FIGURE OF 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
• FIGURE OF EARTH
• EARTH, FIGURE OF THE

EARTH  THE) . The basis of every extensive survey is an accurate triangulation, and the operations of See also:

• GEODESY (from the Gr. y, the earth, and SatEty, to divide)

geodesy consist in the measurement, by theodolites, of the angles of the triangles; the measurement of one or more sides of these triangles on the ground; the determination by astronomical observations of the See also:

• AZIMUTH (from the Arabic)

azimuth of the whole network of triangles; the determination of the actual position of the same on the See also:

• SURFACE

surface of the 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

earth by observations, first for See also:

• LATITUDE (Lat. latitudo, latus, broad)

latitude at some of the stations, and secondly for See also:

• LONGITUDE (from Lat. longitudo, " length ")

longitude; the determination of See also:

• ALTITUDE (Lat. altitudo, from altus, high)

altitude for all stations . For the computation, the points of the actual surface of the earth are imagined as projected along their plumb lines on the mathematical figure, which is given by the stationary See also:

• SEA (in O. Eng. sae, a common Teutonic word; cf. Ger. See, Dutch Zee, &c.; the ultimate source is uncertain)
• SEA, COMMAND OF THE

sea-level, and the See also:

• EXTENSION (Lat. ex, out ; tendere, to stretch)

extension of the sea through the continents by a See also:

• SYSTEM

system of imaginary canals . For many purposes the mathematical surface is assumed to be a See also:

• PLANE

plane; in other cases a See also:

• SPHERE (Gr. vclsa?pa, a ball or globe)

sphere of See also:

• RADIUS

radius 6371 kilometres (20,900,000 ft.) . In the See also:

• CASE
• CASE, JOHN (d. 1600)

case of extensive operations the surface must be considered as a compressed See also:

• ELLIPSOID

ellipsoid of rotation, whose See also:

• MINOR
• MINOR (Lat. for smaller, lesser)
• MINOR, ROBERT CRANNELL (1839-1904)

minor See also:

• AXIS (Lat. for " axle ")

axis coincides with the earth's axis, and whose See also:

• COMPRESSION

compression, flattening, or See also:

• ELLIPTICITY

ellipticity is about 1/298 . Measurement of See also:

• BASE

Base Lines . To determine by actual measurement on the ground the length of a See also:

• SIDE
• SIDE (mod. Eski Adalia)

side of one of the triangles (" base See also:

• LINE

line "), wherefrom to infer the lengths of all the other sides in the triangulation, is not the least difficult operation of a trigonometrical survey . When the problem is stated thus—To determine the number of times that a certain See also:

• STANDARD
• STANDARD, BATTLE OF THE

standard or unit of length is contained between two finely marked points on the surface of the earth at a distance of some See also:

• MILES, NELSON APPLETON (1839— )

miles asunder, so that the See also:

• ERROR (Lat. error, from errare, to wander, to err)

error of the result may be pronounced to See also:

• LIE, JONAS LAURITZ EDEMIL (1833—1908)
• LIE, MARIUS SOPHUS (1842–1899)

lie between certain very narrow limits,—then the question demands very serious See also:

• CONSIDERATION (from Lat. considerare, to look at closely, examine, generally taken to be from con-, and the base seen in sidus, sideris, a star, the word being supposed to be originally an astrological or astronomical term)

consideration . The See also:

• REPRESENTATION

representation of the unit of length by means of the distance between two See also:

• FINE

fine lines on the surface of a See also:

• BAR
• BAR (0. Fr. barre, Late Lat. barra, origin unknown)
• BAR, CONFEDERATION OF
• BAR, FRANCOIS DE (1538-1606)
• BAR, THE

bar of See also:

• METAL
• METAL (through Fr. from Lat. metallum, mine, quarry, adapted from Gr. µATaXAov, in the same sense, probably connected with ,ueraAAdv, to search after, explore, µeTa, after, aAAos, other)

metal at a certain temperature is never itself See also:

• FREE

free from uncertainty and probable error, owing to the difficulty of knowing at any moment the precise temperature of the bar; and the transference of this unit, or a multiple of it, to a measuring bar will be affected not only with errors of observation, but with errors arising from uncertainty of temperature of both bars . If the measuring bar be not self-compensating for temperature, its expansion must be determined by very careful experiments . The thermometers required for this purpose must be very carefully studied, and their errors of See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

division and See also:

• INDEX

index error determined . In See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order to avoid the difficulty in exactly determining the temperature of a bar by the See also:

• MERCURY
• MERCURY (MERCU1uus)
• MERCURY (symbol Hg, atomic weight = 2oo)

mercury thermometer, F .

W . See also:

• BESSEL, FRIEDRICH WILHELM (1784-1846)

Bessel introduced in 1834 near See also:

• KONIGSBERG (Polish Krolewiec)

Konigsberg a See also:

• COMPOUND
• COMPOUND (from Lat. componere, to combine or put together)

compound bar which constituted a metallic thermometer.' A See also:

• ZINC

zinc bar is laid on an See also:

• IRON [symbol Fe, atomic weight 55.85 (0=16)]

iron bar two toises See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long, both bars being perfectly planed and in free contact, the zinc bar being slightly shorter and the two bars rigidly See also:

• UNITED

united at one end . As the temperature varies, the difference of the lengths of the bars, as perceived by the other end, also varies, and affords a quantitative correction for temperature See also:

• VARIATIONS
• VARIATIONS, CALCULUS
• VARIATIONS, CALCULUS OF

variations, which is applied to reduce the length to standard temperature . During the measurement of the base line the bars were not allowed to come into contact, the See also:

• INTERVAL

interval being measured by the insertion of See also:

• GLASS
• GLASS (O.E. glees, cf. Ger. Glas, perhaps derived from an old Teutonic root gla-, a variant of glo-, having the general sense of shining, cf. " glare," " glow ")
• GLASS, STAINED

glass wedges . The results of the comparisons of four measuring rods with one another and with the See also:

• STANDARDS

standards were elaborately computed by the method of least-squares . The probable error of the measured length of 935 toises (about 6000 ft.) has been estimated as 1/863500 or 1.2 µ (r+ denoting a millionth) . With this apparatus fourteen base lines were measured in See also:

• PRUSSIA
• PRUSSIA (Ger. Preussen; Lat. Borussia)

Prussia and some neighbouring states; in these cases a somewhat higher degree of accuracy was obtained . The See also:

• PRINCIPAL

principal triangulation of See also:

• GREAT

Great See also:

• BRITAIN (Gr. Hperavuml vi7vot, Bperravia; Lat. Britannia, rarely Britannia)

Britain and See also:

• IRELAND
• IRELAND, CHURCH
• IRELAND, CHURCH OF
• IRELAND, JOHN (1761-1842)
• IRELAND, JOHN (1838- )
• IRELAND, WILLIAM HENRY (1777-1835)

Ireland has seven base lines: five have been measured by See also:

• STEEL, FLORA ANNIE (1847– )

steel chains, and two, more exactly, by the See also:

• COMPENSATION (from Lat. compensare, to weigh one thing against another)

compensation bars of See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

General T . F . See also:

• COLBY, THOMAS FREDERICK (1784-1852)

Colby, an apparatus introduced in 1827—1828 at Lough Foyle in Ireland . Ten base lines were measured in See also:

• INDIA
• INDIA, FRENCH

India in 1831—1869 by the same apparatus . This is a system of six compound-bars self-correcting for temperature .

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

• BRASS
• BRASS (O. Eng. braes)

brass and the other of iron, are laid in See also:

• PARALLELISM, PSYCHOPHYSICAL

parallelism side by side, firmly united at their centres, from which they may freely expand or See also:

• CONTRACT
• CONTRACT (Lat. contract us, from contrahere, to draw together, to bind)

contract; at the standard temperature they are of the same length . Let AB be one bar, A'B' the other; draw lines through the corresponding extremities AA' (to P) and BB' (to Q), and make A'P=B'Q AA' being equal to BB' . If the ratio A'P/AP equals the ratio of the coefficients of expansion of the bars A'B' and AB, then, obviously, the distance PQ is See also:

• CONSTANT, BENJAMIN (1845-1902)

constant (or nearly so) . In the actual See also:

• INSTRUMENT (Lat. instrumentum, from insincere, to build up, furnish, arrange, prepare)

instrument i An arrangement acting similarly had been previously introduced by See also:

• BORDA, JEAN CHARLES (1733-1799)

Borda . P and Q are finely engraved dots so ft. apart . In practice the bars, when aligned, are not in contact, an interval of 6 in. being allowed between each bar and its See also:

• NEIGHBOUR (O. Eng. neahgebiir, from Walt, " nigh," " near ")

neighbour . This distance is accurately measured by an ingenious micrometrical arrangement constructed on exactly the same principle as the bars themselves . The last base line measured in India had a length of 8913 ft . In consequence of some suspicion as to the accuracy of the compensation apparatus, the measurement was repeated four times, the operations being conducted so as to determine the actual values of the probable errors of the apparatus . The direction of the line (which is at Cape See also:

• COMORIN, CAPE

Comorin) is See also:

• NORTH
• NORTH, BARONS
• NORTH, MARIANNE (1830—1890)
• NORTH, ROGER (1653-1734)
• NORTH, SIR THOMAS (1535?-16o1?)

north and See also:

• SOUTH
• SOUTH, ROBERT (1634–1716)

south . In two of the measurements the brass component was to the See also:

• WEST
• WEST, BENJAMIN (1738-1820)
• WEST, NICHOLAS (1461-1533)

west, in the others to the See also:

• EAST
• EAST, ALFRED (1849- )

east; the See also:

• DIFFERENCES, CALCULUS OF (Theory of Finite Differences)

differences between the individual measurements and the mean of the four were +0.0017, -0.0049, -0.0015, +0.0045 ft . These differences are very small; an elaborate investigation of allsources of error shows that the probable error of a base line in India is on the See also:

• AVERAGE

average =2.8 A .

These compensation bars were also used by See also:

• SIR

Sir See also:

• THOMAS
• THOMAS (c. 1654-1720)
• THOMAS (d. 110o)
• THOMAS, ARTHUR GORING (1850-1892)
• THOMAS, CHARLES LOUIS AMBROISE (1811-1896)
• THOMAS, GEORGE (c. 1756-1802)
• THOMAS, GEORGE HENRY (1816-187o)
• THOMAS, ISAIAH (1749-1831)
• THOMAS, PIERRE (1634-1698)
• THOMAS, SIDNEY GILCHRIST (1850-1885)
• THOMAS, ST
• THOMAS, THEODORE (1835-1905)
• THOMAS, WILLIAM (d. 1554)

Thomas Maclear in the measurement of the base line in his extension of See also:

• LACAILLE, NICOLAS LOUIS DE (1713-1762)

Lacaille's arc at the Cape . The See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of this operation will be found in a See also:

• VOLUME

volume entitled Verification and Extension of Lacaille's Arc of See also:

• MERIDIAN
• MERIDIAN (from the Lat. meridianus, pertaining to the south or mid-day)

Meridian at the Cape of See also:

• GOOD, JOHN MASON (1764-1827)

Good See also:

• HOPE, ANTHONY
• HOPE, THOMAS (c. 1770-1831)

Hope, by Sir Thomas Maclear, published in 1866 . A rediscussion has been given by Sir See also:

• DAVID
• DAVID (a Hebrew name meaning probably beloved 1)
• DAVID, FELICIEN (1810—1876)
• DAVID, GERARD [GHEERAERT DAVIT], (?=1523)
• DAVID, PIERRE JEAN (1789–1856)
• DAVID, ST (Dewi, Sant)

David Gill in his See also:

• REPORT (O.Fr. report or raport, modern rapport, from O.Fr. reporter, mod. rap porter, Lat. reportare, to bring back, in poetical use only, of bringing back an account, news, &c.)

Report on the See also:

• GEODETIC

Geodetic Survey of South See also:

• AFRICA
• AFRICA, ROMAN

Africa, eec., 1896 . A very See also:

• SIMPLE

simple base apparatus was employed by W . See also:

• STRUVE, FRIEDRICH GEORG WILHELM (1793-1864)

Struve in his triangulations in See also:

• RUSSIA
• RUSSIA (Rossiya)

Russia from 1817 to 1855 . This consisted of four wrought-iron bars, each two toises (rather more than 13 ft.) long; one end of each bar is terminated in a small steel See also:

• CYLINDER (Gr. KvAwSpos, from KvXivaety, to roll)

cylinder presenting a slightly See also:

• CONVEX

convex surface for contact, the other end carries a contact See also:

• LEVER (through O. Fr. leveour, levere, mod. levier, from Lat. levare, to lift, raise)
• LEVER, CHARLES JAMES (1806-1872)

lever rigidly connected with the bar . The shorter See also:

• ARM (a common Teutonic word; the Indo-European root is ar, to join or fit; cf. the Lat. armus, shoulder, and the plural word arma, weapons, Gr. apphs, joint, and the reduplicated apapilKSV, to join)

arm of the lever terminates below in a polished hemisphere, the upper and longer arm traversing a See also:

• VERTICAL (from Lat. vertex, highest point)

vertical divided arc . In measuring, the plane end of one bar is brought into contact with the See also:

• SHORT, FRANCIS JOB (1857– )

short arm of the contact lever (pushed forward by a weak See also:

• SPRING (from " to spring," " to leap or jump up," " burst out," O. Eng., springau, a common Teut. word, cf. Ger. springer, possibly allied to Gr. QnrFpxecOac, to move rapidly)

spring) of the next bar . Each bar has two thermometers, and a level for determining the inclination of the bar in measuring . The manner of transferring the end of a bar to the ground is simply this: under the end of the bar a stake is driven very firmly into the See also:

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

round, carrying on its upper surface a disk, capable of See also:

• MOVEMENT

movement in the direction of the measured line by means of slow-See also:

• MOTION (Lat. motio, from movere, to move)
• MOTION, LAWS OF

motion screws . A fine See also:

• MARK
• MARK, CARL (1858– )
• MARK, GOSPEL OF ST
• MARK, ST

mark on this disk is brought vertically under the end of the bar by means of a See also:

• THEODOLITE

theodolite which is planted at a distance of 25 ft. from the stake in a direction perpendicular to the base . Struve investigated for each base the probable errors of the measurement arising from each of these seven causes: See also:

• ALIGNMENT (from Fr. d and ligne, the Lat. Linea, a line)

Alignment, inclination, comparisons with standards, readings of index, See also:

• PERSONAL

personal errors, uncertainties of temperature, and the probable errors of adopted rates of expansion .

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)

rod . Twenty-two base lines were measured in 1840—1899 . General See also:

• CARLOS, DON (1545-1568)
• CARLOS, DON (1788-1855)
• CARLOS, DON (CHARLES MARIA DE LOS DOLORES JUAN ISIDOR.E JOSEPH FRANCIS QUIRIN ANTONY MICHAEL GABRIEL RAPHAEL) (1848—1909)

Carlos Ibanez employed in 1858—1879, for the measurement of nine base lines in See also:

• SPAIN
• SPAIN (Espana)

Spain, two apparatus similar to the apparatus previously employed by Porro in See also:

• ITALY
• ITALY (Italia)

Italy; one is complicated, the other simplified . The first, an apparatus of the See also:

• BROTHERS, RICHARD (1757-1824)

brothers See also:

• BRUNNER, HENRY (184o– )

Brunner of See also:

• PARIS
• PARIS (also called ALEXANDROS)
• PARIS, ALEXIS PAULIN (1800-x881)
• PARIS, BRUNO PAULIN GASTON (1839-1903)
• PARIS, FRANCOIS DE (169o-1727)
• PARIS, LOUIS PHILIPPE ALBERT
• PARIS, TREATIES OF (1814-1815)

Paris, was a thermometric See also:

• COMBINATION (Lat. combinare, to combine)

combination of two bars, one of See also:

• PLATINUM [symbol Pt, atomic weight 145.0 (0=16)]

platinum and one of brass, in length 4 metres, furnished with three levels and four thermometers . Suppose A, B, C three See also:

• MICROMETER (from Gr. wcp6c, small, jArpov, a measure)

micrometer microscopes very firmly supported at intervals of 4 metres with their axes vertical, and aligned in the plane of the base line by means of a transit instrument, their micrometer screws being in the line of measurement . The measuring bar is brought under say A and B, and those micro-meters read ; the bar is then shifted and brought under B and C . By repetition of this See also:

• PROCESS

process, the See also:

• READING

reading of a micrometer indicating the end of each position of the bar, the measurement is made . Quite similar apparatus (among others) has been employed by the See also:

• FRENCH
• FRENCH, DANIEL CHESTER (1850– )
• FRENCH, NICHOLAS (1604-1678)

French and Germans . Since, however, it only permitted a distance of about 300 M. to be measured daily, Ibanez introduced a simplification; the measuring rod being made simply of steel, and provided with inlaid mercury thermometers . This apparatus was used in See also:

• SWITZERLAND

Switzerland for the measurement of three base lines . The accuracy is shown by the estimated probable errors: to•2 s to to•8 i .

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

notice that a large See also:

• STAFF (O. Eng. staef, cf. Du. staf, Ger. Stab, &c.; Icel. stafr meant also a written letter, and O. Eng. stafas, the letters of the alphabet; " stave," one of the thin pieces of wood of which a cask is made, is a doublet)

staff and favourable ground are necessary . An important improvement was introduced by See also:

• EDWARD

Edward Jaderin of Stock-holm, who See also:

• MEASURES

measures with stretched wires of about 24 metres long; these wires are about 1.65 mm. in See also:

• DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, and when in use are stretched by an accurate spring See also:

• BALANCE (derived through the Fr. from the Late Lat. bilantia, an apparatus for weighing, from bi, two, and lanx, a dish or scale)

balance with a tension of to kg., The nature of the ground has a very trifling effect on this method . The difficulty of temperature determinations is removed by employing wires made of See also:

• INVAR

invar, an alloy of steel (64 °A) and See also:

• NICKEL
• NICKEL (symbol Ni, atomic weight 58.68 (0=16))

nickel (36%) which has practically no linear expansion for small thermal changes 2 Geodetic Survey of South Africa, vol. iii . (1905), p. viii ; See also:

• LES

Les Nouveaux Appareils pour la mesure rapide See also:

• DES

des bases geod., See also:

• PAR (Lat. par, equal)

par J . Rene See also:

• BENOIT, PETER LEONARD LEOPOLD (1834—1901)

Benoit et Ch . Ed . See also:

• GUILLAUME
• GUILLAUME, JEAN BAPTISTE CLAUDE EUGENE (1822-1905)

Guillaume (1906) . at See also:

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

ordinary temperatures; this alloy was discovered in 1896 by BenSit and Guillaume of the See also:

• INTERNATIONAL, THE

International See also:

• BUREAU (a Fr. word from burel or bureau, a coarse cloth used for coverings)

Bureau of Weights and Measures at See also:

• BRETEUIL, LOUIS CHARLES AUGUSTE LE TONNELIER, BARON DE (1730-1807)

Breteuil . Apparently the future of base-line measurements rests with the invar wires of the Jaderin apparatus; next comes Porro's apparatus with invar bars 4 to 5 metres long . Results have been obtained in the United States, of great importance in view of their accuracy, rapidity of determination and See also:

• ECONOMY

economy .

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

• TOTAL

total length of 69.2 km. were measured in six months . The total cost of one base was $1231 . At the beginning and at the end of the See also:

• FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
• FIELD, CYRUS WEST (1819-1892)
• FIELD, DAVID DUDLEY (18o5-1894)
• FIELD, EUGENE (1850-1895)
• FIELD, FREDERICK (18o1—1885)
• FIELD, HENRY MARTYN (1822-1907)
• FIELD, JOHN (1782—1837)
• FIELD, MARSHALL (183 1906)
• FIELD, NATHAN (1587—1633)
• FIELD, STEPHEN JOHNSON (1816-1899)
• FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)

field-See also:

• SEASON (0. Fr. seson, seison, mod. saison, Lat. satio, sowing time, the spring, from serere, to sow; in Late Lat. the word is found with its present meaning, the spring being considered as particularly the season of the year)

season a distance of exactly too m. was measured with R . S . See also:

• WOODWARD, JOHN
• WOODWARD, SAMUEL (179o-1838)

Woodward's " 5-m. See also:

• ICE (a word common to Teutonic languages; cf. Ger. Eis)

ice-bar " (invented in 1891) ; by means of the remeasurement of this length the standardization of the apparatus was done under the same conditions as existed in the case of the base measurements . For the measurements there were employed two steel tapes of Too m. long, provided with supports at distances of 25 m., two of 5o m., and the duplex apparatus of Eimbeck, consisting of four 5-m. rods . Each base was divided into sections of about woo m.; one of these, the " test kilometre," was measured with all the five apparatus, the others only with two apparatus, mostly tapes . The probable error was about to•8 p, and the See also:

• DAY (O. Eng. dreg, Ger. Tag; according to the New English Dictionary, " in no way related to the Lat. dies")
• DAY, JOHN (1574-1640?)
• DAY, THOMAS (1748-1789)

day's See also:

• WORK

work a distance of about 2000 M . Each of the four rods of the duplex apparatus consists of two bars of brass and steel . Mercury thermometers are inserted in both bars; these serve for the measurement of the length of the base lines by each of the bars, as they are brought into their consecutive positions, the contact being made by an elastic-sliding contact . The length of the base lines may be calculated for each bar only, and also by the supposition that both bars have the same temperature . The apparatus thus affords three .sets of results, which mutually See also:

• CONTROL (Fr. contrdle, older form contre rolle, from Med. Lat. contra-rotulus, a counter roll or copy of a document used to check the original; there is no instance in English of the use of " control " in this, its literal, meaning)

control themselves, and the contact adjustments permit rapid work .

The same See also:

• DEVICE

device has been applied to the older bimetallic-compensating apparatus of See also:

• BACHE, ALEXANDER DALLAS (1806-1867)
• BACHE, FRANCIS EDWARD (1833–1888)

Bache-Wurdemann (six bases, 1847–1857) and of Schott . There was also employed a single rod bimetallic apparatus on F . Porro's principle, constructed by the brothers See also:

• REPSOLD, JOHANN GEORG (1771–1830)

Repsold for some base lines . Excellent results have been more recently obtained with invar tapes . The following results show the lengths of the same See also:

• GERMAN
• GERMAN, DUTCH AND SCANDINAVIAN

German base lines as measured by different apparatus: metres . Base at See also:

• BERLIN
• BERLIN, CONGRESS AND TREATY OF
• BERLIN, ISAIAH (1725–1799)

Berlin 1864 Apparatus of Bessel 2336.3920 T88o „ Brunner .3924 Base atStrehlen 1854 „ Bessel 2762.5824 1879 „ Brunner .5852 Old base at See also:

• BONN

Bonn 1847 Bessel 2133.9095 1892 New base at Bonn 1892 2512.9612 „ 1892 Brunner .9696 It is necessary that the altitude above the level of the sea of every See also:

• PART

part of a base line be ascertained by spirit levelling, in order that the measured length may be reduced to what it would have been had the measurement been made on the surface of the sea, produced in See also:

• IMAGINATION

imagination . Thus if l be the length of a measuring bar, h its height at any given position in the measurement, r the radius of the earth, then the length radially projected on to the level of the sea is l(1-h/r) . In the See also:

• SALISBURY
• SALISBURY, EARLS OF
• SALISBURY, ROBERT ARTHUR TALBOT GASCOYNECECIL, 3RD MARQUESS OF (1830-1903)
• SALISBURY, ROBERT CECIL, 1ST EARL OF (c. 1565-1612)
• SALISBURY, THOMAS DE MONTACUTE, 4TH EARL OF (1388-1428)
• SALISBURY, WILLIAM LONGSWORD (or LONGESPEE), EARL OF (d. 1226)

Salisbury See also:

• PLAIN (O. Fr. plain, from Lat. plenum)

Plain base line the reduction to the level of the sea is -0.6294 ft . The total number of base lines measured in See also:

• EUROPE

Europe up to the See also:

• PRESENT

present See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time is about one See also:

• HUNDRED

hundred and ten, nineteen of which do not exceed in length 2500 metres, or about If miles, and three—one in See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France, the others in See also:

• BAVARIA (Ger. Bayern)

Bavaria—exceed 19,000 metres . The question has been frequently discussed whether or not the See also:

• ADVANTAGE

advantage of a long base is sufficiently great to See also:

• WARRANT (Med. Lat. warantum; O. Fr. garant, warant, derived from O.H.G. root represented in modern German bygewdhren)

warrant the See also:

• EXPENDITURE

expenditure of time that it requires, or whether as much precision is not obtain.. able in the end by careful triangulation from a short base . But the See also:

• ANSWER (derived from and, against, and the same root as swear)

answer cannot be given generally; it must depend on the circumstances of each particular case . With Jaderin's apparatus, provided with invar wires, bases of 20 to 30 km. long are obtained with-out difficulty .

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

external stations, as h, k, the angles of the triangles bhp, phq, hqk, kqa are measured . From these angles can be computed the ratios of the segments, which must agree, if all operations are correctly performed, with the ratios resulting from XI . 20609 the measures . Leaving the base line, the sides increase up to to, 30 or 50 miles occasionally, but seldom reaching too miles . The triangulation points may either be natural See also:

• OBJECTS

objects presenting them-selves in suitable positions, such as See also:

• CHURCH
• CHURCH (according to most authorities derived from the Gr. Kvpcaxov [&wµa], " the Lord's [house]," and common to many Teutonic, Slavonic and other languages under various forms—Scottish kirk, Ger. Kirche, Swed. kirka, Dan. kirke, Russ. tserkov, Buig. cerk
• CHURCH, FREDERICK EDWIN (1826-1900)
• CHURCH, GEORGE EARL (1835–1910)
• CHURCH, RICHARD WILLIAM (1815–189o)
• CHURCH, SIR RICHARD (1784–1873)

church towers; or they may be objects specially constructed in See also:

• STONE
• STONE (0. Eng. shin; the word is common to Teutonic languages, cf. Ger. Stein, Du. steen, Dan. and Swed. sten; the root is also seen in Gr. aria, pebble)
• STONE, CHARLES POMEROY (1824-1887)
• STONE, EDWARD JAMES (1831-1897)
• STONE, FRANK (1800-1859)
• STONE, GEORGE (1708—1764)
• STONE, LUCY [BLACKWELL] (1818-1893)
• STONE, MARCUS (184o— )
• STONE, NICHOLAS (1586-1647)

stone or See also:

• WOOD, ANTHONY A2 (1632-1695)
• WOOD, JOHN GEORGE (1827—1889)
• WOOD, MRS HENRY [ELLEN] (1814—1887)
• WOOD, SEARLES VALENTINE (1798—188o)

wood on See also:

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

mountain tops or other prominent ground . In every case it is necessary that the precise centre of the station be marked by some permanent mark . In India no expense is spared in making permanent the principal trigonometrical stations—costly towers in See also:

• MASONRY

masonry being erected . It inessential that every trigonometrical station shall present a fine See also:

• OBJECT

object for observation from surrounding stations . See also:

• HORIZONTAL

Horizontal Angles . In placing the theodolite over a station to be observed from, the first point to be attended to is that it shall See also:

• REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest upon a perfectly solid See also:

• FOUNDATION (Lat. fundatio, from fundare, to found)

foundation . The method of obtaining this desideratum must depend entirely on the nature of the ground; the instrument must if possible be supported on See also:

• ROCK
• ROCK (O.Fr. rake, Sp. rota, Ital. rocca; possibly from a Lat. form rupica, from rupes, rock)
• ROCK, DANIEL (1799–187t)

rock, or if that be impossible a solid foundation must be obtained by digging .

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

outer one to carry the See also:

• OBSERVATORY

observatory, the inner one to carry the instrument,—and these two edifices must have no point of contact . Many cases of high scaffolding have occurred on the See also:

• ENGLISH

English See also:

• ORDNANCE (a syncopated form of " ordinance " or " ordonnance," so spelt in this sense since the 17th century)

Ordnance Survey, as for instance at Thaxted church, where the See also:

• TOWER (Lat. turris; Fr. tour, clocker; Ital. torre; Ger. Thurm)

tower, 8o ft. high, is surmounted by a See also:

• SPIRE

spire of 90 ft . The See also:

• SCAFFOLD
• SCAFFOLD, SCAFFOLDING (from the O. Fr. escafaut, originally escafalt, modern echafaud, a corruption of the Italian or Spanish calafalco, a platform, especially a canopy over a bier, a catafalque; this word is composed of O. Span. altar, O. Ital. catare, t

scaffold for the observatory was carried from the base to the See also:

• TOP (cf. Dan. top, Ger. Topf, also meaning pot)

top of the spire; that for the instrument was raised from a point of the spire 140 ft. above the ground, having its bearing upon timbers passing through the spire at that height . Thus the instrument, at a height of 178 ft. above the ground, was insulated, and not affected by the See also:

• ACTION

action of the See also:

• WIND
• WIND (a common Teut. word, cognate with Skt. vats, Lat. ventus, cf. " weather," to be of course distinguished from to " wind," to coil or twist, O.Eng. windan, cf. "wander," "wend," &c.)

wind on the observatory . At every station it is necessary to examine and correct the adjustments of the theodolite, which are these: the line of collimation of the See also:

• TELESCOPE

telescope must be perpendicular to its axis of rotation; this axis perpendicular to the vertical axis of the instrument; and the latter perpendicular to the plane of the See also:

• HORIZON (Gr. 6pfTwv, dividing)

horizon . The micrometer microscopes must also measure correct quantities on the divided circle or circles . The method of observing is this . Let A, B, C .. . be the stations to be observed taken in.order of azimuth; the telescope is first directed to A and the See also:

• CROSS

cross-hairs of the telescope made to bisect the object presented by A, then the microscopes or verniers of the horizontal circle (also of the vertical circle if necessary) are read and recorded . The telescope is then turned to B, which is observed in the same manner; then C and the other stations . Coming round by continuous motion to A, it is again observed, and the agreement of this second reading with the first is some test of the stability of the instrument . In taking this round of angles—or " arc,” as it is called on the Ordnance Survey—it is desirable that the interval of time between the first and second observations of A should be as small as may be consistent with due care .

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

common, to which all angular measurements are thus referred,—the observations on each arc commencing and ending with this point, which is on the Ordnance Survey called the " referring object.” It is usual for this purpose to select, from among the points which have to be observed, that one which affords the best object for precise observation . For mountain tops a " referring object " is constructed of two rectangular plates of metal in the same vertical plane, their edges parallel and placed at such a distance apart that the See also:

• LIGHT

light of the See also:

• SKY (M. Eng. skie, cloud; O. Eng. skua, shade; connected with an Indo-European root sku, cover, whence " scum," Lat. obscurus, dark, &c.)

sky seen through appears as a vertical line about to” in width . The best distance for this object is from I to 2 miles . This method seems at first sight very advantageous.? but if, however, it.be desired to attain the highest accuracy, it is better, as shown by General See also:

• SCHREIBER, LADY CHARLOTTE ELIZABETH (1812-1895)

Schreiber of Berlin in 1878, to measure only single angles, and as many of these as possible between the directions to be determined . Division-errors are thus more perfectly eliminated, and errors due to the variation in the stability, &c., of the See also:

• INSTRUMENTS

instruments are diminished . This method is rapidly gaining See also:

• PRECEDENCE (from Lat. praecedere, to go before, precede)

precedence . The theodolites used in geodesy vary in See also:

• PATTERN

pattern and in See also:

• SIZE

size—the horizontal circles ranging from to in. to 36 in. in diameter . In See also:

• RAMSDEN, JESSE (1735-1800)

Ramsden's 36-in. theodolite the telescope has a See also:

• FOCAL

focal length of 36 in. and an See also:

• APERTURE (from Lat. aperire, to open)

aperture of 2.5 in., the ordinarily used magnifying See also:

• POWER [WILLIAM GRATTAN] TYRONE (1797-1841)

power being 54; this last, however, can of course be changed at the requirements of the observer or of the See also:

• WEATHER (O. Eng. weder; the word is common to Teutonic languages; cf. Du. weder, Dan. veir, Icel. ve8r, and Ger. Wetter and Gewitter, storm; the root is wa- to blow, from which is derived " wind ")

weather . The probable error of a single observation of a fine object with this theodolite is about o"•2 . Fig . 2 represents an altazimuth theodolite, of an improved pattern used on the Ordnance Survey .

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

angle is measured twice in each position of the zero of the horizontal circle, of which there are generally ten; the entire II number of measures of an angle is never less than 20 . An examination of 1407 angles showed that the probable error of an observed angle is on the average = o"•28 . For the observations of very distant stations it is usual to employ a See also:

• HELIOTROPE
• HELIOTROPE, or TURNSOLE

heliotrope (from the Gr. ijXcos, See also:

• SUN
• SUN (0. Eng. sonne, Ger. sonne. Fr. soleil, Lat. sol, Gr. ijXior, from which comes helio- in various English compounds)

sun; rpo,ror, a turn), invented by See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Gauss at See also:

• GOTTINGEN

Gottingen in 1821 . In its simplest See also:

• FORM (Lat. forma)

form this is a plane See also:

• MIRROR (through O. Fr. mirour, mod. miroir, from a sup-posed Late Lat. miratorium, from mirari, to admire)

mirror, 4, 6, or 8 in. in diameter, capable of rotation round a horizontal and a vertical axis . This mirror is placed at the station to be observed, and in fine weather it is kept so directed that the rays of the sun reflected by it strike the distant observing telescope . To the observer the heliotrope presents the See also:

• APPEARANCE (from Lat. apparere, to appear)

appearance of a See also:

• STAR

star of the first or second magnitude, and is generally a pleasant object for observing . Observations at See also:

• NIGHT

night, with the aid of light-signals, have been repeatedly made, and with good results, particularly in France by General See also:

• FRANCOIS (1558-1614)

Francois Perrier, and more recently in the United States by the See also:

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

Coast and Geodetic Survey; the See also:

• SIGNAL

signal employed being an See also:

• ACETYLENE

acetylene See also:

• BICYCLE (from prefix bi = twice, and Gr. KuKXOr, a circle, wheel)

bicycle-See also:

• LAMP (from Gr. Xag ras, a torch, Xaµaav, to shine)

lamp, with a See also:

• LENS
• LENS (from Lat. lens, lentil, on account of the similarity of the form of a lens to that of a lentil seed)

lens 5 in. in diameter . Particularly noteworthy are the trigonometrical connexions of Spain and See also:

• ALGERIA
• ALGERIA (Algerie)

Algeria, which were carried out in 1879 by Generals Ibanez and Perrier (over a distance of 270 km.), of See also:

• SICILY (Ital. Sicilia)

Sicily and See also:

• MALTA
• MALTA (or MEDITERRANEAN) FEVER

Malta in 1900, and of the islands of See also:

• ELBA (Gr. AiWaXla; Lat. Ilva)

Elba and See also:

• SARDINIA (Gr. 'IXs'o"uva, from a fancied resemblance to a footprint in its shape, Ital. Sardegna)

Sardinia in 1902 by Dr Guarducci (over distances up to 230 km.); in these cases artificial Astronomical Observations . The direction of the meridian is determined either by a theodolite or a portable transit instrument . In the former case the operation consists in observing the angle between a terrestrial object—generally a mark specially erected and capable of See also:

• ILLUMINATION

illumination at night—and a See also:

• CLOSE
• CLOSE (from Lat. clausum, shut)
• CLOSE, MAXWELL HENRY (1822-1903)

close circumpolar star at its greatest eastern or western azimuth, or, at any See also:

• RATE

rate, when very near that position .

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)

sin 1" sin 25/ sin z, in seconds of angle, omitting ,smaller terms, S being the star's See also:

• DECLINATION (from Lat. declinare, to decline)

declination and z its See also:

• ZENITH (from the Arabic)

zenith distance . The collimation and level errors are very carefully determined before and after these observations, and it is usual to arrange the observations by the reversal of the telescope so that collimation error shall disappear . If b, c be the level and collimation errors, the correction to the circle reading is b cot ztc cosec z, b being See also:

• POSITIVE (or PORTABLE) ORGAN

positive when the west end of the axis is high . It is clear that any uncertainty as to the real See also:

• STATE
• STATE, GREAT OFFICERS OF

state of the level will produce a corresponding uncertainty in the resulting value of the azimuth an uncertainty which increases with the latitude and is very large in high latitudes . This may be partly remedied by observing in connexion with the star its reflection in mercury . In determining the value of " one division " of a level See also:

• TUBE (Lat. tuba)

tube, it is necessary to See also:

• BEAR
• BEAR, BLACK
• BEAR, BROWN
• BEAR, GRIZZLY
• BEAR, ISABELLINE
• BEAR, WHITE

bear in mind that in some the value varies considerably with the temperature . By experiments on the level of Ramsden's 3-See also:

• FOOT

foot theodolite, it was found that though at the ordinary temperature of 66° the value of a division was about one second, yet at 32° it was about five seconds . In a very excellent portable transit used on the Ordnance Survey, the uprights carrying the telescope are constructed of See also:

• MAHOGANY

mahogany, each upright being built of several pieces glued and screwed together; the base, which is a solid and heavy See also:

• PLATE

plate of iron, carries a See also:

• REVERSING

reversing apparatus for lifting the telescope out of its See also:

• BEARINGS

bearings, reversing it and letting it down again . Thus is avoided the See also:

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

change of temperature which the telescope would incur by being lifted by the hands of the observer . Another form of transit is the German See also:

• DIAGONAL (Gr. &a, through, ywvia, a corner)

diagonal form, in which the rays of light after passing through the object-glass are turned by a total reflection See also:

• PRISM (Gr. rrpivµa, properly a thing sawn, Irpii"ety, to saw)

prism through one of the trans-See also:

• VERSE (from Lat. versus, literally a line or furrow drawn by turning the plough, from vertere, and afterwards signifying an arrangement of syllables into feet)

verse arms of the telescope, at the extremity of which arm is the See also:

• EYE
• EYE (O. Eng. edge, Ger. Auge; derived from an Indo-European root also seen in Lat. oc-ulus, the organ of vision (q.v.)

eye-piece . The unused See also:

• HALF

half of the ordinary telescope being cut away is replaced by a counterpoise . In this instrument there is the advantage that the observer without moving the position of his eye commands the whole meridian, and that the level may remain on the pivots whatever be the See also:

• ELEVATION

elevation of the telescope .

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)

pole star crosses the vertical of each mark a short time before and after attaining its greatest eastern and western azimuths . If now the instrument, perfectly levelled, is adjusted to have its centre See also:

• WIRE (A.S. wir, a wire; cf. Swed. vire, to twist, M.H.G. wiere, a gold ornament, Lat. viriae, armlets, ultimately from the root wi, to twist, bind)

wire on one of the marks, then when elevated to the star, the star will See also:

• TRAVERSE

traverse the wire, and its exact positipn in the field a,t any moment can be measured by the micrometer wire . Alternate observations of the star and the terrestrial mark, combined with careful level readings and reversals of the instrument, will enable one, even with only one mark, to determine the direction of the meridian in the course of an See also:

• HOUR

hour with a probable error of less than a second . The second mark enables one to See also:

• COMPLETE

complete the station more rapidly and gives a check upon the work . As an instance, at See also:

• FINDLAY
• FINDLAY, JOHN RITCHIE (1824—1898)
• FINDLAY, SIR GEORGE (1829—1893)

Findlay Seat, in latitude 57° 35', the resulting azimuths of the two marks were 177° 45' 37"•2940"•2o and 182° 17' 15"•61 to"•13, while the angle between the two marks directly measured by a theodolite was found to be 4° 31' 37"•43E0"•23• We now come to the consideration of the determination of time with the transit instrument . Let fig . 3 represent the sphere stereo-graphically projected on the plane of the horizon,—ns being the meridian, we the See also:

• PRIME, PRIMER AND PRIMING

prime vertical, Z,P the zenith and the pole . Let p be the point in which the See also:

• PRODUCTION (Lat. productionem, from producere, to pro-duce)

production of the axis of the instrument meets the See also:

• CELESTIAL, OR STELLAR

celestial sphere, S the position of a star when observed on a wire whose distance from the collimation centre is c . Let a be the azimuthal deviation, namely, the angle wZp, b the level error so that Zp=9o°—b . Let also the hour angle corresponding to p be 90°—n, and the declination of the same =m, the star's declination being S, and the Flo . latitude ..

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)

cos m cos S sin (n—r), Sin m= sin b sin 0—cos b cos d sin a, Cos m sin n = sin b cos +cos b sin cis sin a . And these equations solve the problem, however large be the errors of the instrument . Supposing, as usual, a, b, m, rt to be small, we have at once r=n+c sec S+m tan S, which is the correction to the observed time of transit . Or, eliminating m and n by means of the second and third equations, and putting z for the zenith distance of the star, t for the observed time of transit, the corrected time is t+ (a sin z+b cos z+c)/ cos S . Another very convenient form for stars near the zenith is r=b sec ¢+c sec S+m (tan S—tan ch) . Suppose that in commencing to observe at a station the' error of the chronometer is not known; then having secured for the instrument a very solid foundation, removed as far as possible level and collimation errors, and placed it by estimation nearly in the meridian, let two stars differing considerably in declination be observed—the instrument not being reversed between them . From these two stars, neither of which should be a close circumpolar star, a good approximation to the , chronometer error can be obtained; thus light was employed: in the first case electric light and in the two others acetylene lamps . let e1, e2, be the apparent See also:

• CLOCK

clock errors given by these stars if 81, 82 be their declinations the real error is e=ei+(e1-e2) (tan 0-tan 81)/(tan Si-tan 82) . Of course this is still only approximate, but it will enable the observer (who by the help of a table of natural tangents can compute s in a few minutes) to find the meridian by placing at the proper time, which he now knows approximately, the centre wire of his instrument on the first star that passes—not near the zenith . The transit instrument is always reversed at least once in the course of an evening's observing, the level being frequently read and recorded . It is necessary in most instruments to add a correction for the difference in size of the pivots .

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

northern extremity of the axis of the instrument produced meets the celestial sphere . Let nZq be the azimuthal deviation=a, and b being the level error, Zq=9o°-b; let also nPq=r and Pq=Ile Let S' be the position of a star when observed on a wire whose distance from the collimation centre is c, positive when to the south, and let h be the observed hour angle of the star, viz . ZPS' . Then the triangles qPS', qPZ give -Sin c=sin 8 cos 4-cos 8 sin ,, cos (h+r), Cos 4, = sin b sin 0-}-cos b cos 4' cos a, Sin ,y sin r=cos b sin a . Now when a and b are very small, we see from the last two equations that 4,=4-b, a =r sin 4,, and if we calculate ¢' by the See also:

• FORMULA
• FORMULA (Lat. diminutive of forma, shape, pattern, &c., especially used of rules of judicial procedure)

formula cot ¢' =cot 8 cos h, the first See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation leads us to this result =4'+(a sin z+b cos z+c)/cos z, the correction for instrumental error being very' similar to that applied to the observed time of transit in the case of meridian observations . When a is not very small and z is small, the formulae required are more complicated . The method of determining latitude by transits in the prime vertical has the disadvantage of being a somewhat slow process, and of requiring a very precise knowledge of the time, a disadvantage from which the zenith telescope is free . In principle this instrument is based on the proposition that when the meridian zenith distances of two stars at their upper culminations—one being to the north and the other to the south of the zenith —are equal, the latitude is the mean of their declinations; or, if the zenith distance of a star culminating to the south of the zenith be Z, its declination being 8, and that of another culminating to the north with zenith distance Z' and declination 8', then clearly the latitude is s(6+6')+ 1(Z-Z') . Now the zenith telescope does away with the divided circle, and substitutes the measurement micrometrically of the quantity Z'-Z . In fig . 4 is shown a zenith telescope by H .

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

• POTSDAM

Potsdam) since about 1890 for the determination of the variations of latitude due to different, but as yet imperfectly understood, influences . The instrument is sup-ported on a strong See also:

• TRIPOD (Gr. rpiTovr, Lat. tripus)

tripod, fitted with levelling screws; to this tripod is fixed the azimuth circle and a long vertical steel axis . Fitting on this axis is a hollow axis which carries on its upper end a short transverse horizontal axis with a level . This latter carries the telescope, which, supported at the centre of its length, is free to rotate in a vertical plane . The telescope is thus mounted eccentrically with respect to the vertical axis around which it revolves . Two extremely sensitive levels are attached to the telescope, which latter carries a micrometer in its eye-piece, with a See also:

• SCREW (O.E. scrue, from O. Fr. escroue, mod. ecrou; ultimate origin uncertain; the word, or a similar one, appears in Teutonic languages, cf. Ger. Schraube, Dan. skrue, but Skeat, following Diaz, finds the origin in Lat. scrobs, a ditch, hole, particularl

screw of long range for measuring differences of zenith distance . Two levels are employed for controlling and increasing the accuracy . For this instrument stars are selected in pairs, passing north and south of the zenith, culminating within a few minutes of time and within about twenty minutes (angular) of zenith distance of each other . When a pair of stars is to be observed, the telescope is set to the mean of the zenith distances and in the plane of the meridian . The first star on passing the central meridional wire is bisected by the micrometer; then the telescope is rotated very carefully through 180° round the vertical axis, and the second star on passing through the field is bisected by the micrometer on the centre wire . The micrometer has thus measured the difference of the zenith distances, and the calculation to get the latitude is most simple . Of course it is necessary to read the level, and the observations are not necessarily confined to the centre wire .

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)

refraction corrections, µ, the micrometer readings of the south and north star, the micrometer being supposed to read from the zenith, then, supposing the observation made on the centre wire, 4, = 1(s+8')+a (l4-A')m+4 (n+n'-s-s')l+1(r-r') . It is of course of the highest importance that the value m of the screw be well determined . This is done most effectually by observing the vertical movement of a close circumpolar star when at its greatest azimuth . In a single night with this instrument a very accurate result, say with a probable error of about 0"•2, could be obtained for latitude from, say, twenty pair of stars; but when the latitude is required to be obtained with the highest possible precision, two nights at least are necessary . The weak point of the zenith telescope lies in the circumstance that its requirements prevent the selection of stars whose positions are well fixed ; very frequently it is necessary to have the declinations of the stars selected for this instrument specially observed at fixed observatories . The zenith telescope is made in various sizes from 30 to 54 in. in focal length; a 3o-in. telescope is sufficient for the highest purposes and is very portable . The See also:

• NET

net observation probable-error for one pair of stars is only t 0"• I . The zenith telescope is a particularly pleasant instrument to work with, and an observer has been known (a sergeant of Royal See also:

• ENGINEERS, MILITARY

Engineers, on one occasion) to take every star in his See also:

• LIST (O.E. lisle, a Teutonic word, cf. Dut. lust, Ger. Leiste, adapted in Ital. lista and Fr. lisle)
• LIST, FRIEDRICH (1789-1846)

list during eleven See also:

• HOURS, CANONICAL

hours on a stretch, namely, from 6 o'clock P.M. until 5 A.M., and this on a very See also:

• COLD (in O. Eng. cald and ceald, a word coming ultimately from a root cognate with the Lat. gelu, gelidus, and common in the Teutonic languages, which usually have two distinct forms for the substantive and the adjective, cf. Ger. Kolte, kalt, Dutch koude

cold See also:

• NOVEMBER (Lat. novem, nine)

November night on one of the highest points of the See also:

• GRAMPIANS, THE

Grampians . Observers accustomed to geodetic operations attain considerable See also:

• POWERS, HIRAM (1805-1873)

powers of endurance . Shortly after the commencement of the observations on one of the hills in the Isle of See also:

• SKYE

Skye a See also:

• STORM (in O. Eng..storm, and so in Du. and Low Ger.; in O. H. Ger. and mod. Ger. Sturm; the root is probably that seen in " stir," to rouse, move, disturb, cf. Ger. storen)
• STORM, THEODOR WOLDSEN (1817-1888)

storm carried away the wooden houses of the men and See also:

• LEFT

left the observatory roofless . Three observatory See also:

• ROOFS

roofs were subsequently demolished, and for some time the observatory was used without a roof, being filled with See also:

• SNOW (in O. Eng. sndw; a common Indo-European word; cf. in Teutonic languages, Ger. Schnee, Du. sneeuw; in Slavonic snieg', Lith. snegas; Gr. vi4a, Lat. nix, nivis, whence the Romanic forms, Ital. neve, Fr. neige, &c.; Ir. and Gael. sneachd; the original

snow every night and emptied every See also:

• MORNING

morning . Quite different, however, was the experience of the same party when on the top of See also:

• BEN (from Old Eng. bennan, within)

Ben See also:

• NEVIS

Nevis, 4406 ft. high .

For about a fortnight the state of the See also:

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

atmosphere was unusually See also:

• CALM

calm, so much so, that a lighted See also:

• CANDLE (Lat. candela, from candere, to glow)

candle could often be carried between the tents of the men and the observatory, whilst at the foot of the See also:

• HILL
• HILL (0. Eng. hyll; cf. Low Ger. hull, Mid. Dutch hul, allied to Lat. celsus, high, collis, hill, &c.)
• HILL, A
• HILL, AARON (1685-175o)