2pn Lat. | Log: sin i Loga 7.9939434 9309 the vertical section AB, and at B near the section BA. The obtained, namely, from the astronomical observations there one greatest distance of the vertical sections one from another is can compute the latitudes of all the other points with any degree of scos de sin 2a./162, in which so and so are the mean latitude precision that may be considered desirable. It is necessary to employ and azimuth respectively of the middle point of AB. For the value for this purpose formulae which will give results true even for the s=64 kilometres, the maximum distance is 3 mm. longest distances to the second place of decimals of seconds, otherwise An idea of the course of a longer geodetic line may be gathered there will arise an accumulation of errors froin imperfect calculation from the following example. Let the line be that joining Cadiz and which should always be avoided. For very long distances, cight St Petersburg, whose approximate positions are places of decimals should be employed in logarithmic calculations; if seven places only are available very great care will be required to Cadiz. St Petersburg." keep the last place true. Now let $. be the latitudes of two stations Lat. 36° 22' N. 59° 56' N. A and B; a, .* their mutual azimuths counted from north by east Long. 6° 18' w. 30° 17' E. continuously from oo to 360°;..w their difference of longitude Il G be the point on the geodetic corresponding to F on that one measured from west to east; and s the distance AB. of the plane curves which contains the normal at Cadiz (by "corre First compute a latitude oi by means of the formula $1= sponding " we mean that F and G are on a meridian) then G is to +(scos a)lo, where is the radius of curvature of the meridian at the the north of F: at a quarter of the whole distance from Cadiz GF latitude o this will require but four places of logarithms. Then, is 458 ft., at half the distance it is 637 ft., and at three-quarters it is in the first two of the following, five places are sufficient from that of the vertical plane, which is the astronomical azimuth. sin a cos a, sin’a tano 2pn The azimuth of a geodetic line cannot be observed, so that the line does not enter of necessity into practical geodesy, although many formulae connected with its use are of great simplicity and *-= cos(a–je) –. elegance. The geodetic line has always held a more important place s sin(a-fe). in the science of geodesy among the mathematicians of France, Germany and Russia than has been assigned to it in the operations n cos(&' +17) of the English and Indian triangulations. Although the observed a*-a=w sin(+'+in)-c+180°. angles of a triangulation are not geodetic angles, yet in the calcula: Here n is the normal or radius of curvature perpendicular to the tion of the distance and reciprocal bearings of two points which meridian; both n and p correspond to latitude 6, and po to latitude are far apart, and are connected by a long chain of triangles, we may |(+$'). For calculations of latitude and longitude, tables of the fall upon the geodetic line in this manner : logarithmic values of p sin r', n sin i', and anp, sin i' are necessary. If A, 2 be the points, then to start the calculation from A, we The following table contains these logarithms for every ten minutes 'obtain by some preliminary calculation the approximate azimuth of latitude from 52° to 53° computed with the elements a = 20926060 of 2, or the angle made by the direction of Z with the side AB or and a : b= 295 : 294 : AC of the first triangle. Let P, be the point where this line intersccts BC; then, to find P2, where the line cuts the next triangle side CD, we make the angle BP.P, such that BP,P:+BP,A= 180°. 2pn sin This fixes Ps, and P, is fixed by a repetition of the same process; so for Po, Ps ... Now it is clear that the points Ps, P., P, so computed are those which would be actually fixed by an observer with 7.9928231 0-37131 á theodolite, proceeding in the following manner. Having set the 8190 instrument up at A, and turned the telescope in the direction of 9185 8148 the computed bearing, an assistant places a mark P, on the line 9060 8107 BC, adjusting it till bisected by the cross-hairs of the telescope at 8936 8065 A. The theodolite is then placed over P, and the telescope turned 8024 to A; the horizontal circle is then moved through 180°. The 53 0 7982 assistant then places a mark P, on the line CD, so as to be bisected by the telescope, which is then moved to Ps, and in the same manner P, is fixed. Now it is clear that the series of points P1, P3, .P: calculation of spherical excesscs, the spherical excess of a triangle The logarithm in the last column is that required also for the approaches to the geodetic line, for the plane of any two consecutive being expressed by ab sin C/2pn sin !'. If the objection be raised that not the geodetic azimuths but the with reference to another point; that is, let a perpendicular arc be It is frequently necessary to obtain the co-ordinates of one point astronomical azimuths are observed, it is necessary to consider that drawn from B to the meridian of A meeting it in P, then, a being the observed vertical sections do not correspond to points on the the azimuth of B at A, the co-ordinates of B with reference to A arc sea-level but to elevated points. Since the normals of the ellipsoid of rotation do not in general intersect, there consequently arises an AP=s cos (a-je), BP=s sin (a-fe), influence of the height on the azimuth. In the case of the measure. ment of the azimuth from A to B, the instrument is set to a point A where e is the spherical excess of APB, viz. so sin a cos a multiplied over the surface of the ellipsoid (the sea-level), and it is then adjusted by the quantity whose logarithm is in the fourth column of the above 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 If it be necessary to determine the geographical latitude and therefore be rotated through a small azimuth in order to contain B. ) longitude as well as the azimuths to a greater degree of accuracy The correction amounts approximately, to-ch' costo sin 2a/20; 1 formula: given the latitude of A, and the azimuth a and the in the case of k' = 1000 m., its value is o".108 cos & sin 2a. This correction is therefore of greater importance in the case of distances of B; to determine the latitude and longitude w of B, observed azimuths and horizontal angles than in the previously and the back azimuth a'; Here it is understood that a'is symmetrical considered case of the astronomical and the geodetic azimuths. The to e, so that a ta'= 360° observed azimuths and horizontal angles must therefore also be Let corrected in the case, where it is required to dispense with geodetic 0 = sale, where A = (1-ė sin *)} lines. and 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 411-ascos o sin 2a, '=61-escos o cos' a; starting from one given point. The calculated latitudes, longitudes 5.5' are always very minute quantities even for the longest distances; and azimuths, which are designated geodetic latitudes, longitudes then, putting «=90°-4, and azimuths, are not to be confounded with the observed latitudes, longitudes and azimuths, for these last are subject to somewhat '+- sin }(«-A-5) tan large errors. Supposing the latitudes of a number of stations in the triangulation to be observed, practically the mean of these determines a'+s+wcos («-6-5). the position in latitude of the network, taken as a whole. So the tanorientation or general azimuth of the whole is inferred from all the azimuth observations. The triangulation is then supposed to be s sin }(a'+$ $-$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 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. On the Course of Geodetic Lines on the Earth's For lines of any length the formulae of F. W. Bessel (Astr. Nach., Surface" in the Phil. Mag. 1870; Helmert, Theorien der höheren 1823, iv. 241) are suitable. Geodäsie, 1. 321. If the two points A and B be defined by their geographical 52 o 10 20 30 40 50 29 8812 1 Sec a paper cot a-cot š= cCOs Q co-ordinates, we can accurately calculate the corresponding astrono- 1 distances and azimuths, of any two points on a spheroid whose mical azimuths, i.e. those of the vertical section, and then proceed, latitudes and difference of longitude are given. in the case of not too great distances, to determine the length and By a series of reductions from the cquations containing 5, ♡ it the azimuth of the shortest lines. For any distances recourse must may be shown that again be made to Bessel's formula. Let a, a' be the mutual azimuths of two points A, B on a spheroid, where do is the mean of andand the higher powers of e are ata' =$+$' +10 w(o'-0) cos do sin dot..., k the chord line joining them, H, H' the angles made by the chord with the normals at A and.B, 6.6,w their latitudes and difference of neglected. A short computation will show that the small quantity longitude, and (x +ya)/2 +226 =! the equation of the surface; on the right hand side of this equation cannot amount even to then if the plane xz passes through A the co-ordinates of A and B the thousandth part of a second for k <o:ld, which is, practically will be speaking, zero; consequently the sum of the azimuths a ta' on the *= (a/A) cos . x = (a/A') cos' cos w, sphcroid is equal to the sum of the spherical azimuths, whence follows this very important thcorem (known as Dalby's theorem). y=0 y' = (a/A') cos' sin w, If 0,6' be the latitudes of two points on the surface of a spheroid, w s=(a/A) (1-e?) sin . .' = (a/4') (1-e) sino', their difference of longitude, a, a' their reciprocal azimuths, where A=(1-esin o)!, A'=(1-e? sin')!, and e is the eccen tan jw=cotilata') {cos (0'-)/sin }(0'++)). tricity. Let f, g, h be the direction cosines of the normal to that The computation of the geodetic from the astronomical azimuths plane which contains the normal at A and the point B, and whose has been given above From we can now compute the length s inclinations to the meridian plane of A is =a; let also l, m, n and of the vertical section, and from this the shortest length. The ľ, m', n' be the direction cosines of the normal at A, and of the difference of length of the geodetic line and either of the plane tangent to the surface at A which lies in the plane passing through curves is 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 e's cos "po sin ?200/360 0%, x'- x, y'-3, 2-2, we have these three equations At least this is an approximate expression. Supposing s=0-13, f(x'- x) +gy' +h(z'--) = 0 this quantity would be less than one-hundredth of a millimetre. The líne s is now to be calculated as a circular arc with a mean radius fltgm thn along AB. If do = }(0+0'), 2= |(180° +a-a'), 10 =(1-esino), fľ+gm' +hn' =o. I_A, Eliminate f.8. h from these cquations, and substitute , and = 1 = cos l'= -sin cos a m' = sin a k/2r. These formulae give, in the case of k=0.10, values certain to n=sin n'=cos cos a, eight logarithmic decimal places. An excellent series of formulae and we get for the solution of the problem, to determine the azimuths, chord (x'—x) sin oty' cot a-(2-2) cos 6=0. and distance along the surface from the geographical co-ordinates, was given in 1882 by Ch. M. Schols (Archives Néerlandaises, vol. xvii.). The substitution of the values of x, 2, x', y'. z' in this equation will give immediately the value of cot a; and if we put si for the Irregularities of the Earth's Surface. corresponding azimuths on a sphere, or on the supposition e=0, In considering the effect of uncqual distribution of matter in the the following relations exist carth's crust on the form of the surfacr, we may simplify the matter by disregarding the considerations of rotation and eccentricity. COS O's In the first place, supposing the earth a sphere covered with a film of water, let the density o be a function of the distance from the centre cot a'-cot s'= -:COS¢'O so that surfaces of cqual density are concentric spheres. Let now a COS A disturbance of the arrangement of matter tako place, so that the A'sin $-A sin d'=Q sin w. density is no longer to be expressed by p, a function of r only, but is If from B we let fall a perpendicular on the meridian plane of A, expressed by eti', where p' is a function of three co-ordinates 0, 4.1. and from A let fall a perpendicular on the meridian plane of B, Then p' is the density of what may be designated disturbing matter; then the following equations become geometrically evident: it is positive in some places and negative in others, and the whole k sinh sin a = (a/S') cos sin w 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 k sin m' sin a' = (a/A) cos o sin w. P be a point on the disturbed surface, p' the corresponding point Now in any surface u=0 we have vertically below it on the undisturbed surface, PP-N. The ka = (x-x)+(-y)+('-2)* 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, du du dua and il 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) (du? , du? / M +V=C-N-MN+V. In the present case, if we put As far as we know, N'is always a very.small quantity, and we have with sufficient approximation N=3V/4000, 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 then 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 cos u = (a/k)AU; cos v' = (a/k) A'U. inclined to that at P', and astronomical observations have shown Let u be such an angle that that this inclination, the deflection or deviation, amounting ordinarily to one or two seconds, may in some cases exceed 10, (1-e?)'sin $ = A sin u or, as at the foot of the Himalayas, even 60". By the expression cos $ = A cosu, mathematical figure of the earth we mean the surface of the sea then on expressing x, x', %, z' in terms of u and u', produced in imagination so as to percolate the continents. We U= 1 -cos u cos u' cos w-sin u sin u'; see then that the effect of the uneven distribution of matter in the also, if v be the third side of a spherical triangle, of which two crust of the earth is to produce small elevations and depressions on sides are fr-u and fr-u' and the included angle w, using a sub- No geodesist can proceed far in his work without encountering the the mathematical surface which would be otherwise spheroidal. sidiary angle such that irregularities of the mathematical surface, and it is necessary that sin sin fv=e sin } (u' – u) cos }(u'+u), he should know how they affect his astronomical observations. The we obtain finally the following equations: whole of this subject is dealt with in his usual elegant manner by k = 2a cos y sin jo Bessel in the Astronomische Nachrichten, Nos. 329, 330, 331, in a cos y =A sec y sin jo paper entitled “Ueber den Einfluss der Unregelmässigkeiten der Figur der Erde auf geodätische Arbeiten, &c." But without entering cos u' = A' sec y sin }o into further details it is not difficult to see how local attraction at sin y sin a = (a/k) cos u' sin w any station affects the determinations of latitude, longitude and sin se sin a' = (a/k) cos u sin w. azimuth there. These determine rigorously the distance, and the mutual zenith the zenith to the south-west, so that it takes in the celestial sphere å Let there be at the station an attraction to the north-east throwing position Z', its undisturbed position being 2. Let the rectangular 1 Helmert, Theorien der höheren Geodäsie, 1. 232, 247 components of the displacement ZZ' be measured southwards -COS = and , measured westwards. Now the great circle joining Z' with! Taking Durham Observatory as the origin, and the tangent plane the pole of the heavens P makes there an angle with the meridian to the surface (determined by = -0.664,7= -4":117) as the plane PZ=n cosec PZ'=7 sec $, where is the latitude of the station. of rand y, the former measured northwards, and zincasured vertically Also this great circle mects the horizon in a point whose distance downwards, the equation to the surface is from the great circle PZ is n seco sin = tan . That is, a meridian -99524953x +.99288005y2 +.9976305232 -0.00671003x2 mark, fixed by observations of the pole star, will be placed that 416550702=0 amount to the east of north. Hence the observed latitude requires the correction &; the observed longitude a correction 7 sec •; and Altitudes. any observed azimuth a correction 7 tan . Here it is supposed The precise determination of the altitude of his station is a matter thát azimuths are measured from north by east, and longitudes of secondary importance to the geodesist; nevertheless it is usual eastwards. The horizontal angles are also influenced by the deflec: to observe the zenith distances of all trigonometrical points. Of tions of the plumb-line, in fact, just as if the direction of the vertical great importance is a knowledge of the height of the base for its reaxis of the theodolite varied by the same amount. This influence. duction to the sea level. Again the height of a station does influence however, is slight, so long as the sights point almost horizontally a little the observation of terrestrial angles, for a vertical line at B at the objects, which is always the case in the observation of distant does not lie generally in the vertical plane of A (see above). The points. height above the sea-level also influences the geographical latitude, The expression given for N enables one to form an approximate inasmuch as the centrifugal force is increased and ihe magnitude and estimate of the effect of a compact mountain in raising the sca-level, direction of the attraction of the earth are altered, and the effect Take, for instance, Ben Nevis, which contains about a couple of upon the latitude is a very small term expressed by the formula cubic miles; a simple calculation shows that the elevation produced g'-8) sin 20/ag, where g, g'are the values of gravity at the equator would only amount to about 3 in. In the case of a mountain mass and at the pole. This is k sin 2015820 seconds, h being in metres, like the Himalayas, stretching over some 1500 miles of country with a quantity which may be neglected, since for ordinary mountain a breadth of 300 and an average height of 3 miles, although it is diffi- heights it amounts to only a few hundredths of a second. We cult or impossible to find an expression for V, yet we may ascertain can assume this amount as joined with the northern component of that an elevation amounting to several hundred feet may exist the plumb-line perturbations. near their base. The geodetical operations, however, rather negative The uncertainties of terrestrial refraction render it impossible to this idea, for it was shown by Colonel Clarke (Phil. Mag., 1878) determine accurately by vertica! angles the heights of distant points. that the form of the sea-level along the Indian arc departs but slightly Generally speaking, refraction is greatest at about daybreak; from from that of the mean figure of the carth. If this be so, the action that time it diminishes, being at a minimum for a couple of hours of the Himalayas must be counteracted by subterrancan tenuity. before and after mid-day: later in the afternoon it again increases. Suppose now that A, B, C, . .: . are the stations of a network of This at least is the general march of the phenomenon, but it is by triangulation projected on or lying on a spheroid of semiaxis major no means regular. The vertical angles measured at the station on and eccentricity a, e, this spheroid having its axis parallel to the axis Hart Fell showed on one occasion in the month of September a of rotation of the earth, and its surface coinciding with the mathe. refraction of double the average amount, lasting from I P. M. to 5 P.M. matical surface of the earth at A. Then basing the calculations The mean value of the coefficient of refraction k determined from a on the observed elements at A, the calculated latitudes, longitudes very large number of observations of terrestrial zenith distances in and directions of the meridian at the other points will be the true Great Britain is .0792.0047; and if we separate those rays which latitudes, &c., of the points as projected on the spheroid. On for a considerable portion of their length cross the sea from those comparing these geodetic elements with the corresponding astro- which do not, the former give k=:0813 and the latter k =.0753. nomical determinations, there will appear a system of differences These values are determined from high stations and long distances; which represent the inclinations, at the various points, of the actual when the distance is short, and the rays graze the ground, the amount irregular surface to the surface of the spheroid of reference. These of refraction is extremely uncertain and variable. A case is noted differences will suggest two things,-first, that we may improve the in the Indian survey where the zenith distance of a station 10.5 miles agreement of the two surfaces, by not restricting the spheroid of off varicd from a depression of 4' 52":6 at 4.30 P.M. to an elevacion reference by the condition of making its surface coincide with the of 2' 24"0 at 10.50 P.M. mathematical surface of the earth ai A; and secondly, by altering ith,'h' be the heights above the level of the sea of two stations, the form and dimensions of the spheroid. With respect to the first 90° +8, 90° to their mutual zenith distances (8 being that observed circumstance, we may allow the spheroid two degrees of freedom, át ), s their distance apart, the earth being regarded as a sphere of that is, the normals of the surfaces at A may be allowed to separate radius = Q, then, with sufficient precision, a small quantity, compounded of a meridional difference and a .28 difference perpendicular to the same. Let the spheroid be so placed -2k hi-h=stan that its normal at A lies to the north of the normal to the earth's surface by the small quantity & and to the east by the quantity n. Il from a station whose height is h the horizon of the sca be observed Then in starting the calculation of geodetic latitudes, longitudes and to have a zenith distance 90° +ö, then the above formula gives for h azimuths from A, we must take, not the observed elements o, a, the valuc but for ø, $+$, and for a, ato tan $, and zero longitude must be a tan? h= replaced by 7 sec o. At the same time suppose the elements of the spheroid to be altered from a, e to c+da, c+de. Confining our attention at first to the two points A, B, let (d'), (a'), (w) be the Suppose the depression 8 to be a minutes, then h= 1.05412 if numerical elements at B as obtained in the first calculation, viz. the ray be for the grcater part of its length crossing the sca; if before the shifting and alteration of the spheroid; they will now otherwise, h= :04on?. . To take an example: the mean of cight observations of the zenith distance of the sea horizon at the top of take the form Ben Nevis is 91° 4'48", or s = 67:8; the ray is pretty equally dis($)+15+87+hda +kde, posed over land and water, and hence h = 1.047n3 = 4396 ít. The la')+15+g'nth'da+k'de, actual height of the hill by spirit-levelling is 4406 it., so that the error (w)+1'5+g"nth"la+k"de, of the height thus obtained is only 10 st. where the coefficients f, g, ... &c. can be numerically calculated. The determination of altitudes by means of spirit-levelling is Now these clements, corresponding to the projection of B on the undoubtedly the most exact method, particularly in its present spheroid of reference, must be equal severally to the astronomically development as precise-levelling, by which there have been deterdetermined elements at B, corrected for the inclination of the sur- mined in all civilized countries close-meshed nets of elevated points faces there. 118'in' be the components of the inclination at that covering the entire land. (A. R. C.; F. R. H.) point, then we have GEOFFREY, sumamed MARTEL (1006-1060), count of Anjou, X'=($')-°'+18+80+hda +kde, son of the count Fulk Nerra (9.0.) and of the countess Hildegarde n'tan '=(a')-a'+l'E+g'rth'da + k'de, n'sec ' = (w)-wti'& +8onth'da+k'de, 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 ', d', w are the observed elements at B. Here it appears (“the Gosling"), count of Vendôme, the son of his half-sister that the observation of longitude gives no additional information, Adela. Fulk having revolted, he confiscated the countship, but is available as a check upon the azimuthal observations. Il now there be a number of astronomical stations in the tri. / which he did not restore till 1050. On the ist of January 1032 angulation, and we form equations such as the above for each point, he married Agnes, widow of William the Great, duke of Aquitaine, then we can from them determine those values of E, 7, da, de, which and taking arms against William the Fat, eldest son and successor make the quantity + m2 +62+72+ ... a minimum. obtain that spheroid which best represents the surface covered by the of William the Great, defeated him and took him prisoner at triangulation. Mont-Couër near Saint-Jouin-de-Marnes on the oth of September In the Account of the Principal Triangulation of Great Brilain and Ireland will be found the determination, from 75 equations, of the the sons of his wife Agnes by William the Great, who were still 1033. He then tried to win recognition as dukes of Aquitaine for spheroid best representing the surface of the British Isles. Its elements are a = 20927005 + 295 ft., 6:0–6=280 +8; and it is so minors, but Fulk Nerra promptly took up arms to defend his placed that at Greenwich Observatory &=1'.864, 7= -0':546. suzerain William the Fat, from whom he held the Loudunois and 20 21-2k Saintonge in fies 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 (roth of March 1039) Geofirey 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 of twenty-one (1173); but though he enjoyed the temporalities affairs of Maine, though without much result, for having sided he was never consecrated and resigned the see in 1183. He then against Gervais, bishop of Le Mans, who was trying to make became his father's chancellor, holding a large number of lucrative himself guardian of the young count of Maine, Hugh, he had been benefices in plurality. Richard nominated him archbishop of beaten and forced to make terms with Gervais in 1038. In 1040 York in 1189, but he was not consecrated till 1191, or enthroned he succeeded his father in Anjou and was able to conquer Touraine till 1194. Geoffrey, though of high character, was a man of (1044) and assert his authority over Maine (see ANJOU). About uneven temper; his history in chiefly one of quarrels, with the 1050 he repudiated Agnes, his first wife, and married Grécie, the sec of Canterbury, with the chancellor Willian Longchamp, with widow of Bellay, lord of Montreuil-Bellay (before August 1052), his half-brothers Richard and John, and especially with his whom he subsequently left in order to marry Adela, daughter of a canons at York. This last dispute kept him in litigation before certain Count Odo. Later he returned to Grécie, but again left Richard and the pope for many years. He led the clergy in their her to marry Adelaide the German. When, however, he died on refusal to be taxed by John and was forced to fly the kingdom in the 14th of November 1060, at the monastery of St Nicholas at 1207. He died in Normandy on the 12th of December 1212. Angers, he lest no children, and transmitted the countship to See Giraldus Cambrensis, Vila Galfridi; Stubbs's prefaces to Geofirey the Bearded, the eldest of his nephews (see ANJOU). Roger de Hoveden, vols. iii. and iv. (Rolls Series). (H. W. C. D.) See Louis Halphen, Le Comté d'Anjou au XXe siècle (Paris, 1906). GEOFFREY DE MONTBRAY (d. 1093), bishop of Coutances A summary biography is given by Célestin Port, Dictionnaire historique, géographique ei biographique de Maine-et-Loirc (3 vols., (Constantiensis), a right-hand man of William the Conqueror, was Paris-Angers, 1874-1878), vol. ii. pp. 252-253, and a sketch of the a type of the great feudal prelate, warrior and administrator at wars by Kate Norgate, England under the Angevin Kings (2 vols., necd. He knew, says Orderic, more about marshalling mailed London, 1887), vol. i. chs. iii. iv. (L. H.) knights than edifying psalm-singing clerks. Obtaining, as a young GEOFFREY, surnamed PLANTAGENET (or PLANTEGENET) | man, in 1048, the sce of Coutances, by his brother's influence (1113-1151), count of Anjou, was the son of Count Fulk the Young (see MOWBRAY), he raised from his fellow nobles and from their and of Eremburge (or Arembourg of La Flèche; he was born on Sicilian spoils funds for completing his cathedral, which was the 24th of August 1113. He is also called “ le bel” or “the consecrated in 1056. With bishop Odo, a warrior like himself, handsome,” and received the surname of Plantagenet from the he was on the battle-field of Hastings, exhorting the Normans lo habit which he is said to have had of wearing in his cap a sprig of victory; and at William's coronation it was he who called on broom (genet). In 1127 he was made a knight, and on the end of themio acclaim their dukeasking. His rewardin England was a June 11 29 married Matilda, daughter of Henry I. of England, and mighty ficf scattered over twelve counties. He accompanied widow of the emperor Henry V. Some months afterwards he william on his visit to Normandy (1067), but, returning, led a succeeded to his father, who gave up the countship when he royal force to the relief of Montacute in September 1069. In 1075 definitively went to the kingdom of Jerusalem. The years of his he again took the field, leading with Bishop Odo a vast host government were spent in subduing the Angevin barons and in against the rebel earl of Norfolk, whose stronghold at Norwich conquering Normandy (see ANJOU). In 1151, while returning they besieged and captured. from the siege of Montreuil-Bellay, he took cold, in consequence of Meanwhile the Conqueror had invested him with important bathing in the Loir at Château-du-Loir, and died on the 7th of judicial functions. In 1072 he had presided over the great September. He was buried in the cathedral of Le Mans. By his Kentish suit between the primate and Bishop Odo, and about the wife Matilda hc had three sons: Henry Plantagenet, born at Le same time over those between the abbot of Ely and his despoilers, Mans on Sunday, the 5th of March 1133; Geoffrey, born at and between the bishop of Worcester and the abbot of Ely, and Argentan on the 1st of June 1134; and William Long-Sword, born there is some reason to think that he acted as a Domesday on the 22nd of July 1136. commissioner (1086), and was placed about the same time in See Kate Norgate, England under the Angevin Kings (2 vols., London, 1887), vol.' i. ch. v.-viii.; Célestin Port, Dictionnaire charge of Northumberland. The bishop, who attended the historique, géographique et biographique de Maine-et-Loire (3 vols.. Conqueror's funeral, joined in the great rising against William Paris-Angers, 1874-1878), vol. ii. pp: 254-256. A history of Rufus next year (1058), making Bristol, with which (as Geoffrey ic Bel has yet to be written; there is a biography of him Domesday shows) he was closely connected and where he had written in the 12th century by Jean, a monk of Marmoutier, Historia Gaufredi, ducis Normannorum et comilis Andegavorum, published by built a strong castle, his base of operations. Heburned Bath and Marchegay et Salmon; “ Chroniques des comtes d'Anjou " (Société ravaged Somerset, but had submitted to the king before the end de l'histoire de France, Paris, 1856), pp. 229-310. (L. H.) of the year. He appears to have been at Dover with William in GEOFFREY (1158-1186), duke of Brittany, fourth son of the January 1099, but, withdrawing to Normandy, died at Coutances English king Henry II. and his wise Elcanor of Aquitaine, was three years later. In his fidelity to Duke Robert he seems to born on the 23rd of September 1958. In 1167 Henry suggested a have there held out for him against his brother Henry, when the marriage between Geoffrey and Constance (d. 1201), daughter and latter obtained the Cotentin. heiress of Conan IV., duke of Brittany (d. 1171); and Conan not See E. A. Freeman, Norman Conquest and William Rufus; J. H, only assented, perhaps under compulsion, to this proposal, but Round, Feudal England; and, for original.authorities, the works of Orderic Vitalis and William of Poitiers, and of Florence of Worcester; surrendered the greater part of his unruly duchy to the English the Anglo-Saxon Chronicle: William of Malmesbury's Gesta pois king. Having received the homage of the Brelon nobles, tificum, and Lanfranc's works, ed. Giles; Domesday Book. Geoffrey joined his brothers, Henry and Richard, who, in alliance (J. H. R.) with Louis VII. of France, were in revolt against their father; but GEOFFREY OF MONMOUTH (d. 1954), bishop of St Asaph he made his peace in 1174, afterwards helping to restore order in and writer on early British history, was born about the year 1100. Brittany and Normandy, and aiding the new French king, Philip of his early life little is known, except that he reccived a liberal Augustus, «to crush some rebellious vassals In July 1181 his education under the eye of his paternal uncle, Uchtryd, who was marriage with Constance was celebrated, and practically the at that time archdeacon, and subsequently bishop, of Llandati. whole of his subsequent life was spent in warfare with his brother In 1129 Geoffrey appears at Oxford among the witnesses of an Richard. In 1183 he made peace with his father, who had come Osency charter. He subscribes himself Geoffrey Arturus; 'to Richard's assistance; but a fresh struggle soon broke out for from this we may perhaps inser that he had already begun bis the possession of Anjou, and Geoffrey was in Paris treating for experiments in the manufacture of Celtic mythology. A first aid with Philip Augustus, when he died on the 19th of August | edition of his Historia Brilonum was in circulation by the year 1139, although the text which we possess appears to date from the Historia Britonum Geoffrey is also credited with a Life of 1147. This famous work, which the author has the audacity Merlin composed in Latin verse. The authorship of this work to place on the same level with the histories of William of has, however, been disputed, on the ground that the style is disMalmesbury and Henry of Huntingdon, professes to be a transla- tinctly superior to that of the Historio. A minor composition, the tion from a Celtic source; "a very old book in the British Prophecies of Merlin, was written before 1136, and afterwards incortongue” which Walter, archdeacon of Oxford, had brought porated with the Historia, of which it forms the seventh book. from Brittany. Walter the archdeacon is a historical personage; For a discussion of the manuscripts of Geoffrey's work, see Sir whether his book has any real existence may be fairly questioned. T: D. Hardy's Descriptive Catalogue Rolls Series), i. pp. 341 tl. The Historia Briton um has been critically edited by San Marte (Halle, There is nothing in the matter or the style of the Historia to 1854). There is an English translation by J. A. Giles (London, 1842). preclude us from supposing that Geoffrey drew partly upon The Vila Merlini has been edited by F. Michel and T. Wright (Paris, confused traditions, partly on his own powers of invention, and 1837). See also the Dublin Unit. Magazine for April 1876, for an to a very slight degree upon the accepted authorities for early article by T. Gilray on the literary influence of Geoffrey; G. Heeger's British history. His chronology is fantastic and incredible; Trojanersage der Brillen (1889); and La Borderie's Eludes historiques . (H. W. C. D.) William of Newburgh justly remarks that, if we accepted the GEOFFREY OF PARIS (d. c. 1320), French chronicler, was events which Geoffrey relaies, we should have to suppose that probably the author of the Chronique métrique de Philippe le they had happened in another world. William of Newburgh | Bd, or Chronique rimée de Geoffroi de Paris. This work, which wrote, however, in the reign of Richard I. when the reputation deals with the history of France from 1300 to 1316, contains of Geoffrey's work was too well established to be shaken by such 7918 verses, and is valuable as that of a writer who had a personal criticisms. The fearless romancer had achieved an immediate knowledge of many of the events which he relates. Various short success. He was patronized by Robert, carl of Gloucester, and historical poems have also been attributed to Geoffrey, but there by two bishops of Lincoln; he obtained, about 1140, the arch- is no certain information about either his life or his writings. deaconry of Llandaff “on account of his learning "; and in The Chronique was published by J. A. Buchon in his Collection des 1151 was promoted to the see of St Asaph. chroniques, tome ix. (Paris, 1827), and it has also been printed in Before his death the Historic Britonum had already become a tome xxii. of the Recueil des historiens des Gaules et de la France (Paris, 1865). See G. Paris, Histoire de la littérature française au model and a quarry for poets and chroniclers. The list of moyen âge (Paris, 1890); and A. Molinier, Les Sources de l'histoire de imitators, begins with Geoffrey Gaimar, the author of the Estorie France, tome iii. (Paris, 1903). des Engles (c. 1147), and Wace, whose Roman de Brut (1155) is GEOFFREY THE BAKER (d. C. 1360), English chronicler, partly a translation and partly a free paraphrase of the Historia. is also called Walter of Swinbroke, and was probably a secular In the next century the influence of Geoffrey is unmistakably clerk at Swinbrook in Oxfordshire. He wrote a Chronicon attested by the Brul of Layamon, and the rhyming English Angliae temporibus Edwardi II. el Edwardi III., which deals chronicle of Robert of Gloucester. Among later historians who with the history of England from 1303 to 1356. From the beginwere deceived by the Historia Brilonum it is only nccdful toning until about 1324 this work is based upon Adam Murimuth's mention Higdon, Hardyng, Fabyan (1512), Holinshed (1580) Continuatio chronicorum, but after this date it is valuable and and John Milton. Still greater was the influence of Geoffrey interesting, containing information not found elsewhere, and upon those writers who, like Warner in Albion's England (1586), closing with a good account of the battle of Poitiers. The author and Drayton in Polyolbion (1613), deliberately made their obtained his knowledge about the last days of Edward II. from accounts of English history as poctical as possible. The stories William Bisschop, a companion of the king's murderers, Thomas which Geoffrey preserved or invented were not infrequently Gurney and John Maltravers. Geoffrey also wrote a Chroni. a source of inspiration to literary artists. The earliest English culum from the creation of the world until 1336, the value of tragedy, Gorboduc (1565), the Mirror for Magistrates (1587), and which is very slight. His writings have been edited with notes Shakespeare's Lear, are instances in point. It was, however, by Sir E. M. Thompson as the Chronicon Galfridi lc Baker de the Arthurian legend which of all his fabrications attained the Swynebroke (Oxford, 1889). Some doubt exists concerning greatest vogue. In the work of expanding and elaborating this Geoffrey's share in the compilation of the Vila et mors Edwardi theme the successors of Geoffrey went as far beyond him as heII., usually attributed to Sir Thomas de la More, or Moor, and had gone beyond Nennius; but he retains the credit due to the printed by Camden in his Anglica scripla. It has been maintained founder of a great school. Marie de France, who wrote at the by Camden and others that More wrote an account of Edward's court of Henry II., and Chrétien de Troyes, her French con reign in French, and that this was translated into Latin by temporary, were the earliest of the avowed romancers to take Geoffrey and used by him in compiling his Chronicon. Recent up the theme. The succeeding age saw the Arthurian story scholarship, however, asserts that More was no writer, and that popularized, through translations of the French romances, as the Vila et mors is an extract from Geoffrey's Chronicon, and far afield as Germany and Scandinavia. It produced in England was attributed to More, who was the author's patron. In the the Roman du Saint Graal and the Roman de Merlin, both from main this conclusion substantiates the verdict of Stubbs, who the pen of Robert de Borron; the Roman de Lancelot; the Roman has published the Vita et mors in his Chronicles of the reigns of de Tristan, which is attributed to a fictitious Lucas de Gast. In Edward I. and Edward II. (London, 1883). The manuscripts the reign of Edward IV. Sir Thomas Malory paraphrased and of Geoffrey's works are in the Bodleian library at Oxford. arranged the best episodes of these romances in English prose. GEOFFRIN, MARIE THÉRÈSE RODET (1699-1777), a His Morte d'Arthur, printed by Caxton in 1485, epitomizes the Frenchwoman who played an interesting part in French literary rich mythology which Geoffrey's work had first called into life, and artistic life, was born in Paris in 1699. She married, on the and gave the Arthurian story a lasting place in the English 19th of July 1713, Pierre François Geoffrin, a rich manufacturer imagination. The influence of the Historia Britonum may be and lieutenant-colonel of the National Guard, who died in 1750. illustrated in another way, by enumerating the more familiar It was not till Mme Geoffrin was nearly fifty years of age that we of the legends to which it first gave popularity. Of the twelve begin to hear of her as a power in Parisian society. She had books into which it is divided only three (Bks. IX., X., XI.) are learned much from Mme de Tencin, and about 1748 began to concerned with Arthur. Earlier in the work, however, we have gather round her a literary and artistic circle. She had every the adventures of Brutus; of his follower Corineus, the vanquisher week two dinners, on Monday for artists, and on Wednesday for of the Cornish giant Goemagol (Gogmagog); of Locrinus and her friends the Encyclopaedists and other men of letters. She his daughter Sabre (immortalized in Milton's Comus); of Bladud received many foreigners of distinction, Hume and Horace the builder of Bath; of Lear and his daughters; of the three Walpole among others. Walpole spent much time in her society pairs of brothers, Ferrex and Porrex, Brennius and Belinus, before he was finally attached to Mme du Deffand, and speaks of Elidure and Peridure. The story of Vortigern and Rowena her in his letters as a model of common sense. She was indeed takes its final form in the Historia Britonum; and Merlin makes somewhat of a small tyrant in her circle. She had adopted the his first appearance in the prelude to the Arthur legend. Besides | pose of an old woman earlier than necessary, and her coquetry, if |