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AVAVA YYAWWWYA
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AVAVA YYAWWWYA , g YAAMY/ AIWA . 146 in which dc and dA represent the errors in the length and See also:azimuth of any See also:side c which have been generated 7 in the course of the triangulation up to • it from the See also:base-See also:line and the azimuth station at the origin. The errors in the See also:latitude and See also:longitude of any station which are due to the triangulation are 3 dX, = [d .AX], and dL, = [d. AL]. Let station i be the origin, and let 2, 3, ... be the succeeding stations taken along a predetermined line of See also:traverse, which may either run from vertex to vertex 2 of the successive triangles, zigzagging between the flanks of the See also:chain, as in fig. 3 (I), or be carried directly along one of the flanks, as in fig. 3 (2). For the See also:general symbols of the See also:differential equations substitute Wk,,, AL,,, AA,,, c,,, A,,, and B,,, for the side between stations n and n+I of the traverse; and let Sc„ and 8A°be the errors generated between the sides and c,,; then 4 dci bc1 dc2 Sci Sc2 do " Sc c1 c1' c2=ci+ c2' '' = i c ; dA1=SA1; dA2=dBi+SA2; ... dA„=dB„_1+SA,,. Performing the necessary substitutions and summations, we get r Sc2 +A Sc° 1[DA17,- +2 [DA]~2 -{-...An c„ +(I+i[AA cot A] See also:sin i")SA1+(I+2[AA cot A] sin I")SA2 +...+(I+AA. cot A. sin I")SA,,. [Axil '+n[x]b C2 2+...+oa„bn" —['[AX tan A15A1+2[Da tan A]SA2+... l +oan tan A.M.] sin rnr 1 Sc2 bc° 1 [ALIs i +2 [AL]c2 +... +L n c„ +{1[AL cot A]SA1+a[.L cot A]SA2+... +AL, cot AnbA„] sin 1". Thus we have the following expression for any See also:geodetic See also:error:—µ,Sci+. +gnb n +,1SA1+... +,„SA„=E, (8) where g and 4) represent the respective summations which are the coefficients of Sc and SA in each instance but the first, in which I is added to the summation in forming the coefficient of SA. The angular errors x, y and z must now be introduced, in See also:place of Sc and SA, into the general expression, which will then take different forms, according as the route adopted for the line of traverse was the zigzag or the See also:direct. In the former, the number of stations on the traverse is ordinarily the same as the number of triangles, and, whether or no, a See also:common numerical notation may be adopted for both the traverse stations and the See also:collateral triangles; thus the angular errors of every triangle enter the general expression in the See also:form = c~x+cot Y . g'y —cot Z . g'z, in which µ'=g sin i ", and the upper sign of ¢ is taken if the triangle lies to the See also:left, the See also:lower if to the right, of the line of traverse. When the direct traverse is adopted, there are only See also:half as many traverse stations as triangles, and therefore only half the number of g's and 4,'s to determine; but it becomes necessary to adopt different numberings for the stations and the triangles, and the form of the coefficients of the angular errors alternates in successive triangles. Thus, if the pth triangle has no side on the line of the traverse but only an See also:angle at the lth station, the form is +sin .xp+cot Y5.gi •yp—cot Z.gt.z5. If the qth triangle has a side between the lth and the (l+I)th stations of the traverse, the form is cot Xq(gl — g't+I)xg + + 11'i+1 cot Yq)yq — (4u+1 — g( cot Z0)zq. As each See also:circuit has a right-See also:hand and a left-hand See also:branch, the errors of the angles are finally arranged so as to See also:present equations of the general form[GEODETIC TRIANGULATION u, v and w being the reciprocals of the weights of the observed angles. This necessitates the simultaneous See also:solution of eighty-three equations to obtain as many values of X. The resulting values of the errors of the angles in any, the pth, triangle, are xp= up[apal; y,= vp[b5)]; zp=w5[cpX]. (9) ii. One of the unknown quantities in every triangle, as x, may be eliminated from each of the eleven circuit and base-line equations by substituting its equivalent—(y+z) for it, a similar substitution being made in the minimum. Then the equations take the form [(b—a)y+(c—a)zJ=E, while the minimum becomes [(y+z)2 Y2 zil L u +;v +w Thus we have now to find only eleven values of a by a simultaneous solution of as many equations, instead of eighty-three values from eighty-three equations; but we arrive at more complex expressions for the angular errors as follows: rip yp = Zip+vp -[-wp[ (up+wp) [(bp— ap)X] —wp[(cp—ap)r]] • (ro) zp up+vp....wp[ (up+vp)[(cp— ap)xl —:zp[(bp — ap)al ] The second method has invariably been adopted, originally be. cause it was supposed that, the number of the factors A being reduced from the See also:total number of equations to that of the circuit and base-line equations, a See also:great saving of labour would be effected. But subsequently it was ascertained that in this respect there is little to choose between the two methods; for, when x is not eliminated, and as many factors are introduced as there are equations, the factors for the triangular equations may be readily eliminated at the outset. Then the really severe calculations will be restricted to the solution of the equations containing the factors for the circuit and base-line equations as in the second method. In the preceding See also:illustration it is assumed that the base-lines are errorless as compared with the triangulation. Strictly speaking, however, as base-lines are fallible quantities, presumably of different See also:weight, their errors should be introduced as unknown quantities of which the most probable values are to be determined in a simultaneous investigation of the errors of all the facts of observation, whether linear or angular. When they are connected together by so few triangles that their ratios may be deduced as accurately, or nearly so, from the triangulation as from the measured lengths, this ought to be done; but, when the connecting triangles are so numerous that the direct ratios are of much greater weight than the trigonometrical, the errors of the base-lines may be neglected. In the reduction of the See also:Indian triangulation it was decided, after examining the relative magnitudes of the probable errors of the linear and the angular See also:measures and ratios, to assume the base-lines to be errorless. The chains of triangles being largely composed of polygons or other networks, and not merely of single triangles, as has been assumed for simplicity in the illustration, the geometrical See also:harmony to be maintained involved the introduction of a large number of " side," " central and " toto-partial " equations of See also:condition, as well as the triangular. Thus the problem for attack was the simultaneous solution of a number of equations of condition =that of all the geometrical conditions of every figure+four times the number of circuits formed by the chains of triangles+the number of baselines—I, the number of unknown quantities contained in the equations being that of the whole of the observed angles' the method of See also:procedure, if rigorous, would be precisely similar to that already indicated for " harmonizing the angles of trigonometrical figures," of which it is merely an expansion from single figures to great See also:groups. The rigorous treatment would, however, have involved the simultaneous solution of about 4000 equations between 9230 unknown quantities, which was impracticable. The triangulation was therefore divided into sections for See also:separate reduction, of which the most important were the five between the meridians of 67° and 92° (see fig. I), consisting of four See also:quadrilateral figures and a trigon, each comprising several chains of triangles and some base-lines. This arrangement had the See also:advantage of enabling the final reductions to be taken in hand as soon as convenient after the completion of any See also:section, instead of being postponed until all were completed. It was subject, however, to the condition that the sections containing the best chains of triangles were to be first reduced; for, as all chains bordering contiguous sections would necessarily be " fixed " as a See also:part of the section first reduced, it was obviously desirable to run no See also:risk of impairing the best chains by forcing them into See also:adjustment with others of inferior quality. It happened that both the See also:north-See also:east and the See also:south-See also:west quadrilaterals contained several of the older chains; their reduction was therefore made to follow that of the collateral sections containing the See also:modern chains. But the reduction of each of these great sections was in itself a very formidable undertaking, necessitating some departure from a purely rigorous treatment. For the chains were largely composed of polygonal networks and not of single triangles only as assumed in the illustration, and therefore See also:cognizance had to be taken of a dB„= dX,,+, _ rl L +, = [ax+by+cz].—[ax+by+cz]i =E. The eleven circuit and base-line equations of condition having been duly constructed, the next step is to find values of the angular error, which will satisfy these equations, and be the most probable of any See also:system of values that will do so, and at the same See also:time will not disturb the existing harmony of the angles in each of the seventy-two triangles. Harmony is maintained by introducing the See also:equation of condition x+y+z=o for every triangle. The most probable results are obtained by the method of minimum squares, which may be applied in two ways. i. A See also:factor X may be obtained for each of the eighty-three equa- tions under the condition that [u2+ v +w] is made a minimum, number of " side " and other geometrical equations of condition, which entered irregularly and caused great entanglement. Equations 9 and ro of the illustration are of a See also:simple form because they have a single geometrical condition to maintain, the triangular, which is not only expressed by the simple and symmetrical equation x+y+z=o, but—what is of much greater importance—recurs in a See also:regular See also:order of sequence that materially facilitates the general solution. Thus, though the calculations must in all cases be very numerous and laborious, rules can be formulated under which they can be well controlled at every See also:stage and eventually brought to a successful issue. The other geometrical conditions of networks are expressed by equations which are not merely of a more complex form but have no regular order of sequence, for the networks pre-sent a variety of forms; thus their introduction would cause much entanglement and complication, and greatly increase the labour of the calculations and the chances of failure. Wherever, therefore, any See also:compound figure occurred, only so much of it as was required to form a chain of single triangles was employed. The figure having previously been made consistent, it was immaterial what part was employed, but the selection was usually made so as to introduce the fewest triangles, The triangulation for final simultaneous reduction was thus made to consist of chains of single triangles only; but all the included angles were " fixed " simultaneously. The excluded angles of compound figures were subsequently harmonized with the fixed angles, which was readily done for each figure per se. This departure from rigorous accuracy was not of material importance, for the angles of the compound figures excluded from the simultaneous reduction had already, in the course of the several See also:independent figural adjustments, been made to exert their full See also:influence on the included angles. The figural adjustments had, how-ever, introduced new relations between the angles of different figures, causing their weights to increase caeteris paribus with the number of geometrical conditions satisfied in each instance. Thus, suppose w to be the See also:average weight of the t observed angles of any figure, and n the number of geometrical conditions presented for See also:satisfaction; then the average weight of the angles after adjustment may be taken as w. t the factor thus being 1.5 for a triangle, 1.8 for a hexagon, 2 for a quadrilateral, 2.5 for the network around the Sironj base-line, &c. In framing the normal equations between the indeterminate factors X for the final simultaneous reduction, it would have greatly added to the labour of the subsequent calculations if a separate weight had been given to each angle, as was done in the See also:primary figural reductions; this was obviously unnecessary, for theoretical requirements would now be amply satisfied by giving equal weights to all the angles of each independent figure. The mean weight that was finally adopted for the angles of each See also:group was therefore taken as t w.ot n' p being the modulus. The second of the two processes for applying the method of minimum squares having been adopted, the values of the errors y and z of the angles appertaining to any, the pth, triangle were finally expressed by the following equations, which are derived from (1o) by substituting u for the reciprocal final mean weight as above determined: yn = 3 [(2bv — av — c5)X] zo = 3 [(2ca — a5 — b5)\] The following table gives the number of equations of condition and unknown quantities—the angular errors—in the five great sections of the triangulation, which were respectively included in the simultaneous general reductions and relegated to the subsequent adjustments of each figure per se: Simultaneous. See also:External Figural. Equations. Equations. Section. Tlc t ot:jz °~ era e Z sl F` m F E'w Side. u ' 1. N.W. Quad. . 23 550 165o 267 104 152 6 761 110 2. S.E. Quad. 15 277 831 164 64 92 2 476 68 3. N.E. Quad. . 49 573 1719 112 56 69 0 341 50 4. Trigon. . . 22 303 909 192 79 101 2 547 77 5. S. W. Quad. 24 172 516 83 32 52 1 237 40 The corrections to the angles were generally See also:minute, rarely exceeding the theoretical probable errors of the angles, and therefore applicable without taking any liberties with the facts of observation. Azimuth observations in connexion with the See also:principal triangulation were determined by measuring the See also:horizontal angle between a referring See also:mark and a circumpolar See also:star, shortly before and after See also:elongation, and usually at both elongations in order to eliminate the error of the star's place. Systematic changes of " See also:face " and of the zero settings of the azimuthal circle were made as in the measurement of the principal angles; but the repetitions on each zero were more numerous; the azimuthal levels were read and corrections applied to the star observations for dislevelinent. The triangulation was not adjusted, in the course of the final simultaneous reduction, to the astronomically determined azimuths, because they are liable to be vitiated by See also:local attractions; but the azimuths observed at about fifty stations around the primary azimuthal station, which was adopted as the origin of the geodetic calculations, were referred to that station, through the triangulation, for comparison with the primary azimuth. A table was prepared of the See also:differences (observed at the origin—computed from a distance) between the primary and the geodetic azimuths; the differences were assumed to be mainly due to the local deflexions of the plumb-line and only partially to error in the triangulation, and each was multiplied by the factor tangent of latitude of origin, =tangent of latitude of comparing station in order that the effect of the local attraction on the azimuth observed at the distant station—which varies with the latitude and is =the deflexion in the See also:prime See also:vertical X the tangent of the latitude —might be converted to what it would have been had the station been situated in the same latitude as the origin. Each See also:deduction was given a weight, w, inversely proportional to the number of triangles connecting the station with the origin, and the most probable value of the error of the observed azimuth at the origin was taken as x = [(observed —computed) p w] (12); [w] the value of x thus obtained was —PI". The formulae employed in the reduction of the azimuth observations were as follows. In the spherical triangle PZS, in which P is the See also:pole, Z the See also:zenith and S the star, the co-latitude PZ and the polar distance PS are known, and, as the angle at S is a right angle at the elongation, the See also:hour angle and the azimuth at that time are found from the equations cosP = tanPScotPZ, cosZ = cosPSsinP. The See also:interval, 6P, between the time of any observation and that of the elongation being known, the corresponding azimuthal angle, SZ, between the two positions of the star at the times of observation and elongation is given rigorously by the following expression —tan EZ 2sin'2SP cotPSsinPZsinP{1+tan2PScosSP+sec2PScotPsinbP} (13)' which is expressed as follows for logarithmic computation SZ = — m tan Z See also:cos' PS 1 — n +1 where m = 2 sine- cosec i', n = 2 sin2PS sin' , and 2 2 l=cot P sin SP; 1, m, and n are tabulated. Let A and B (fig. 4) be any two points the normals at which meet at C, cutting the See also:sea-level at p and q; take Dq=Ap, then BD is the difference of height; draw Height and ¢ .8 the tangents Aa and Bb at See also:Refraction. A and B, then aAB is the depression of B at A and bBA that of A at B; join AD, then BD is determined from the triangle ABD. The triangulation gives the distance between A and B at the sea-level, whence pq=c; thus, putting Ap, the height of A above the sea-level, =H, and pC= r, AD = c (t H c2 ) + r—24,.2 Putting Da and Db for the actual depressions at A and B, S for the angle at A, usually called the " subtended angle," and h for BD S = a(Db—Da) (15), and h = AD sin s (16) cos Db Azimuth Observations. (i4). The angle at C being=Db-f-Da, S may FiG' 4' be expressed in terms of a single vertical angle and C when observations have been taken at only one of the two points. P C, the "contained arc," =c—cosec 1" in seconds. Putting D'a PvY and D's for the observed vertical angles, and Oa, ¢b for the amounts by which they are affected by refraction, Da=D'a+4a and Ds=D'b-i-0b; and 4'b may differ in amount, but as they cannot be separately ascertained they are always assumed to be equal; the See also:hypothesis is sufficiently exact for See also:practical purposes when both verticals have been measured under similar atmospheric conditions. The retractions being taken equal, the observed verticals are substituted for the true in (15) to find S, and the difference of height is calculated by (16); the third See also:term within the brackets of (14) is usually omitted. The mean value of the refraction is deduced from the See also:formula ct.-= 2(C—D'.+D'b)) (17). An approximate value is thus obtained from the observations between the pairs of reciprocating stations in each See also:district, and the corresponding mean " coefficient of refraction," 4=C, is computed for the district, and is employed when heights have to be deter-See also:mined from observations at a single station only. When either of the vertical angles is an elevation—E must be substituted for D in the above expressions.' 2. LEVELLING Levelling is the See also:art of determining the relative heights of points on the See also:surface of the ground as referred to a hypothetical surface which cuts the direction of gravity everywhere at right angles. When a line of instrumental levels is begun at the sea-level, a See also:series of heights is determined corresponding to what would be found by perpendicular measurements upwards from the surface of See also:water communicating freely with the sea in underground channels; thus the line traced indicates a hypothetical prolongation of the surface of the sea inland, which is everywhere conformable to the See also:earth's curvature. The trigonometrical determination of the relative heights of points at known distances apart, by the measurements of their mutual vertical angles—is a method of levelling. But the method to which the term " levelling " is always applied is that of the direct determination of the differences of height from the readings of the lines at which graduated staves, held vertically over the points, are cut by,the horizontal See also:plane which passes through the See also:eye of the observer. Each method has its own advantages. The former is less accurate, but best suited for the requirements of a general See also:geographical survey, to obtain the heights of all the more prominent See also:objects on the surface of the ground, whether accessible or not. The latter may be conducted with extreme precision, and is specially valuable for the determination of the relative levels, however minute, of easily accessible points, however numerous, which succeed each other at See also:short intervals apart; thus it is very generally undertaken pari passu with geographical surveys to furnish lines of level for ready reference as a check on the accuracy of the trigonometrical heights. In levelling with staves the measurements are always taken from the horizontal plane which passes through the eye of the observer; but the line of levels which it is the See also:object of the operations to trace is a curved line, everywhere conforming to the normal curvature of the earth's surface, and deviating more and more from the plane of reference as the distance from the station of observation increases. Thus, either a correction for curvature must be applied to every See also:staff See also:reading, or the See also:instrument must be set up at equal distances from the staves; the curvature correction, being the same for each staff, will then be eliminated from the difference of the readings, which will thus give the true difference of level of the points on which the staves are set up.
Levelling has to be repeated frequently in executing a See also:long line of levels—say seven times on an average in every mile—and must be conducted with precaution against various errors. Instrumental errors arise when the visual See also:axis of the See also:telescope is not perpendicular to the axis of rotation, and when the focusing See also:tube does not move truly parallel to the visual axis on a See also:change of See also:focus. The first error is eliminated, and the second avoided, by placing the instrument at equal distances from the staves; and as this procedure has also the advantage of eliminating the corrections for both curvature and refraction, it should invariably be adopted.
' In topographical and levelling operations it is sometimes convenient to apply small corrections to observations of the height for curvature and refraction simultaneously. Putting d for the distance, r for the earth's See also:radius, and ic for the coefficient of refraction, and expressing the distance and radius in See also:miles and the correction to height in feet, then correction for curvature = d2; correction for refraction = —ticd2; correction for both
3Errors of staff readings should be guarded against by having the staves graduated on both faces, but differently figured, so that the observer may not be biased to repeat an error of the first reading in the second. The staves of the Indian survey have one face painted See also: Cumulative error, not eliminable by working in a circuit, may be caused when there is much northing or southing in the direction of the line, for then the See also:sun's See also:light will often fall endwise on the bubble of the level, See also:illuminating the See also:outer edge of the rim at the nearer end and the inner edge at the farther end, and so biasing the observer to take scale readings of edges which are not equidistant from the centre of the bubble; this introduces a tendency to raise the south or depress the north ends of lines of level in the See also:northern hemisphere. On long lines, the employment of a second observer, working independently over the same ground as the first, station by station, is very desirable. The great lines are usually carried over the See also:main roads of the See also:country, a number of " See also:bench marks " bring fixed for future reference. In the See also:ordnance survey of Great See also:Britain lines have been carried across from See also:coast to coast in such a manner that the level of any common See also:crossing point may be found by several independent lines. Of these points there are 166 in See also:England, See also:Scotland and See also:Wales; the discrepancies met with at them were adjusted simultaneously by the method of minimum squares. The sea-level is the natural datum plane for levelling operations, more particularly in countries bordering on the ocean. The earliest surveys of coasts were made for the use sea-,See also:eve, of navigators and, as it was considered very important that the charts should everywhere show the minimum See also:depth of water which a See also:vessel would meet with, See also:low water of See also:spring-tides was adopted as the datum. But this does not See also:answer the requirements of a See also:land survey, because the tidal range between extreme high and low water differs greatly at different points on coast-lines. Thus the generally adopted datum plane for land surveys is the mean sea-level, which, if not absolutely See also:uniform all the See also:world over, is much more nearly so than low water. Tidal observations have been taken at nearly fifty points on the coasts of Great Britain, which were connected by levelling operations; the local levels of mean sea were found to differ by larger magnitudes than could fairly be attributed to errors in the lines of level, having a range of 12 to 15 in. above or below the mean of all at points on the open coast, and more in tidal See also:rivers? But the general mean of the coast stations for England and Wales was practically identical with that for Scotland. The observations, however, were seldom of longer duration than a fortnight, which is insufficient for an exact determination of even the short See also:period components of the tides, and ignores the See also:annual and semi-annual components, which occasionally attain considerable magnitudes. The mean sea-levels at See also:Port Said in the Mediterranean and at See also:Suez in the Red Sea have been found to be identical, and a similar identity is said to exist in the levels of the See also:Atlantic and the Pacific oceans on the opposite coasts of the See also:Isthmus of See also:Panama. This is in favour of a uniform level all the world over; but, on the other hand, lines of level carried across the See also:continent of See also:Europe make the mean sea-level of the Mediterranean at See also:Marseilles and See also:Trieste from 2 to 5 ft. below that of the North Sea and the Atlantic at See also:Amsterdam and Brest—a result which 2In tidal estuaries and rivers the mean water-level rises above the mean sea-level as the distance from the open coast-line increases; for instance, in the Hooghly See also:river, passing See also:Calcutta, there is a rise of to in. in 42 M. between See also:Sagar (See also:Saugor) See also:Island at the mouth of the river and See also:Diamond See also:Harbour, and a further rise of 20 in. in 43 m. between Diamond Harbour and Kidderpur. it is not easy to explain on See also:mechanical principles. In See also:India various tidal stations on the east and west coasts, at which the mean sea-level has been determined from several years' observations, have been connected by lines of level run along the coasts and across the continent; the differences between the results were in all cases due with greater See also:probability to error generated in levelling over lines of great length than to actual differences of sea-level in different localities. The sea-level, however, may not coincide everywhere with the geometrical figure which most closely represents the earth's Qeoldor surface, but may be raised or lowered, here and there, Deformed under the influence of local and abnormal attrac- tions, presenting an equipotential surface—an See also:ellipsoid or See also:spheroid of revolution slightly deformed by bumps and hollows—which H. Bruns calls a " See also:geoid." See also:Archdeacon See also:Pratt has shown that, under the combined influence of the See also:positive attraction of the Himalayan Mountains and the negative attraction of the Indian Ocean, the sea-level may be some 56o ft. higher at See also:Karachi than at Cape See also:Comorin; but, on the other hand, the Indian pendulum operations have shown that there is a deficiency of See also:density under the Himalayas and an increase under the See also:bed of the ocean, which may wholly compensate for the excess of the See also:mountain masses and deficiency of the ocean, and leave the surface undisturbed. If any bumps and hollows exist, they cannot be measured, instrumentally; for the instrumental levels will be affected by the local attractions precisely as the sea-level is, and will thus invariably show level surfaces even should there be considerable deviations from the geometrical figure. . 3. TOPOGRAPHICAL SURVEYS The See also:skeleton framework of a survey over a large See also:area should be triangulation, although it is frequently combined with traversing. The method of filling in the details is necessarily influenced to some extent by the nature of the framework, but it depends mainly on the magnitude of the scale and the requisite degree of minutiae. In all instances the principal triangles and circuit traverses have to be broken down into smaller ones to furnish a sufficient number of fixed points and lines for the subsequent operations. The filling in may be performed wholly by linear measurements or wholly by direction intersections, but is most frequently effected by both linear and angular measures, the former taken with chains and tapes and offset poles, the latter with small theodolites, sextants, See also:optical squares or other reflecting See also:instruments, magnetized needles, prismatic compasses and plane tables. When the scale of a survey is large, the linear and angular measures are usually recorded on the spot in a See also: ~When a considerable area has to be treated by traverses it is divided into a number of blocks of convenient See also:size, bounded by roads, rivers or See also:parish boundaries, and a " traverse on the See also:meridian of the origin " is carried round the periphery of each See also:block. Be-ginning at a trigonometrical station, the theodolite is set to circle reading o° o' with the telescope pointing to the north, and at every " forward " station of the traverse the circle is set to the same reading when the telescope is pointed at the " back " station as was obtained at the back station when the telescope was pointing to the forward one. When the circuit is completed and the theodolite again put up at the origin and set on the last back station with the appropriate circle reading, the circle reading, with the telescope again pointed to the first forward station, will be the same as at first, if no error has been committed. This system establishes a convenient check on the accuracy of the operations and enables the angles to be readily protracted on a system of lines parallel to the meridian of the origin. As a further check the traverse is connected with all contiguous trigonometrical stations by measured angles and distances. Traverses are frequently carried between the points already fixed on the sides of the minor triangles; the initial side is then adopted, instead of the meridian, as the axis of co-ordinates for the plotting, the telescope being pointed with circle reading o° o' to either of the trigonometrical stations at the extremities of the side. The plotting is done from the field-books of the surveyors by a separate agency. Its accuracy is tested by examination on the ground, when all necessary addenda are made. The examiner —who should be surveyor, plotter and draughtsman—verifies the accuracy of the detail by intersections and productions and occasional direct measurements, and generally endeavours to cause the details under examination to prove the accuracy of each other rather than to obtain direct See also:proof by remeasurement. He fixes conspicuous trees and delineates the woods, footpaths, rocks, precipices, steep slopes, embankments, &c., and supplies the requisite See also:information regarding minor objects to enable a draughtsman to make a perfect See also:representation according to the scale of the map. In examining a coast-line he delineates the See also:foreshore and sketches the strike and See also:dip of the stratified rocks. In tidal rivers he ascertains and marks the highest points to which the See also:ordinary tides flow. The examiner on the 25.344 in. scale (=-2510) is required to give all necessary information regarding the parcels of ground of different character—whether arable, pasture, See also:wood, See also:moor, See also:moss, sandy—defining the limits of each on a separate tracing if necessary. He has also to distinguish between See also:turnpike, parish and occupation roads, to collect all names, and to furnish notes of military, baronial and ecclesiastical antiquities to enable them to be appropriately represented in the final maps. The latter are subjected to a double examination—first in the office, secondly on the ground; they are then handed over to the officer in See also:charge of the levelling to have the levels and See also:contour lines inserted, and finally to the hill sketchers, whose See also:duty it is to make an See also:artistic representation of the features of the ground. In the Indian survey all filling in is done by plane-tabling on a basis of points previously fixed; the methods differ simply in the extent to which linear measures are introduced to supplement the direction rays of the plane-table. When the scale of the survey is small, direct measurements of distance are rarely made and the filling is usually done wholly by direction intersections, which See also:fix all the principal points, and by eye-sketching; but as the scale is increased linear measures with chains and offset poles are introduced to the extent that may be desirable. A See also:sheet of See also:drawing paper is mounted on See also:cloth over the face of the plane-table; the points, previously fixed by triangulation or otherwise, are projected on it—the collateral meridians and See also:parallels, or the rectangular co-ordinates, when these are more convenient for employment than the spherical, having first been drawn; the plane-table is then ready for use. Operations are begun at a fixed point by aligning with the sight rule on another fixed point, which brings the meridian line of the table on that of the station. The magnetic See also:needle may now be placed on the table and a position assigned to it for future reference. Rays are drawn from the station point on the table to all conspicuous objects around with the aid of the sight rule. The table is then taken to other fixed points, and the process of See also:ray-drawing is repeated at each; thus a number of objects, some of which may become available as stations of observation, are fixed. Additional stations may be established by setting up the table on a ray, adjusting it on the back station—that from which the ray was drawn—and then obtaining a cross intersection with the sight rule laid on some other fixed point, also by interpolating between three fixed points situated around the observer. The magnetic needle may not be relied on for correct See also:orientation, but is of service in enabling the table to be set so nearly true at the outset that it has to be very slightly altered afterwards. The error in the setting is indicated by the rays from the surrounding fixed points intersecting in a small triangle instead of a point, and a slight change in azimuth suffices to reduce the triangle to a point, which will indicate the position of the station exactly. Azimuthal error being less apparent on short than on long lines, See also:interpolation is best performed by rays drawn from near points, and checked by rays drawn to distant points, as the latter show most strongly the magnitude of any error of the primary magnetic setting. In this way, and by self-verificatory traverses " on the back ray " between fixed points, plane-table stations are established over the ground at appropriate intervals, depending on the scale of the survey; and from these stations all surrounding objects which the scale permits of being shown are laid down on the table, sometimes by rays only, sometimes by a single ray and a measured distance. The general configuration- of the ground is delineated simultaneously. In checking and examination various methods are followed. For large scale work in plains it is customary to run arbitrary lines across it and make an independent survey of the See also:belt of ground to a distance of a few chains on either side for comparison with the See also:original survey; the smaller scale hill See also:topography is checked by examination from commanding points, and also by traverses run across the finished work on the table. 4. GEOGRAPHICAL SURVEYING The introduction by mechanical means of See also:superior See also:graduation in instruments of the smaller class has enabled surveyors to effect Base See also:good results more rapidly, and with less See also:expenditure Measure- on equipment and on the staff necessary for transport meats. in the field, than was formerly possible. The 12-in. theodolite of the present See also:day, with See also:micrometer adjustments to assist in the reading of minute subdivisions of angular graduation, is found to be equal to the old 24-in. or even 36-in. instruments. New Methods for the measurement of bases have largely superseded the laborious process of measurement by the alignment of " See also:compensation " bars, though not entirely independent of them. The Jaderin apparatus, which consists of a See also:wire 25 metres in length stretched along a series of cradles or supports, is the simplest means of measuring a base yet devised; and experiments with it at the Pulkova See also:observatory show it to be capable of producing most accurate results. But there is' a measurable defect in the apparatus, owing to the liability of the wires to change in length under variable conditions of temperature. It is therefore considered necessary, where base measurements for geodetic purposes are to be made with scientific exactness, that the Jaderin wires should be compared before and after use with a See also:standard measurement, and this standard is best attained by the use of the See also:Brunner, or See also:Colby, bars. The direct process of measurement is not extended to such lengths as formerly, but from the ends of a shorter line, the length of which has been exactly determined, the base is extended by a process of triangulation. There are vast areas in which, while it is impossible to apply the elaborate processes of first-class or " geodetic " triangulation, secondary it is nevertheless desirable that we should rapidly Triangula- acquire such geographical knowledge as will enable tien. us to See also:lay down See also:political boundaries, to project roads and railways, and to attain such exact knowledge of See also:special localities as will further military ends. Such surveys are called by various names—military surveys, first surveys, geographical surveys, &c.; but, inasmuch as they are all undertaken with the same end in view, i.e. the acquisition of a See also:sound topographical map on various scales, and as that end serves See also:civil purposes as much as military, it seems appropriate to designate them geographical surveys only. The governing principles of geographical surveys are rapidity and See also:economy. Accuracy is, of course, a recognized See also:necessity, but Principles the term must admit of a certain See also:elasticity in See also:gee-which graphical work which is inadmissible in geodetic govern Geo- or cadastral functions. It is obviously foolish to graphical expend as much See also:money over the elaboration of toposurveys, graphy in the unpeopled See also:sand wastes which border the See also:Nile valley, for instance (albeit those deserts may be full of triangulation, or at least by some process analogous surveds of 3' Survey. to triangulation, which will furnish the necessary skeleton on which to adjust the topography so as to ensure a See also:complete and homogeneous map. This base may be found in a variety of ways. If geodetic triangulation exists in the country, that triangulation should of course include a wide extent of secondary determina- TieBase. tions, the fixing of peaks and points in the landscape far away to either flank, which will either give the data for further See also:extension of geographical triangulation, or which may even serve the purposes of the map-maker without any such extension at all. In this manner the See also:Indus valley series of the triangulation of India has furnished the basis for surveys across See also:Afghanistan and See also:Baluchistan to the See also:Oxus and See also:Persia. Should no such preliminary determinations of the value of one or two.starting-points be available, and it becomes necessary to measure a base and to work ab initio, the Jaderin wire apparatus may be adopted. It is cheap (cost about 50), and far more accurate than the process of measuring either by any known " subtense " system (in which the distance is computed from the angle subtended by a See also:bar of given length) or by measurement with a See also:steel chain. This latter method may, however, be adopted so long as the base can be levelled, repeated measurements obtained, and the chain compared with a standard steel tape before and after use. The initial data on which to start a comprehensive See also:scheme of triangulation for a geographical survey are: (1) latitude; Initial Data. (2) longitude;. (3) azimuth; and (4) See also:altitude, and this data should, if possible, be obtained past passu with the measurement of the base. A 6-in. transit theodolite, fitted with a micrometer eyepiece and extra vertical wires, is the instrument See also:par excellence for work of this, nature; and it possesses the advantages of portability and See also:comparative cheapness. The method of using it for the purposes of determining values for (1) and (3), i.e. for ascertaining the latitude of one end of the base and the azimuth of the other end from it, are Latitude and fully explained in See also:Major See also:Talbot's paper on Military Azimuth. Surveying in the Field (J. See also:Mackay & Co., See also:Chatham, 1889), which is not a theoretical See also:treatise, but a practical illustration of methods employed successfully in the geographical survey of a very large area of the Indian transfrontier districts. It should be noted that these observations are not merely of an initial See also:character. They should be constantly repeated as the survey advances, and under certain circumstances (referred to subsequently) they require daily repetition. The problems connected with the determination of (2) longitude have of See also:late years occupied much of the See also:attention of scientific surveyors. No system of See also:absolute determination is Longitude. accurate enough for See also:combination with triangulation,
as affording a check on the accuracy of the latter, and the spaces in the world across which geographical surveying has yet to be carried are rapidly becoming too restricted to admit of any liability to error so great as is invariably involved in such determinations. It is true that absolute values derived from the observation of lunar distances, or occultations, have often proved to be of the highest value; but there remains a degree of uncertainty (possibly due to the want of exact knowledge of the See also:moon's position at any instant of time), even when observations have been taken with all the advantages of the most elaborate arrangements and the most scientific manipulation, which renders the roughest form of triangulation more trustworthy for ascertaining differential longitude than any comparison between the absolute determination of any two points. Consequently, if an absolute determination is necessary it should be made once, with all possible care, and the value obtained should be carried through the whole scheme of triangulation. It rests with the surveyor to decide at what point of the general survey this value can best be introduced, provided he
topographical detail), as in the valley itself—the great centre of See also:Egyptian cultivation, the great military See also:highway of northern See also:Africa. On the other hand, the most careful accuracy attainable in the art of topographical delineation is requisite in illustrating the nature of a district which immediately surrounds what may prove hereafter to be an important military position. And this, again, implies a class of technical accuracy which is quite apart from the rigid attention to detail of a cadastral survey, and demands a much higher intelligence to See also:compass.
The technical principles of procedure, however, are the same in geographical as in other surveys. A geographical survey must equally start from a base and be supported by
can estimate the probable See also:longitudinal value of his initial base within a few minutes of the truth. A final correction in longitude is constant, and can easily be applied. With reference to such absolute determinations of longitude, Major S. See also: See also:Soc. Journ. for See also:June 1896) will afford the observer valuable assistance. But the recognized method of obtaining a longitude value in See also:recent geographical See also:fields is by means of the telegraph—a method so simple and so accurate that it may be applied with See also:Telegraph advantage even to the checking of long lines of tri-Determina- angulation. No effort should be spared to introduce a dons. telegraphic longitude value into any scheme of geographical survey. It involves a clear line and an instructed observer at each end, but, given these desiderata, the interchange of time signals sufficient for an accurate See also:record only requires a See also:night or two of clear See also:weather. But inasmuch as rigorous accuracy in the observations for time is necessary, it would be well for the surveyor in the field to be provided with a sidereal chronometer. Under all other circumstances demanding time observations (and they are an essential supplement to every class of astronomical determination) an ordinary mean time See also:watch is sufficient. With reference to altitude determinations, there has lately been observable amongst surveyors a growing distrust of barometric Altitude. results and a reaction in favour of direct levelling, or of differential results derived from direct observation with the theodolite (or clinometer) rather than from comparison of those determined by aneroid or See also:hypsometer. It is indeed impossible to eliminate the uncertainties due to the variable atmospheric pressure introduced by " weather " changes from any barometric record. A See also:mercurial See also:barometer advantageously placed and carefully observed at fixed diurnal intervals throughout a comparatively long period may give fairly trustworthy results if a constant comparison can be maintained throughout that period with similar records at sea-level, or at any fixed altitude. Yet observations extending over several months have been found to yield results which compare most unfavourably with those attained during the process of triangulation by continued lines of vertical observations from point to point, even when the uncertainties of the correction for refraction are taken into See also:account. Errors introduced into vertical observations by refraction are readily ascertainable and comparatively unimportant in their effect. Those due to variable atmospheric conditions on barometric records are still indefinite, and are likely to remain so. The result has been that the latter have been relegated to purely local conditions of survey, and that whenever practicable the former are combined with the general process of triangulation. The conditions under which geographical surveys can be carried out are of See also:infinite variety, but those conditions are rare which absolutely preclude the possibility of any such expression) of the topography, even when the configuration of the land surface is favourable. In such circumstances the method of observing azimuths to points situated approximately near to the probable route in advance, and of deter- Triangulamining the exact position of those points in latitude ilon or as one by one they are passed by the moving force, Oil IV . has been found to yield results which are quite sufficiently accurate to ensure the final adjustment of the entire route See also:geography to any subsequent system of triangulation which may be extended through the country traversed, without serious discrepancies in compilation. It is, however, obvious that as accuracy depends greatly on the exact determination of absolute latitude values, this method is best adapted to a route See also:running approximately parallel to a meridian, and is at complete disadvantage in one running east and west. Where the conditions are favourable to its application, it has been adopted with most satisfactory results; as, for instance, on the route between See also:Seistan and See also:Herat, where the initial data for the Russo-Afghan boundary delimitation was secured by this means, and more recently on the boundary surveys of western See also:Abyssinia. When an active enemy is in the field, and topographical operations are consequently restricted, it is usually possible to obtain the necessary See also:control " (i.e. a few well-fixed points determined by triangulation) for topography in advance MGeography. of a position securely held. With a very little assist- ance from the triangulator an experienced topographer will be able to See also:sketch a field of See also:action with far more certainty and rapidity than can be attained by the ordinary so-called " military surveyor," and he may, in favourable circumstances, combine his work with that of the military balloonist in such a way as to represent every feature of importance, even in a widely extended position held by the enemy. The application of the See also:camera and of telephotography to the See also:evolution of a map of the enemy's position is well understood in See also:France (vide See also:Colonel Laussedat's treatise on " The See also:History of Topography "), as it is in See also:Russia, and we must in future expect that all advantages of an See also:expert and professional map of the whole See also:theatre of a See also:campaign will See also:lie in the hands of the general who is best supplied with professional experts to compass them. Geographical surveying and military surveying are convertible terms, and it is important to See also:note that both equally require the services of a highly trained staff of professional topographers. During the See also:war between Russia and. See also:Turkey (1817–78) upwards of a See also:hundred professional geographical surveyors were pressed into military service, besides the regular survey staff which is attached to every See also:army See also:corps. Triangulation was carried across the Balkans by eight different series; every pass and every notable feature of the Balkans and Rhodope Mountains was accurately surveyed, as well as the plains intervening between the Balkans and See also:Constantinople. Surveys on a scale which averaged about 1 m. = r in. were carried up to the very See also:gates of the See also:city. The use of the camera as an See also:accessory to the plane table (i.e. the art of photo-topography) has been applied almost exclusively to geographical or exploratory surveys. The camera is specially prepared, resting on a graduated horizontal photo-topoplate which is read with verniers, and with a small•0aphs' telescope and vertical arc attached. Cross wires are fixed in the See also:focal plane of the camera, which is also fitted with a magnetic needle and a scale so placed that the magnetic declination, the scale, and the intersection of the cross wires are all photographed on the See also:plate containing the view. A panoramic group of views (slightly overlapping each other) is taken at each station, and the angular distance between each is measured on the horizontal circle. The process of constructing the horizontal See also:projection front these See also:perspective views involves plotting the skeleton triangulation, as obtained from the primary triangulation, with the theodolite (which precedes the photo-topographical survey), or from the horizontal plate of the camera. kWith several stations so plotted, the view from each of them of a certain portion of the country may be projected on the plane of the map, and salient points seen in perspective may be fixed by intersection. The field work of a photo-topographic party consists primarily in See also:execution of a triangulation by the usual methods which would be adapted to any ordinary topographical survey. To this is added a secondary triangulation, which is executed pari passe with the See also:photography for the purpose of fixing the position of the camera stations. From such stations alone the topographical details are finally secured with the aid of the photographs. Great care is necessary in the selection of stations that 'will be suitable both for the extension of triangulation and the purposes of closely overlooking topographical details. In order to obtain means for correctly orienting the photographic views when plotting the map from them, it is usual, whilst making the exposures, to observe two or three points in each view with the aft-azimuth attached to the camera, in order to ascertain the horizontal and vertical angles between them. It is also advisable to keep an outline sketch of the landscape for the purpose of recording names of roads, buildings, &c.
The process of projecting the map from the photographs involves the use of two drawing-boards, on one of which the graphical determination of the points is made, and on the other the details
Conditions surveys at all. Perfect freedom of action, and the
under underwhich
Geographi- recognition of such work as a public benefit, are not cal Surveys often attainable. Far more frequently the opporare carried tunity offers itself to the surveyor with the progress
out.
of a political See also:mission or the advance of an army in the field. It cannot be too strongly insisted on that geographical surveys are functions of both civil and military operations. Very much of such work Is also possible where a country lies open to exploration, not actively hostile, but yet unsettled and adverse to strangers. The geographical surveyor has to See also:fit himself to all such conditions, and it may happen that a continuous, comprehensive scheme of triangulation as a map basis is impossible. Under such circumstances other expedients must be adopted to ensure that accuracy of position which cannot be attained by the topographer unaided.
During a long-continued See also: Occasionally a hill can be reached in the course of the day's march, or (luring a day's See also:halt, which will materially assist to consolidate and strengthen the series. It may. however, frequently be impossible to maintain a consistent series of triangulation for the " control " (to use an See also:American 152 of the final topography are drawn. The principal trigonometrical points are plotted on both these boards by their co-ordinates, and the camera stations either by their co-See also:ordinate values or by intersection. Intermediate points, selected as appearing on two or more negatives, are then projected by intersection. The horizontal projection of a See also:panorama consisting of any given number of plates is a regular geometrical figure of as many sides as there are plates, enclosing an inscribed circle whose radius is the focal length of the camera. Having correctly plotted the position of one plate, or view, with reference to the projected camera station by means of the angle observed to some known point within it, it is possible to See also:plot the position of the See also:rest of the series, with reference to the camera station and the orienting triangulation point, by the angular differences which are dependent on the number of photographs forming the sides of the geometrical figure. Having secured the correct orientation of the horizontal See also:plan, direction lines are drawn from the plotted camera station to points photographed, and the position of topographical features is fixed by intersection from two or more camera stations. The plane-table is the instrument, par excellence, on which the geographical surveyor must depend for the final mapping of the See also:physical features of the country under survey. The Plane- methods of adapting the plane-table to geographical table, requirements differ with those varying See also:climatic conditions which affect its construction. In the comparatively dry See also:climate of See also:Asiatic Russia or of the See also:United States, where errors arising from the unequal expansion of the plane-table See also:board are insignificant, the plane-table is largely made use of as a triangulating instrument, and is fitted with slow-See also:motion screws and with other appliances for increasing the certainty and the accuracy of observations. Such an See also:adaptation of the plane-table is found to be impossible in India, where the great alternations of temperature, no less than of atmospheric humidity, tend to vitiate the ac-curacy of the projections on the surface of the board by the unequal effects of expansion in the material of which it is composed. The Indian plane-table is of the simplest possible construction, and it is never used in connexion with the stadia for ascertaining the distances of points and features of the ground (as is the See also:case in See also:America) ; and in place of the complicated American See also:alidade, with its telescope and vertical arc, a simple sight rule is used, and a chirometer for the measurement of vertical angles. The Indian plane-table approximates closely in general construction to the " Gannett " See also:pattern of America, which is specially constructed for exploratory surveys. The scale on which geographical surveys are conducted is necessarily small. It may be reckoned at from I : 500000 to I : 125000, or from 1 in. = 8 m. to I in. = 2 m. The r in. = I m. Scale• scale is. the normal scale for rigorous topography, and although it is impossible to fix a definite line beyond which geographical scales See also:merge into topographical (for instance, the 1-in. scale is classed as geographical in America whenever the continuous line contour system of ground representation gives place to hachuring), it is convenient to assume generally that geographical scales of mapping are smaller than the 1-in. scale. On the smaller scales of I : 500000 or I : 250000 an experienced geographical surveyor, in favourable country, will complete an area Out-fora. of mapping from day to day which will practically See also:cover nearly all that falls within his range of See also:vision; and he will, in the course of five or six months of continuous travelling (especially if provided with the necessary " control ") cover an area of geographical mapping illustrating all important topographical features representable on the small scale of his survey, which may be reckoned at tens of thousands of square miles. But inasmuch as everything depends upon his range of vision, and the constant occurrence of suitable features from which to extend it, there is obviously no guiding rule by which to reckon his probable out-turn. The same uncertainty which exists about " out-turn " manifestly exists about " cost." The normal cost of the 1-in. rigorous topo-Cost. graphical survey in India, when carried over districts which present an average of hills, plains and forests, may be estimated as between 35 to 40 shillings a square mile. This compares favourably with the rates which obtain in America over districts which probably present far more facilities for surveying than India does, but where cheap native labour is unknown. The geographical surveyor is simply a topographer employed on a smaller scale survey. His equipment and staff are somewhat less but, on the other hand, his travelling expenses are greater. It is found that, on the whole, a See also:fair average for the cost of geographical work may be struck by applying the square of the unit of scale as a factor to 1-in. survey rates; thus a See also:quarter-inch scale survey (i.e. 4m. to the in.), should be one-sixteenth of the cost per mile of the 1-in. survey over similar ground. A geographical See also:reconnaissance on the scale of I : 500000 (8 m. = I in.) should be one-sixtyfourth of the square-mile cost of the 1-in. survey, &c. This is, indeed, a See also:close approximation to the results obtained on the Indian transfrontier, and would probably be found to hold good for See also:British colonial possessions. In processes of map See also:reproduction an invention for the reproduction of drawings by a method of direct See also:printing on See also:zinc without the intervention of a negative has proved of great value. By this[TRAVERSING AND FISCAL method a considerable quantity of work has been turned out in much less time and at a much lower cost than would be Map Rvroinvolved by any process of photo-zincography or daclon. See also:lithography. A large number of cadastral maps have been reproduced at about one-ninth of the ordinary cadastral See also:rate. For the rapid reproduction of geographical maps in the field in order to meet the requirements of a general conducting a campaign, or of a political officer on a boundary mission, no better method has been evolved than the ferrotype process, by which See also:blue prints can be secured in a few See also:hours from a drawing of the original on tracing-cloth. The sensitized paper and printing-See also:frame are far more portable than any photo-lithographic apparatus. Sketches illustrative of a field of action may be placed in the hands of the general commanding on the day following the action, if the weather conditions are favourable for their development. The necessity for darkness whilst dealing with the sensitized material is a draw-back, but it may usually be arranged with blankets and waterproof sheets when a See also:tent is not available. 5. TRAVERSING AND FISCAL, OR See also:REVENUE, SURVEYS Traversing is a combination of linear and angular measures in equal proportions; the surveyor proceeds from point to point, measuring the lines between them and at each point the angle between the back and forward lines; he runs his lines as much as possible over level and open ground, avoiding obstacles by working round them. The system is well suited for laying down roads, boundary lines, and circuitous features of the ground, and is very generally resorted to for filling in the interior details of surveys based on triangulation. It has been largely employed in certain districts of British India, which had to be surveyed in a manner to satisfy fiscal as well as topographical requirements; for, the See also:village being the administrative unit of the district, the boundary of every village had to be laid down, and this necessitated the survey of an enormous number of circuits. Moreover, the traverse system was better adapted for the country than a network of triangulation, as the ground was generally very See also:flat and covered with trees, villages, and other obstacles to distant vision, and was also devoid of hills and other commanding points of view. The principal triangulation had been carried across it, but by chains executed with great difficulty and expense, and therefore at wide intervals apart, with the intention that the intermediate spaces should be provided with points as a basis for the general topography in some other way. A system of traverses was obviously the best that could be adopted under the circumstances, as it not only gave all the village boundaries, but was practically easier to execute than a network of minor triangulation. In the Indian survey the traverses are executed in minor circuits following the periphery of each village and in major circuits comprising groups of several villages; the former are done with 4" to 6" theodolites and a single chain, the latter with 7" to ro" theodolites and a pair of chains, which are compared frequently with a standard. The main circuits are connected with every station of the principal triangulation within reach. The meridian of the origin is determined by astronomical observations; the angle at the origin between the meridian and the next station is measured, and then at each of the successive stations the angle between the immediately preceding and following stations; summing these together, the " inclinations " of the lines between the stations to the meridian of the origin are successively determined. The distances between the stations, multi-plied by the cosines and sines of the inclinations, give the distance of each station from the one preceding it, resolved in the directions parallel and perpendicular respectively to the meridian of the origin; and the algebraical sums of these quantities give the corresponding rectangular co-ordinates of the successive stations relatively to the origin and its meridian. The area included in any circuit is expressed by the formula area =half algebraical sum of products (xi +X2) (y2—Y1) (18), x,, y, being the co-ordinates of the first, and x2, y2 those of the second station, of every line of the traverse in See also:succession round the circuit. Of geometrical tests there are two, both applicable at the close of a circuit: the first is angular, viz. the sum of all the interior angles of the described See also:polygon should be equal to twice as See also:man, right angles as the figure has sides, less four; the second is linear, viz. the algebraical sum of the x co-ordinates and that. of the y co-ordinates should each be=o. The astronomical test is this: at any station of the traverse the azimuth of a referring mark may be determined by astronomical observations; the inclination of the line between the station and the referring mark to the meridian of the origin is given by the traverse, the two should differ by the convergency of the meridians of the station and the origin. In practice the angles of the traverse are usually adjusted to satisfy their special geometrical and astronomical tests in the first instance, and then the co-ordinates of the stations are calculated and adjusted by corrections applied to the longest, that the angles may be least disturbed, as no further corrections are given them. The exact value of the convergence, when the distance and azi- Conver- muth of the second astronomical station from the first gency of are known, is that of B — (rr+A) of equation (5) ; Meridians. but, as the first term is sufficient for a traverse, we have convergency = x tan Xcosec 11" substituting x, the co-ordinate of the second station perpendicular to the meridian of the origin, for c sin A. The co-ordinates of the principal stations of a trigonometrical survey are usually the spherical co-ordinates of latitude and longi-AdJvstment tude; those of a traverse survey are always rectangular, ofTra• plane for a small area but spherical for a large one. See also:corn- verses to It is often necessary, therefore, for purposes of com- See also:verse to parison and check at stations common to surveys of See also:lion. both descriptions, to convert either rectangular co- ordinates into latitudes and longitudes, or See also:vice versa, in order that the errors of traverses may be dispersed by proportion over the co-ordinates of the traverse stations, if desired, or adjusted in the final mapping. The latter is generally all that is necessary, more particularly when the traverses are referred to successive trigonometrical stations as origins, as the operations are being extended, in order to prevent any large See also:accumulation of error. Similar conversions are also frequently necessary in map projections. The method of effecting them will now be indicated. Let A and B be any two points, Aa the meridian of A, Bb the parallel of latitude of B; then Ab, Bb will be their differences in a Transforms• latitude and longitude; from B draw BP lion sf0r perpendicular to Aa; then AP, BP P of co- will be the rectangular spherical co-ordin- ordinates. ates of B relatively to A. Put BP =x, AP=y, the arc Pb=n, and the arc Bb, the difference of longitude, = w; also let A°, Xb and Xp be the latitudes of A, B, and the point P, p, the radius of curvature of the meridian, and vp the normal terminating in the axis minor for the latitude Xp; and z (x°+x,,). Then, when the rectangular co-ordinates are given, we have, taking A as the origin, the latitude of which is known, Xp = X° + ycosec 1"; rt = x tan Xp cosec I"; Po 2Ppvp ?b — a° =P cosec 1"—n; w =Y sec(Xs ;n) cosec 1" And, when the latitude and longitude are given, we have s 2 '1 = \ i/2 JPbsin 2 Xb sin I" y= poPh, — 7t° + n1sin I" x = esvpcos (Xb+ an)sin I" When a hill See also:peak or other prominent object has been observed from a number of stations whose co-ordinates are already fixed, the Co-ordinates converging rays may be projected graphically, and from of Unvisited an examination of their several intersections the most probable position of the object may be obtained almost Point. as accurately as by calculations by the method of least squares, which are very laborious and out of place for the determination of a secondary point. The following is a description of the application of this method to points on a plane surface in the calculations of the ordnance survey. Let s1, s2, . . be stations whose rectangular co-ordinates, x1, x2, . . . perpendicular, and y,, y2, . . . parallel, to the meridian of the origin are given; let a1, a be the bearings—here the direction-inclinations with the meridian of the origin—of any point P, as observed at the several stations; and let p be an approximate position of P, with co-ordinates xp, yp, as determined by graphical projection on a district map or by rough calculation. Construct a diagram of the rays converging around p, by taking a point to represent p and drawing two lines through it at right angles to each other to In the Indian survey, tables are employed for these calculations which give the value of 1" of arc in feet on the meridian, and on each parallel of latitude, at intervals of 5' apart ; also a corresponding table of arc-versines (Pb) of spheroidal arcs of parallel (Bb) I° in length, from which the arc-versines for shorter or longer arcs are obtained proportionally to the squares of the arcs; x is taken as the difference of longitude converted into linear measure.indicate the directions of north, south, east and west. Calculate accurately (yp —yi) tan al, and compare with (x5—x1); the difference will show how far the direction of the ray from s1 falls to the east or west of p. Or calculate (xp—x1) cot a1, and compare with (y,,—yl) to find how far the direction falls to the north or south of p. Set off the distance on the corresponding axis of p, and through N S the point thus fixed draw the direction a1 with a common protractor. All the other rays around p may be drawn in like manner; they will intersect each other in a number of points, the centre of which may be adopted as the most probable position of P. The co-ordinates of P will then be readily obtained from those of p =the distances on the meridian and perpendicular. In the annexed diagram (fig. 6) P is supposed to have been observed from five stations, giving as many intersecting rays, (1, I), (2, 2), ; there are ten points of intersection, the mean position of which gives the true position of P, the assumed position being p. The advantages claimed for the method are that, the bearings being independent, an erroneous bearing may be redrawn without disturbing those that are correct ; similarly new bearings may be introduced without disturbing previous work, and observations from a large number of stations may be readily utilized, whereas, when calculation is resorted to, observations in excess of the minimum number required are frequently rejected because of the labour of computing them. Au'rxoxrTIEs.—Clarke, See also:Geodesy (See also:London) ; See also:Waller, " India's Contribution to Geodesy," Trans. Roy. Soc., vol. clxxxvi. (1895) ; Thuillier, See also:Manual of Surveying for India (Calcutta) ; See also:Gore, Hand-book of Professional Instructions for the Topographical Branch Survey of India See also:Department (Calcutta) ; D'A. See also:Jackson, Aid to Survey Practice (London, 1899) ; Woodthorpe, Hints to Travellers (Plane-tabling section); Grant, "Diagram for Determining Parallaxes," &c., Geog. Journ. (June 1896); See also:Pierce, " Economic Use of the Plane-Table," vol. xcii. pt. ii., See also:Pro. Inst. Civ. Eng.; See also:Bridges-See also: Nautical surveys vary much in character according to the nature of the work, its importance to nav'ga`'on, and the time available. The elaborate methods and rigid accuracy of a triangulation for geodetic purposes on See also:shore are unnecessary, (19)• and are not attempted; astronomical observations at intervals in an extended survey prevent any serious accumulation of errors consequent upon a triangulation which is usually carried out with instruments, of which an 8-in. theodolite is the largest size used, whilst 5-in. theodolites generally suffice, and the See also:sextant is largely employed for the minor triangulation. The scales upon which nautical surveys are plotted range from a in. to 2 or 3 in. to the sea-mile in coast surveys for the ordinary purposes of See also:navigation, according to the requirements; for detailed surveys of harbours or anchorages a scale of from 6 to 12 in. is usually adopted, but in special cases scales as large as 6o in. to the mile are used. The following are the principal instruments required for use in the field: Theodolite, 5 in., fitted with large telescope of high See also:power, /nstru- with coloured shades to the eye-piece for observing meats- the sun for true bearings. Sextant, 8 in. observing, stand and artificial See also:horizon. Chronometers, eight See also:box, and two or three See also:pocket, are usually supplied to surveying vessels. See also:Sounding sextants, differing from ordinary sextants in being lighter and handier. The arc is cut only to minutes, reading to large angles of as much as 140°, and fitted with a tube of See also:bell shape so as to include a large field in the telescope, which is of high power. Measuring chain too ft. in length. Ten foot pole for coast-lining, is a light pole carrying two oblong frames, 18 in. by 24 in., covered with See also:canvas painted white, with a broad vertical black stripe in the centre and fixed on the pole lo ft. apart. Station-pointer, an instrument in constant requisition either for sounding, coast-lining, or topographical plotting, which enables an observer's position to be fixed by taking two angles between three objects suitably situated. The movable legs being set to the observed angles, and placed on the plotting sheet, the chamfered edges of the three legs are brought to pass through the points observed. The centre of the instrument then indicates the observer's position. Heliostats, for reflecting the rays of the sun from distant stations to indicate their position, are invaluable. The most convenient form is See also:Galton's sun See also:signal; but an ordinary See also:swing See also:mirror, mounted to turn horizontally, will answer the purpose, the flash being directed from a hole in the centre of the mirror. Pocket aneroid barometer, required for topographical purposes. Prismatic compass, patent logs (taffrail and See also:harpoon), See also:Lucas wire sounding See also:machine (large and small size), and See also: The first two legs, weighted, are let go together; using the third leg as a prop, the tripod is hauled into position and secured by guys to anchors, and 'by additional weights slipped down the legs. A vertical pole with bamboo can now be added, its weighted heel being on the ground and lashed to the See also:fork. On this a See also:flag 14 ft. square may be hoisted. Floating beacons can be made by filling up flush the heads of two 27-See also:gallon casks, connected by nailing a piece of thick plank at See also:top and bottom. A barling spar passing through holes cut in the planks between the casks, projecting at least 20 ft. below and aoout lo ft. above them, is toggled securely by See also:iron pins above the upper and below the lower plank. To the upper part of the spar is lashed a bamboo, 30 to 35 ft. long, carrying a, black flag 12 to 16 ft. square, which will be visible from the ship lo m. in clear weather. The ends of a span of l-in. chain are secured round the spar above and below the casks with a long link travelling upon it, to which the See also:cable is attached by a slip, the end being carried up and lightly stopped to the bamboo below the flag. A wire strop, kept open by its own stiffness, is fitted to the casks for convenience in slipping and picking up. The beacon is moored with chain and rope half as long again as the depth of water. Beacons have been moored by sounding line in as great depth as 3000 fathoms with a weight of Too lb. There is nothing in a nautical survey which requires more attentioli than the " fix "; a knowledge of the principles involved is essential in order to select properly situated "Fixing." objects. The method of fixing by two angles between three fixed points is generally known as the " two-circle method," but there are really three circles involved. The station-pointer " is the instrument used for plotting fixes. Its contruction depends upon the fact that angles subtended by the chord of a segment of a circle measured from any point in its circumference are equal. The lines joining three fixed points form the chords of segments of three circles, each of which passes through the observer's position and two of the fixed points. The more rectangular the angle at which the circles intersect each other, and the more sensitive they are, the better will be the fix; one condition is useless without the other. A circle is " sensitive " when the angle between the two objects responds readily to any small movement of the observer towards or away from the centre of the circle passing through the observer's position and the objects. This is most markedly the case when one object is very close to the observer and the other very distant, but not so when both objects are distant. Speaking generally, the sensibility of angles depends upon the relative distance of the two objects from the observer, as well as the absolute distance of the nearer of the two. In the accompanying diagram A, B, C are the objects, and X FIG. 7. the observer. Fig. 7 shows the circle passing through C, B and X, cutting the circle ABX at a good angle, and therefore fixing X independently of the circle CAX, which is less sensitive than either of the other two. In fig. 8 the two first circles are very sensitive, but being nearly tangential they give no cut with each other. The third circle cuts both at right angles; it is, however, far less sensitive, and for that See also:reason if the right and left hand objects are both distant the fix must be See also:bad. In such a case as this, because the angles CXB, BXA are both so sensitive, and the accuracy of the fix depends on the precision with which the angle CXA is measured, that angle should be observed direct, together with one of the other angles composing it. Fig. q represents a case where the points are badly disposed, approaching the condition known as " on the circle," passing through the three points. All three circles cut one another at such a See also:fine angle as to give a very poor fix. The centre of the station-pointer could be moved considerably without materially affecting the coincidence of the legs with the three points. To avoid a bad fix the following rules are safe: T. Never observe objects of which the central is the furthest unless it is very distant relatively to the other two, in which case the fix is admissible, but must be used with caution. 2. Choose objects disposed as follows: (a) One outside object distant and the other two near, the angle between the two near objects being not less than 300 or more than 1400. The amount of the angle between the See also:middle and distant object is immaterial. (b) The three objects nearly in a straight line, the angle between any two being not less than 300. (c) The observer's position being inside the triangle formed by the objects. A fix on the line of two points in transit, with an angle to a third point, becomes more sensitive as the distance between the transit points increases relatively to the distance between the front transit point and the observer; the more nearly the angle to the third point approaches a right angle, and the nearer it is situated to the observer, the better the fix. If the third point is at a long distance, small errors either of observation or plotting affect the result largely. A good practical test for a fix is afforded by noticing whether a very slight movement of the centre of the station-pointer will throw one or more of the points away from the leg. If it can be moved without appreciably disturbing the coincidence of the leg and all three points, the fix is bad. Tracing-paper answers exactly the same purpose as the station-pointer. The angles are laid off from a centre representing the position, and the lines brought to pass through the points as before. This entails more time, and the angles are not so accurately measured with a small protractor. Nevertheless this has often to be used, as when points are close together on a small scale the central part of the station-pointer will often hide them and prevent the use of the instrument. The use of tracing-paper permits any number of angles to different points to be laid down on it, which under certain conditions of fixing is sometimes a great advantage. Although marine surveys are in reality founded upon triangulation and measured bases of some description, yet when plotted irregularly the system of triangles is not always apparent. The triangulation ranges from the rough triangle of a running survey to the carefully formed triangles of detailed surveys. The measured base for an extended survey is provisional only, the scale resting ultimately mainly upon the astronomical positions observed at its extremes. In the case of a plan the base is absolute. The main triangulation, of which the first triangle contains the measured base as its known side, establishes a series of points known as main stations, from which and to which angles are taken to fix other stations. A sufficiency of secondary stations and marks enables the detail of the chart to be filled in between them. The points embracing the area to be worked on, having been plotted, are transferred to field boards, upon which the detail of the work in the field is plotted; when complete the work is traced and re-transferred to the plotting-sheet, which is then inked in as the finished chart, and if of large extent it is graduated on the gnomonic projection on the astronomical positions of two points situated near opposite corners of the chart. The See also:kind of base ordinarily used is one measured by chain on flat ground, of Z to r a m. in length, between two points visible from one another, and so situated that a triangulation can be readily extended from them to embrace other points in the survey forming well-conditioned triangles. The error of the chain is noted before leaving the ship, and again on returning, by cd'mparing its length with the standard length of too ft. marked on the ship's See also:deck. The correction so found is applied to obtain the final result. If by reason of water intervening between the base stations it is impossible to measure the direct distance between them, it is permissible to deduce it by traversing. A Masthead Angle Base is useful for small plans of harbours, &c., when circumstances do not permit of a base being measured on shore. The ship at See also:anchor nearly midway between two base stations is the most favourable condition for employing this method. Theodolite reading of the masthead with its See also:elevation by sextant observed simultaneously at each base station (the mean of several observations being employed) give the necessary data to calculate the distance between the base stations from the two distances resulting from the elevation of the masthead and the simultaneous theodolite-angies between the masthead and the base stations. The height of the masthead may be temporarily increased by securing a spar to extend 3o ft. or so above it, and the exact height from See also:truck to netting is found by tricing up the end of the measuringchain. The angle of elevation should not be diminished below about 1° from either station. Base by Sound.—The interval in seconds between the flash and See also:report of a See also:gun, carefully noted by counting the beats of a watch or pocket chronometer, multiplied by the rate per second at which sound travels (corrected for temperature) supplies a means of obtaining a base which is sometimes of great use when other methods are not available. Three miles is a suitable distance for such a base, and guns or small brass Cohorn mortars are fired alternately from either end, and repeated several times. The arithmetical mean is not strictly correct, owing to the retardation of the sound against the See also:wind exceeding the See also:acceleration when travelling with it; the formula used is therefore T = 2i t, where T is the mean interval required, t the interval observed one way, t' the interval the other way. The method is not a very accurate one, but is suffi- ciently so when the scale is finally determined by astronomical observations, or for sketch surveys. The measurement should be across the wind if possible, especially if guns can only be fired from one end of the base. Sound travels about 1090 ft. per second at a temperature of 32° F., and increases at the rate of 1.15 ft. for each degree above that temperature, decreasing in the same proportion for temperatures below 32°. Base by Angle of Short Measured Length.--An angle measured by sextant between two well-defined marks at a carefully measured distance apart, placed at right angles to the required base, will give a base for a small plan. Astronomical Base.—The difference of latitude between two stations visible from each other and nearly in the same meridian, combined with their true bearings, gives an excellent base for an extended triangulation; the only See also:drawback to it is the effect of local attraction of masses of land in the vicinity on the pendulum, or, in other words, on the See also:mercury in the artificial horizon. The base stations should be as far apart as possible, in order to minimize the effect of any error in the astronomical observations. The observation spots would not necessarily be actually at the base stations, which would probably be situated on summits at some little distance in order to command distant views. In such cases each observation spot would be connected with its corresponding base station by a subsidiary triangulation, a short base being measured for the purpose. The ship at anchor off the observation spot frequently affords a convenient means of effecting the connexion by a masthead angle base and simultaneous angles. If possible, the observation spots should be east or west of the mountain stations from which the true bearings are observed. If the base stations A and B are so situated that by reason of distance or of high land intervening they are invisible from one another, but both visible from some main station C between them, when the main triangulation is completed, the ratio of the sides AC, BC can be determined. From this ratio and the observed angle ACB, the angles See also:ABC, BAC can be found. The true bearing of the lines AC or BC being known, the true bearing of the base stations A and B can be deduced. Extension of Base.—A base of any description is seldom long enough to plot from directly, and in order to diminish errors of plotting it is necessary to begin on the longest side possible so as to work inwards. A short base measured on flat ground will give a better result than a longer one measured over inequalities, provided that the triangulation is carefully extended by means of judiciously selected triangles, great care being taken to plumb the centre of each station. To facilitate the extension of the base in as few triangles as possible, the base should be placed so that there are two stations, one on each side of it, subtending angles at them of from 30° to 40°, and the distances between which, on being calculated in the triangles of the quadrilateral so formed, will constitute the first extension of the base. Similarly, two other stations placed one on each side of the last two will form another quadrilateral, giving a yet longer side, and so on. The angles to be used in the main triangulation scheme must be very carefully observed and the theodolite placed exactly over the centre of the station. Main angles are usually repeated several times by resetting the See also:vernier Main Tel-«regulation. at intervals equidistant along the arc, in order to eliminate instrumental errors as well as errors of observation. The selection of an. object suitable for a zero is important. It should, if possible, be another main station at some distance, but not so far or so high as to be easily obscured, well defined, and likely to be permanent. Angles to secondary stations and other marks need not be repeated so many times as the more important angles, but it is well to check all angles once at least. Rough sketches from all stations are of great assistance in identifying objects from different points of view, the angles being entered against each in the sketch. False Station.—When the theodolite cannot for any reason be placed over the centre of a station, if the distance be measured Bases. and the theodolite reading of it be noted, the observed angles may be reduced to what they would be at the centre of the station. False stations have frequently to be made in practice; a simple rule to meet all cases is of great assistance to avoid the possibility of error in applying the correction with its proper sign. This may very easily be found as follows, without having to bestow a moment's thought beyond applying the rule, which is a See also:matter of no small gain in, time when a large number of angles have to be corrected. Rule.—Put down the theodolite reading Which it is required to correct (increased if necessary by 360°), and from it subtract the theodolite reading of the centre of the station. See also:Call this See also:remainder B. With o as a " course " and the number of feet from the theodolite to the station as a " distance," enter the traverse table and take out the greater increment if o lies 6rtater between 45° and 135°, or between 225° and 315°, and the lesser increment for other angles. The accompanying dia- See also:gram (fig. to) will assist the memory. Lesiser. \ Refer this increment to the " table of Z25' lncreinurcG 135 subtended angles by various lengths at different distances " (using the distance of the object observed) and find the corresponding correction in arc, which mark + or — according as 0 is under or over 18o°. Apply this correction to the observed theodolite angle. A " table of subtended angles " is unnecessary if the formula Angle in seconds=number of feet subtended X34 be used instead. distance of object in sea-miles Convergency of Meridians.—The difference of the reciprocal true bearings between two stations is called the " convergency." The formula for calculating it is : Conv. in minutes =dist. in sea-miles X sin. See also:Mere. bearing X tan. See also:mid. See also:lat. Whenever true bearings are used in triangulation, the effect of convergency must be considered and applied. In north latitudes the southerly bearing is the greater of the two, and in south latitudes the northerly bearing. The Mercatorial bearing between two stations is the mean of their reciprocal true bearings. After a preliminary run over the ground to note suitable positions for main and secondary stations on prominent See also:head-Trlangu- lands, islands and summits not too far back from laced coast the coast, and, if no former survey exists, to make Survey. at the same time a rough plot of them by compass and patent See also:log, a scheme must be formed for the main triangulation with the object of enclosing the whole survey in as few triangles as possible, regard being paid to the limit of vision of each station due to its height, to the existing meteorological conditions, to the limitations imposed by higher land intervening, and to its accessibility. The triangles decided upon should be well-conditioned, taking care not to introduce an angle of less than 300 to 35°, which is only permissible when the two longer sides of such a triangle are of nearly equal length, and when in the calculation that will follow one of these sides shall be derived from the other and not from the short side. In open country the selection of stations is comparatively an easy matter, but in country densely wooded the time occupied by a triangulation is mainly governed by the judicious selection of stations quickly reached, sufficiently elevated to command distant views, and situated on summits capable of being readily cleared of trees in the required direction, an all-round view being, of course, desirable but not always attainable. The positions of secondary stations will also generally be decided upon during the preliminary reconnaissance. The object of these stations is to break up the large primary triangles into triangles of smaller size, dividing up the distances between the primary stations into suitable lengths; they are selected with a view to greater accessibility than the latter, and should therefore usually be near the coast and at no great elevation. Upon shots from these will depend the position of the greater number of the coast-line marks, to be erected and fixed as the detailed survey of each section of the coast is taken in hand in regular order. The nature of the base to be used, and its position in order to fulfil the conditions specified under the head of Bases must be considered, the base when extended forming a side of one of the main triangles. It is immaterial at what part of the survey the base is situated, but if it is near one end, a satisfactory check on the accuracy .f the triangulation is obtained by comparing the length of aside at the other extreme of the survey, derived by calculation through the whole system of triangles, with its length deduced from a check base measured in its vicinity. It is generally a saving of time to measure the base at some anchorage or harbour that requires a large scale plan. The triangulation involved in extending the base to connect it with the main triangulation scheme can thus be utilized for both purposes, and while the triangulation is being calculated and plotted the survey of the plan can be proceeded with. True bearings are observed at both ends of the survey and the results subsequently compared. Astronomical observations for latitude are obtained at observation spots near the extremes of the survey and the meridian distance run between them, the observation spots being connected with the primary triangulation; they are usually disposed at intervals of from Frio to rso m., and thus errors due to a triangulation carried out with theodolites of moderate See also:diameter do not accumulate to any serious extent. If the survey is greatly extended, intermediate observation spots afford a satisfactory check, by comparing the positions as calculated in the triangulation with those obtained by direct observation. Calculating the Triangulation.—The triangles as observed being tabulated, the angles of each triangle are corrected to bring their sum to exactly 18o°. We must expect to find errors in the triangles of as much as one minute, but under favourable conditions they may be much less. In distributing the errors we must consider the general skill of the observer, the size of his theodolite relatively to the others, and the conditions under which his angles were observed; failing any particular reason to assign a larger error to one angle than to another, the error must be divided equally, bearing in mind that an alteration in the small angle will make more difference in the resulting position than in either of the other two, and as it approaches 30° (the limit of a receiving angle) it is well to change it but very slightly in the See also:absence of any strong reason to the contrary. The length of base being determined, the sides of all the triangles involved are calculated by the ordinary rules of See also:trigonometry. Starting from the true bearing observed at one end of the survey, the bearing of the side of each triangle that forms the immediate line of junction from one to the other is found by applying the angles necessary for the purpose in the respective triangles, not forgetting to apply the convergency between each pair of stations when reversing the bearings. The bearing of the final side is then compared with the bearing obtained by direct observation at that end of the survey. The difference is principally due to accumulated errors in the triangulation; half of the difference is then applied to the bearing of each side. Convert these true bearings into Mercatorial bearings by applying half the convergency between each pair of stations. With the lengths of the connecting sides found from the measured base and their Mercatorial bearing, the Mercatorial bearing of one observation spot from the other is found by middle latitude sailing. Taking the observed astronomical positions of the observation spots and first reducing their true difference longitude to departure, as measured on a spheroid from the formula Dep. =T. D. long, no. ft. in i m. of long. then with the no. ft. in i m. of lat. d. lat. and dep. the Mercatorial true bearing and distance between the observation spots is calculated by middle latitude sailing, and compared with that by triangulation and measured base. To adjust any discrepancy, it is necessary to consider the probable error of the observations for latitude and meridian' distance; within those limits the astronomical positions may safely be altered in order to harmonize the results; it is more important to bring the bearings into close agreement than the distance. From the amended astronomical positions the Mercatorial true bearings and distance befween them are re-calculated. The difference between this Mercatorial bearing and that found from the triangulation and measured base must be applied to the bearing of each side to get the final corrected bearings, and to the See also:logarithm of each side of the triangulation as originally calculated must be .added or subtracted the difference between the logarithms of the distance of the amended positions of the observation spots and the same distance by triangulation. Calculating Intermediate Astronomical Positions.—The latitude and longitude of any intermediate main station may now be calculated from the finally corrected Mercatorial true bearings and lengths of sides. The difference longitude so found is what it ,would be if measured on a true See also:sphere, whereas we require it as measured on a spheroid, which is slightly less. The correction = d. long cos2midd.lat. must therefore be subtracted; or the true difference longitude may be found direct from the formula ep. no. ft. in r m. of lat. From the foregoing it is seen that d no. ft. in i m. of long. in a triangulation for hydrographical purposes both the bearings of the sides and their lengths ultimately depend almost entirely often invaluable in carrying on an irregular triangulation, as it upon the astronomical observations at the extremes of the survey; I may remain visible when all other original points of the survey the observed true bearings and measured base are consequently have disappeared, and " back-angles " from it may be continually more in the nature of checks than anything else. It is obvious, therefore, that the nearer together the observation spots, the greater effect will a given error in the astronomical positions have upon the length and direction of the sides of the triangulation, and in such cases the bearings as actually observed must not be altered to any large extent when a trifling change in the astronomical positions might perhaps effect the required harmony. For the reasons given under Astronomical Base, high land near observation spots may cause very false results, which may often account for discrepancies when situated on opposite sides of a mountainous country. Great care is requisite in projecting on paper the points of a survey. The paper should be allowed to stretch and shrink as it pleases until it comes to a stand, being exposed to the See also:air for four or five hours daily, and finally well flattened out by being placed on a table with drawing boards placed over it heavily weighted. If the triangulation has been calculated beforehand throughout, and the lengths of all the different sides have been found, it is more advantageous to begin plotting by distances rather than by chords. The main stations are thus got down in less time and with less trouble, but these are only a small proportion of the points to be plotted, and long lines must be ruled between the stations as zeros for plotting other points by chords. In ruling these lines care must be taken to draw them exactly through the centre of the pricks denoting the stations, but, however carefully drawn, there is liability to slight error in any line projected to a point lying beyond the distance of the stations between which the zero line is drawn. In plotting by distances, therefore, all points that will subsequently have to be plotted by chords should lie well within the area covered by the main triangulation. Three distances must be measured to obtain an intersection of the arcs cutting each other at a sufficiently broad angle; the plotting of the main stations once begun must be completed before distortion of the paper can occur from change in the humidity of the See also:atmosphere. Plotting, whether by distance or by chords, must be begun on as long a side as possible, so as to plot inwards, or with decreasing distances. In plotting by chords it is important to remember in the selection of lines of reference (or zero lines), that that should be preferred which makes the smallest angle with the line to be projected from it, and of the angular points those nearest to the object to be projected from them. Irregular Methods of Plotting.—In surveys for the ordinary purposes of navigation, it frequently happens that a regular system of triangulation cannot be carried out, and recourse must be had to a variety of devices; the judicious use of the ship in such cases is often essential, and with proper care excellent results may be obtained. A few examples will best illustrate some of the methods used, but circumstances vary so much in every survey that it is only possible to meet them properly by studying each case as it arises, and to improvise methods. Fixing a position by means of the " back-angle " is one of the most ordinary expedients. Angles having been observed at A, to the station B, and certain other fixed points of the survey, C and D for instance; if A is shot up from B, at which station angles to the same fixed points have been observed, then it is not necessary to visit those points to fix A. For instance, in the triangle ABC, two of the angles have been observed, and there-fore the third angle at C is known (the three angles of a triangle being equal to 180°), and it is called the " calculated or back-angle from C." A necessary condition is that the receiving angle at A, between any two lines (direct or calculated), must be sufficiently broad to give a good cut ; also the points from which the " back-angles " are calculated should not be situated at too great distances from A, relatively to the distance between A and B. A station may be ?lotted by laying down the line to it from some other station, and teen placing on tracing-paper a number of the angles taken at it, including the angle to the station from which it has been shot up. If the points to which angles are taken are well situated, a good position is obtained, its accuracy being much strengthened by being able to plot on a line to it, which, moreover, forms a good zero line for laying off other angles from the station when plotted. Sometimes the main stations must be carried on with a point plotted by only two angles. An effort must be made to check this subsequently by getting an " angle back " from stations dependent upon it to some old well-fixed point; failing this, two stations being plotted with two angles, pricking one and laying down the line to the other will afford a check. A well-defined mountain peak, far inland and never visited, when once it is well fixed is ?lofting. obtained, or it may be used for plotting on true bearing lines of it. In plotting the true bearing of such a peak, the convergency must be found and applied to get the reversed bearing, which is then laid down from a meridian drawn through it; or the reversed bearing of any other line already drawn through the peak being known, it may simply be laid down with that as a zero. A rough position of the spot from which the true bearing was taken must be assumed in order to calculate the convergency. Fig. If will illustrate the foregoing remarks. A and B are astronomical observation spots at the extremes of a survey, from both of which the high, inaccessible peak C is visible. D, E, F are intermediate stations; A and D, D and E, E and F, F and B being respectively visible from each other. G is visible from A and D, and C is visible from all stations. The latitudes of A and B and meridian distance between them A being determined, and the true bearing of C being observed from both observation spots, angles are observed at all the stations. Calculating the spheroidal correction (from the formula, correction= d. long. cos' idd. lat.) and adding it to the true (or chronometric) difference longitude between A and B to obtain the spherical d. long. ; with this spherical d. long. and the d. lat., the Mercatorial true bearing and distance is found by middle latitude sailing (which is an equally correct but shorter method than by spherical trigonometry, and may be safely used when dealing with the distances usual between observation spots in nautical surveys). The convergency is also calculated, and the true bearing of A from B and B from A are thus determined. In the plane triangle ABC the angle A is the difference between the calculated bearing of B and the observed bearing of C from A; similarly angle B is the difference between calculated bearing of A and observed bearing of C from B; The distance AB having been also calculated, the side AC is found. Laying down AC on the paper on the required scale,D is plotted on its direct shot from A, and on the angle back from C, calculated in the triangle ACD. G is plotted on the direct shots from A and D, and on the angle back from C, calculated either in the triangle ACG or GCD. The perfect intersection of the three lines at G assures these four points being correct. E, F and B are plotted in a similar manner. The points are now all plotted, but they depend on calculated angles, and except for the first four points we have no check whatever either on the accuracy of the angles observed in the field or on the plotting. Ancther well-defined object in such a position, for instance as Z, visible from three or more stations, would afford the necessary check, if lines laid off to it from as many stations as possible gave a good intersection. If no such point, however, exists, a certain degree of check on the angles observed is derived by applying the sum of all the calculated angles at C to the true bearing of A from C (found by reversing observed bearing of C from A with convergency applied), which will give the bearing of B from C. See also:Reverse this bearing with convergency applied, and compare it with the observed bearing of C from B. If the discrepancy is but small, it will be a strong presumption in favour of the substantial accuracy of the work. If the calculated true bearing of B from A be now laid down, it is very unlikely that the line will pass through B, but this is due to the discrepancy which must always be expected between astronomical positions and triangulation. If some of the stations between A and B require to be placed somewhat closely' to one another, it may be desirable to obtain fresh true bearings of C instead of carrying on the original bearing by means of the calculated angle. In all cases of irregular plotting the ship is very useful, especially if she is moored taut without the swivel, and angles are observed from the See also:bow. Floating beacons may also assist an irregular triangulation. Surveys of various degrees of accuracy are included among sketch surveys. The roughest description is the ordinary running survey, when the work is done by the ship sketch steaming along the coast, fixing points, and sketching surveys. in the coast-line by bearings and angles, relying for her position upon her courses and distances as registered by patent log, necessarily regardless of the effect of wind and current and errors of steerage. At the other extreme comes the modified running survey, which in point of practical accuracy falls little short of that attained by irregular triangulation. Some of these modifications will be briefly noticed. A running survey of a coast-line between two harbours, that have been surveyed independently and astronomically fixed, may often be carried out by fixing the ship on the points already laid down on the harbour surveys and See also:shooting up prominent intermediate natural objects, assisted possibly by theodolite lines from the shore stations. Theodolite lines to the ship at any of her positions are particularly valuable, and floating beacons suitably placed materially increase the value of any such work. A sketch survey of a coast upon which it is impossible to land may be well carried out by dropping beacons at intervals of about lb m., well out from the land and placed abreast prominent natural objects called the " breastmarks," which must be capable of recognition from the beacons anchored off the next " breastmark " on either side. The distance between the beacons is found by running a patent log both ways, noting the time occupied by each run; if the current has remained constant, a tolerably good result can be obtained. At the first beacon, angles are observed between the second beacon and the two " breastmarks," an " intermediate " mark, and any other natural object which will serve as " points." At the second beacon, angles are observed between the first beacon and the same objects as before. Plotting on the line of the two beacons as a base, all the points observed can be pricked in on two shots. At a position about midway between the beacons, simultaneous angles are observed to all the points and laid off on tracing-paper, which will afford the necessary check, and the See also:foundation is thus laid for filling in the detail of coast-line, topography, and soundings off this particular stretch of coast in any detail desired. Each section of coast is complete in itself on its own base; the weak point lies in the junction of the different sections, as the patent log bases can hardly be expected to agree precisely, and the scales of adjacent sections may thus be slightly different. This is obviated, as far as possible, by fixing on the points of one section and shooting up those of another, which will check any great irregularity of scale creeping in. The bearing is preserved by getting occasional true bearing lines at the beacons of the most distant point visible. Space does not here permit of dwelling upon the details of the various pre-cautions that are necessary to secure the best results the method is capable of; it can only be stated generally that in all cases of using angles from the ship under weigh, several assistants are necessary, so that the principal angles may be taken simultaneously, the remainder being connected immediately after-wards with zeros involving the smallest possible error due to the ship not being absolutely stationary; these zeros being included amongst the primary angles. When close to a beacon, if its bearing is noted and the distance in feet obtained from its elevation, the angles are readily reduced to the beacon itself. Astronomical positions by See also:twilight stars keep a check upon the work. Sketch Surveys by Compass Bearings and Vertical Angles.—In the case of an island culminating in a high, well-defined See also:summit visible from all directions, a useful and accurate method is to steam round it at a sufficient distance to obtain a true horizon, stopping to make as many stations as may be desirable, and fixing by compass bearing of the summit and its vertical angle. The height is roughly obtained by shooting in the summit, from two positions on a patent log base whilst approaching it. With this approximate height and See also:Lecky's vertical danger angle tables, each station may be plotted on its bearing of the'summit. From these stations the island is shot in by angles between its tangents and the summit, and angles to any other natural features, plotting the work as we go on any convenient scale which must be considered only as provisional. On completing the circuit of the island, the true scale is found by measuring the total distance in inches on the plotting-sheet from the first to the last station, and dividing it by the distance in miles between them as shown by patent log. The final height of the summit bears to the rough height used in plotting the direct proportion of the provisional scale to the true scale. This method may be utilized for the sketch survey of a coast where there are well-defined peaks of sufficient height at convenient intervals, and would be superior to an ordinary running survey. From positions of the ship fixed by bearings and elevations of one peak, another farther along the coast is shot in and its height determined; this second peak is then used in its turn to fix a third, and so on. The smaller the vertical angle the more liability there is to error, but a glance at Lecky's tables will show what effect an error of say I' in altitude will produce for any given height and distance, and the limits of distance must depend upon this See also:consideration. Surveys of See also:Banks out of Sight of Land.—On striking shoal soundingsunexpectedly, the ship may either be anchored at once and the shoal sounded by boats starring round her, using prismatic compass and masthead angle; or if the shoal is of large extent and may be prudently crossed in the ship, it is a good plan to get two beacons laid down on a bearing from one another and patent log distance of 4 or 5 M. With another beacon (or mark-See also:boat, carrying a large black flag on a bamboo 3o ft. high) fixed on this base, forming an equilateral triangle, and the ship anchored as a See also:fourth point, soundings may be carried out by the boats fixing by station-pointer. The ship's position is determined by observations of twilight stars. In a detailed survey the coast is sketched in by walking along it, fixing by theodolite or sextant angles, and plotting by tracing-paper or station-pointer. A sufficient number of fixed marks along the shore afford a constant check coast.trningon the minor coast-line stations, which should be plotted on, or checked by, lines from one to the other wherever possible to do so. When impracticable to fix in the ordinary way, the ten-foot pole may be used to traverse from one fixed point to another. With a coast fronted by broad drying, See also:coral See also:reef or flats over which it is possible to walk, the distance between any two coast-line stations may be found by measuring at one of them the angle subtended by a known length placed at right angles to the line joining the stations. There is far less liability to error if the work is plotted at once on the spot on field board with the fixed points pricked through and circled in upon it; but if circumstances render it necessary, the angles being registered and sketches made of the bits of coast between the fixes on a scale larger than that of the chart, they may be plotted after-wards; to do this satisfactorily, however, requires the surveyor to appreciate instinctively exactly what angles are necessary at the time. It is with the high-water line that the coast-See also:liner is concerned, delineating its character according to the admiralty symbols. The officer sounding off the coast is responsible for the position of the dry line at low-water, and on large scales this would be sketched in from a small boat at low-water springs. Heights of cliffs, rocks, islets, &c., must be inserted, either from measurement or from the formula, height in feet = angle of elevation in seconds X distance in miles, 34 and details of topography close to the coast, including roads, houses and enclosures, must be shown by the coast-liner. Rocks above water or breaking should be fixed on passing them. Coast-line may be sketched from a boat pulling along the shore, fixing and shooting up any natural objects on the See also:beach from positions at anchor. The most important feature of a chart is the completeness with which it is sounded. Small scale surveys on anything less than one inch to the mile are See also:apt to be very misleading; sounding such a survey may appear to have been closely sounded, but in reality the lines are so far apart that they often fail to disclose indications of shoal-water. The work of sounding may be proceeded with as soon as sufficient points for fixing are plotted; but off an intricate coast it is better to get the coast-line done first. The lines of soundings are run by the boats parallel to one another and perpendicular to the coast at a distance apart which is governed by the scale; five lines to the inch is about as close as they can be run without overcrowding; if closer lines are required the scale must generally be increased. The distance apart will vary with the depth of water and the nature of the coast; a rocky coast with shallow water off it and projecting points will need much closer examination than a steep-to coast, for instance. The line of prolongation of a point under water will require special care to ensure the See also:fathom lines being drawn correctly. If the soundings begin to decrease when pulling off-shore it is See also:evidence of something suspicious, and intermediate lines of soundings or lines at right angles to those previously run should be obtained. Whenever possible lines of soundings should be run on transit lines; these may often be picked up by fixing when on the required line, noting the angle on the protractor between the line and some fixed mark on the field board, and then placing the angle on the sextant, reflecting the mark and noting what obiects are in line at that angle. On large scale surveys whitewash marks or flags should mark the ends of the lines, and for the back transit marks natural objects may perhaps be picked up; if not, they must be placed in the required positions. The boat is fixed by two angles, with an occasional third angle as a check; the distance between the fixes is dependent upon the scale of the chart and the rapidity with which the depth alters; the 3, 5 and ro fathom lines should always be fixed, allowing roughly for the tidal reduction. The nature of the bottom must be taken every few casts and recorded. It is best to plot each fix on the sounding board at once, joining the fixes by straight lines and numbering them for See also:identification. The tidal reduction being obtained, the reduced soundings are written in the field-book in red underneath each sounding as originally noted; they are then placed in their proper position on the board between the fixes. Suspicious ground should be closely examined; a small See also:nun See also:buoy anchored on the shoal is useful to See also:guide the boat while trying for the least depth. Sweeping for a reported See also:pinnacle See also:rock may be resorted to when sounding fails to discover it. Local information from fishermen and others is often most valuable as to the existence of dangers. Up to depths of about 15 fathoms the hand lead-line is used from the boats, but beyond that depth the small Lucas machine for wire effects a great saving of time and labour. The deeper soundings of a survey are usually obtained from the ship, but steamboats with wire sounding See also:machines may assist very materially. By the aid of a steam winch, which by means of an endless rounding line hauls a too-lb lead forward to the end of the lower See also:boom rigged out, from which it is dropped by a slipping apparatus which acts on striking the water, soundings of 40 fathoms may be picked up from the sounding See also:platform aft, whilst going at a See also:speed of 42 knots. In deeper water it is quicker to stop the ship and sound from aft with the wire sounding machine. In running long lines of soundings on and off shore, it is very essential to be able to fix as far from the land as possible. Angles will be taken from aloft for this purpose, and a few floating beacons dropped in judiciously chosen positions will often well repay the trouble. A single fixed point on the land used in See also:conjunction with two beacons suitably placed will give an admirable fix. A line to the ship or her See also:smoke from one or two theodolite stations on shore is often invaluable; if watches are compared, observations may be made at stated times and plotted after-wards. True bearings of a distant fixed object cutting the line of position derived from an altitude of the sun is another means of fixing a position, and after dark the true bearing of a light may be obtained by the time azimuth and angular distance of a star near the prime vertical, or by the angular distance of Polaris in the northern lremigphere. A very large percentage of the bugbears to navigation denoted by vigias' on the charts eventually turn out to have no exvlgtas. istence, but before it is possible to expunge them a large area has to be examined. No-bottom soundings are but little use, but the evidence of positive soundings should be conclusive. Submarine banks rising from great depths necessarily stand on bases many square miles in area. Of recent years our knowledge of the angle of slope that may be expected to occur at different depths has been much extended. From depths of upwards of 2000 fathoms the slope is so See also:gradual that a See also:bank could hardly approach the surface in less than 7 m. from such a sounding; therefore anywhere within an area of at least 1 50 sq. m. all round a bank rising from these depths, a sounding must show some decided indications of a rise in the bottom. Under such circumstances, soundings at intervals of 7 m., and run in parallel lines 7 M. apart, enclosing areas of only 50 sq. m. between any four adjacent soundings, should effectually clear up the ground and lead to the See also:discovery of any shoal; and in fact the soundings might even be more widely spaced. From depths of 1500 and woo fathoms, shoals can scarcely occur within 3 M. and 2 m. respectively; but as the depth decreases the angle of slope rapidly increases, and a shoal might occur within three-quarters of a mile or even half a mile of such a 1 A See also:Spanish word meaning " look-out," used of marks on the chart signifying obstructions to navigation.sounding as goo fathoms. A full appreciation of these facts will indicate the distance apart at which it is proper to place soundings in squares suitable to the general depth of water. Contour lines will soon show in which direction to prosecute the See also:search if any irregularity of depth is manifested. When once a decided indication is found, it is not difficult to follow it up by paying attention to the contour lines as See also:developed by successive soundings. Discoloured water, ripplings, See also:fish See also:jumping or birds hovering about may assist in locating a shoal, but the sub-marine sentry towed at a depth of 40 fathoms is here invaluable, and may save hours of See also:hunting. Reports being more liable to errors of longitude than of latitude, a greater margin is necessary in that direction. Long parallel lines east and west are prefer-able, but the necessity of turning the ship more or less head to wind at every sounding makes it desirable to run the lines with the wind abeam, which tends to disturb the dead reckoning least. A good See also:idea of the current may be obtained from the general direction of the ship's head whilst sounding considered with reference to the strength and direction of the wind, and it should be allowed for in shaping the course to preserve the See also:parallelism of the lines, but the less frequently the course is altered the better. A good position in the morning should be obtained by pairs of stars on opposite bearings, the lines of position of one pair cutting those of another pair nearly at right angles. The dead reckoning should be checked by lines of position from observations of the sun about every two hours throughout the day, preferably whilst a sounding is being obtained and the ship stationary. Evening twilight stars give another position. Tides.-The datum for reduction of soundings is low-water ordinary springs, the level of which is referred to a permanent bench mark in order that future surveys may be reduced to the same datum level. Whilst sounding is going on the height of the water above this level is observed by a See also:tide See also:gauge. The time of high-water at full and change, called the " See also:establishment," and the heights to which spring and See also:neap tides respectively rise above the datum are also required. It is seldom that a sufficiently long series of observations can be obtained for their discussion by See also:harmonic See also:analysis, and therefore the graphical method is preferred; an abstract form provides for the projection of high and low See also:waters, lunitidal intervals, moon's meridian passage, declination of sun and moon, apogee and See also:perigee, and mean time of high-water following superior transit, and of the highest tide in the twenty-four hours. A good portable automatic tide gauge suitable for all requirements is much to be desired. Tidal Streams and Surface Currents are observed from the ship or boats at anchor in different positions, by means of a current log; or the course of a buoy drifted by the current may be followed by a boat fixing at regular intervals. Tidal streams often run for some hours after high and low water by the shore; it is important to find out whether the change of stream occurs at a regular time of the tide. Undercurrents are of importance from a scientific point of view. A deep-sea current See also:meter, devised (1876) by Lieut. Pillsbury, U.S.N., has, with several modifications, been used with success on many occasions, notably by the U.S. Coast and Geodetic Survey steamer " See also:Blake " in the investigation of the Gulf Stream. The instrument is first lowered to the required depth, and when ready is put into action by means of a heavy weight, or messenger, travelling down the supporting Deep-sea line and striking on a See also:metal plate, thus closing the Current jaws of the levers and enabling the instrument to meter. begin working. The See also:rudder is then See also:free to revolve inside the framework and take up the direction of the current; the small cones can revolve on their axis and See also:register the number of revolutions, while the compass needle is released and free to take up the north and south line. On the despatch of a second messenger, which strikes on top of the first and fixes the jaws of the levers open, every part of the machine is simultaneously locked. Having noted the exact time of starting each of the messengers, the time during which the instrument has been working at the required depth is known, and from this the velocity of the current can be calculated, the number of revolutions having been recorded, while the direction is shown by the angle between the compass needle and the direction of the rudder. The instrument is shown in fig. 12. AA are the jaws of the levers through which the first messenger passes and strikes on the metal plate B. The force of the See also:blow is sufficient to See also:press B down, thus bringing the jaws as close together as possible, and putting the meter into action. The second messenger falling on the first opens the levers again and prevents their closing, thus keeping all parts of the machine locked. C is the rudder which takes up the direction of the current when the levers are unlocked. D is a set of small levers on the rudder in connexion with AA. The outer end on the tail of the rudder fits into the notches on the outer See also:ring of the frame when the machine is locked and thus keeps the rudder fixed, but when the first messenger has started the machine by pressing down B and opening the levers AA, this small See also:lever is raised and the rudder can revolve freely. EE are four small cones which revolve on their axis in a vertical plane, similar to an See also:anemometer; the axis is connected by a See also:worm See also:screw to geared wheels which register the number of revolutions up to 5000, corresponding to about 4 nautical miles. There is a small lever in connexion with AA which prevents the cones revolving when the machine is locked, but allows them to revolve freely when the machine is in action. Below the rudder-See also:post is a compass-bowl F, which is hung in gimbals and capable of removal. The needle is so arranged that it can be lifted off the See also:pivot by means of a lever in connexion with AA; when the meter is in action the needle swings freely on its pivot, but when the levers are locked it is raised off its pivot by the inverted See also:cup-piece K placed inside the triple claws on the top of the compass and screwed to the lever, thus locking the needle without See also:chance of moving. The compass bowl should be filled with fresh water before lowering the instrument into the sea, and the top screwed See also:home tightly. The needle should be removed and carefully dried after use, to pre-vent corrosion. The long See also:arm G is to keep the machine steady in one direction; it See also:works u0 and down a jackstay which passes between two sheaves at the extremity of the long arm. This also assists to keep the machine in as upright a position as possible, and prevents it from being drifted astern with the current. A weight of as much as 8 or lo cwt. is required at the bottom of the jackstay in a very strong current. An elongated weight of from 6o to 8o lb must be suspended from the eye at the bottom of the meter to help to keep it as vertical as possible. On the outer part of the horizontal notched ring forming the frame, and placed on the side of the machine opposite to the projecting arm G, it has been found necessary to See also:bolt a short arm supported by stays from above, from which is suspended a leaden counterpoise weight to assist in keeping the apparatus upright. This additional fitting is not shown in fig. 12. A a-in. phosphor-See also:bronze wire rope is used for lowering the machine; it is rove through a metal sheave H and india-See also:rubber washer, and spliced round a See also:heart which is attached to metal plate B. The messengers are fitted with a hinged See also:joint to enable them to he placed round the wire rope, and secured with a screw bolt. To obtain the exact value of a revolution of the small cones it is necessary to make experiments when the actual speed of the current is known, by immersing the meter just below the surface and taking careful observations of the surface-current by means of a current log or weighted pole. From the number of revolutions registered by the meter in a certain number of minutes, and taking the mean of several observations, a very fair value for a revolution can be deduced. On every occasion of using the meter for under-current observations the value of a revolution should be re-determined, as it is apt to vary owing to small differences in the See also:friction caused by want of oil or the presence of dust or grit; while the force of the current is probably another important factor in influencing the number of revolutions recorded. The features of the country should generally be delineated as far back as the skyline viewed from seaward, in order to assist Topography. the navigator to recognize the land. The summits of hills and conspicuous spurs are fixed either by fines to or by angles at them; their heights are determined by theodolite elevations or depressions to or from stations whose height above high-water is known. As much of the ground as possible is walked over, and its shape is delineated by contour lines sketched by eye, assisted by an aneroid barometer. In wooded country much of the topography may have to be shot in from the ship; sketches made from different positions at anchor along the coast with angles to all prominent features, valleys, ravines, spurs of hills, &c., will give a very fair idea of the general lie of the country. Circum-meridian altitudes of stars on opposite sides of the zenith observed by sextant in the artificial horizon is the method adopted wherever possible for observations for Latitudes. latitudes. Arranged in pairs of nearly the same altitude north and south of zenith, the mean of each pair should give a result from which instrumental and See also:personal errors and errors due to atmospheric conditions are altogether eliminated. The mean of several such pairs should have a probable error of not more than 1". As a rule the observations of each star should be confined to within 5 or 6 minutes on either side of the meridian, which will allow of from fifteen to twenty observations. Two stars selected to " pair " should pass the meridian within an hour of each other, and should not differ in altitude more than 2° or 3°. Artificial horizon roof error is eliminated by always keeping the same end of the roof towards the observer; when observing a single object, as the sun, the roof must be reversed when half way through the observations. The observations are reduced to the meridian by Raper's method. When pairs of stars are not observed, circum-meridian altitudes of the sun alone must be resorted to, but being observed on one side of the zenith only, none of the errors to which all observations are liable can be eliminated. Sets of equal altitudes of sun or stars by sextant and artificial horizon are usually employed to discover chronometer errors. Six sets of eleven observations, a.m. and p.m., Chronoobserving both limbs of the sun, should give a result meter which, under favourable conditions of latitude and Errors. declination, might be expected to vary less than two-tenths of a second from the normal personal equation of the observer. Stars give equally good results. In high latitudes sextant observations diminish in value owing to the slower movement in altitude. In the case of the sun all the chronometers are compared with the " standard " at apparent See also:noon; the comparisons with the chronometer used for the observations on each occasion of landing and returning to the ship are worked up to noon. In the case of stars, the chronometer comparisons on leaving and again on returning are worked up to an intermediate time. A convenient system, which retains the advantage of the equal altitude method, whilst avoiding the necessity of waiting some hours for the p.m. observation, is to observe two stars at equal altitudes on opposite sides of the meridian, and, combining the observations, treat them as See also:relating to an imaginary star having the mean R.A. and mean declination of the two stars selected, which should have nearly the same declination and should differ from 4h to 8h in R.A. The error of chronometer on mean time of place being obtained, the local time is transferred from one observation spot to another by the ship carrying usually eight box chronometers. The best results are found by using travelling rates, Mertdlances which are deduced from the difference of the errors Distan. found on leaving an observation spot and returning to it; from this difference is eliminated that portion which may have accumulated during an interval between two determinations of error at the other, or any intermediate, observation spot. A travelling rate may also be obtained from observations at two places, the meridian distance between which is known; this rate may then be used for the meridian distance between places observed at during the passage. Failing travelling rates, the mean of the harbour rates at either end must be used. The same observer, using the same instrument, must be employed throughout the observations of a meridian distance. If the telegraph is available, it should of course be used. The error on local time at each end of the wire is obtained, and a number of telegraphic signals are exchanged between the observers, an equal number being transmitted and received at either end. The local time of sending a signal from one place being known and the local time of its reception being noted, the difference is the meridian distance. The retardation due to the time occupied by the current in travelling along the wire is eliminated by sending signals in both directions. The relative personal equation of the observers at either end, both in their observations for time, and also in receiving and transmitting signals, is eliminated by changing ends and repeating the operations. If this is impracticable, the personal equations should be deter-mined and applied to the results. Chronometers keeping See also:solar time at one end of the wire, and sidereal time at the other end, materially increase the accuracy with which signals .can be exchanged, for the same reason that comparisons between sidereal clocks at an observatory are made through the See also:medium of a solar See also:clock. Time by means of the sextant can be so readily obtained, and within such small limits of error, by skilled observers, that in hydrographic surveys it is usually employed; but if transit instruments are available, and sufficient time can be devoted to erecting them properly, the value of the work is greatly enhanced in high latitudes. True bearings are obtained on shore by observing with theodolite the horizontal angle between the object selected as the zero and the sun, taking the latter in each quadrant True as defined by the cross-wires of the telescope. The Bearings. altitude may be read on the vertical arc of the theodolite; except in high latitudes, where a second observer with sextant and artificial horizon are necessary, unless the precise errors of the chronometers are known, when the time can be obtained by carrying a pocket chronometer to the station. The sun should be near the prime vertical and at a low altitude; the theodolite must be very carefully levelled, especially in the position with the telescope pointing towards the sun. To eliminate instrumental errors the observations should be repeated with the vernier set at intervals equidistant along the arc, and a.m. and p.m. observations should be taken at about equal altitudes. At sea true bearings are obtained by measuring with a sextant the angle between the sun and some distant well-defined object making an angle of from too° to 1200 and observing the altitude of the sun at the same time, together with that of the terrestrial object. The sun's altitude should be low to get the best results, and both limbs should be observed. The sun's true bearing is calculated from its altitude, the latitude, and its declination; the horizontal angle is applied to obtain the true bearing of the zero. On shore the theodolite gives the horizontal angle direct, but with sextant observations it must be deduced from the angular distance and the elevation.
For further information see See also:Wharton, Hydrographical Surveying (London, 1898) ; Shortland, Nautical Surveying (London, 1890). (A. M. F.*)
" SURVILLE, CLOTILDE DE," the supposed author of the Poesies de Clotilde. The generally accepted See also:legend gave the following account of her. See also:Marguerite Eleonore Clotilde de Vallon Challis, See also:dame de Surville, was See also:born in the See also:early years of the 15th See also:century at Vallon. In 1421 she married See also:Berenger de Surville, who was killed at the See also:siege of See also: The manuscript had been in the See also:possession of See also:Jean See also:Francois See also:Marie, See also:marquis de Surville, an emigre who returned to France in 1798 to raise an insurrection in See also:Provence, and had paid the See also:penalty with his See also:life. In 1863 Antonin See also:Mace made turther inquiries on the subject and discovered letters from Vanderbourg to Surville's widow. This See also:correspondence makes it clear that Vanderbourg was See also:innocent of See also:forgery and believed that See also:xxv1. 6the poems were of 15th-century date, and-that the anachronisms of matter and form were due to retouching by Surville. But the researches of M. Mace interested local antiquarians, and documentary evidence was produced that the wife of Berenger de Surville was Marguerite Chalis, not Clotilde, and that the See also:marriage dated only from 1428. Moreover Berenger, whose death at the siege of Orleans was one of the leading motives of the book, lived for twenty years after that date. See also:Friends of M. de Surville also disclosed the fact that the marquis had contributed archaic See also:poetry to a See also:Lausanne See also:journal. See A. Mace, Un prods d'hisloire litteraire (187o); A. Mazon, Marguerite Chalis el la legende de Clotilde de Surville (1875); articles by Gaston Paris in the Revue critique dhi sb ire et de littirature (March I, 1873 and May 30, 1874), by See also:Paul See also:Cottin in the Bulletin du bibliophile (1894); E. K. See also:Chambers, See also:Literary Forgeries (1891); and further references in the Bibliographie See also:des femmes celebres (See also:Turin and Paris, 1892, &c.). Additional information and CommentsThere are no comments yet for this article.
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