See also:

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

W. See also:

• BESSEL, FRIEDRICH WILHELM (1784-1846)

The bars may be thus described: Two bars, one of See also:

• BRASS
• BRASS (O. Eng. braes)

These compensation bars were also used by See also:

• SIR

He found that to•8 g was the mean of the probable errors of the seven bases measured by him. The Austro-Hungarian apparatus is similar; the distance of the rods is measured by a slider, which rests on one of the ends of each See also:

• ROD (O.E. rodd, probably related to Norw. rudda, stick, rodda, stake)
• ROD, EDOUARD (1857-1910)

The distance measured daily amounts at least to 800 m. A greater daily distance can be measured with the same accuracy by means of Bessel's apparatus; this permits the ready measurement of 2000 M. daily. For this, however, it is important to See also:

• NOTICE

For the measurement of the arc of meridian in longitude 98° E., in 1900, nine base lines of a See also:

• TOTAL

The same See also:

• DEVICE

In working away from a base line ab, stations c, d, e, f are carefully selected so as to obtain from well-shaped triangles gradually increasing sides Before, how- ever, finally leaving the base line, it is usual to verify it by triangulation. thus: during the measurement two or more points, as p; q (fig. I), are marked in the base in positions such that the lengths of the different segments of the line are known ; then, taking suitable See also:

• EXTERNAL

When the theodolite is required to be raised above the surface of the ground in order to command particular points, it is necessary to build two scaffolds,—the See also:

• OUTER

Before taking the next arc the horizontal circle is moved through 2o° or 30°; thus a different set of divisions of the circle is used in each arc, which tends to eliminate the errors of division. It is very desirable that all arcs at a station should contain one point in See also:

• COMMON

The horizontal circle of t4-in. diameter is read by three micrometer microscopes; the vertical circle has a diameter of 12 in., and is read by two micro-scopes. In the great trigonometrical survey of India the theodolites used in the more important parts of the work have been of 2 and 3 ft. diameter—the circle read by five equidistant microscopes. Every See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

If the observation be made t minutes of time before or after the time of greatest azimuth, the azimuth then will differ from its maximum value by (4501)2 See also:

• SIN
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

But there is the disadvantage that the flexure of the transverse axis causes a variable collimation error depending on the zenith distance of the star to which it is directed; and moreover it has been found that in some cases the personal error of an observer is not the same in the two positions of the telescope. To determine the direction of the meridian, it is well to erect two marks at nearly equal angular distances on either side of the north meridian line, so that the See also:

• POLE (FAMILY)
• POLE, REGINALD (1500-1558)
• POLE, RICHARD DE LA (d. 1525)
• POLE, WILLIAM (1814—1900)

Then to find the hour 3. angle ZPS=r of the star when observed, in the triangles pPS, pPZ we have, since pPS=9o+r—n, —Sin c=sin m sin S+See also:

• COS
• COS, or STANKO (Ital. Stanchio, Turk. Islan-keui, by corruption from Etc rav KW)

The transit instrument is also used in the prime vertical for the determination of latitudes. In the preceding figure let q be the point in which the See also:

• NORTHERN

Wanschaff of Berlin, which is the type used (according to the Central Bureau at See also:

• POTSDAM

In fact if n, s be the north and south readings of the level for the south star, n', s' the same for the north star, l the value of one division of the level, m the value of one division of the micrometer, r, r' the See also:

• REFRACTION
• REFRACTION (Lat. refringere, to break open or apart)

For about a fortnight the state of the See also:

• ATMOSPHERE (Gr. fir µ6r, vapour; orkaipa, a sphere)

The determination of the personal errors of the observers in this delicate operation is a See also:

• MATTER

The principal triangulations of France, Spain, See also:

• AUSTRIA
• AUSTRIA, LOWER (Ger. Niederosterreich or Osterreich unter der Enns, " Austria below the river Enns ")
• AUSTRIA, UPPER (Ger. Oberosterreich or Osterreich ob der Enns, " Austria above the river Enns ")

Now the angle A of the triangle as measured by a theodolite is the inclination of the planes BAa and CAa, and the angle at B is that contained by the planes AB/3and CB O. But the planes See also:

• ABA

If we retain small quantities of the second order only, and put A, B, @1 for the angles of the geodetic triangle, while A, B, C are those of a plane triangle having sides equal respectively to those of the geodetic triangle, then, a being the See also:

• AREA

Now if AB, BC be two contiguous elements of a geodetic, then BM must be a normal to the surface, and since Sl, 3m, Sn are in this case represented by S(dx/ds), 3(dy/ds), S(dz/ds), and if the equation of the surface be u=o, we have d'x /du d'y du–dzz /du ds2/dx=ds'/dy ds'/Tz' which, however, are See also:

• EQUIVALENT

If we imagine the geodetic AB, it will generally trisect the angles between the vertical sections at A and B, so that the geodetic at A is near the vertical section AB, and at B near the section BA.' The greatest distance of the vertical sections one from another is e2sa cos' ¢o sin 2ao/16a', in which 00 and ao are the mean latitude and azimuth respectively of the middle point of AB. For the value s =64 kilometres, the maximum distance is 3 mm. An See also:

• IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

The azimuth of the geodetic at Cadiz differs 20" from that of the vertical plane, which is the astronomical azimuth. The azimuth of a geodetic line cannot be observed, so that the line does not enter of See also:

• NECESSITY (Lat. necessitas)

Since the normals of the ellipsoid of rotation do not in general intersect, there consequently arises an See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

Mag. 1870; Helmert, Theorien der hoheren Geodasie, I. 32I.obtained, namely, from the astronomical observations there—one can compute the latitudes of all the other points with any degree of precision that may be considered desirable. It is necessary to employ for this purpose formulae which will give results true even for the longest distances to the second place of decimals of seconds, otherwise there will arise an See also:

• ACCUMULATION (from Lat. accumulare, to heap up)

52 0 7.9939434 7.9928231 0.37131 to 9309 8190 29 20 9185 8148 28 30 9060 8107 26 40 8936 8065 24 5o 8812 8024 23 53 0 8688 7982 22 The See also:

• LOGARITHM (from Gr. Abyos, word, ratio, and apx0µos, number)

By a series of reductions from the equations containing ;'' it may be shown that a+a'=3+I'+ae4w(4,'-0)2 cos 4¢o sin 4,o+... , where ¢o is the mean of 4, and 4', and the higher powers of e are neglected. A short computation will show that the small quantity on the right-hand side of this equation cannot amount even to the thousandth part of a second for k<o•1a, which is, practically speaking, zero; consequently the sum of the azimuths a+a' on the spheroid is equal to the sum of the spherical azimuths, whence follows this very important theorem (known as Dalby's theorem). If rk, See also:

• GYP

These determine rigorously the distance, and the mutual zenith Helmert, Theorien der hokeren Geodasie, 1. 232, 247.2 then i = a° 1 +i e2e2 cos 24,o cos See also:

• GAOL, or JAIL

Let P be a point on the disturbed surface, P' the corresponding point vertically below it on the undisturbed surface, PP'=N. The knowledge of N over the whole surface gives us the form of the disturbed or actual surface of the sea; it is an equipotential surface, and if V be the potential at P of the disturbing matter p', M the See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

At least this is an approximate expression. Supposing s=o•ia, this quantity would be less than one-hundredth of a millimetre. The line s is now to be calculated as a circular arc with a mean radius r along AB. If eo=a(4'+4'), ao=1(18o°+a—a'), Ao—(i—e2 sin 200)1, and n measured westwards. Now the great circle joining Z' with the pole of the heavens P makes there an angle with the meridian PZ =n cosec PZ' =n sec ¢, where 4) is the latitude of the station. Also this great circle meets the horizon in a point whose distance from the great circle PZ is n sec 4) sin 4) =n tan 0. That is, a meridian mark, fixed by observations of the pole star, will be placed that amount to the east of north. Hence the observed latitude requires the correction E; the observed longitude a correction n sec 4); and any observed azimuth a correction n tan ¢. Here it is supposed that azimuths are measured from north by east, and longitudes eastwards. The horizontal angles are also influenced by the deflections of the plumb-line, in fact, just as if the direction of the vertical axis of the theodolite varied by the samc amount. This influence, however, is slight, so long as the See also:

• SIGHTS

Take, for instance, Ben Nevis, which contains about a couple of cubic miles; a simple calculation shows that the elevation produced would only amount to about 3 in. In the case of a mountain mass like the Himalayas, stretching over some 1500 miles of See also:

• COUNTRY (from the Mid. Eng. contre or contrie, and O. Fr. cuntree; Late Lat. contrata, showing the derivation from contra, opposite, over against, thus the tract of land which fronts the sight, cf. Ger. Gegend, neighbourhood)

Then in starting the calculation of geodetic latitudes, longitudes and azimuths from A, we must take, not the observed elements ¢, a, but for 0, 4)+f, and for a, a+n tan 0, and zero longitude must be replaced by n sec O. At the same time suppose the elements of the spheroid to be altered from a, e to a+da, e+de. Confining our See also:

• ATTENTION (from Lat. ad-tendo, await, expect; the condition of being " stretched " or " tense ")

In the Account of the Principal Triangulation of Great Britain and Ireland will be found the determination, from 75 equations, of the spheroid best representing the surface of the See also:

• BRITISH

The vertical angles measured at the station on See also:

• HART, ALBERT BUSHNELL (1854– )
• HART, CHARLES (d. 1683)
• HART, ERNEST ABRAHAM (1835–1898)
• HART, SIR ROBERT
• HART, WILLIAM (1823–1894)