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CHAPTER VII ISOSTASY WILLLIAM BO,WIE U. S. Coast and Geodetic Survey The outer Abortion off-' the earth rests on the material of' the interior :n a condition of' equilibrium which, presumably, is only disturbed by the shiftings, of loads over the earth's surface. This condition of equilib- ri-un~ is tenanted " isostasy." The word is derived from Greek words which may be considered to mean " equal standing " or " equal pressure." The outer portion of' the earth is generally called the crust. It has been found by geodetic investigations to extend to a depth of' approximately 60 miles below sea-level. In this outer shell-are materials of different densities at different places. The higher the ground the less is the density of the material below, and the lower the solid surface of' the earth, the greater is the density of' the crustal material underneath. According, to the principle of isostasy, if' the earth's crust were cut into prisms of the same cross section by imaginary vertical planes the prisms would have the same Glass if the isostatic condition were perfect. This means that the pressure exerted by these prisms on the subcrustal material at the depth of' (40 miles below sea-level would be uniform throughout. It is inconceivable that these prisms could have a very small cross section, say one mile square or ten miles square. One of' the outstanding problems in geodesy is to (letermine the cross section of' the imaginary prisms of the earth's crust which might be independently in isostatic equilibrium. Investigations carriecl on up to this time have led one to the belief that the cross section of' the prism would be of the order of' magnitude of 50 to 100 miles square. It is possible that the cross section is somewhat smaller than o0 miles square but there seems to be no letdown method by which this matter may be tested. There must be change in the physical characteristics of the earth's material as we pass from the outer shell to the suberustal material. The geodetic data have shown conclusively that the heterogeneous densities existing, in the crust extend to approximately the 60-mile depth. Below that depth any layer of material extending, around the earth should have uniform density, and it is likely that this condition applies to all other i~na:,inary layers of' materials down to the center of' the earth. The 103

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104 FI G URE 0113 THE EAR TH subcrustal material must be plastic to long continued stresses. It acts as if the materal has no residual rigidity. On the other hand, the ma- terial of the crust has residual rigidity and can maintain a very irregular surface. The highest point of land is Mt. Everest, in the Himalayan Mountains, which is 29,141 feet in elevation. The greatest known depression of the earth's surface occurs in the Planet Deep, just to the eastward of the island of ~indanao of the Philippine Archipelago. The Ernden, a vessel of the German Navy, using the sonic method, obtained a depth of 10,?03 meters, which is equivalent to 5,902 fathoms or 3d,410 feet. The greatest known difference of elevation is, therefore, 64,501 feet, more than 12 miles. This great difference does not truly represent the stress difference that might exist between two prisms of the earth's crust, one under the Himalayan Mountains and the other under the Planet Deep, for the weight of water in the latter case must be talker into account. But if we assume that the weight of the water is equivalent to approximately two miles of normal surface material, the stress difference between the Planet Deep and the highest part of the Himalayan Mountains would be equivalent to the weight of about ten miles of rock. It is well known that there is no earth material that could withstand crushing under such a great weight, and, by inference, the material at the base of the earth's crust could not maintain such great stress differ- ences as would exist if all the crustal material had a uniform density. This is corroborative evidence in favor of the existence of the isostatic condition of the earth's crust, a condition that calls for material in different places varying in density with the elevation of the surface above. The data secured from observations for the variation of latitude, earth and ocean tides, and the transmission of seismic waves indicate that the earth is either solid throughout with the rigidity of steel, or that it is solid to a distance approximately 2,000 miles below sea-level, with the solid portion having a rigidity greater than that of steel. This seems to indicate a contradiction between isostasy and geophysical data. This, however, cannot be, for isostasy certainly exists, and, besides, there are many substances which are solid and resist deformation when stresses less than the elastic limit are applied for a short time but which will yield without fracturing when stresses much smaller than the elastic limit are applied for long periods of time. Since the earth's crust is in isostatic equilibrium to a very marked clegree, it is reasonable to assume that this condition has obtained in the past and that it will continue in the geological future. The proof of isostasy furnishes evidence regarding at least the outer portion of the earth which should be of value to the geophysicist and to the geologist

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ISOSTASY 105 in their studies of' the physical properties of' the earth and in the effort to interpret geological history. There are enormous loads shifted over the earth's surface as a result of' rainfall, erosion, and the transportation of material to tide water. This shi]:'tin~, of' load disturbs the equilibrium of the earth's crust. There is downwarping of' those areas which receive great beds of sediments, and upward movement of' those areas from which material is removed. The sinking and rising could only occur as a result of horizontal move- ment of material in subcrustal space. This transfer could not occur above the lower limit of' the crust, for the stress difference is from the hitcher area towards the lower one until the bottom of the crust has been reached. The isostatic condition of the earth's crust has been proved to be true by the work of the ,eodesist, although isostasy is fundamentally a geolog;.- cal subject. The principal work of the geodesist is the determination of' the figure of the earth. The share and size may be determined from triangulation and astronomical observations for latitude and longitude; the shape may be determined from observed values of the earth's attraction or gravity. The father of isostasy is generally recognized to be George B. Airy, at one time Astronomer Royal, Greenwich Observatory, England, who on February 1b, 18~D, delivered a paper ~ before the Royal Society of London, in which he gave an explanation of the apparent deficiency in the attraction of mountain masses on the direction of gravity to which the astronomical observations are referred. On December 7, 1854, an extensive reporter by John Henry Pratt, Archdeacon of Calcutta, was read at a meeting of' the Royal Society of London. Pratt,.in attempting to determine the figure of the earth from triangulation and connected astronomical stations in India found that, in his judgment, the arc of meridian in India was quite different from that derived by Colonel Everest for ~ whole quadrant of the meridian. Pratt had applied corrections to the astronomical latitudes in order to take into account the attraction of the nearby mountain masses. He realized that he had not advanced a wholly satisfactory hypothesis as to the geodetic and astronomical data of India for he closed his paper by saying: " The whole subject, however, deserves careful examination as no anomaly should, if' possible, remain unexplained in a work conducted with such care, labor and ability as the measurment of the Indian arc has exhibited." Airy in his paper re-l'erred to the one by Pratt and then proceeded to set forth his views as to how the anomalies, or unexplained differences be- tween the latitudes bv astronomical observat~iolls and by triangulation, could best be interpreted. He says, in part: I conceive that there can be no other support [for mountains and table-lands] than that arising from the downward projection of a portion of the earth's light

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106 FI CURE OF THE EAR TH crust into the dense lava; the horizontal extent of. that projection corresponding rudely with the horizontal extent of the table-land, and the depth of its projec- tion downward being such that the increased power of flotation thus gained is roughly equal to the increase of weight above. from the prominence of the table- la.nd. It appears to me that the state of the earth's crust lying upon the lava may be compared with perfect correctness to the state of a raft of timber floating upon water; in which, if we remark one log whose upper surface floats much higher than the upper surfaces of the others, we are certain that its lower sur- face lies deeper in the water than the lower surfaces of the others. It would appear from the above quotation, that Airy had the idea that the higher the elevation of a portion of the earth's surface the deeper would the crustal material extend into the subcrustal space. Airy had loo definite opinion as to the condition of the suberust.al material since lie said that the fluidity of the ~nat.eria1 below the crust must be very imperfect and, in fact, might be mere viscidity. FIe claimed that it night be even little more than that degree of yielding which shows itself lay cha.~,es in the floors of sul~terra~.eous chambers at a great deftly below the surface in mines.. I-Ie said, however, that in order to present his ideas in the clearest borne he would suppose the interior of the earth to be perfectly fluid. It was more than three years after Airy advanced his hypothesis that Pratt presented his paper in which, referring to Airy's hypothesis, he advanced his own views as to the equilibrium of the earth. In that paper i4 he said: The Astronomer Royal (Airy), ire ~ paper published in the Transactions for 1855, suggested that immediately beneath the mountain-mass there was most probably a deficiency of matter, which would produce, as it were. a negative .~ttr;lctIon, and so counteract the effect on the plumb-line. Pratt, re:ferrill~ to Airy's views, makes the statement that., in his jud~- ment, Airy's hypothesis is untenable. The principal reason for differing with him is stated as follows: The same reasoning by which Mr. Airy makes it appear that every protuberance outside this thin crust must be accompanied by a protuberance inside, down into the fluid mass, would equally pros e that wherever there was a hollow, as in deep seas, in the outward surface, there must be one also in the inner surface of the crust corresponding to it; thus leading to a law of va.ryi:~g thickness which no process of cooling could have produced. However, he gave credit to Airy for first making the suggestion that there is a deficiency of material below elevated portions of the earth's surface, which also is the basis of the alternate hypothesis proposed by Pratt. Pratt first fourld: It is nevertheless to this source I mean a Deficiency of Matter below that He must fool<, I feel fully assured, for a compensating cause, if any is to be ford.

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ISOSTASY 107 My present object is to propose another hypothesis regarding deficiency of matter below the mountain-mass, as first suggested by Mr. Airy; and to reduce my hypothesis to the test of calculation. Pratt then outlines, in a rather indefinite way, his views that the crust of the earth resulted from a cooling of the outer portion of a liquid earth and that the difference in the amount of contraction of the different parts of the earth's material had caused an irregular surface. In a later paper, read before the Royal Society of Londoll on December 22, INTO, he out- lined his hypothesis more definitely, as is indicated by the following quotation: A few years ago I proposed the following hypothesis regarding the Constitu- tion of the Earth's Solid Crust, viz.: that the variety we see in the elevation and depression of the earth's surface, in mot.tntains and plains and ocean-beds. has arisen from the mass having contracted unequally in becoming solid from ~ fluid or semifluid condition: and that below the sea-level under mountains en cl plains there is ~ deficiency of matter, approximately equal in amount to the mass above sea-level; and that below ocean-beds there is an excess of matter, approximately equal to the deficiency in the ocean when compared with rock; so that the amount of matter in any vertical column drawn frown the surface to ~ level surface below the crust is now, and ever has been. approximately the same in every part of the earth. In a footnote to this article, Pratt says " Or. Niry was flee first to s-uo~,est in Phil. Trans. 1855, p. 101, a deficiency of matter below moun- tai~ regions." iVe have here a definite statement by Pratt that Airy was the real father of the hypothesis which was later developed into the principle of isostasy. TVe may sum up the hypotheses of Pratt and Airy by saying that Airy held to the idea of an earth's crust with varying thicknesses, the thicken- int, varying directly as the elevation of the surface, and that Pratt., on the other hand, held to the idea of a crust of uniform depth with densities varying, inversely as the elevation of the earth's surface. In his hypothesis as to the geological process by which the earth's surface became irregular, Pratt sug,estecl that the differences in the density of the crustal material were due to the non-unifor~ity in the contraction with cooling. This idea has now been abandoned, for the ana.l:-ses off- igneous rocks found on oceanic islands and on the continents i~.~clicate that the heavier elements are present in greater proportion in the rocks of the oceanic areas than in the continental areas. This leads to the definite conclusion that there is a fundamental difference in density due to the chemical composition of the rocks that causes a difference in the density of the suboceanic alla subcontinental crustal material. The cause of this difference in density is not known, but undoubtedly it resulted :tro~l1 the process by wl~;cl-~ the oceans and continents were formed.

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108 FIGURE OF THE EARTH The idea of a crust resting on plastic matter met much OppOSitiOl1 by the advocates of the theory that the earth's material is very strong, and can withstand the great stress differences that would be caused by masses such as continents, mountains and plateaus. After long argument and discussion of its merits and demerits, the equilibrium or isostatic theory has now been generally accepted as a scientific fact, or principle. The general acceptance of isostasy may be said to be due to the investi- gations made by members of the U. S. Coast and Geodetic Survey, in which the deflection of the vertical and gravity data were used. Much has been done by others in this country and in other countries in the isostatic field. The numbers of books and papers dealing with or referring to isostasy have reached large proportions. The first comprehensive isost.atic investigations were in connect.io~ with the determination of the shape and size of the earth by means of triangulation and astronomical Ula.ta, in the U:~itecl States. It was. :I-'oun~l that at the triangulation stations there were differences between the latitudes, longitudes and azimuths determined by triangulation and by astronomical methods. It was assumed that the isostatic condition of the earth's crust is perfect and confutations based on that hypothesis were made of the effect of land and water masses and of their compensa- t.ion on the astronomical data. Computations were made on the basis of a distribution of the isostatic compensation to various sleuths extending from the surface down to approximately 20V miles. It was found that at the depth of 120.2 kills. below sea-level the astronomical and tria.n~u- lation latitudes and longitudes were brought into the closest agreement. It was therefore concluded that that depth was the most probable one as the limit for crustal material. Gravity values were also used in testing the isostatic condition of the earth's crust, and it has been found that the results are in complete a~ree- n~ent with those obtained from triangulation and astronomical data. The depth of compensation now considered to be the most reliable is 96 kilo- meters or about 60 miles. This value was derived :from gravity and deflection data in the elevated parts of the United States. Gravity observations have been made at many places in the IJnited States, Canada, India, a number of the countries of' Europe, Japan, Mexico. and some other countries, and on a number of' oceanic islands. In recent years observations have been made even over the oceans. W'here- ever the isostatic principle has been applied to the gravity data the ob- served values of gravity, except for certain restricted areas, agree very closely with the theoretical values. The c om.putations and map reading connected with the isostatic reduc- tio~s Fan ity data anal the deflections of' the vertical are quite laborious. .. . . . .

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ISOSTASY 109 In order to facilitate that part of the world certain assumptions had to be made. They are: ~ ~ That the isostatic compensation of topographic features is complete; 2) That the compensation is distributed uniformly with depth directly beneath the topographic features; 3) That the compensation extends to a uniform depth below sea-level; 4) That the material above sea-level has a density of 2.~7 and that the deficiency of mass in tidal waters is 1.65. The investigators realized that none of these assumptions is exactly true but they believed that the outstanding differences between the observed and the theoretical values of' gravity and the deflections of' the vertical would be a measure of the degree to which the actual conditions deviate from the assumed ideal ones. There is marked uniformity in the results of' the isostatic investi`~,a- tions made for different portions of' the land areas of' the world and also over some portions of the oceans. It is therefore apparent that isostasy exists in all portions of the earth and not merely under the United States, where the early tests were made. There is no working in a circle; the principle is of general application. In order that the investigations might be carried out, tables were com- puted i'or use in connection with the reading from maps and charts of' the elevations for land areas, and of the depths for water areas. The whole earth's surface was divided into zones to facilitate the readings of elevations and depths. In order to secure a high degree of accuracy in the computed topographic effects on the value of gravity the zones close to the gravity station have very small radii. The zones widen out as the distance increases from the station, since the attraction of the masses varies inversely as the square of the distance, and for any given mass its effect on the value of gravity decreases rapidly with the distance away. In making the isostatic reductions for the gravity stations it is not necessary to read the maps and charts all around the earth for each one of! the stations. After they have been read for the whole world for three or more stations for any given limited area, then for the intermediate stations values for the effect of topography and compensation in the outer zones can be interpolated from the completed stations. The closer the stations are together the less per station is the work involved in the map and chart reading. In the isostatic investigations, factors are used to determine the effect of compensation distributed to various depths. As was mentioned earlier, the most probable depth of' the earth's crust, determined from deflection of' the Vertical and gravity data, is 96 lams. It seems probable that l'uture

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110 FIGURE OF THE EARTH values of the depth of the earth's crust, based on many more data than have already been used, will lie between 80 and 110 kms. In the isostatic investigations made at the Coast and Geodetic Survey-, it was assumed that the Pratt idea of isostasy is the correct one. That, act will be recalled, postulates varying, densities of crustal material with a. rather uniform depth to which this heterogeneous material extends. There has been much discussion as to whether the Pratt or the Airy hypothesis is the correct one but, up to the present time, no conclusive ~vid~ne.e is; available. It may be that the matter will have to be settler! ~ P ~ 1 _ _~ 1 ~ 1 ~ __ 71 ~ ~ ~1~ ; ^m 1 ~L ~ O ^o ^f +L ~ by a consideration of the geopr-lyslca1 alla geoc~le~llc~1 Ala U1 b11 problem. The radii of the inner zones are made small in order that the topo- graphic effects, computed I'rom the average elevations for a zone or a compartment of a zone, may not be subject to errors which would appreciably affect the r eductions. ~ See Special Publication No. 10, IJ. S. Coast and Geodetic Survey.) It should not be assumed that the investigators who prepared the reduction tables believed that a topo- ~,raphic feature, a small Mueller of' meters in horizontal diameter, is compensated I'or in a very narrow prism extending some 60 miles below sea-level. One entry of the tables with the elevation of the zone or compartment males it possible to quickly obtain the value of the topo- graphic and compensation effects. It is most improbable that a topographic -E'eature one Utile square or even ten miles square in horizontal extent is inclepenclentlv co~npensatecl. Some tests of' a limited nature have been made to learn the extent to which the compensation of' a topographic :feature may extend horizontally. No conclusive results were obtained. This is due to the fact that the effect on the value of' gravity of the compensation of topographic features is exceedingly small for the inner zones and is about the same in amount when distributed }~orizontallv out to some clistar~ce -i'rom the features. ., There are probably several causes o-E a gravity anomaly and it is exceed- i~lLgly difficult or perhaps impossible to detern~il:le accurately the effect of eacl~ of' them. This question is of importance only as a detail of the large general problems of' isostasy. After applying, the isostatic principle to deflections o-I' the vertical ancl values of' gravity, there will still be outstanding, differences called residuals or anomalies. The gravity anomaly is the difference between the observed value of gravity and the value computed according, to a definite method. The isostatic anomaly is the difference that is found when the principle of isostasy is applied in obtainin, the computed value of' gravity. For some large areas of the country the isostatic anomalies are very small, but for other parts the anomaly changes greatly between

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ISOSTASY stations that are con~parat.ively close together. The a~-~.o~naly would seem to be a measure of the degree to which the ideal conditions assumed by met.hocl deviate front the true conclitions. The attraction of a love- of rock 30 -feet in th.;c:L::r~ess anal 2.6rY ifs ,, density is 0.001 dynes Should the layer be of-' <~oat horizontal extent the effect is the since on a Pendulum placed at rI;ff'erent distances above the ~-natexial. A~ a,~:~aly of' -~().()~0 dyne ulna therefore indicate the presence of aft extra mass Lea the station equ.;~alent to a layer o:t' rocl: 1,500 feet in thickness. In makir~g isostatic reductions we assume that A` h topographic :f'eature is. balanced by a deficiency of excess of materiel `:lirectly beneath it, that the increase in density along all radii is the salve, except as modified by the isostatic compensation, that the compensation is complete, and that the density of the land topography is 2.(;: while the deficiency of density for tidal waters is 1.~. lye know that there are variations i'rom each of:' these conditions at different gravity stations It is remarkable, however, that the isostatic anomalies without reboard to sign average less than 0.020 dyne for North America while for Europe and Asia, as far as is known, the average gravity anomaly is not greater than 0.020. On oceanic islands, however, the isostatic anomaly is considerably more than it is for continental areas. G cavity stations at sea, established by 1)~. F. A. Venial, 3Teines% on various submarines, have isostatic anomalies that tend to be strongly positive. The average anomaly with regarcl to sign for a continent may stand out as positive or negative. This may be due to an erroneous value for the base gravity station to which all field stations are referred or to erroneous values for the constants in the gravity formula. In general it has been found that, for continental stations, a large Positive or negative anomaly is due to very local causes which exist in the outer portion of the crust near the stations involved. This has been definitely proved by having additional observations made around each of a number of stations which have lar,,e gravity anomalies. In each case the surrounding stations have shown smaller and, in most cases, much smaller anomalies than the station that was being tested. There is only one extensive region of persistent positive anomalies for the United States and that is in the western part of the Dakotas, eastern Montana and eastern Wyoming. It is rather noteworthy that this positive area in the United States has been found to extend over into the plains of Canada. It is difficult to understand why this region is so decidedly positive. Perhaps it may be merely accidental and due to the location of the gravity stations now existing on structural anticlines which have been found to be positive in practically every case, or it is possible that this 8

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112 FIGURE OF THE EAR TH region represents a portion of the earth's surface which is not. in isostatic equilibrium. Further tests should be made to try to discover the real cause of the persistent character of the anomalies. On oceanic islands the cause of the lar~,e anomalies may be due to three things. First, the depression o:l the geoi.cl below the spheroid which places the station closer to the center of attraction of the earth than are stations n the same latituJ.e on continents; seconUl.l~y, most of the oceanic islands are volcanic in character and perhaps the density of the material of the island, the platform on which it rests, and. the crust i.~nmedi.atel;y beneath allay be greater than normal; alla tl.~i.rd].y, ~ lacl; of equilibrium -for the local area.. It is believed that, at least for continental stations, a large positive anomaly is due to heaver material very close, horizontal!: and vertically, to the gravity station, and, conversely-, a large negative anomaly is due to material near the station that is lighter than Cornball It is rather significant that wherever any stations are t,roupecl ire ~ small area these are found to be many irregularities in the curves clra.wn to represent the gravity anomalies. If we could discover the exact distribution of densities from the earth's surface down to the depth of compensation, approximately 60 miles below sea-level, corrections could be applied to the computed value which would make it agree almost exactly with the observed value. It is believed bit many that the ~,ravity pendulum can be used success- fully in discovering the presence of, and in outlinin,, the buried structure. If this should prove to be true it would be another geophysical method for exploring for oil and minerals. Definitions of terms used and a short list of references follow. GLOSSARY ASTRONOMICAL Post. The latitude and longitude of a point on the earth's surface as determined by observations on the stars. The latitude is the angle be- tsseen the plumb line at the point and the plane of the earths equator. The longitude is the angle beween two planes containing the earths axis, one of which contains the plumb line at the station and the other the plumb line at some initial station usually Greenwich. DEFLECTION OF THE VERTICAL. The angular difference between the direction of the plumb line at a point on the earth's surface and the normal to the adopted spheroid of reference at that point. The deflection is usually given by its trio components, one in the meridian and the other in the prime vertical. D.EPTH OF COMPENSATION. The depth below sea-level to which the compensa- tion extends. According to the Pratt hypothesis, the depth of compensation is uniform. By the Airy hypothesis. the depth varies from place to place, being greatest under the highest mountains and smallest under the deepest beds of the oceans.

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110 EARIO ~ CR1TST.-ThE outer layer Off the soLd earth within whim surface i~egu- l~Hi~ are compensated by deviations from norm~1 densities of the m~ed~1 below. [UNSTICK term applied to uDy substance which odors res~t~Dce to forces that tend to deform it and which resumes its oh~iD~1 form Then the forces cease, pro- vided the latter are within the elastic limit. FIGURE OF TUE [ARTU~LD defining elements of the muthematicuI surface which approximates the ~eoidu1 surface. The Share of the Crib has bean proved to be pproxim~t~y an ablate amberoid. GEODESY. That branch of Science which deals with the determination of the shape add size of the earth, and Huh Surveys in ~bicb the shape and size of the eurtb must he taken into consideration. GEODESIC FOSITIO~hO lut~ude and 1oD~iblde of ~ point OD the earthy ~lr- fuce referred to an adopted Spheroid of reference. Ceodetic positions are de- termined hy triangulation from an iniHu1 Cation whose position bus been ~rbi- tr~rdy adopted after ~ consideration of ~stronomic~1 data. CHOIR. An eglEpoteDtiu1 surface coinciding with the surface of the maters of the ocean, if they were free from the periodic disturbing ejects of the sun and moon, the mind, the varying b~ronletric pressure, and differences of temperature Aid density of the Hater. Adder land areas tbe Redid surface is abut ~bicb would coincide gab the Hater surfaces in narrow se~-leveI canals if they were o~tcnded inland through the continents CREMATION. The attractive eject of HI bodies or purticIes for each other. GRAVITY. Tbe resultant erect of the e~rtb's gravitation add the centrKug~ force due to the eurtb's rotation. Angie A~o~^LY~be disgrace baleen the observed and tbeor~1 vaults of Fruity at ~ pant. Tbe theoretic value is obtunded by taking Count of the latitude add elevation of the station, and, in the iso~t~tic m~bod, by further taking into consideration the ejects of the topography of the bole eurtb add As is6st~tic compensation. Isos~^~1c ADJ~s~ExT.~be movement, mostly vertical of sections of the e~rth's crust and the movement, mostly borizoDt~t of subcrUst~1 m~t~i~1 neces- s~ry to balance the loading and unloading of the e~rtb's surface by erosion and sedim~t~ti~. ISOS=T1C COMPENSATION. A deficiency of mass under land areas and in excess of mass adder oceans. Tbe i~o~tutic compensation is in the crust of the Crib below se~-level and is assumed to equal the mass of the topographic features. ISOSI^TIC EQUILIBRIA. Ibe condition of rest Flab the outer materials of the Crib tend to Require. Tbe equibbIium is bct~een the crust and the suh- crustu1 ~uteri~1 and Dot vitbin the crust itselL It is bused on the idea that the 1nuss of each unit section of the earth' Hurt exerts the same pressure OD the sub- cru~1 matehul. PLASTIC.- A term applied to m~teria1 ~bicb may brave rigidity under ~ su~- ciently smog stress and ~y break if the stress is beyond ~ certain limit yet Blob may be distorted Abbott fracturing by ~ Cress within the rupture Wait acting for ~ su~cieDtly TODD time. PRIME VE~lIc^.-Tbe great cycle, parsing through ~ poiDt OD the ebb s sur- f~ce, ~bicb is per~^dicul~r to the horizon add the meridian. RESIDUAL DEFLECTION. Tbe uDexpl~iDed difference between the direction of gravity and the normal to the spberoid best representing the figure of the eurtb,

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~4 FIGURE OF THE EAR TH after corrections for the effect of topography and compensation have been applied to the former. It is usually specified by its components in the meridian and in the prime vertical. RESIDUAL RIGIDITY. That property of ~ate~ial which enables it to maintain its form under stresses which act for ~ long tine but are within the elastic limit of the material. SPHEROID.-An ellipsoid of revolution with its minor axis parallel with the axis of rotation and having dimensions so chosen as to approximate the earth as a whole, or so as to make a small portion coincide as nearly as possible with the corresponding portion of the geoid belonging to a particular region. TOPOGRAPHY. The masses above sea-level of continents and islands and the deficiency of mass in spaces occupied by the waters of oceans, seas and gulfs. TRIANGULATION. A method for determining r elative geographic positions. It . .. .. . . ~ .. . . ~ ~ ~ _1 1 1_ involves the direct measurement of the length of one or more lines anct the measurement of the angles of <~ system of triangles of which the measured bases form occasional sides. REFEREA-CES 1. Airy, George B. On the computation of the effect of the attraction of moun- tain masses as disturbing the apparent astronomical latitude of stations in geodetic surveys. Roy. Soc., Phil. Trans. 145:101-104 (1855); Roy. Astron. Soc., Mo. Notices 16: 42-43 (1855-56). 2. Bowie, William. Investigations of gravity and isostasy. U. S. Coast and Geodetic Survey Spec. Pub. No. 40:1-196 (1917). 3. . Isostatic investigations and data for grravity stations in the United States established since 1915. U. S. Coast and Geodetic Survey Spec. Pub. No. 99: l-91 (1924). 4.- . Isostasy. E. P. Dutton Co., New York. p. 1-275 (1927). 5. Burr ard, S. G. Investigations of isostasy in Himalayan and neighboring regions. Survey of India Prof. Paper No. 17:1-38 (1918). 6. Hayford, John F. The figure of the earth and isostasy from measurements in the United States. U. S. Coast and Geodetic Survey' p. 1-78 (1909). 7. . Supplementary investigation in 1909 of the figure of the earth and isostasy. U. S. Coast and Geodetic Survey, p. 1-80 (1910). S. . and Bowie, William. The effect of topography and isostatic compensa tion upon the intensity of gravity. U. S. Coast and Geodetic Survey Spec. Pub. No. 10: 1-132 (1912) . 9. Heiskanen, W. Untersuchungen uber Schwerl~raft und Isostasie. Veroffentl. Finnischen geodatischen Instituts, No. 4: 1-96 (1924). 10. Jeffreys, Harold. The earth, its origin, history and physical constitution (arm ea.) Cambridge (Eng.) Univ. Press. p. 1-278 (1929). 11. Miller, A. H. Gravity in western Canada. Pubs. of the Dominion Observatory, VIII, No. 9: 245-329 (1929) . 12. Nansen, Fridtjof. The strandflat and isostasy. I komr~ission hos Jacof, Dybwad. Oslo. p. 1-313 (1922). 12a. The Earth's crust, its surface-forms, and isostatic adjustment. Oslo. p. 1-116 (19~28) . 13. Pratt, John Henry. On the attraction of the Himalaya Mountains and of the elevated regions beyond them upon the plumb-line in India. Roy. Soc., Phil. Trans. 145: 53-100 (1855).

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ISOSTASY 115 14. Pratt, John Henry. On the deflection of the plumb-line in India caused by the attraction of the Himalaya Mountains and of the elevated regions be- yond; and its modification by the compensating, effect of a deficiency of matter below the mountain mass. Roy. Soc., Phil. Trans. 149 (1859), p. 746. 15. Putnam, G. R. Relative determinations of gravity with half-second pendulums and other pendulum investigations. U. S. Coast and Geodetic Survey, An- nua.1 Report for 1894, Appendix 1: 9-50 (1895). 16. Sans Huelin, Guillermo. La reduction isostatica de nu.estras estaciones de gravedad. Memorials del Instituto Geografic.o y Catastral. XV, N. 5: 1-18 (1926) . l7. White, David. Gravity observ`a,t.ions flora the standpoint of the local geology. Bull. Geol. Surv. Ant. 35: 207-278 (1924).