... ...
VAI:? IATIOiV OF LATITUDE 2~9 period is greatly magnified.
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From page 260... ...
2 60 FI GURE OF THE EAR TH t.ions from non-seasonal non-climatic causes, and of these more will be said hereafter. Attempts to evaluate a priory the effects of seasonal causes in displacing the pole of' figure and thence to deduce the motion of the pole of' rotation have been made by Spitaler, Jerseys, Schweydar, and Rosenhead.
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From page 261... ...
of the polar motion thus dedu.cecl ~ priory with the actually- observed notion is as good as could be expected in view of the uncertainty of the cla.t.a. Thus far we have discussed only the annual component of the polar emotion.
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From page 262... ...
8. Annual component of the Polar motion, 1900-1911.
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From page 263... ...
Die Chandlersche und die Newcombsche Periode der Polbewegung. Zentralbureau der International Erdmessung.
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From page 264... ...
Even apart from the inevitable but not :-et quantitatively determineLl damping, out due to friction, the I'ourteen-month motion is variable in phase and also in an~plitude because something,, or ~ variety of' thins, disturbs it, just as the motion of' a pendulums swint,in~ on a ship at sea is subject to irregular disturbances by the shoals to which the vessel is subjected through the action of' wind and wave. The a.nnua.1 motion is variable because in the first place the cause is seasona1~.~1 meteorological ancl each year differs somewhat front every other, and in tl~e second because the irregular perturbations of' the l'ourteen-mouthly motion affect the annual motion also.' The causes of these perturbations, other than those that Plight be termed met.eorolo`~ical, are something, of' a mystery.
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From page 265... ...
There is now fairly clear evidence that there are irregularities in the rate of rotation of the earth * and the only plausible expla.nation is that the earth's moment of Inertia about It's axis of rotation is chan~,in~, since it' the angular velocity of rotation is chan,~,ed, the moment off inertia, must change in the opposite direction in order that the an¢,ula.r momentum mar remain constant This change in the monument of inertia means ail effective shrinking, or swelling, of the earth.
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From page 266... ...
266 FI GURE OF THE EAR TH that in recent geologic time coverecl Scandinavia and Northern Germany and in North America came down to the latitude of New York City ancl below, are evidences that chances in climate have been both great and widespread. 01 course, if the pole approaches any given region, thereby giving it presumably a colder climate, it recedes from a region in the same hemisphere but clifferin3 180° in lon~,it.ude, thereby placing, the latter region nearer the equator.
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From page 267... ...
_ · ~ The effect of the error i s ~ ,, ~ There is but little adequate and direct evidence from astronomic al observations bearing on the question of a secular shi:ftin~, of the pole. Since the days when accurate astronomical observations began to be made there have been apparent changes in latitude at various observatories when redetermina.tions have been made; these chances are in general only a few tenths of a seconcl.
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From page 268... ...
~n] tbe free motions, b~9e been dedUre]
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From page 269... ...
FJ~IZO~ OF [~7~E 2G9 of the pole of Ague ty amounts by no Glenda in~precT~ble in comparison with twos that bare been discussed. But the periods of the tiff forces that Erect the position of die Pole of figure are so swat that the erect on the position of the pole of rotation is negligible.
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From page 270... ...
Nevertheless the statement that the earth is on the average about twice as rigid as steel is as satisfactory a brief statement as can be made at present. What the latitude observations really determine is not a.
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From page 271... ...
VARIATION OF LATITUDE 271 where r is the distance of the point in question, a is the radius of the earth treated as a sphere and S is a surface spherical harmonic of the second degree; in the present problem the harmonic is of special type but the idea behind the definition of 7c allows any surface spherical harmonic of degree two to be used.
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From page 272... ...
The radius of this core is more than bolt the radius of To earth. Outside of this liquid or nearly liquid core comas Solid matter decreasing in density and rigidity as the surf~cc is ~ppro~bed.
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From page 273... ...
results are somewhat puzzling. The explanation may lie partly in the enclosed character of the Baltic, which is almost an inland lake, for the levels of tide stations on the North Sea conformed more nearly to the statical law, partly in the smallness of the quantities dealt with, and partly in the fact that changes of sea-level, whether due to meteorological or climatic causes or to small hypothetical changes in the Pure of the earth, are themselves causes in some degree of the variation of latitude.
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From page 274... ...
regions Scar lines or center of seismic activity. [or determining carte movements of this sort, latitude otser~tions cannot compete in ~ccUT~cy with good geodetic surveys of the region in question repeated at suitable intervals provided gusts abut the survey can Start from ~ line far enough Achy from the suspected region to he considered as stable.
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From page 275... ...
to eliminate systematic errors in star places. It is easy to see now tat insufficient prcc~utio~s were t~kcn fly earlier observers with tab meridian circle ~]
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From page 276... ...
Schlesinger bus also suggested that ordinary l~titnie observations such as brave been carried OUt for example, iD CoDDOCtIoD with the geodetic surveys of the Baited States RD] magi, mi~bt he re _ ~ ~ ~ petted with the oxpect~tioU of delving Irom them much v~lu~hle inform~tio~ as to the proper motions of the stars concerned.
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From page 277... ...
Geopb~sic~1 Anion ~itb Kimul~ ~ cab. Its reports of ~ fen gages act, gem the title ~ [rQ`ision~I Besults of the MOTH of the Intern~tio~1 Latitude Scrvice In the born gel 39° 8' for the period ....
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