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If G be the point on the geodetic corresponding to F on that one of the plane curves which contains the normal at Cadiz (by" sponding" we mean that F and G are on a meridian) then G is to the north of F; at a quarter of the whole distance from Cadiz GF is 458 ft., at half the distance it is 637 ft., and at three-quarters it is 473 ft. The azimuth of the geodetic at Cadiz differs 20" from that of the vertical plane, which is the astronomical azimuth.

The azimuth of a geodetic line cannot be observed, so that the line does not enter of necessity into practical geodesy, although many formulae connected with its use are of great simplicity and elegance. The geodetic line has always held a more important place in the science of geodesy among the mathematicians of France, Germany and Russia than has been assigned to it in the operations of the English and Indian triangulations. Although the observed angles of a triangulation are not geodetic angles, yet in the calculation of the distance and reciprocal bearings of two points which are far apart, and are connected by a long chain of triangles, we may fall upon the geodetic line in this manner:

If A, Z be the points, then to start the calculation from A, we obtain by some preliminary calculation the approximate azimuth of Z, or the angle made by the direction of Z with the side AB or AC of the first triangle. Let P1 be the point where this line intersects BC; then, to find P2, where the line cuts the next triangle side CD, we make the angle BP P2 such that BP,P2+BP,A=180°. This fixes P2, and P, is fixed by a repetition of the same process; so for P., P... Now it is clear that the points P1, P2, P3 so computed are those which would be actually fixed by an observer with a theodolite, proceeding in the following manner. Having set the instrument up at A, and turned the telescope in the direction of the computed bearing, an assistant places a mark Pi on the line BC, adjusting it till bisected by the cross-hairs of the telescope at A. The theodolite is then placed over P1, and the telescope turned to A; the horizontal circle is then moved through 180°. The assistant then places a mark P2 on the line CD, so as to be bisected by the telescope, which is then moved to P2, and in the same manner P is fixed. Now it is clear that the series of points P1, P2, P3 approaches to the geodetic line, for the plane of any two consecutive elements P-1 Pa, Pa P41 contains the normal at P.

If the objection be raised that not the geodetic azimuths but the astronomical azimuths are observed, it is necessary to consider that the observed vertical sections do not correspond to points on the sea-level but to elevated points. Since the normals of the ellipsoid of rotation do not in general intersect, there consequently arises an influence of the height on the azimuth. In the case of the measurement of the azimuth from A to B, the instrument is set to a point A' over the surface of the ellipsoid (the sea-level), and it is then adjusted to a point B', also over the surface, say at a height h'. The vertical plane containing A' and B' also contains A but not B: it must therefore be rotated through a small azimuth in order to contain B. The correction amounts approximately to-eh' cos sin 2a/20; in the case of h'= 1000 m., its value is o" 108 cos sin 2a.

This correction is therefore of greater importance in the case of observed azimuths and horizontal angles than in the previously

considered case of the astronomical and the geodetic azimuths. The observed azimuths and horizontal angles must therefore also be corrected in the case, where it is required to dispense with geodetic lines.

obtained, namely, from the astronomical observations there-one
can compute the latitudes of all the other points with any degree of
precision that may be considered desirable. It is necessary to employ
for this purpose formulae which will give results true even for the
longest distances to the second place of decimals of seconds, otherwise
there will arise an accumulation of errors from imperfect calculation
which should always be avoided. For very long distances, eight
places of decimals should be employed in logarithmic calculations;
if seven places only are available very great care will be required to
keep the last place true. Now let , be the latitudes of two stations
A and B; a, a their mutual azimuths counted from north by east
continuously from o° to 360°; their difference of longitude
measured from west to east; and s the distance AB.
First compute a latitude by means of the formula =
+(s cos a)/p, where p is the radius of curvature of the meridian at the
latitude; this will require but four places of logarithms. Then,
in the first two of the following, five places are sufficient-

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The logarithm in the last column is that required also for the calculation of spherical excesses, the spherical excess of a triangle being expressed by ab sin C/2pn sin 1".

It is frequently necessary to obtain the co-ordinates of one point with reference to another point; that is, let a perpendicular are be the azimuth of B at A, the co-ordinates of B with reference to A are drawn from B to the meridian of A meeting it in P, then, a being AP s cos (aje), BP=s sin (a−je),

where is the spherical excess of APB, viz. s2 sin a cos a multiplied by the quantity whose logarithm is in the fourth column of the above

table.

longitude as well as the azimuths to a greater degree of accuracy If it be necessary to determine the geographical latitude and formula: given the latitude of A, and the azimuth a and the than is given by the above formulae, we make use of the following distance s of B, to determine the latitude ' and longitude w of B, and the back azimuth a'. Here it is understood that a' is symmetrical to a, so that a*+a' = 360°

Let

and

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=sA/a, where A = (1-c2 sin 2)}

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4(1) cos2 sin 2a, {'=6(1-e) cos2 cos2 a;

tan

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2

=

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a

When the angles of a triangulation have been adjusted by the method of least squares, and the sides are calculated, the next process is to calculate the latitudes and longitudes of all the stations starting from one given point. The calculated latitudes, longitudes, are always very minute quantities even for the longest distances; and azimuths, which are designated geodetic latitudes, longitudes then, putting =90°-, and azimuths, are not to be confounded with the observed latitudes, longitudes and azimuths, for these last are subject to somewhat large errors. Supposing the latitudes of a number of stations in the triangulation to be observed, practically the mean of these determines the position in latitude of the network, taken as a whole. So the orientation or general azimuth of the whole is inferred from all the azimuth observations. The triangulation is then supposed to be projected on a spheroid of given elements, representing as nearly as one knows the real figure of the earth. Then, taking the latitude of one point and the direction of the meridian there as given

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tan

a2+} +w_cos | (x-0-5)
2 cos(x+0+) cot

s sin (a'+-a) 02
sin(a'+s+a) 12

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here po is the radius of curvature of the meridian for the mean latitude (+). These formulae are approximate only, but they are sufficiently precise even for very long distances.

For lines of any length the formulae of F. W. Bessel (Astr. Nach., 1823, iv. 241) are suitable.

If the two points A and B be defined by their geographical

co-ordinates, we can accurately calculate the corresponding astrono- | mical azimuths, i.e. those of the vertical section, and then proceed, in the case of not too great distances, to determine the length and the azimuth of the shortest lines. For any distances recourse must again be made to Bessel's formula.1 Let a, a' be the mutual azimuths of two points A, B on a spheroid, k the chord line joining them, p, the angles made by the chord with the normals at A and.B, 4, ', their latitudes and difference of longitude, and (x2+y2)/a2+b2= the equation of the surface; then if the plane xz passes through A the co-ordinates of A and B will be x=(a/A') cos o' cos w, y' = (a/A') cos' sin w,

x=(a/A) cos +, y=0

g= = (a/A) (1−e2) sin o, z′ = (a/^′) (1 —eo) sin ø′, where A= (1-e2 sin2 ¢)1, A′=(1—e2 sin? '), and e is the eccentricity. Let f, g, h be the direction cosines of the normal to that plane which contains the normal at A and the point B, and whose inclinations to the meridian plane of A is a; let also l, m, n and l', m', n' be the direction cosines of the normal at A, and of the tangent to the surface at A which lies in the plane passing through B, then since the first line is perpendicular to each of the other two and to the chord k, whose direction cosines are proportional to x' -x, y'-y, z'-z, we have these three equations

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(1-e)'sin A sin # cos += A cos u,

then on expressing x, x', z, z' in terms of u and w',

U=1-cos u cos u' cos w-sin u sin u';

also, if v be the third side of a spherical triangle, of which two sides are - and -' and the included angle w, using a subsidiary angle such that

sin sin ve sin (u'-u) cos (u'+u), we obtain finally the following equations:k=2a cos sin v sin v

cos μ =▲ sec

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distances and azimuths, of any two points on a spheroid whose latitudes and difference of longitude are given. By a series of reductions from the equations containing 5, šit may be shown that a+a'=5+5'+}e1w(ø′−6)a cos 1¢ɑ sin +..., where is the mean of and ', and the higher powers of e are neglected. A short computation will show that the small quantity on the right-hand side of this equation cannot amount even to the thousandth part of a second for k<0.1e, which is, practically speaking, zero; consequently the sum of the azimuths a+a' on the spheroid is equal to the sum of the spherical azimuths, whence follows this very important theorem (known as Dalby's theorem). If . ' be the latitudes of two points on the surface of a spheroid, their difference of longitude, a, a' their reciprocal azimuths,

tan w=cot (a+a') {cos (p′-¢)/sin }(ø′+ø)}. The computation of the geodetic from the astronomical azimuths has been given above From k we can now compute the length s of the vertical section, and from this the shortest length. The difference of length of the geodetic line and either of the plane curves is

e's'cos o sin 22a0/360 a1.

At least this is an approximate expression. Supposing s=0-14, this quantity would be less than one-hundredth of a millimetre. The line s is now to be calculated as a circular arc with a mean radius! along AB. If =}(0+ø′), ao=}(180°+a-a'), A=(1—e2 sin 2)*,

then=(1+ cos cos cos o cos a), and approximately sin (s/2r) =

a

k/2r. These formulae give, in the case of k=0.1a, values certain to eight logarithmic decimal places. An excellent series of formulae for the solution of the problem, to determine the azimuths, chord and distance along the surface from the geographical co-ordinates, was given in 1882 by Ch. M. Schols (Archives Néerlandaises, vol. xvii.).

Irregularities of the Earth's Surface.

In considering the effect of unequal distribution of matter in the carth's crust on the form of the surface, we may simplify the matter by disregarding the considerations of rotation and eccentricity. In the first place, supposing the earth a sphere covered with a film of water, let the density be a function of the distance from the centre so that surfaces of equal density are concentric spheres. Let now a disturbance of the arrangement of matter take place, so that the density is no longer to be expressed by p, a function of r only, but is expressed by p+p', where p' is a function of three co-ordinates 8, 4, 7. Then p' is the density of what may be designated disturbing matter; it is positive in some places and negative in others, and the whole quantity of matter whose density is p' is zero. The previously spherical surface of the sea of radius a now takes a new form. Let P be a point on the disturbed surface, P' the corresponding point vertically below it on the undisturbed surface, PP-N. The knowledge of N over the whole surface gives us the form of the disturbed or actual surface of the sea; it is an equipotential surface, and if V be the potential at P of the disturbing matter p', M the mass of the earth (the attraction-constant is assumed equal to unity)

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As far as we know, N'is always a very small quantity, and we have with sufficient approximation N=3V/48a, where & is the mean density of the earth. Thus we have the disturbance in elevation of the sea-level expressed in terms of the potential of the disturbing matter. If at any point P the value of N remain constant when we pass to any adjacent point, then the actual surface is there parallel to the ideal spherical surface; as a rule, however, the normal at P is inclined to that at P', and astronomical observations have shown that this inclination, the deflection or deviation, amounting ordinarily to one or two seconds, may in some cases exceed 10 or, as at the foot of the Himalayas, even 60". By the expression "mathematical figure of the earth "we mean the surface of the sea produced in imagination so as to percolate the continents. We see then that the effect of the uneven distribution of matter in the crust of the earth is to produce small elevations and depressions on the mathematical surface which would be otherwise spheroidal. No geodesist can proceed far in his work without encountering the irregularities of the mathematical surface, and it is necessary that he should know how they affect his astronomical observations. whole of this subject is dealt with in his usual elegant manner by Bessel in the Astronomische Nachrichten, Nos. 329, 330, 331, in a paper entitled "Ueber den Einfluss der Unregelmässigkeiten der Figur der Erde auf geodätische Arbeiten, &c." But without entering into further details it is not difficult to see how local attraction at any station affects the determinations of latitude, longitude and azimuth there.

The

the zenith to the south-west, so that it takes in the celestial sphere a Let there be at the station an attraction to the north-east throwing position Z', its undisturbed position being Z. Let the rectangular components of the displacement ZZ' be measured southwards

and ŋ measured westwards. 17

Now the great circle joining Z' with the pole of the heavens P makes there an angle with the meridian PZ = cosec PZ'n seco, where is the latitude of the station. Also this great circle meets the horizon in a point whose distance from the great circle PZ is n sec sin on tan p. That is, a meridian mark, fixed by observations of the pole star, will be placed that amount to the east of north. Hence the observed latitude requires the correction; the observed longitude a correction 7 sec ; and any observed azimuth a correction tan . Here it is supposed that azimuths are measured from north by east, and longitudes eastwards. The horizontal angles are also influenced by the deflec tions of the plumb-line, in fact, just as if the direction of the vertical axis of the theodolite varied by the same amount. This influence, however, is slight, so long as the sights point almost horizontally at the objects, which is always the case in the observation of distant points. The expression given for N enables one to form an approximate estimate of the effect of a compact mountain in raising the sea-level. Take, for instance, Ben Nevis, which contains about a couple of cubic miles; a simple calculation shows that the elevation produced would only amount to about 3 in. In the case of a mountain mass like the Himalayas, stretching over some 1500 miles of country with a breadth of 300 and an average height of 3 miles, although it is difficult or impossible to find an expression for V, yet we may ascertain that an elevation amounting to several hundred feet may exist near their base. The geodetical operations, however, rather negative this idea, for it was shown by Colonel Clarke (Phil. Mag., 1878) that the form of the sea-level along the Indian arc departs but slightly from that of the mean figure of the earth. If this be so, the action of the Himalayas must be counteracted by subterranean tenuity. Suppose now that A, B, C,... are the stations of a network of triangulation projected on or lying on a spheroid of semiaxis major and eccentricity a, e, this spheroid having its axis parallel to the axis of rotation of the earth, and its surface coinciding with the mathematical surface of the earth at A. Then basing the calculations on the observed elements at A, the calculated latitudes, longitudes and directions of the meridian at the other points will be the true latitudes, &c., of the points as projected on the spheroid. On comparing these geodetic elements with the corresponding astronomical determinations, there will appear a system of differences which represent the inclinations, at the various points, of the actual irregular surface to the surface of the spheroid of reference. These differences will suggest two things,-first, that we may improve the agreement of the two surfaces, by not restricting the spheroid of reference by the condition of making its surface coincide with the mathematical surface of the earth at A; and secondly, by altering the form and dimensions of the spheroid. With respect to the first circumstance, we may allow the spheroid two degrees of freedom, that is, the normals of the surfaces at A may be allowed to separate a small quantity, compounded of a meridional difference and a difference perpendicular to the same. Let the spheroid be so placed that its normal at A lies to the north of the normal to the earth's surface by the small quantity and to the cast by the quantity n Then in starting the calculation of geodetic latitudes, longitudes and azimuths from A, we must take, not the observed clements, a, but for ø, +§, and for a, a+ tan , and zero longitude must be replaced by see p. At the same time suppose the elements of the spheroid to be altered from a, e to a+da, e‡de. Confining our attention at first to the two points A, B, let (p'), (a'), (w) be the numerical elements at B as obtained in the first calculation, viz. before the shifting and alteration of the spheroid; they will now take the form

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The precise determination of the altitude of his station is a matter of secondary importance to the geodesist; nevertheless it is usual to observe the zenith distances of all trigonometrical points. Of great importance is a knowledge of the height of the base for its reduction to the sea-level. Again the height of a station does influence a little the observation of terrestrial angles, for a vertical line at B does not lie generally in the vertical plane of A (see above). The height above the sea-level also influences the geographical latitude, inasmuch as the centrifugal force is increased and the magnitude and direction of the attraction of the earth are altered, and the effect upon the latitude is a very small term expressed by the formula (g'-g) sin 24/ag, where g, g' are the values of gravity at the equator and at the pole. This is h sin 24/5820 seconds, h being in metres, a quantity which may be neglected, since for ordinary mountain heights it amounts to only a few hundredths of a second. We can assume this amount as joined with the northern component of the plumb-line perturbations.

The uncertainties of terrestrial refraction render it impossible to determine accurately by vertical angles the heights of distant points. Generally speaking, refraction is greatest at about daybreak; from that time it diminishes, being at a minimum for a couple of hours before and after mid-day; later in the afternoon it again increases. This at least is the general march of the phenomenon, but it is by no means regular. The vertical angles measured at the station on Hart Fell showed on one occasion in the month of September a refraction of double the average amount, lasting from I P.M. to 5 P.M. The mean value of the coefficient of refraction k determined from a very large number of observations of terrestrial zenith distances in Great Britain is 07920047; and if we separate those rays which for a considerable portion of their length cross the sea from those which do not, the former give k=0813 and the latter k=0753. These values are determined from high stations and long distances; when the distance is short, and the rays graze the ground, the amount of refraction is extremely uncertain and variable. A case is noted in the Indian survey where the zenith distance of a station 10.5 miles off varied from a depression of 4′ 52°-6 at 4-30 P.M. to an elevation of 2' 240 at 10.50 P.M.

If h, h' be the heights above the level of the sea of two stations, 90°+8, 90°+8' their mutual zenith distances (& being that observed at h), s their distance apart, the earth being regarded as a splicre of radius=a, then, with sufficient precision,

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Suppose the depression & to be n minutes, then h=1-054m2 if the ray be for the greater part of its length crossing the sca; if otherwise, h=1.040n2. To take an example: the mean of eight observations of the zenith distance of the sea horizon at the top of Ben Nevis is 91° 4′ 48′′, or 564.8; the ray is pretty equally disposed over land and water, and hence h=1047n2=4396 ft. The actual height of the hill by spirit-levelling is 4406 ft., so that the error of the height thus obtained is only 10 ft.

The determination of altitudes by means of spirit-levelling is undoubtedly the most exact method, particularly in its present development as precise-levelling, by which there have been determined in all civilized countries close-meshed nets of elevated points covering the entire land. (A. R. C.; F. R. H.)

GEOFFREY, surnamed MARTEL (1006-1060), count of Anjou, son of the count Fulk Nerra (q.v.) and of the countess Hildegarde or Audegarde, was born on the 14th of October 1006. During his father's lifetime he was recognized as suzerain by Fulk l'Oison

where ', a', w are the observed elements at B. Here it appears that the observation of longitude gives no additional information," the Gosling "), count of Vendôme, the son of his half-sister but is available as a check upon the azimuthal observations.

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Adela. Fulk having revolted, he confiscated the countship, which he did not restore till 1050. On the 1st of January 1032 he married Agnes, widow of William the Great, duke of Aquitaine, and taking arms against William the Fat, eldest son and successor of William the Great, defeated him and took him prisoner at Mont-Couër near Saint-Jouin-de-Marnes on the 20th of September 1033. He then tried to win recognition as dukes of Aquitaine for the sons of his wife Agnes by William the Great, who were still minors, but Fulk Nerra promptly took up arms to defend his suzerain William the Fat, from whom he held the Loudunois and

Saintonge in fief against his son. In 1036 Geoffrey Martel had to | 1186. He left a daughter, Eleanor, and his wife bore a liberate William the Fat, on payment of a heavy ransom, but the posthumous son, the unfortunate Arthur. latter having died in 1038, and the second son of William the GEOFFREY (c. 1152-1212), archbishop of York, was a bastard Great, Odo, duke of Gascony, having fallen in his turn at the son of Henry II., king of England. He was distinguished from siege of Mauzé (10th of March 1039) Geoffrey made peace with his his legitimate half-brothers by his consistent attachment and father in the autumn of 1039, and had his wife's two sons recog-fidelity to his father. He was made bishop of Lincoln at the age nized as dukes. About this time, also, he had interfered in the affairs of Maine, though without much result, for having sided against Gervais, bishop of Le Mans, who was trying to make himself guardian of the young count of Maine, Hugh, he had been beaten and forced to make terms with Gervais in 1038. In 1040 he succeeded his father in Anjou and was able to conquer Touraine (1044) and assert his authority over Maine (see ANJOU). About 1050 he repudiated Agnes, his first wife, and married Grécie, the widow of Bellay, lord of Montreuil-Bellay (before August 1052), whom he subsequently left in order to marry Adela, daughter of a certain Count Odo. Later he returned to Grécie, but again left her to marry Adelaide the German. When, however, he died on the 14th of November 1060, at the monastery of St Nicholas at Angers, he left no children, and transmitted the countship to Geoffrey the Bearded, the eldest of his nephews (See ANJOU).

See Louis Halphen, Le Comté d'Anjou au XIe siècle (Paris, 1906). A summary biography is given by Célestin Port, Dictionnaire historique, géographique et biographique de Maine-et-Loire (3 vols., Paris-Angers, 1874-1878), vol. ii. pp. 252-253, and a sketch of the wars by Kate Norgate, England under the Angevin Kings (2 vols., London, 1887), vol. i. chs. iii. iv. (L. H.*) GEOFFREY, surnamed PLANTAGENET [or PLANTEGENET] (1113-1151), count of Anjou, was the son of Count Fulk the Young and of Eremburge (or Arembourg of La Flèche; he was born on the 24th of August 1113. He is also called "le bel" or "the handsome," and received the surname of Plantagenet from the habit which he is said to have had of wearing in his cap a sprig of broom (genêt). In 1127 he was made a knight, and on the 2nd of June 1129 married Matilda, daughter of Henry I. of England, and widow of the emperor Henry V. Some months afterwards he succeeded to his father, who gave up the countship when he definitively went to the kingdom of Jerusalem. The years of his government were spent in subduing the Angevin barons and in conquering Normandy (see ANJOU). In 1151, while returning from the siege of Montreuil-Bellay, he took cold, in consequence of bathing in the Loir at Château-du-Loir, and died on the 7th of September. He was buried in the cathedral of Le Mans. By his wife Matilda he had three sons: Henry Plantagenet, born at Le Mans on Sunday, the 5th of March 1133; Geoffrey, born at Argentan on the 1st of June 1134; and William Long-Sword, born on the 22nd of July 1136.

See Kate Norgate, England under the Angevin Kings (2 vols., London, 1887), vol. i. chs. v.-viii.; Célestin Port, Dictionnaire historique, géographique et biographique de Maine-et-Loire (3 vols., Paris-Angers, 1874-1878), vol. ii. pp. 254-256. A history of Geoffrey le Bel has yet to be written; there is a biography of him written in the 12th century by Jean, a monk of Marmoutier, Historia Gaufredi, ducis Normannorum et comitis Andegavorum, published by Marchegay et Salmon; "Chroniques des comtes d'Anjou" (Société de l'histoire de France, Paris, 1856), pp. 229-310. (L. H.*)

GEOFFREY (1158-1186), duke of Brittany, fourth son of the English king Henry II. and his wife Eleanor of Aquitaine, was born on the 23rd of September 1158. In 1167 Henry suggested a marriage between Geoffrey and Constance (d. 1 201), daughter and heiress of Conan IV., duke of Brittany (d. 1171); and Conan not only assented, perhaps under compulsion, to this proposal, but surrendered the greater part of his unruly duchy to the English king. Having received the homage of the Breton nobles, Geoffrey joined his brothers, Henry and Richard, who, in alliance with Louis VII. of France, were in revolt against their father; but he made his peace in 1174, afterwards helping to restore order in Brittany and Normandy, and aiding the new French king, Philip Augustus, to crush some rebellious vassals In July 1181 his marriage with Constance was celebrated, and practically the whole of his subsequent life was spent in warfare with his brother Richard. In 1183 he made peace with his father, who had come to Richard's assistance; but a fresh struggle soon broke out for the possession of Anjou, and Geoffrey was in Paris treating for aid with Philip Augustus, when he died on the 19th of August

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of twenty-one (1173); but though he enjoyed the temporalities he was never consecrated and resigned the see in 1183. He then became his father's chancellor, holding a large number of lucrative benefices in plurality. Richard nominated him archbishop of York in 1189, but he was not consecrated till 1191, or enthroned till 1194. Geoffrey, though of high character, was a man of uneven temper; his history in chiefly one of quarrels, with the see of Canterbury, with the chancellor Willian Longchamp, with his half-brothers Richard and John, and especially with his canons at York. This last dispute kept him in litigation before Richard and the pope for many years. He led the clergy in their refusal to be taxed by John and was forced to fly the kingdom in 1207. He died in Normandy on the 12th of December 1212. See Giraldus Cambrensis, Vita Galfridi; Stubbs's prefaces to Roger de Hoveden, vols. iii. and iv. (Rolls Series). (H. W. C. D.) GEOFFREY DE MONTBRAY (d. 1093), bishop of Coutances (Constantiensis), a right-hand man of William the Conqueror, was a type of the great feudal prelate, warrior and administrator at need. He knew, says Orderic, more about marshalling mailed knights than edifying psalm-singing clerks. Obtaining, as a young man, in 1048, the see of Coutances, by his brother's influence (see MOWBRAY), he raised from his fellow nobles and from their Sicilian spoils funds for completing his cathedral, which was consecrated in 1056. With bishop Odo, a warrior like himself, he was on the battle-field of Hastings, exhorting the Normans to victory; and at William's coronation it was he who called on them to acclaim their duke as king. His reward in England was a mighty ficf scattered over twelve counties. He accompanied William on his visit to Normandy (1067), but, returning, led a royal force to the relief of Montacute in September 1069. In 1075 he again took the field, leading with Bishop Odo a vast host against the rebel earl of Norfolk, whose stronghold at Norwich they besieged and captured.

Meanwhile the Conqueror had invested him with important judicial functions. In 1072 he had presided over the great Kentish suit between the primate and Bishop Odo, and about the same time over those between.the abbot of Ely and his despoilers, and between the bishop of Worcester and the abbot of Ely, and there is some reason to think that he acted as a Domesday commissioner (1086), and was placed about the same time in charge of Northumberland. The bishop, who attended the Conqueror's funeral, joined in the great rising against William Rufus next year (1088), making Bristol, with which (as Domesday shows) he was closely connected and where he had built a strong castle, his base of operations. He burned Bath and ravaged Somerset, but had submitted to the king before the end of the year. He appears to have been at Dover with William in January 1090, but, withdrawing to Normandy, died at Coutances three years later. In his fidelity to Duke Robert he seems to have there held out for him against his brother Henry, when the latter obtained the Cotentin.

See E. A. Freeman, Norman Conquest and William Rufus: J. H. Round, Feudal England; and, for original authorities, the works of Orderic Vitalis and William of Poitiers, and of Florence of Worcester; the Anglo-Saxon Chronicle; William of Malmesbury's Gesta pontificum, and Lanfranc's works, ed. Giles; Domesday Book. (J. H. R.)

GEOFFREY OF MONMOUTH (d. 1154), bishop of St Asaph and writer on early British history, was born about the year 1100. Of his early life little is known, except that he received a liberal education under the eye of his paternal uncle, Uchtryd, who was at that time archdeacon, and subsequently bishop, of Llandaff. In 1129 Geoffrey appears at Oxford among the witnesses of an Oseney charter. He subscribes himself Geoffrey Arturus; from this we may perhaps infer that he had already begun his experiments in the manufacture of Celtic mythology. A first edition of his Historia Brilonum was in circulation by the year

1139, although the text which we possess appears to date from 1147. This famous work, which the author has the audacity to place on the same level with the histories of William of Malmesbury and Henry of Huntingdon, professes to be a translation from a Celtic source; "a very old book in the British tongue" which Walter, archdeacon of Oxford, had brought from Brittany. Walter the archdeacon is a historical personage; whether his book has any real existence may be fairly questioned. There is nothing in the matter or the style of the Historia to preclude us from supposing that Geoffrey drew partly upon confused traditions, partly on his own powers of invention, and to a very slight degree upon the accepted authorities for early British history. His chronology is fantastic and incredible; William of Newburgh justly remarks that, if we accepted the events which Geoffrey relates, we should have to suppose that they had happened in another world. William of Newburgh wrote, however, in the reign of Richard I. when the reputation of Geoffrey's work was too well established to be shaken by such criticisms. The fearless romancer had achieved an immediate success. He was patronized by Robert, carl of Gloucester, and by two bishops of Lincoln; he obtained, about 1140, the archdeaconry of Llandaff "on account of his learning "; and in 1151 was promoted to the see of St Asaph.

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the Historia Britonum Geoffrey is also credited with a Life of
Merlin composed in Latin verse. The authorship of this work
has, however, been disputed, on the ground that the style is dis-
tinctly superior to that of the Historia. A minor composition, the
Prophecies of Merlin, was written before 1136, and afterwards incor-
porated with the Historia, of which it forms the seventh book.
For a discussion of the manuscripts of Geoffrey's work, see Sir
T. D. Hardy's Descriptive Catalogue (Rolls Series), i. pp. 341 ff. The
Historia Britonum has been critically edited by San Marte (Halle,
1854). There is an English translation by J. A. Giles (London, 1842).
The Vila Merlini has been edited by F. Michel and T. Wright (Paris,
1837). See also the Dublin Unit. Magazine for April 1876, for an
article by T. Gilray on the literary influence of Geoffrey; G. Heeger's
Trojanersage der Brillen (1889); and La Borderic's Études historiques
bretonnes (1883).
(H. W. C. D.)

GEOFFREY OF PARIS (d. c. 1320), French chronicler, was probably the author of the Chronique métrique de Philippe le Bel, or Chronique rimée de Geoffroi de Paris. This work, which deals with the history of France from 1300 to 1316, contains 7918 verses, and is valuable as that of a writer who had a personal knowledge of many of the events which he relates. Various short historical poems have also been attributed to Geoffrey, but there is no certain information about either his life or his writings.

The Chronique was published by J. A. Buchon in his Collection des chroniques, tome ix. (Paris, 1827), and it has also been printed in tome xxii. of the Recueil des historiens des Gaules et de la France (Paris, 1865). See G. Paris, Histoire de la littérature française au moyen âge (Paris, 1890); and A. Molinier, Les Sources de l'histoire de France, tome iii. (Paris, 1903).

GEOFFREY THE BAKER (d. c. 1360), English chronicler, is also called Walter of Swinbroke, and was probably a secular clerk at Swinbrook in Oxfordshire. He wrote a Chronicon Angliae temporibus Edwardi II. et Edwardi III., which deals with the history of England from 1303 to 1356. From the begin

Continuatio chronicarum, but after this date it is valuable and interesting, containing information not found elsewhere, and closing with a good account of the battle of Poitiers. The author obtained his knowledge about the last days of Edward II. from William Bisschop, a companion of the king's murderers, Thomas Gurney and John Maltravers. Geoffrey also wrote a Chroniculum from the creation of the world until 1336, the value of which is very slight. His writings have been edited with notes by Sir E. M. Thompson as the Chronicon Galfridi le Baker de Swynebroke (Oxford, 1889). Some doubt exists concerning Geoffrey's share in the compilation of the Vita et mors Edwardi II., usually attributed to Sir Thomas, de la More, or Moor, and printed by Camden in his Anglica scripla. It has been maintained by Camden and others that More wrote an account of Edward's reign in French, and that this was translated into Latin by Geoffrey and used by him in compiling his Chronicon. Recent scholarship, however, asserts that More was no writer, and that the Vila et mors is an extract from Geoffrey's Chronicon, and was attributed to More, who was the author's patron. In the main this conclusion substantiates the verdict of Stubbs, who has published the Vita et mors in his Chronicles of the reigns of Edward I. and Edward II. (London, 1883). The manuscripts of Geoffrey's works are in the Bodleian library at Oxford.

Before his death the Historia Britonum had already become a model and a quarry for poets and chroniclers. The list of imitators begins with Geoffrey Gaimar, the author of the Estorie des Engles (c. 1147), and Wace, whose Roman de Brut (1155) is partly a translation and partly a free paraphrase of the Historia. | In the next century the influence of Geoffrey is unmistakably attested by the Brut of Layamon, and the rhyming English | chronicle of Robert of Gloucester. Among later historians who were deceived by the Historia Britonum it is only needful toning until about 1324 this work is based upon Adam Murimuth's mention Higdon, Hardyng, Fabyan (1512), Holinshed (1580) and John Milton. Still greater was the influence of Geoffrey upon those writers who, like Warner in Albion's England (1586), and Drayton in Polyolbion (1613), deliberately made their accounts of English history as poctical as possible. The stories which Geoffrey preserved or invented were not infrequently a source of inspiration to literary artists. The earliest English tragedy, Gorboduc (1565), the Mirror for Magistrates (1587), and Shakespeare's Lear, are instances in point. It was, however, the Arthurian legend which of all his fabrications attained the greatest vogue. In the work of expanding and elaborating this theme the successors of Geoffrey went as far beyond him as he had gone beyond Nennius; but he retains the credit due to the founder of a great school. Marie de France, who wrote at the court of Henry II., and Chrétien de Troyes, her French contemporary, were the earliest of the avowed romancers to take up the theme. The succeeding age saw the Arthurian story popularized, through translations of the French romances, as far afield as Germany and Scandinavia. It produced in England the Roman du Saint Graal and the Roman de Merlin, both from the pen of Robert de Borron; the Roman de Lancelot; the Roman de Tristan, which is attributed to a fictitious Lucas de Gast. In the reign of Edward IV. Sir Thomas Malory paraphrased and arranged the best episodes of these romances in English prose. His Morte d'Arthur, printed by Caxton in 1485, epitomizes the rich mythology which Geoffrey's work had first called into life, and gave the Arthurian story a lasting place in the English imagination. The influence of the Historia Britonum may be illustrated in another way, by enumerating the more familiar of the legends to which it first gave popularity. Of the twelve books into which it is divided only three (Bks. IX., X., XI.) are concerned with Arthur. Earlier in the work, however, we have the adventures of Brutus; of his follower Corineus, the vanquisher of the Cornish giant Goemagol (Gogmagog); of Locrinus and his daughter Sabre (immortalized in Milton's Comus); of Bladud the builder of Bath; of Lear and his daughters; of the three pairs of brothers, Ferrex and Porrex, Brennius and Belinus, Elidure and Peridure. The story of Vortigern and Rowena takes its final form in the Historia Britonum; and Merlin makes his first appearance in the prelude to the Arthur legend. Besides

GEOFFRIN, MARIE THÉRÈSE RODET (1699-1777), a Frenchwoman who played an interesting part in French literary and artistic life, was born in Paris in 1699. She married, on the 19th of July 1713, Pierre François Geoffrin, a rich manufacturer and lieutenant-colonel of the National Guard, who died in 1750. It was not till Mme Geoffrin was nearly fifty years of age that we begin to hear of her as a power in Parisian society. She had learned much from Mme de Tencin, and about 1748 began to gather round her a literary and artistic circle. She had every week two dinners, on Monday for artists, and on Wednesday for her friends the Encyclopaedists and other men of letters. She received many foreigners of distinction, Hume and Horace Walpole among others. Walpole spent much time in her society before he was finally attached to Mme du Deffand, and speaks of her in his letters as a model of common sense. She was indeed somewhat of a small tyrant in her circle. She had adopted the pose of an old woman earlier than necessary, and her coquetry, if

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