See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

See also:

• PTOLEMY (CLAUDIUS PTOLEMAEUS)

In 1637 an Englishman, See also:

• RICHARD
• RICHARD (d. 1184)
• RICHARD, FRANCOIS MARIE BENJAMIN (18,9-1908)
• RICHARD, HENRY (1812-1888)
• RICHARD, ST

This astronomer, having been sent by the See also:

• ACADEMY, GREEK
• ACADEMY, ROYAL

The second party consisted of Pierre Louis See also:

• MOREAU, GUSTAVE (1826-1898)
• MOREAU, HEGESIPPE (18ro-1838)
• MOREAU, JEAN VICTOR MARIE (1763-1813)

From this, the southern extremity of their arc, they carried a chain of triangles northward to the See also:

• MOUNTAIN (0. Fr. montaigne; popular Lat. montanea, an adjectival form from the classical mons, montis, whence Eng. " mount," a form usually used along with the name of an individual mountain, e.g. Mt Everest)
• MOUNTAIN, THE (La Montagne)

Passing over the measurements made between See also:

• ROME
• ROME (Roma)

J. D. Arago and Claude Louis Mathieu on the French. The publication in 1838 of See also:

• FRIEDRICH, JOHANN (1836— )

Colby, Colonel L. A. See also:

• HALL
• HALL (generally known as SCHWABISCH-HALL, tc distinguish it from the small town of Hall in Tirol and Bad-Hall, a health resort in Upper Austria)
• HALL (O.E. heall, a common Teutonic word, cf. Ger. Halle)
• HALL, BASIL (1788-1844)
• HALL, CARL CHRISTIAN (1812–1888)
• HALL, CHARLES FRANCIS (1821-1871)
• HALL, CHRISTOPHER NEWMAN (1816—19oz)
• HALL, EDWARD (c. 1498-1547)
• HALL, FITZEDWARD (1825-1901)
• HALL, ISAAC HOLLISTER (1837-1896)
• HALL, JAMES (1793–1868)
• HALL, JAMES (1811–1898)
• HALL, JOSEPH (1574-1656)
• HALL, MARSHALL (1790-1857)
• HALL, ROBERT (1764-1831)
• HALL, SAMUEL CARTER (5800-5889)
• HALL, SIR JAMES (1761-1832)
• HALL, WILLIAM EDWARD (1835-1894)

The See also:

• AVERAGE

. . See also:

• COL
• COL (Fr. for " neck," Lat. collum)

The survey is detailed in eighteen volumes, published at See also:

• DEHRA

In 186o Friedrich Georg Wilhelm See also:

• STRUVE, FRIEDRICH GEORG WILHELM (1793-1864)

Assuming that the earth is composed of concentric ellipsoidal strata having a See also:

• COMMON

If the fluid be heterogeneous then it is to be remarked that for forces of attraction according to the See also:

• ORDINARY (med. Lat. ordinarius, Fr. ordinaire)

In other words, the body is composed of homogeneous spheroidal shells of variable density and ellipticity. On this sup-position we shall express the attraction of the mass upon a particle in its interior, and then, taking into account the centrifugal force, form the equation expressing the condition of fluid equilibrium. The attraction of the homogeneous spheroid x2+y2+z2(r +2e) =c2(1 +2e), where e is the ellipticity (of which the square is neglected), on an See also:

• INTERNAL

Here we must now put c for c1, c for r; and 1+2e under the first integral sign may be replaced by unity, since small quantities of the second order are neglected. Two differentiations See also:

• LEAD
• LEAD (pronounced iced)

Trans. viii.; see also Camb. Dub. Math. Journ., 1849, iv.) proved that if the external form of the sea—imagined to percolate the See also:

• LAND

H. Pratt, who deduced it from observations made in India. The sin224, term in the expression for G, and the corresponding deviation of the meridian from an See also:

• ELLIPSE (adapted from Gr. EXkei 'tc, a deficiency, iXXeirely, to fall behind)

On this assumption the depression in latitude 45° is 23—1 metres, and the coefficient of sine ¢ cos2cl) is, in See also:

• ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

H. Darwin, " The Theory of the Figure of the Earth carried to the Second Order of Small Quantities," Mon. Not. R.A.S., 1899; E. Wiechert, " fiber See also:

• DIE
• DIE (Fr. de, from Lat. datum, given)

H. Jeans, " On the Vibrations and Stability of a Gravitating See also:

• PLANET (Gr. ssXavirrns, a wanderer)

Love, " The Gravitational Stability of the Earth," Phil. Trans. 207, p. 237; Proc. Roy. Soc. vol. 80. this surface should turn out, after precise measurements, to be exactly an ellipsoid of revolution is a priori improbable. Al-though it may be highly probable that originally the earth was a fluid mass, yet in the cooling whereby the present crust has resulted, the actual solid surface has been See also:

• LEFT

In the vicinity of mountains it may See also:

• CHANGE (derived through the Fr. from the Late Lat. cambium, cambiare, to barter; the ultimate derivation is probably from the root which appears in the Gr. «a urmu', to bend)

At sixteen astronomical stations in the English survey the disturbance of latitude due to the form of the ground has been computed, and the following will give an idea of the results. At six stations the deflection is under 2", at six others it is between 2" and 4", and at four stations it exceeds 4",. There is one very exceptional station on the north See also:

• COAST (from Lat. costa, a rib, side)

where r= (r1+r2). This form suggests the following See also:

• PROCEDURE (Fr. procedure, from Lat. procedere, to go for-ward)

The maximum value of y is at Q, where it is y=aµu(I—u). The deflection at the distance ae is A=1u sin 0(1—2u cos O + u2) L, or since B is small, putting h+u=1, we have A=µO(h2+B2) 1. The maximum deflec- tion takes place at a point whose distance from Q is to the depth of the mass as 1: See also:

• J2(z)

Faye (See also:

• COMET (Gr. Koµieiis, long-haired)

(See also:

• FIT

The probable error in the length of the earth's quadrant is t 336 M. We now give a series of some meridian-arcs measurements, which were utilized in 1866 by A. R. Clarke in the Comparisons of the See also:

• STANDARDS

48 50 47.98 3710827.13 Dunkirk . 51 2 8.41 4509790.84 The distance of the parallels of Dunkirk and Greenwich, deduced from the extension of the triangulation of England into France, in 1862, is 161407.3 ft., which is 3.9 ft. greater than that obtained from Captain Kater's triangulation, and 3.2 ft. less than the distance calculated by Delambre from General Roy's triangulation. The following table shows the data of the English arc with the distances in standard feet from Formentera. 0 If Ft. Formentera 51 28 38.30 4671198.3 Greenwich Arbury . . 52 13 26.59 4943837'6 See also:

• CLIFTON

The mean of these three is that entered in the above table. For the Indian arc in long. 770 40' we have the following data :- if Ft. Punned . 8 9 31.132 1029174.9 Putchapolliam 10 59 42.276 1756562.0 Dodagunta 12 59 52.165 2518376.3 Namthabad . 15 5 53.562 3591788.4 Daumergida . 18 3 15.292 4697329.5 Takalkhera . 21 5 51.532 5794695.7 Kalianpur . 24 7 11.262 7755835.9 Kaliana .. 29 30 48.322 The data of the Russian arc (long. 26° 40') taken from Struve's work are as below :- ° Ft. Staro Nekrasovsk 45 20 24.98 616529.81 Vodu-Luy .

Suprunkovzy 477 45 3'04 1246762.17 4 See also:

• KREMENETS (Polish, Krzemieniec)

. 34 21 6.26 1678375.7 And, finally, for the Peruvian arc, in long. 281° o', ° Ft. Tarqui 3 4 32.068 Cotchesqui . . 0 2 31.387 1131036.3 Having now stated the data of the problem, we may seek that oblate ellipsoid (spheroid) which best represents the observations. Whatever the real figure may be, it is certain that if we suppose it an ellipsoid with three unequal axes, the arithmetical See also:

• PROCESS

In the Russian arc the largest corrections are + 3.76", at Torne., and-3.31", at Staro Nekrasovsk. Of the whole 40 corrections, 16 are under 1•o", ro between 1•o" and 2•o", 10 between 2.0" and 3•o", and 4 over 3•o". The probable error of an observed latitude is + 1'42"; for the spheroidal it would be very slightly larger. This quantity may be taken therefore as approximately the probable amount of local deflection. If p be the radius of curvature of the meridian in latitude 43, p' that perpendicular to the meridian, D the length of a degree of the meridian, D' the length of a degree of longitude, r the radius drawn from the centre of the earth, V the angle of the vertical with the radius-vector, then Ft. p =20890606.6 -106411.5 cos 20 + 225.8 cos 44 p' =20961607.3 - 35590.9 cos 20 + 45.2 cos 495 D = 364609.87 - 1857.14 cos 24, + 3.94 cos 44, D' = 365538.48 cos 4,- 310.17 cos 30 + 0.39 COS 50 Log r/a=9.9992645 + .0007374 cos 24' -•0000019cos40 V = 700.44" sin 2¢-1.19" sin 44). A. R. Clarke has recalculated the elements of the ellipsoid of the earth; his values, derived in 188o, in which he utilized the measurements of parallel arcs in India, are particularly in practice. These values are a =20926202 ft. =6378249 metres. b=20854895 ft. = 6356515 metres. b : a= 292.465 : 293.465.

The calculation of the elements of the ellipsoid of rotation from measurements of the curvature of arcs in any given azimuth by means of geographical longitudes, latitudes and azimuths is indicated in the article GEODESY ; reference may be made to Principal Triangulation, Helmert's Geodiisie, and the publications of the Kgl. Preuss. Geod. Inst.:-Lotabweichungen (1886), and Die europ. Langengradmessung in 52° Br. (1893). For the calculation of an ellipsoid with three unequal axes see Comparison of Standards, See also:

• PREFACE (Med. Lat. prefatia, for classical praefatio, praefari, to speak beforehand)

Such relative measurements are easier and more exact than absolute ones. In some cases the ordinary See also:

• THREAD (0. Eng. praed, literally, that which is twisted, prawan, to twist, to throw, cf. " throwster," a silk-winder, Ger. drehen, to twist, turn, Du. draad, Ger. Draht, thread, wire)

B. Lutke (1826-1829), a Russian See also:

• REAR

This is supposed to take into account the attraction of the elevated strata or See also:

• PLATEAU (a French term, older platel, for a flat piece of wood, metal, &c., from plat, flat)
• PLATEAU, JOSEPH ANTOINE FERDINAND (1801-1883)

The small term involving sin224 could not be calculated with sufficient exactness from the observations, and is therefore taken from the theoretical views of Sir G. H. Darwin and E. Wiechert. For the constant g=978•o3 cm. another correction has been suggested (1906) by the absolute determinations made by F. Kuhnen and Ph. See also:

• FURTWANGLER, ADOLF (1853–1907)

G. Stokes) the vertical condensation of the masses on the sea-level, without its form being considerably altered (scarcely t metre radially). Further, the value of gravity (g) measured at the height H is corrected to sea-level by +2gH/R, where R is the radius of the earth. Another correction, due to P. Bouguer, is —igbH/pR, where 8 is the density of the strata of height H, and p the mean density of the earth. These two corrections are represented in " Bouguer's See also:

• RULE

Inst., N.F., No. 27). 90° 100° 110° I20° 130° 140° 1500 16o° 170° 18o° -0.91 -0.62 -0.27 +o•o8 0.36 0.53 o•56 0.46 o•26 0 have approximately __3g SD. Ag —N 2 A. p) . Since N slowly varies empirically, it follows that in restricted regions (of a few too km. in diameter) Ag is a measure of the variation of D. By applying the reduction of Bouguer to g, D is diminished by H and only gives the thickness of the ideal disturbing mass which corresponds to the perturbations due to subterranean masses. Ag has See also:

• POSITIVE (or PORTABLE) ORGAN

F. G. W. Struve, who is to be regarded as the See also:

• FATHER

The number of longitude stations originally arranged for was 15; and the determinations of the differences in longitude were uniformly commenced by the Russian observers E. I. von Forsch, J. I. Zylinski, B. See also:

• TIELE, CORNELIS PETRUS (1830-1902)

Inst. The following figures are quoted from Helmert's report " Die Grosse der Erde " (Sitzb. d. Berl. Akad. d. Wiss., 1906, P. 535) Easterly Deviation of the Astronomical Zenith. Name. Longitude. ° Feaghmain . —I0 2I Killorglin . - 9 47 +2.8 See also:

• HAVERFORDWEST (Welsh Hwlfordd, the English name ,being perhaps a corruption of the Scandinavian Hafna-Fjord)

. + 7 6 -4.4 See also:

• GOTTINGEN

Clarke instituted an extensive series of comparisons at See also:

• SOUTHAMPTON
• SOUTHAMPTON, EARL OF
• SOUTHAMPTON, HENRY WRIOTHESLEY, 3RD EARL OF (1J73—1624)

The International Geodetic Association (Internationale Erdmessung). On the proposition of the Prussian See also:

• LIEUTENANT

Gradmessung, See also:

• OCTOBER

This will give a long arc of parallel, really projected in the first half of the 19th century. The calculation of the Russian section gives, with an assumed ellipticity of 1/299.15, the value a= 6377350 metres; this is rather uncertain, since the arc embraces only 19° in longitude. We may here recall that in France geodetic studies have recovered their former expansion under the vigorous impulse of Colonel (afterwards General) Francois Perrier. When occupied with the triangulation of See also:

• ALGERIA
• ALGERIA (Algerie)

The operations concerning the revision of the French arc were completed only in r896. Meanwhile the French geodesists had accomplished the junction of Algeria to Spain, with the help of the geodesists of the See also:

• MADRID

Ferrero, Rapport sur See also:

• LES

41 37'0 -0.2 Javalon . 40 13'8 -0.2 Desierto 40 5.0 -4.5. See also:

• CHINCHILLA
• CHINCHILLA, LA PLATA
• CHINCHILLA, PERUVIAN

The west-European and the Russo-Scandinavian meridians indicate another See also:

• ANOMALY (from Gr. lwvw)

In See also:

• CROSSING

Breitengradmessung " (Verhandlungen der 9. Allgem. Conf. d. I. E. in Paris, 1889, Ann. xi.). z U.S. Coast and Geodetic Survey; H. S. Pritchett, superin- tendent. The Transcontinental Triangulation and the American Arc of the Parallel, by C. A. Schott (Washington, 1900).

' U.S. Coast and Geodetic Survey; O. H. Tittmann, superin- tendent. The Eastern Oblique Arc of the United States, by C. A. Schott (1902). parallel. The astronomical data have been afforded by 71 latitude stations, 17 longitude stations, and 56 azimuth stations, distributed over the whole extent of the arc. The resulting dimensions of an osculating spheroid were found to be a = 6378157 metres =90 (prob. error), e(ellipticity) =1/304.5 t 1.9 (prob. error). With the ellipticity 1/3 99. I 5, a= 63 78041 metres t 8o (prob. era).

During the years 1903-1906 the United States Coast and Geodetic Survey, under the direction of O. H. Tittmann and the See also:

• SPECIAL

A new measurement of the meridian arc of Quito was executed in the years 1901-1906 by the Service geographique of France under the direction of the Academie des Sciences, the ground having been previously reconnoitred in 1899. The new arc has an amplitude in latitude of 5° 53' 33", and stretches from Tulcan (lat. o° 48' 25") on the See also:

• BORDERS, THE

Lacombe, A. Lallemand, and Lieut. Georges Perrier (son of General Perrier). It is conceivable that the chain of triangles in longitude 98° in North America may be united with that of Ecuador and Peru: a continuous chain over the whole of America is certainly but a question of time. During the years 1899-1902 the measurement of an arc of meridian was made in the extreme north, in Spitzbergen, between the latitudes 76° 38' and 8o° 5o', according to the project of P. G. Rosen. The southern part was determined by the Russians—O. Backlund, Captain D. D. Sergieffsky, F. N.

Tschernychev, A. Hansky and others—during 1899-1901, with the aid of T base-line, 15 trigonometrical, 11 latitude and 5 gravity stations. The northern part, which has one side in common with the southern part, bas been determined by Swedes (Professors Rosen, father and son, E. Jaderin, T. Rubin and others), who utilized T base-line, g azimuth measurements, 18 trigonometrical, 17 latitude and 5 gravity stations. The party worked under excessive difficulties, which were accentuated by the See also:

• ARCTIC (Gr. "ApKroc, the Bear, the northern constellation of Ursa Major)

It has ensured that the relative measurements made at the stations in different countries should be reduced conformably with the absolute determinations made at Potsdam; the result was that, in 1906, the intensities of gravitation at some 2000 stations had been co-ordinated. The intensity of gravity on the sea has been determined by the comparison of barometric and hypsometric observations (Mohn's method). The association, at the proposal of Helmert, provided the necessary funds for two expeditions:—English Channel—Rio de Janeiro, and the Red Sea—Australia—San Francisco—Japan. Dr O. See also:

• HECKER, FRIEDRICH FRANZ KARL (1811-1881)
• HECKER, ISAAC THOMAS (1819-1888)

(1885) 157)• The deviations of the geoid from the flattened ellipsoid of rotation with regard to the heights (the directions of normals being nearly the same) will scarcely exceed +too metres (Helmert).3 The basis of the degree- and gravity-measurements is actually formed by a stationary sea-surface, which is assumed to be level. However, by the influence of winds and ocean currents the mean surface of the sea near the coasts (which one assumes as the fundamental sea-surface) can deviate somewhat from a level surface. According to the more recent levelling it varies at the most by only some decimeters.' ' Sir David Gill, Report on the Geodetic Survey of South Africa, 1833–1892 (Cape Town, 1896), vol. ii. 1901, vol. iii. 19o5. 2 O. Hecker, Bestimmung der Schwerkraft a. d. Atlantischen Ozean (Veroffentl. d. Kgl. Preuss. Geod. Inst.

No. 11), Berlin, 1903. 2F. R. Helmert, Neuere Fortschritte in der Erkenntnis der math. Erdgestalt " (Verhandl. des VII. Internationalen Geographen-Kongresses, Berlin, 1899), London, 1901. ' C. Lallemand, " Rapport sur les travaux du service du nivellement general de la France, de 1900 a 190;, " (See also:

• CAMP (from Lat. campus, field)

It is well known that the masses of the earth are continually undergoing small changes; the earth's crust and sea-surface reciprocally oscillate, and the axis of rotation vibrates relatively to the body of the earth. The investigation of these problems falls in the See also:

• PROGRAMME, or PROGRAM