PN = l7.OO kg:f il7.oo) = il7.oo)5 - 5il7.OO)2 - 4044.96-= - 576.96

;

PN = 17 .5O kg:fil7.50) = il7.60)5 - 5il7.50)2 - 4044.96 = -2t6.83PN = 17,78 kg:t(n.7e') = u7.78f - S l7.7ef - 4044.96 = - 4.AC

Try

'f ry

Try

Try PN = t7.79kg:f UT.7gl " ur.79t3 - 5u7.7g)z - 4044.96 = + z.g7

Try Pn = 17 .8O kg:t itz.eot = il7.Bof -s (ft.ao'tz - 4044.96 = + to.59

From tha obove five triols, it con bs seen thot the volue of px whichgives o solution neoresl to zero is 17.79 kg, therelor",-Fp: f,ZlZS kg. fhexoct volu is ac?uolly somewhere between- lz.zg- ond' ti'.zg kg. Sifice'-only two digits ofter rhedecimor potnt- woull tii'iutt'iiieni', the votua tz.zgwos selecled.

IOR ue.iunEt.tr ILesson ll

-.Wgiif,ff.g. -[o!,

I}TEASUNEIfiENTOF IIONTZONTALDISTANCES

l

n-,. curBTlE c0RREcTrolrstt-t. suRvEys ulTH TME

l. Etprting Pe4etdiulan To Litoal Chnd-Bi.uttion kthodbl 3:1:5 llelhod

2. thr.attLing Atgl2A Uith Tape.3. tqitg o{l AtrgbL Uifi Tape1. Oetehinhg Obeunted Oi.ttarcet

tr-t. il.r.us'n nvE PR6rEl{st. Cffiinen Cor,r:ettioru2. Cortinen Conxettiorut. Cffiinen Cotuegtiona1. ,btutring Anglz,s Uith Tape5. ,eaatilLitg Angfra Uitth Tape.6. Atuhuctun gi,ttarcet

11-1. COXBTf,ED CORABCTTOIfS.The correctionE for the ef,fects of lncorrect length of,tape, ternperature, tension, alope, and sag rnay be comblnedas a single net correctisn per tape length. Each correctlonis computed separately and lt ls lnportant to ldenttfywhlch correction tends to nake the taPe too I'onq or tooshort.

Since the sign of each correction can be determined du-rlng computation, it is then a matter of addlng these guan-tities algebralcally to arrlve at a single and overall cor-rection to lengths vhich are measured or lald out. Comblnedcoirections are usually determlned on the basls of thcnominal tape length siice each correctlon is relatlvelysmall and do not appreciably affect each other. The result-ing net correction per tape length nay bq used as long atconditions renain constant during taplng. Variation in con-ditlons mry be due to changes ln temperature durinQ thalday, non-uniformity of pull exerted on the ends of thataF, the ground may be such that it becones necessary toEupport the tape at varlous lntervala, and some othcrfactors which may affect the taping operatlon

11-2. ST'RYBTS gITH TIPE.The tape is'not necesEarily linlted only to the measuremsntof distanceE. There are various problems arlsing in survey-lng fiel.duork whlch can be solved just by the use of Itape. Some of thgse surveylng operatS.ons include: erecttngpbrpendicular to a line, measuring angles, laying off ang-Ies, determining obstructed diEtances, locating irregulr!bounderies, and determlning, areas of dlfferent shapes. :

1. Erectlng Perpendicular To Line. There nay be 6instances when it would be necessary to erect on the groa perpendicular to an eEtablished line. For example,the floor dlmensions of a building or aare to be laid out, it becomes necessarycular lines. Commonly employed for suchments are the chord-bisectlon method and

road interseetlto erect perpendlparticular regulrlthe 3ltl:5 method.

a) Chord-Blsectlon lGthod. In Flg. l1-1' lt ls ragulred to erect.a perpendlcul.ar to the }Ine AB at polnt ITwo egual lengths, tlb and rc, are measured on each side opoint n. htith b as center and taking any convenient Lof tape as radlusr iln arc of a clrcle la descrlbed.same procedure is repeated at point c. The intersectlon othe two arcs locate'polnt d, and line dn ls the deglperpendicular to AB.

b) 3:l:5 llethod. This method of erectlng a perpendlcular to a given llne is illustrated ln 8ig. 11-2. Thcthod involves the setting up on the ground of a tltanguhose three sldei are made ln the proportlong of 3,,l lO- ltftff#tlicfhs

,lFIe. ll-1. Cticrd-bdrnrjol- nntd. Fig. ll-r. l-1-i nfrd.

5. Polnt A ls seleqted on line X}f, where a perpendicular isto be erected. From A and along llne MN, measure 3.0 m totet polnt 8. Then, with the zero end of the tape held bythe flrst tapeman at B and the 10-n mark held by the secondtepernan at A, a loop ls formed by the third tapeman tobrlng the 5-m and 6-m marks together. The third tapenanthan pulls each part of the tape taut tcj locate point C onthc Around. The ltne joining polnts A and C ia the desiredgrrpendlcular to llne HN.Althouqh thls task is better and e4sier performed bythree tapemeno it is st1l1 posaibl.e for Just one person togrrform the layout by fastening the tape ends to stakeslrcurely anchored at polnts A and B. Alsoi any otheftrngths ln the proportlons of 31 4, and 5 can be used Euchtr 5:8:10, 9:12:15, and L2zL6z2O.

2. l{easurlng Anglea lltlr Ta5n. A tape ls not frequent-ly used ln engineering condtructions for measqring or lay-llt. ,l-t. ,at^saing atryrl bg ahrlrd rhd.

Itlhere:l- e ony convenicnt length(; chord dlsloncaQ. = ongle to be meosured

,,c,frrrWitfhti

-Jll

tItttIIII

tf2

--\It,

IIttI

tf2

I

lng out angles. There may be some occaslons, however, whena theodorite or transit is not readlly avallabre that thetape is instead used. The measurement of very smalr angleswlth tape usual].y gives satisfactory results. Arl angurarmeasurements by tape are accomplished by the apprication of

the aielevery basic geometric and trigonometric principles.In Fig. 11-3, let it be reguired to measureBOC (orO). One way to do it'is to lay out anylength (L) along lines oB and OC to establish-b, If the chord distance ab (or d) is'measureded, the angle BOC can be c.omputed as folLoys

convq.qient'points-i andand blsect-

/

' sintlt'Y Eq'(l)Equation 1 is only valid if the lengths of Oa and, Ob areequal. If unegual lengths are laid out, as AB and AC inFig. 11-4, then upon measuring the distance gC, the anglcBAC (or{A) can be computed using any of the following tri-gonometric equationsFiA. ll-1. ,kt.str.ilg atqlt uith tape..

A -

(AC)z+(AB)2-(BC)e@

lfhete AB, AC, and EC are the sides of triangle ABC and S(L/21 (AB+AC+BC).The accuracy of measuring angles with tape depends,the care taken in laylng out lengths and in establ,isfrlthe needed points on the ground. It would be dlfficult

measure angl.es when the terrain is very irregular or rhetavegetation obstructs the desired measurement.

The use of the tape in measurtng angles ls rather sland should only be empJ.oyed on aurveys covering relatlvelsmalI areas. A transit or theodolite should be used to meesure or lay out angles on surveys of wlder scope and wtrerdhigher degrees of precision would be required.3. Laying Off Angles Uith Tape. There are diffezent mr-thods which may be used to lay off an angle using a tapa.In F'ig. 11-5 ls illustrated a method vhlch employa a alprinciple of trigonometry. Along line AB a convenlcntlength, AP, is first laid out. Then pp' is erected perpcn-dlcular to the llne at P by using a length whlch ls detcr-mined by multiplying the 1engtn oi ap toi'f,) by the naturrltangent of ,the angle to be lald off or ppt = ! (Tan0l.Aqgle PAP| (or0) should glve the desired angle at A.'Another method reguires the determlnation of a chorCl, t taatutEvatr uI r 1G- H*tqt4 Urtreaa

fig. tl-5. Lulutg ol[ at an4ltwhg a pe4enniuilat li*.

tag. ,r-6. taqing oll an atglttuitts. o ehud langth.

\

Ec.(31

Icngth whtch will define the desired angJ.e. In Fig. 11-6,tt is required to Lay off an angle fn (or0) from line PA.The chord length is first determined from the iiquation d =ZLaLnlQ/2), where g is the desired angle and L is any con-venient length laid out along tine PA. Then, point n isrstablished by laying out from P, and along line PA, aconvenient length of tape. The tape is then swung throughln arc and accordingly the arc traced is marked on theground. Wlth ! now as center, the computed chord length is1160 laid out and swtrng through an arc, and its inter-rection wlth the first arc establishes point n. Line nn isthe required chord length, and the angle fn is the desiredrngle.

oeterrrning obstructed Distances. rn some instancestt may not be possible to directly measure distances due toen obstruction. The required J.ength lnay also be inaccessi-ble or difficult to measure. The fol.lowing are some of thelndirect methods which could be employed to determine obs-tructed or lnaccessible distances

a) In Fig. 11-7, point C is established at a conve-nlent location away from the obstruction and it is seen toIt that lines AC and BC intersect at right angIes. BothIlnes are measured as accurately as possible. If A and Bdefine the end points of the required llne, the length ofltne AB can be computed by the pythagorean theorem or

ABg Eq.(4)b) The length of llne AB ln F19. 11-8 could not be

determined because of an obstruction somewhere at the mid-dle of the llne. To dbtermine its length, the head tapemananchors one end of the tape at B and swings it using anyconvenient radius. The rear tapernan positions himself atpolnt A and llnes in the other end of the tape with a dis-tant polnt as D and directs'ttre marking of points a and bon the ground where the end of the tape crosses line AD.Tha mld-pbint of llne ab is located to establish point C.

*,f&?!["o15ll{,

-

l13.

llal| /.,

-u,3Ob!l ruclion

Fig. rr-7. Fig. tl-t.

Flg. ,l-9.

Fis. ,r-r0

I l4- itiifrjff{,ofio,"*&';fi1!"iili:*%

-

I 15,

\lftn 1ln9 BC eatabllahcd pctptndlcular to llnc AC, thclcngth oE AB can be tndlrsctly,detcrmlned also by thcpythagorean theorem slnce AC and BC are known.

c, In Flg. 11-9, the length of AB.can be determineddue to the slnilarlty of triangl.es ABD and BCD. A line' BDof predetermlned length is first established $erpendicularto llne ABC. The length of line BC is then measured and ABls computed as fol lows:

# = 3 or AB " (BD)2^Bc). . . . . . . . Eq.(5)d) The length of AB in Fig. 11-10 is determined by

using the tangent function of trigonometry. At a convenientlocatlon along the shore Ilne, AC is set out perpendicular'to AB and lts length measured. tlith the use of a tape,angle BCA is determined by the chord method. The reguiredlength is then determined as follows

AB = (AC) Ton ({BCA} " " 'Eq.(6)e) In Fig. 11:11, polnt C'ls established at a sulta-

ble location away from tbe.obstruction and the lengths ofAC and BC are measured. On the extension of both linesr'potnts D and E are established such that CD = (Ac)/2 and CE= (BCl/2. The length of AB is parallel to and twice' theIength of DE which can be measured.

fl The method illustrated in Fiig. 11-12 is one wheretwo 1lnes, BD and CE, are established perpendlcqlar to theline ABC. The distance betueen the two perpendiculars (orBC) is measured an with polnts D and E both lined up withA, the length of AB can then be determined by similarity oftriangles or

g =

(AB j- Bc) i AB (cE) = BD {AB + Bc)BD CEAB (CE) = BD (AB) + BD(BC)AB (CE) . BD (AB) = BD ( BC)AB (cE. BD) - BD(BC) or AB = ffi. . Eq.(7)

g) In Flg. 11-13, it is required to deternine thelength of line AB which apparently could not be measureddlrectly because of an intervening body of water. The re-quired length ls determined by establishlng a Iine cD whichis parallel to and equal ln tength to A8. In thiq method,.perpendicular offsets AC and BD are established by tape. IfAC and BD are egual in length, CD, when measured, should beequal to the length of AB

- h) In Fig. 11-14, the obstructed length of AB may belndlrectly determined if the length DE can be measured. Inthls rnethod, polnt C is first selected such that it is a

llA teatunatEtr 6

errtaln dtctancG away from the obatructed llne. The lengthsof AC and EC are then meaaured and thelr respective middlepotnta (D 6 E) establlshed.. The length of AB is ttrice thatot DE

1) One convenient method of getting around obstruct-tonc such as a large building, involves uslng an equilate-rel trlangle as illustrated in Fig. 11-15. From the prolon-getlon of the preceding llne, a 60-deg angle is laid off atA and a sufficient length is laid out to cleai the obs-tructlon. Another 50-deg angle is laid off at C and thedlatance CB is taped equal to AC. Point B should fall 'onthc prolongation of the original line and the measurement'rney be continued further. The length of AB should be equalto elther AC or CB..

J) Shown in Fig. 11-16 is a typical problem encoun-tcred when determining the width of a stream or a tride ri-vcr. Here, BD is set out perpendicular to the requiredlcngth and point C is located at its mid-length. DE is nextrct out perpendicular to BD and polnt E is located so thatIt ls ln line wlth points A and C. If the length of DE isrccurately measured, it should be equal to the length ofthe regulred Line AB.11-3. ILLUSTRTTIIIE PROBLEI{S.l. COHBIIIEO COnnECnOItS. A line wos determined ro be 2395.25 mwhon meosured with 'o 30-m steel lope supported throughoul its lengthundor o pull of 4kg onO ot o rn?on tmproture of 35oC. Determine the cor-rcct length of tha line if tho ?op6 used ls of stondord lngth ot ZOoCunder o pul.l of 5kg. The cross-soctionol oro of the topi is O.O3 sqcm, its coeff icient of lineor erponsion ls o.ooooll6/1"c. dnd the modu-lur of elosllclty of sleel ls 2.O x 106kq,/cm2.Glvcn:

t-

NL=9=

Solu lion:

2395.25 m30m4ks

T = 35'c A = o.o3cm2T. = ?o0c c =o.ooooll6/t'cF; = 5kg E = 2.a xlo6kg/cm2

o) Ct = CL (T - Tr) = O.OOOOI16 (2395.25)(35 - 20)= + O,42 m '(Corrcc?lon for lht moorur.d lcngth du. lo t.rip.rotur..

Thc porlliv. slgn lndlcot!r tiot top. h too long)hr . - (Pm- P3)L - (4-5)2395.25et

-P - AE - o.og t2.o x 106)= - O,04 m (Corr.ctlon lor th. m.orur.d lln. dur ?o l.nrion.Th. n.go-tlva rlgn lndlcol.r lhot tqp. lt too rhorll

c) L, =LtCrtCp" 2595.63 m

2. COilONEO COnnECf lOIlS. A SO-m sleel tope is of stondord lengthunder o pull of 5.5 kg whn supportod lhroughout its entiro length. Tho

= 2395.25 + O.42 - O.O4(Lgngth ot mgosurod llng corr.ct.d fol cft.cls of tompa-roturo ond pull)

,orlfi""r!trtf,,fl& ; I I L

top6 wclghs O.O5 kg,/m, hor o crosr-s.ctlonol or.o of O.Orr_T,-i".liri,**iil;',r'itl'"'-Tir'rldlllTiiii,{:iirffi iili458'650m. Ar the trmc rhe mcosurcmsnt. wos mooe, rn.'.on"ronr guilopplled. wos I kg lt_r!..rhs

-rop" -!3neJiil'a iiiy';;-trt'oic polnr. orrrrmine ?he correct tength of rhe 1lni.-

G ivan:NL=P3:ut=

'p!'m

Solutlon:

50m5.5 kgO.O5 kglm8ks

O.O4 cm2-2.lO x tfU,stcmz458.650 m

" O.ooOOil6 (459.65Otil8 -20)(Corrrctlon loi th. mrorurid tln. du. tonrgotlvr. rign indicotor thot' topr j. too

l?:r_l:-"tlol. duo ro 3oe qT Og-,r,. spon. Th. .ff.c, ot,o0orwoys molo thc topc too 3horr,

24r2{Co?r.ctlon dur to toe tor th. g.e6m rponl

l8'co.ooooil 6/toc458.650 m

A=F=l-:

o) cp = (Pm I-PJL= + O.Ol4m

_

(8 - 5.5) 458.650

O.O4(2.tO x tO0(Corr.cllon lor lho mcarurod llnc ducsltlvc rlgn lndicoto, thof toOr tr toob) c. =_',rr'L: _ _ (o.o5f (5o)g

-r 24e;z 24 rcF= - O.2O3 m

_

.r,'aL3%--4 =-= - O.OOlm

Nolc: sinca lhare ora nlle 5_o--yt,spons ond one g.65m span in moo-suring o totol dlstonca of 4Sg.650m.g(-ql)

- Cr2 = 9(-O. 2O3'l - O.OO1- L828m - (Totot corrootlon du. ro toglL l Cp tCa = 458.650 + O.Ot4 - t.82g456.836m (Lrnerh ot m.o!ur.d lin. corr.ct.d lor .ft.cr3 ot r.n.ion

ond .og)

(0.o5)a (8.65)3'

to l.nrlon. Tho porlong)

t.mp.rctutt. Tlt.horl)

cr=

c)Lt=

t cot?ltED coilnEcrtolls. rn probrem no.z,ft rhs ropo usod wosstondordized ot 2o"c,ond durrng tne ireosurement-tne' m"--on t"mp.rorureobserved wos r8oc, .derermine't-tre coiicct rengih'oi'rne"riis for rhe com-

11111 "lf-"-"ls,o_f

reniion, so9, ono iemierq?uro. Assume rhe coefficrenr ofrrnoor oxponsion of rhe rope to be equor to o.ooooil6 per r creg c.6lven:

Cp - +O.Ol4mCa = -1.828mT3 = 2O"C

'Solutloa:

o) Cf : CL(T - T.)= -O.Ollm

, I I g_ i5iffiff,f,i"r"f,_'

T!

lg

!cr ' 458.66o .'l.o,o - 1.828 - o.oll.lL.nelh ct lhr rnoo.ur.d llnr oorroot.d to? lh' oenblnrd'rtfoitr ol lonrionr .oer ond l.nD.rolura)

a, nEAgunwo ANOLES Vt7H.7AP.E. The onsle P_e^twe6n lwo-intsr-idoiir,e-lin"ej r" to-6"-aet"rmtnec wllh o l-oP' A polnt on eoch fencellnr lr orlobllshed SO.O m f rom the poinl-of interse'cllon. lf lhe dlslonceuli"i-.n- in-,i'i-riiuriixii'i"ii.,il" ii"izliii'i", '"iii.ii, ile tnrersedlon onele?Jlt, tt-tt

llL'ra

Polnt otlarrtcllon

Eolutioa:o) Delermining

Cos 4CAD

12-1. LEVELIIIG.Lcveltng ls the process of dtrectly or indlrectly measurlngvertical aistanles-io a"t.tmine the elevation of polnts orthelr differences in eLevation' It is a vital and lmportantaspect of surveyi"g

"ince leveting operations are underta-

ken to provlde-nicessar'y data f6r Lngineering.design andconstruction, ."J-in. priductiori of topographic napE' The

";;t;;;iilv Lt

" "it" ftrg development can be better deter-

mined by using in" resutts obtiined from levefing opera-tions. Through in. pt"".sses of levelinE' buildings' roads'i;;ir, ana 6tn.i vlrtical and horlzontal structur,es can.bedesigned ana raLa ;;a-io tiest conform to the configurationof the ground.

L2-2. DBFIIIITION OF TBRHS.To better understand leveling operations-' . fht followingbasictermsaredefinedbelo',"n-dsomeofwhichareillus-trated in Figure 12-1.

1. Level Surface. It is a curved surface which is atany point perpendicular to the direction of gravity or the;i-;d rini. rt is best represented by the surface of -aIarge body of still water' However, a level surface is nota plane and does not have a regular for-m because of localdeviations ot tne p}umb line. ro sorne ef fect, t|re Qirectionof gravity depends on the distribution of the nasses of theearthlscrust",,do,,-theirdensities.Suchthatifaplumbbob is held vetiicalry at the base of a mountain, it willhavethetenaencyto.deflecttowardthemountaln.Althoughthe deflection woufa be small and negligible' nevertheleasit makes the level surfase sIightly irregul'ar'

2. Level Line. A level line is-a curved line irp a levelsurfaceallpointsofwhicharenormalto.thedirectionofgravity ana equiaistant from the center of the earth

3. ttorizsntal Surface' It is a plane that is tangent to"

r"J"r"J"ii"""-"t a particular point' t!9 horizontal sur-face is also perpendiculaE to the plumb line at the same

A straight line in a horizontala level iine at one Point' Thisthe dlrection of gravitY at thethe mean radiuE of the earth is

point.l. Horizontal Line.plane which is tangent to

Iine is PerPendicular topoint of tangencY. SiPce:;il;t";i,rJiv'i".i", it is

-practical foT most purposes toassume that a tev6t'line and a horizontal line are the same

line paralleI to the direction of gravity' It ls exempli-ii"a 'by the direction taken bv. a strl"?

":Plo:::i:-"-.. ::"-:irrr*i uol-p"""ing throus}t " point' For ordinary pur-it i" conven'ient -to as.sume that the earth is a truewith a smooth surfacer'and that a plumb line held at

for short distances.5. Vertical Line.

pendedposessphere

A vertical line at anY Point is

1 A 'EA'U.EIIN| OF.l 1+lt- t.Dlta4 otsr.dc6t ,,{f i|,t""if l,',{'-J?5

\Fi4. tl-r.i.t/l,tionthlp be&., Itvd tnlantt.

any point on its surface is al.ways directed toward the cen-ter of the s.phere.

6. l{ean Sea Level. Mean sea }evel is an inraginary sur-face of the sea which is midway between high and 1ow tides.It is taken as the reference surface to which most groundelevations. are referred. This surface is determined by ave-raging the height of' the sea's surface for aII its tidestages over a long'period of time which may extend lo about20 years. Readings are usually taken at hourly intervals onvarious properly distributed stations. Mean sea leveI isnot a steady frame of reference due to the melting of icein the polar regions, the effects of volcanic activity, andnnny other influencing factors; It is for these reasonsthat it is/necessdry to have a continuing observation ofsea leveI fluctuations to detect changes. This surface,which is 'considered to be at zero elevation, conforms tothe spheroidal shape of the earth and is perpendicular tothe direction of gravity at every point.?. Datun. Datum is any convenient level surface coinci-dent or parallel with mean sea level to which elevations ofa particular area are referred.

.Any surface nay be used asa datum when relative elevations over a limited area needsto be established. It is done by assigning an assumedelevation to a reference point and determining the eleva-tion of other points in the vicinity with regard to thisvalue

8. Blevatlon. For a particular point, its elevation isthe vertical. "distance above or bel.ow mean sea level or anyother selected datum. Points on or near'the surfa-ce of theearth have either positive or negative elevations, depend-ing if,the point is above or below mean sea level.

9. Differenee in Elevation. The difference in elevationbetween two points is the vertical distance between the twolevel. surfaces in which the points 1ie.

L2-3. LBVBLITG IIBEHODS.There are valio,rt ,i"tnodg whtch could be emgloyed to deter-mine the eLevatlon of points and their differences ln ele-vation. These methods nalt be undertaken either dlrectly orindirectly ln the fte1d. The princlpJ.e involved ln eachmethod dllfer in some aspects. Also, they nay dlffer vlthrcspect to the type of lnstruments used, the procedure em-ployed, and the attalnable degrees of preclalon. Traditio-nal methods of levellng have been used for so rnany yearsand they stiIl continue to be useful in the present .tln9'such methods lncludel dlrect leveling, trigonogfetric level-ing, and barometric leveling. IConcurrent. with recent developnents in surveying ins-ituments, newer and more prectse technlques have been deve-loped. gome of these utilize el.ectronic instrumente such astolal geodetic statlone, the airborne proflle recorder, 8a-tellite doppler systerns, and lnertial surveylng systems' 1nthe following llssons no attenpt will be made to discussthese new Leveting methods. concentratlon-yl11 be rnade onlyon conventional and traditlonal methods of levellng, thlgbetng an el.ementary course o.f st.udy in surveying.

1. Dlrect or Splrlt Leve1lng. Direct leveling ls thecominon!.y employed method of determining the. elevatlon ofpolnts some dlstance aPart by a series of set ups of a le-veling instrument along a selected route. Thls method oflevellng is also referred to as spirit leveling since thedevice used ls a splrlt level. Differential I'eveling, dou-ble:fgdd3d *l_eveJ!-gg, and tlr-ee-::tj Lng are forms. ofaireEt Leve-fing. In direcf leveling vertlcal distances aremeasured above or below a level llne and these.values areused to compute the elevatlon of points or thelr differen-ces in elevitlon. Being the most:.preclse nethod of levei.1 ing, it ts used rrhen a htgh degree of accuracy is re-quired

2. ReclProcal Leveltng. Reciprocal levellng is the pro-ce6s of accurately determinlng the difference in elevationbetween tvo intervlsible polnta located at a considerabledlstance apart and between vhich points leveling could notbe performed in thel usual nranner. This method ls commonlyemployed when leveling across a wide river, a deep raviner'or across canyons and gull.les where it would be -dlfflcultor impossible to nraintain a foresight and a backsl.ght dis-tance of nearly egual lengths. Reciprocal levellng providesa faster nrethod of determining dlfferences in elevation andwhen it ls carefully conducted, it could be as precise asdirect Leveling. In determtning the dlfference in elevatlonbetween the two points, it will require two setE of obser-'vations and the mean of whlch, is used. Sinee there ls ine-quality between the sights taken, the plocess of recipro-cal, leveling ls expected to elimlnate the errprs resultingfrom crirvature of the earth and the refraction of the at-

,)26- ffifi{ff1i&ff c,

mosphere, provlded that atmospherlc condltlons do notchange durlng the process of Iev-Iing.

3. Profllc Lcvellng. This method of leveling ls used todetermlne dlfferences in elevation between points at desig-nated short measured intervals along an established line toprovlde data from whtch a verttcal section of the groundsurface can be plotted. In the deslgn of roads, railioads,canals, dralnage 6ystema, and transmission Ilnes, it Is ne-ceasary to flrst obtaln a profile of the existlng groundsurface.. I't lE this'method of leveltng which yill best suitsuch requirements.

l. Trlgonoretric Leveling. Thls method of level.ing ,lsemployed 1n determining by trlgonometric computations thedifference ,in elevation between two points from measure-ments of its horlzontal or slope distance and the verticalangle betyeen the points. The reguired distances.are usual-ly obtained by stadia, triangulation, or by direct taping.By most leveling standards, trigonometric leveling onlyprovides a very rough deterninatlon of dlfferences in eIe-vation. Its degree of precision may be improved by usingprecise measuring instruments such as optical theodolitesand total geodetlc statlons which measure angles to 6e-conds. However, there are certain occasior,"

"udh a. in map-ping or surveying ovef very rugged terrain when it rrould befully Justified to undertake trigonometric leveIing. .It tsalso a convenient'method to adapt when it is required onlyto determ.r-ne the elevation. of principal stations or con-ttttultlliii" Levettng. stadia revering combines featuresof direct leveling with those of trigonometrlc leveling.This method is in fact a form of trigonometric leveling. Itcan provide, reasonable accuracy for preliminary surveys,napping, and r,ough leveling, where quisl neasuremeBts areneeded. In stadia leveling, differences ln elevatlon bet-ween polnts are computed from observed vertlcal angles andthe three lntercepts on a rod held. at each potnt backs"ight-ed or foreslghted. Any surveylng lnstrument rnay be employedin stadia leveling as long as lt has a telescope to readvertical angles and is equipped with stadia hairs in addi-tion to the standard cross hairs.6. Baroretric Leveling. Barometric leveling involvesthe determination of differenees in elevation betweenpoints by'measuring the variation ln atmospheric pressureat each point by means of a barometer. Thts leveling methoddepends on the basic princlple that differences in eleva-tlon are progortionaf to the differences in atmosphericpressure. The readings of a badqmeter at differ.ent pointson the earthrs surface provides a measure of the relativeelevations of these points. It is an accepted fact that thepressure 'caused by the weight of 'a column of air above theobserver decreases as the observer goes higher in altitude.The method is. particularly useful for lorr precision level-lng over rough terrain yhere extensive areas need to be

olfilt [Elllo?I

-l3z

covered and dlfferenceg ln elevation are large. It lsprlncipall.y employed on reconnalssance surveya or otherwork requiring only approxlrnate values. However, lt ls notdesirable to employ when the atmospheric pressure in thearea changes rapidly.

7. Cross-Section Level.lng. In hlghway or raitroad cons-tructions it is often necessary to obtain a representationof .the groupd surfac,e on elther side of the centerline.

"Short profiles at right angles to the line of work areusually plotted at regular intervals for this purpose. Thtstype of data'is obtalned in the field by a precess referredto as cross-section leveling.8. BorrorPit Leve1ing. Borrow-pit leveling is a methodof determining the relative elevations of points in borrow-pit excavations for the purpose of calculating volumes ofearthwork. This type of nork is usually encountered in theconstruction of roads and railroads.L2-1. TTPBS OF LBVELSThere are various types of instruments. used in levelingjwerk, the basic instrument used, however, is the spirit le-vel. Other instrumeirts employed in leveling work includethe hand leveI, alidade, translt, theodolite, aneroid baro-meter, and EDM instruments. Although these instruments maydiffer somewhaL in design, each can be used to establish ahorizontal line of sight by means of a tel.escope fittedwith a set of cross hairs and a level bubble.Fig. ll-2. tutry1 ltvt.

l

ItA tE.tuuEJEflr ofrrLv- tEnncaL ottfatcet

l. DurBy Lcvcl. The dumpy level (FIg. L2-21 Ig the mostwldely uEed dlrect levellng lnstrument. It has a long te-leacope whlch is rigldly attached to the leveL bar. Theteleacope, which can be rotated through 350 degrees, fixegthe direction of the line of sight. Attached to the levelbar is a 1evel vial which always rernaing in the same verti-cal plane as the telescope. A leveling head supports theteLescope and permits the bubble in the tube to be centeredby means of the Ieveling screws. The whole. instrument is inturn supported by neans of a tripod.

The dumpy level is simple in construction. Its mainparts are all made in one casting which are fastened rigid-Iy together. Since therb are only a few moving parts whichcould be worn out or displaced, the irlstrument requizesfewer adjustments.

2. Uye Level. The wye level (Fig. L2-3') is very. identi-cal to the dumpy level. The only distinct.difference bet-Fig, l2-3. 9e bvcL.

Lav.l Vlol Focualnc xnob D.tochobla lalarcoPr

Coprtcn - xoodaa ScrarCllrt

Wtt Sug9otl Yra Sugpotl

Crorr AorTtlarcopa ClomD

L.v.llnf Scr.:

Eool Plol.

loaganl Scr.r

Trlgod l.rgr

neen these two lnstruments is in the manner by which theirtelescopes are attached to the supporting leveI bar. Thewye, level has a detachable telescope which rests in sup-[rorts called wyes. It can be removed from the Y-shapedsupports pnd turned end for end during adjustment by relea-slng the two clamping collars which fit across the tops 'of

,,!,'ii!"i i!',n&

-

I 29,

the Yrg. curved crlps are used to facten the tcrcacopc lnplaceThe wye level iE non almogt obEo],ete and acldomly uscdsince newer levels are better congtructed and satlsfactoryfor most Leveling work. Although this Leveltng lnstrunenl

was not as popular as the other revels, many of lts' oldermodels have more sensitive bubbre tubes than the othertypes of engineerrs level.3- Buirderrs Lever. This inEtrunent is used prirnarrryin the different phases of bqilding ionstruction where Ihigh degree of precision is not a prlmary requislte. En_gineers, architects, and builders use it in the settlng ofcqncrete forms, batter boards, and tn establlshlng gridesfor earthwork.Fi4. ,2-1. &ildtt't bve!.

It is often called a construction Level or an archl-tectts level. The level. vlal is not as sensltive as inother levels and lts telescope haE a lrch lesser magnlfyingporrer. The horizontal circle, which is found between thelevel vial and the leveling head, is its special feature.This circle ls used when measurlng or laying out horizontalangles

,1. Autonatic Level. Self-Leveling features are incorpo-rated ln automatic levels. This type of 1evel has becomepopuLar for conventional leveling work because of the easeand speed of their operation. It does not use a level vialand lts abillty to Level. ltself depends upon.the actlon ofa complex pendulum-and-prlsm device.An automatic level is equipgrcd with a prismatic devlcecalled a compensator yrhich is suspended on fine, non-nlgne-tic wires. l{hen the instrument is approximately centered bymeans of a bullrs-eye'Ievel, the force of grlvity on th;compensator alLows the optical system to swlng into a posi-tion which wiLL autotnaticat ly rnake the line of sight hori-zontal. The line of sight renains horizontal as long as thecircular bubble remains approximately centered.l?,n alatueEtElt cUIZ:U.I vc?rtctL otstaicEt

"\Flg. ,l-t. ,ttanl.ac &,ve/..

1 The level is not affected by any slight novement orsettlement which wouLd disturb the bubble or Iine of sight.Its pendulum actlon autornatically shifts to maintain atruly horizontal 1lne of sighf whenever the instrument isslightly disturb. This type of Leveling instrument is par-ticularly useful where the ground is soft or rrhen strongwinds blow agalnst the instrument since it can autornatical-Iy relevel itself

Fig. l2-7. giH gadetie tavat,2-6. Uitt ilning lzva, *ith tstalahlt&leu.on d rcvuaihil2 ttthia.q. Izvet.Fis.

,e!,'ii!,fE1IL,%

-

l3l ,

r5. Tllttng Levelg. ,Thls type of levellng lrlgtrument(F19. 12-5) can be tilted or rotated about lts horlzontal

axis. A bulI's-eye level is employed for its guick andapproximate ,leveling. The tilting knob is used to rotatethe telescope into a correct horizontal positlon. Tiltlnglevels are cotnmonly employed for very precise levellngoperations and in other general leveling worl. It ls a'Isoequipped with a horizontal eircle which rnakes lt suitablefor layout and construction surveys.

5. Geodetic Level. The geodetic level is basicaLly ano-ther type of tilting level. Most of its metal parts aremade of invar to reduce the effects of temperature. Geode-tic levels (Fig. L2-7 ) are.employed in first-order levelingwork where extreme precision is an important

_requirement.The instrument is equipped with stadia hairs ih addition tothe standard vertical and horlzontal cross halrs to nake itsuitable for three-wlre leveIlng. .llhen uslng the lnstrurnentthe obqerver has.to stand erect since it is designed with ahlgh tripod to bring the line of s19ht way above any inter-vening ground surface. This was purposely done to lessenthe effects of differential refraction of extra long llnesof sight.

?. Translt as a Level. The engineerrs translt has al-ways been referred to as the ttuniversal surveying lnstru-mentrr because of its variety of uses. There is no doubtthat it can also be used for leveling work. It can prdvlderesults which are fairly precise although not as good asthose obtained with conventional levels. This is becausethe transit has a relatively shorte.r telescope and 1ev91vial.

Fig. ,2-t. uiLd N 2 convc tcd to a. It^u.Iuel uing a GUz ItAl egepic-ct. Fag. l2-9. La.u a!.ttn rasrtal or-o'.lzvgllng it^t^un,rrt.

8. Laser Level. A new innovation introduced to aurvey-ing operations is the use of lasers. A laser system ls aseparate unit equipped with a portable power supply and naybe 'a hellum-neon laser or gas laser. They are usuallymounted or attached to conve4tional. surveylng instrumentssuch as leve1s, transits, and theqdolltes. The Wlld NA2

l7o aEtsutarEtr *, r vc- vErllctL gt5rttcE

(Flg. 12-8) wtth an attached laacr eycplece la an cxamplcof i Laser convertcd lavcl. The eyeplece lncludes a spectalretlcle yhlch hag a snall free spot ln lts center to allovthe laser llght beam to pass freely. surveylng lnstrumentsvlth laser attachments are 1dea1,ly sulted for appllcatlonsln levellng work, bullding constructlon and layout, and lnmany other englneerlng activitles wher.e reference lineghave to be establlshed accurately.

Laser llght is a low-powered bea.m of red l, 19ht which lssultable for projectlng a llne of slght since lt is cohe-rent and hlghly colllmated. A sharply deflned llght spot lsfocused at the target when the telescope lmage ls focused.The laEer beam.can be proJected along an optically stralghtpath and lt spreads only very sllghtly as the distance fromtfre Eource to target lncreases. Projected ls a vislbletrstrlng

.1 lnerr beam whtch can be seen on targets under dlf-ferent lightlng condittons. The rnaximum range of the laserdepends on aimospheric condttlons and thc nature of thetaiget surface. During dayllght the range is about 300 mand at nlghtlrne lt ls about 600 m.FiS. lt-rl. Litut 4.t2n put*n ot a hildet't lzvo/.

hand level. (Flg. 12-11) is a hand-The9. Hend Level.rEtsutEtEtr il I aa

vznftcaL ot'f.*cEs rc

hcld lnstrument ugcd on lurveyc rnvolvrng rhort atghte andvhere a row order of.accuracy ra suff'lclJni.--rt n", bccnproven to be ugeful 1n reconnalssance r"i"ay", tn cro!3-sectlonlng to obtaln additlonal ,o9 -r."airri"' on al.optngground' and ln taplng to determrne rf trr.-t-ip" rs herd ho-rizontally during rneasurement. Thls instrumint atso pro-vides a quick qi o5 o"t.i'lii"s-;;; ii;;'ll=iio, row thaengineer'|s level should be set up tn oia"i-to u. iui.read a leveling rod held a certain-Oirti"".

"rly.Fig. ,l-rt. ,tard txieI.

The hand lever' consrsts of a brass tube about 15 cmlong having a plain glass objectlve_anA i-p".p sight eye_piece' on top of the tube is a snalr revel viar refrecti.ngthrough a pri:I which appears to move vertlcally whenviewed through tne eyeSireci. when the 'uuuui"'-"ppears to beon the cro6s line it is in the center of the tube and ahorizontal line extends across the hand i;";i.; Durlng reve-ling, the instrument is held in one nana iii r.evered byraising or louering the oUjecttve end uniti--ifr" crose linebisects 'the bubbre. ro obtain a steiot ;;;h;; ir may beherd beside a vertrcar staff or by uringrrif-rt close toone16 cheekbone. The user of a hand level-i"i." a backsightor foresight on a rod whrle standrng in-one---positron andthen moves ahead. to repeat the process. The.re is no magnl_f ication by the hand r.iver and il. i"nettr-oi-s-ignt is linri-ted by the vtslbirity of rod readinEs ising-tne naked eye.The use of a hand revel courd piovrde i.""it" wlth suf-f.'cient accuracy and it is rnore convenient and rapid to usethan the englneerrs level. They are designed to stand upunder rough usage and do not require freguent adjustmentbelng simpre in constructron. Th; nana revei-irlir"--;;:tremely useful in different phases of construetion such aEin excavationsr...setting.of grades f or curbs ;il-- ;;;;"r;;and in checkins the posiiioniig ot t.irr"ii-Ioi tr," pourrngof concrete.

l7d nEatuntEfrt 6!..!- yErftc& OtStatCES

Lessott lr'",

ii| it' E i!'#, "T,

-

I 35.

IilEASUREITENTOF YENTICALDISTANCESI3-1. LEVELII'G RO'S

l. Srll-Retding Rod2. tatget ?od

,3-2. on{rjt Ty?es oF R00l. Rotu Nand Alte,2. Rod Ribboru3. Pr.rtite Rod1. @odetlc Rod.5.. Tape. Rod.

t3-3. k00 LEuELt3-4. TARqETSt 3-5.

_

TEt ESCoPES

l. 0bjettive Le:u2. Egepiete3\ ?s"ou lta,ira

t3-5. 'IAGNIFICATT0ilt3-7. LEVEL.VTAL

I 3-t. eollrcIoEt/f;E 8{rE8r.Et3-9. TRLPfiQS

Citiu on Statet

13-1. LBI'ELITIG BOD8.A. lPveling rod ls a graduated rod which ls used for measu-rtng the vertlcal distance between the 11ne of slghtthr6ugh d 1eveling instrument and the potnt whose elevatlon'is ei{her required or known. Rods are made of wood, flber-gLass, or metal and have graduations in meters and declnalswnrcrr'start from zero at the bottom and extendlng upvard toIengths of 3 or 4 meters. Wooden tods are rnade from select-ed stralght graln, hard wood, carefully sanded and treatedwlth a preservatlve staln that reElgts moisture.absorptlon.The endi of the rod are protected by a hard metal. shoes andcap6. A wide cholce of colors, gatterns, and gradubtlonE isavitlable. Some are nade 1n one, two, or thrAe sectlons andm.ly be either telescoping ot hlnged for ease_ln transpor-ting. Most levellng rods have convenlently deslgned pat-terns whlch allow readlngs to be taken eaaily and vith lesschance of commlttlng mlstakes. Levellng rods rnay be eltherof the follovlng:

1. Self-Readlng Rod. Thls. ls the most comnonly usedtype of levellng rod. It can be read directl.y by the ins-trumentman through the telescope by noting the apparent in-tersection of the horlzontal halr on the rod.

2. Target Bod. Thls type of rod has a slldlng targetwhich is set and read by a rodman at the posltlon sel'ectedby the lnstrumentman.It can be expected that results obtalned by reading the roddlrectly is practlcally as accurate as that done by readlngthe rod with the atd of a target. Under favorable condl-tlons, leveling rods are readable through the telescope fordlstances up to about 90 meters frorn the lnstrument. A tar-get should be used when longer dlstances are lnvolved. Thetarget is extrernely useful shen readings are taken in dlm-ltghted areas, In dense vegetatlon, and when establlshlngseveral points on the same straight grade llne.Lt-2. OTHEN. TTPBS OF ROD.There are Eeveral other types of rod used ln leveling work.Arnong these are:

1. Rods Nand tfter Ctttes or Stateg. Levellng rodgnamed after citles or states include the PhlladelphiatDebroit, Chicago, Florida, Boston, New York, Troy, and SanFrancisco rods.

The Philadetphia rod (Fig. 13-1) ls a comblnatlon self-readlng and target rod and ls the commonly used type ofrod. It ls made in two sections in vhlch the rear aectlonslldes over the front sectlon. Readlngs less than tuometers are taken uslng the rear sectlon of the rod and lsreferred to as readlngs on the short rod. For readlngs bet-lza tatrurcactr oaI rvv- fJrttcaL orsfatcat

Fis. t3-1. Philade2dtia. todt.lliptlcol Torg.l(Motol Plor.)

ncd

ClompScrawJ Tor0ol

Clonp

BrosrSloovot

tbllbtti.c. Gtfu.tion

lclEng/-i,th @ufutionlalEqliA Gnnilnlion

rlilit'Effi:,:E

-.192,

rreen two and four meters, the long (or hlgh) rod ls used byfully extending the rear section.

The' zero mark is at the bottom of the rod and the gra-duations extend upward to usually four meters. Red colorednumbers are used to portray the full meter marks on theface of the rod. Black numbers are used for tenths, and thehundredths are shown by alternate black and white horizon-taf bars. The graduations on the rod are continuous whenthe rod is fully extended. The Philadelphia rod can be readaccurately with a leveLing instrument ai distanges "uP to 90meters. For much longer distances a target shbuld be used.

The Chicago rod comes in three sliding Eections "ld,usually extends to either three or four. meters' It iEgraduated . similar to 'the Philadelphia rod except that ,t.1"

iig,rr." on the face of the rod are wider and thus more sui-taute for longer-distances. . The rod is designed to be col-lapsible for ease in transporting. This type of rod iswidely used in construction'surveys.

2-. Rod Ribbons. This is an improvised type of rod usedin leveling work. The graduations on this rod. are

-markedeither on canvass or metal strlps. whtch are attached to along piece of selected lumber by staples. Rod ri.bbons arequiie nandy as these can be easily removed from the wood to,ni"n it is attached, rolIed, and put into oners pocketafter it is used. since rod ribbons can be'easily comparedwith a standardized tape before it is used., they are suffi-ciently Precise for ordinary leveling operations'3. Freclse Rod. The plecise rbd is a f,orm of rod rib-bon vhich uses a graduated invar strip permanently fastenedto a four-meter long wooden or metal .frame. It is eguippedwith a rod level to alLow the rodnan to hold the rod verti-caLly when used. For. precise leveIing work'a thermometer isattalhed to it for purposes of reading the air temperature.

l. Geodetlc Bod. This rod is similar to a preclse rod,except that a nilvar metal strip is used instead of invar.Nilvir is an al1oy of. metal with a very low coefficlent oflinear expansion. The graduations on a geodetlc rod arepalnted upiiae down fo,r use with inverting telescopes, andare shown in meters, decimeters, and centimeters.- 5. Tape Rod. This seldomly used rod is also known asthe automatic rod. Jt iE used advantageously when numerouselevations are to be'..determlned from a single set-up of theJ.eveling instrument. lfhen empl'oyed in Ieveling work, the

' tape rod elimlnates the need to add backsight readings todelermine the height of instrument or to subtract .foresightreadlngs to determine the elevation of sighted points

Th; tape rod is useful in profile leveling, in takingcross sections, and for the different phases involved inbuilding construction and layout. A three-meter long gra-duated metal tape is looped.around the frame of the rod bymeans of rollers located at uottr ends of the frame. Thetape can be rotated or fixed temporarily in any positionfor a sequence of de_sired rod readings. Harks inscribed on

Jlg- ffifi[ii|ihlicn

Ene rod are slmilar to those used in'Phil.adelphia rodsexcept that graduations increase downward. -

'To illustrate. the use of this rod, assume that a taperod is held vertically on a poi-nt whose elevation is L23.45meters. The rodman then rotates thertape around the frameuntil the line of sight of the leveling instrument falls on3.45 m. The tape is then clamped into this position. Therod is next moved to a point whose elevation is to bedetermined. A rod reading on the point of, say 2,86 m meansan elevation of J.22.85 m; f or 3.0? m the .recorded elevationts 123.07 m; for 1.98 m the recorded elevation is L21.98 m;etc. The foresight readlngs on the rod gives elevations di-rectly and eliminates the need to perform subtraction,until the instrume.nt is moved to another set-up. Shouldthere be a need to transfer the instrument to another loca-tlon, the clamps of the rod erre released and the tape loopIs reset. This is done by again sighting on a point afknown elevation. The process of determining elevations o.fforesighted points is continuecl in a similar manner as ear-I ier explained.

I3-3. ROD LE!'EL.The rod level (Fig. 13-2) is a deviceused for fast and correct plumbing of aIeveling rod. It is t-shape in design'andcohsists of a srna1I circular spirit levelfastened'to the rod or to a small bracketheld against the side of the rod. llhenthe bull's-eye bubble is centered, therod is plumb or correctly held vertical.A different type consists o'f a hingedcasting on each wing. It is mounted on aIevel tube and held parallel to the faceof the rod. The rod is plunb when both ofthe bubbles are centered.13-{,. TARGBTSA target is a small device attached tothe rod when extremely long sights rnakedirect readinE of the rod difficult orlmposslble. Targets are made of metal and

flg. l3-2. P.od lzvil.

may be circular, e1liptical, or rectangular inzontal. and vertical lines are formed by thealternating red and white quadrants painted onusual"ly has a'rectangular opening in the frontportion of the rod in order Llrat readings cansmal1 vernier may be attached to the target toaccurate readings on the rod.

Targets are used not only on extrmg1y long sights, butalso when the rod is held in poorly )ighted places, whereatmospheric conditions may cause adverse effects on rea-

shape. Hori-junction ofits face. Itto expose a

be made. Aallow more

,, i,l ltrf ii'/IL 3!',

-

I 3.9

Fig. l3-3. fltiptical *tal ta'aget'

Fig. l3-1. 0the.t' lotnrr of, tatgett.

r Op.nlng

Whii. Point.dOuodronl

R.d PointodO uodront

ato

dlng a rod accurately. They are also ::ed yhen vegetationor othe! obstruction; to a tine of slght make the readlngdlfflcult t oE rrhen setttng a llne of stakes at the sameelevatlon. tne target ls moved up or down under the direc-tlon of. the Instruirentman untlf ft app93r9 to be bisectedUy-[n"-.io", nafis, but lt ls. r+ad-b1r-the rodman. Shown lnrigot. 13-4 are otirer forms of targets used on rods'

ffi(c)@

13-5. TBLBSCOPES.The telescoPe of acontaining a systemtr19'; I E i I iif,' 5 i!, li "'

surveYlng instrument lsof lenses which are used

metal tubeflx the dl-

rectlon of the llne of slght and ln nagnifying the apparentsize of objects in lts field of view. A Dutchman, JanLippershey, ltnvented the first telescope in 1608. The greatmathematician Johannes Kepler was the one who suggested howthe telescope could be employed for use in surveying ins-truments. This Led to the devel.opment of the Keplerian orastronornical telescope which consists of a tube with varia-ble length which has an objective lens, cross wlres, and aneyepiece.F ig. I 3-5. l*ttrcnnical teteJ:opc.t.

dust cop

Irte ruL Foctrtittg Telzu.oP.

Erte^nat F oetting T ele-x.opo.

In some telescopes the objective lens is mounted on agleeve which moves back and forth in the telescope barrelaa an object is brought into fdcus. This ls called externalfocusing. Internal focusing telescopes have an additional'auxiliary lens which movesrback and forth between theobJective and the cross hairs as the focusing dcrew isturned. Both types of tel,escope are illustrated in Figure13-5.

l. ObJectlve Lens. It is a compound lens composed ofcrown and flint glass mounted in fh"e objective end of thetelescope and has its optical axiF concentric with the tubeaxis. The function of the objective lens is to allow liqhtrays to enter'the telescope and form an image of the objectsighted within its field of view.

2. Byepiece. The eyepiece is a form of microscope con-taining either two or four lenses and is used to enlargealtogether the image and the cross hairs. It allows theInstrumentman to sight and read accurately'the graduationson a leveling rod. Leveling instruments may have either anerecting or 'inverting eyepiece depending on the ar.rangementof the lenses. Each type of eyepiece has a focusing move-ment ao that lt can be focused on the image to suit each

ttttuettr|| or I Al..vtaftc.L ottratclS

-r

rt,a

Ilndlvldual eye7 'An eiecting eyepiece consists of four lenses whtch both

magnify and erect the lrnage. Thls type of eyePtece ls PoPu-1arly used slnce it allows slghted lringes to be observedright side up. The lnverting eyepiece is another type whlchhas only two lenses. It can only miignify the lrnage but noterect it. Although the observer sees the lrrage upslde down,it is clearer and better illuminated'since a lesEer amountof light is absorb by the two lenses. The lnvertlng eye-piece is supe,rior in its optlcal properties and is grefer-red by most engtneers and surveyors. l{ost preclse I'eveIsernploy invertlng eyepleces.

3. Cross 'Hairs. The cross hairs (Fig. 13-51 conslstsof a pair of lines whtch are Perpendicular to .each otherand are used to define the instrument's line of sight. Theyare mounted on a reticle or cross hair rlng near the eye-piece of the telescope and located at tne princlp4l focuSof the objective optical system. It is flxed into posltlonby ,two pairs of capstan screws placed at rlght, angles toeach other. These screus are also used to adjust the posl-tlonlng of the cross halrs. In telescopes of older'surve-ying instruments, cross hairs were made of splder web orfine filaments of blatlnum wlre. Some are $ade of fineglass threads and others have a glass diaphragn on whlchltnes are etched. The dtsadvantage of spider threads isthat they slacken when noist and reqpire some skill tomount with Just the rlght amount of tensionFig. l3-5. Uou hrit ring ott ,,etielt.

uPPcrHo ir

Tola!copoTubc

Hor lzonlolHolr

Crocr

Cross

Stod io

In newer lnstruments, cross hairs are ruled and etchedon a thin glass plate, with dark metal filaments depositedto make the lines visible. Cross hatrs mounted on glaseal,so have a disadvantage since it cauEes a slight loss oflight and al1ows dust to collect on the glass vhich fogsthe image. llost levels used for ordinary leveling uork onl'y,t42- iiitilft|illi*

a

VerticolHoir

\\l|

jlg. ,t-1. OtlRt rl'ttcttu uxtl 6ott (tou ta.ira attd.tadit ha,att.

hevd one horizontal and one vertlcal hair. Instruments usedtor precise,, Ieveling have two additional horizontal hairscrIled stadia hairs. Stadia hairs are shorter, are paraIIelto and equidistant from the horizontal. hair. One of thertadia hairs is positioned above the horizontal hair andthc other ls positioned below. Various patterns of crosshrlrs and stadia hairs are used. Some of these are 111us-trated in Figure 13-7.I3-5. I{AGNIFICATION.Thc magnification of a telescope is the ratio of the appa=rsnt size of an object viewed through a telescoPe to itstlze as seen by tle uriaided eye from the same distance. Itnrry also be taken as the.amount by which an object is in-crcased in aBparent size. The amount of magniflcation isflxed by the ratio of the focal length of the objective andthc eyepiece lenses. Magnification is expressed in terms ofdlameters. For mos! leveIs, the magnification may vary from25 to 40 diameters. Hlgh magnification,is not always an ad-vantage since it limits the field of view of the telescopeand reducds the brightness or illumination of the. viewedobJects.I3-7. LBY'BL VIIL.A level. vi.al ( Fig. 13-8 ) is a sealed graduated glass tubecontilnlng some amount of liquid and a small air bubble. Itlc used to determine the directlon of gravity. The type ofItquld used must have a low viscosity and freezing point.It mugt be able to move quickly with very slight shlfting

wift',t'ii'ilffi

-.1{Il

ortlltlngofthevlalrandshouldberelatlvelystable-lnlength under norlmal variations in temperalure. Alcohol mix-edwithetherrandpentanehydrocarbonswerepopuJ'arlyusedearlier. Xewiy designed I'evel vials now use purified'syn-

' thetlc alcohol.Fig. 13.t. Level vial.

AdjurtlngSaratv

Uniformly spaced graduations, about 2 mm long' etchedon the tubE's-surfaJe locate the bubblers relative posi-tion. When the liquid drops to the lower part of the vlal'inr

"ttt"pped air 6ubble mot.s to the highest point in the

tube. A line tangent to the top center of the bubble is ahorlzontal line which is perpendicular to a plumb line' Theline of sight of the telescope is sald to be horizontalwhen the UuUUte ls located at Lne center of the graduationson the tube.Fig. l3-9. Coincidence hrbbll.

o aAppeoroncc ofDlroclion Tokon

Bubblcs Ecforc C.ntorlng ondln.Turnlng th. L.v.ling Sor.w3.

App.oronco of Bubbla rh.n Ccnl.rad

(c)

13.8. COINCIDBNCE BUBBLBThis type of bubbte is used on most modern and precise lns-trumenli such as the tilting and automatic levels' It em?ploys' an optical device which splits the bubble longitudl-nally, then turns one end around to make it appear adjacent'totheotherend.lfhenthetgoendsformasmoothcurvG,ni"n apparently-'Iooks llke the tlp of a hot dog, the bubblr

,I44- iiifillfth."k,'

eoled Glocsub. (groduotodl

Adj u!tingScrcY,

1s correspondingly centetedhtith the use of a coincidence bubble, the set u'p and

Ieveling of an instrument can be rnade more accurately thanby means of the conventional level vlal. The use of a cgin-cldence bubble, however, has a dlsadvantage slnce lt is nottluays clear which way the leveL needs to be tllted tobrlng the lnaggs together.

f ig. 13-10. Tgpe-t ol tl.ipodt.

lclFixcr'-Leg Ttipd

lblExtttuion Tti+od

Aluminum

l3-9. TRTPODS.Trlpods serve as a base to prevent movement of the instru-ncnt after It ls set up. A trlpod conslsts of three woodenor aluminum Legs which are securely fastened to the tripodhead by means of a hinged Jotnt. The legs are spread widecnough to provlde a stable platform for the instrument.then settlng up tt is good practiee to center and level thelngtrument flrst by adJusting the trlpod legs. If the leve-Ilng head is establlshed nearly horlzontal by means of thetrtpod, only a minimum of shiftlng and adjustment with theIevellng screws would be necessary.

Tvo types of tripod are used with a leveling instru-mcnt. A trlpod rrhose legs are made of a solld piece of woodlg catled a flxed-leg (or hlgh) tripod. If the legs have arlldlng sectlon 1t 1s called an extension trlpod. The

",

1,122t'5lr',*t%

-

| 49,

d ls more rtsld. and FI":-l:--Pot:l?:" .::;::;:-i;: r;;;';i "igni llenei lboy: _!l:-:::":1;--lll'^. ':;:;::' ::;'i;'i;";iv- ;;;'.;;;;t- oi- it'o'ph:i l:-::I'?lj t,?l: ?l

.?il!'l.xJl-il;;;--;"-"it"""io" t.lpod is suitable' for use tn-t r..-la,ll {.A:::n;"fi;.'il,,"!.t-;e;-;!;;i-tn'-i-esi "eea to be adrusted tqiit'lni-.-nflguratlon of the ground'At each end of a ttipod is iiiacned a. polntgd ?it::--:I

*"t"i' I"'iI.E"'"""n1":--;;; ;;.4;-ot tn. titpoa are forced^! trarr:1 I glill'.n!'n'ii'u-oi';;;epi;; l; l:. :i:!-'1:l:. I:ot;'-u'::lll:::; ":;.3"ilfJ'."ip;;-;fii;; ii'iiii"tes pushi.ns -:n:--?"ll:?ll

"

.''i l= "'jl-.'l "-' ;- ;'

"

; ; ; ;' - t l' l- d e e p 1 v : l: : ?l- " :.,: :" t- : l:'#J;'ir'il'=iil'J.iir5-JJi."l"iri-'r'"i sertins over softor unsta!,l'e ground.

J46- iliffifSilu%o,,Lessott 14

-,, it trlt'fffiliafl

-

l -{Z

II]EASUNEIilENTOF YENTICAL

.IIISTANCESI'-'. SETTINE UP Tl'lE LEVELI'-2. LEVELIIrc THE II'$XUTEilT

l. lndtnmrtt Uith Foutt Leve/ing Y)Leua2. lttttrtunt/-a Uith Ttnee Leveling *tetu

la-t. ,t0Lollrc T,E LevELlltG 200la-l. TAX7jG A k00 PEA9rtrc

l. Potition The Rd2. F;st^ 0n Tte Rod3. Retd Tlrc ?,od

I'-5. OETEFI{INIITC OTFFEIEIreE TN ELEVXNON[Et,GfflS 0F SIC'$|u$vnt} TrE, knclrfuvilrc TrE 7JsrRum{rAil AilD

"

lO SrGlrA[sl. lbve P,ig/ltr. at Le[t2. Give a Sightt. AIL Risrrt1. Thia ia a Poirt5. lbve knk 13. Fase The Rod6. Pieh. Up Intttunnb 14. Revenae The R'od7. lnile lot Lotps.l TatgQf. 15. lbve fotw^dl. Cm. ln 16. lt6e The Long Rad

l1-5.tl-t.la-t.l1-e.

9. P'ttt* the Rod10. E&tahliah a Tutrhg ?oirt,1. ThU i,* a Twtning Poirt12. lhve The Rod

1'-1. SBTTING T'P THB LEYTL.The leveling instrument may be set up at any suitable ordesired location. When starting a Lbveling operation theinstrumentman should first consider where he intends toposition the instrument. The level is then puIled out froits box by holding the. leve1 bar or base plate and screrredsecurely onto the tripod head. Care should be exercised inscrewing the leve1. The instrument'should fit snugly andbear firmly. If loosely fitted, the instruinent will wobbleand be unstable; if too tight due to excessive pressure, itwould be difficult to unscrew the instrument later and rrEycause some damage.Solid ground should be selected when setting up theinstrument. Muddy and wet areas should be avoided as theseare unstable to stand on and may only cause serious errorsin leveling work. Tripod legs are spread so that the footplate will be approximately horizontal,. It will be easierand quicker to level the instrument later if ttre pJ-ate isalready horizontally positioned. The legs should be farenough apart fdr a rigid set up, and they shoul.d be pushedfirmLy into the ground to make it stand stable. The instru-mentman should see to it that the telescope is at a conve-nient height for sighting and he must be able to standcomfbrtably between the tripod legs. A preferable'and con-venient height of setup is one which will enable the ins-trumentman to sight through the telescope without having tostretch or stoop. !

llhen setting up the instrument on hillsides or along aslope, one of its legs shoul.d extend uphill and two down-hi11. It ia a{vtsable for the instrumentman to carry al.ong ahand 1evel to determine the approximate height at which theinstrument should be set up in order that points to besighted wilt fall within the established Iine of sight.L{r-z. LBVELING THB If,STBUIIBf,T.A considerable amount of practice in leveling the, instru-ment will be needed by a begi4ner. It is oniy by constantPractice that one would really be able to feel and ex-perience the proper turning of leveling screws to bring tliebubble in a level viar to its center. Most conventlonallevels are designed uith fo_ur leveling screws. The screwsare used to center the bubble in a leve1 tube which isattached to the telescope of the instr.ument. Newer modelsoften

-

have only three reveling screws to center the bubbleof either a level tube or a circular bullrs-eye level. T,heprocedures followed in leveling each type of instrument areoutlined as follows:1. Instrurents Uith Four Leveling Screus. The bubble isfirst centered approximately over one pair of opposlte Ie-

veling screws (Fig. l4-1). Time is wasted by exact cente-IAA tEatuactgtT oFr r-.w- yEattctl otttatcat

rlng ln the flrst attempt, slnce the bubble wllL be thrownoff during cross leveling. The telescope is next turned 90degrees (either clockwise or counterclockwise) and posi-tioned over the two other opposite leveling screws. Thebubble ls agaln centered approximately. This procedure isrepeated about three or more times with lncreasing careuntil the bubble finally remains centered in any directionthe telescope is pointed. The instrument is leveled if thebubble thus remain centered. This condition wi.Il occur onlyvlth a properly adjuste! level vial since its vertical axisassumes a truly vertical position when the bubble is cen-tered

+- oitaclim ot Subbla ltlovanrnt

trlotion of \L.tt Thmb

fig. l1-l . Cctttt itq hthb|2 ttith (ou.n leveLi.4g lcr.clvll.

The thumb and the index finger of each hand are used toturn the screws. Screws are turned always in opposite di-rectionsl that ts, the thumbs should move either away fromeach other or toward each other. It is only during finalcentering when just one screw needs to be turned to movethe bubble thru a small graduation on the level' vial. Itul11 be important to remenber that when the leveling screwsare turned, the bubble moves in the direction of motion ofthe teft thunb. Since all screws have exactly the samethread length, one should be extended and the other Ehor-tened by turning in opposite dlrectlons. Turning oppositeccrews should be at the same time and also at about theaame rate. This procedure wlll altow the screws to cons-tantly bear evenly on the foot pl.ate while the instrumentts being leveled. The instrumentman must see to it that theacrews.should be snug and not set too tight to avoid damageto threads and the base plate. It should yield easily to aturn when held between the thumb and index finger.

2. Instrurents Uith Three Level.ing Screrr. For instru-ments wlth only three leveling screws, the telescope isturned until. the bubble tube is positioned parallel to thellne through any two of the screws. The bubble is then cen-tered on the level vlal by turning these tso screws in oP-poalte dlrectlons. As usual, the thumb and the index finger

a%

ttttutrnl u I dOtaattcaL ctttAnctt a'-| |Ar

of each hanal are used to turn the screws. Also, the bubblewillstillmovelnthedirectionofmotionoftheleftthumb

Thetelescopeisnextrotatedaboutthevertlcalaxlsof the instrom.it so that the bubble tube is brought per-pendicular to a line through.the two Fcrews turned earlier.igai.t, the bubble !s brought carefully to center by meansof the third screw alone. inis Pro6ess of leve.ling is il-lustrated in Fig. L4-2Dirrction ol Bubbl. Lov.n.nl.+

"t)

Molion ot \Lrtl lhumb

Fig. t1-2. Certz itg txthb,' tiil tl*ce 2zveling tfte/y4b;

The instrument is leveled if the bubble remains ".rrt"r-ed on the Level vial when the telescope is brought back toitsfirstposition.Ifthebubbledoesnotremainwithinit. center graduations, the process is repeated until iti"n"i"" in lne center for. any position of the telescope'inir-r""tnoa ot repeated Benteiing wilI only.work if the Ie-vel vial is in aaiustmeft. snould it be out of adjustrnent'no amount of repeated centering will workIn automatic and tilting livels, a three-screw head anda circular bullrs-eye level are usually empLoyed' Frigr toir;;ii;;-,* ii i" inpirtant thar the 1e9s of the. tripod arepo"itioii.d so that leveling head is nearly horizonta.l , andirr*-u"uufe in the circular level is brought as close to thecenter of the vial. tlith the telescope in any convenientpiriti""l- t;; bull's-eye bubble is centered in one direc-iion UV operatint two leielingtcrews. It is then centeredin the other diiection by meins of the third screrd. The1o""."" of centering the bubblei is done by alternately tur-ning two screw"

"nd then the other one singly' The teles-

.opJ ao"= not hive to be turried to. any direction during theprocess of leveling.1I-3. HOLDIHG THE LB\IBLING ROD'The leveling rod is held on /a point by a rodman when asightis.tobetaken.onit.Toobtainthecorrectdistanceti6rn the line of sight to the point on which the rod 'is

,l5o- ;[irf![i'f],i,,

ooo oo

Fig. l1-t. Ito{litg thc tod. placed, lt ls extremely lmportant thatthe rod be held plumb when the readingis nade. The instrumentman checks therda by observing through the telescopeand notlng lf it is held parallel tothe vertical cross hair. If the rod isnot correctly plumbed, the instrument-rnan gives out a signdl to plumb therod.. The accuracy of a leveling opera-tion is significantly improved if therod is alvays held correctly, hnd italso increases the speed with which theuork may be performed.

The rodman either stands beside therod or behind it. He should face theinstrumentman and see to it that the'rod is held nearly at right angles tothe line of sight. The vertical side ofa building, a smokestack, or a flagpoleare convenient aids to the rodman injudging if his rod is pl.umbed properlywhen a reading is taken on it. The 'rodis llqhtly supported between the fin-gers of both hands and is allowed tobalance on its own rdeight. The f ingersmust not cover the face of the rod. Therodman should see to ,it that the gra-duations are always clearly visible andnot obstructed.

In high precision surveys the leve-J.ing rods used are eguipped with a rodleve1. AlthouEh thls device is notgenerally used in ordinary }evelingwork, it is advisable to use one wheninexpe/lenced rodmen are empl'o1ted. Arod level. is securely held against theback of a rod"or it'rnay be permanentlyattached to it. It should not i,n anywayobstruct the rod graduations.LI-I. TTf,If,G A ROD RBADING.Before readings are taken on a rod, it'ls important to first examine how thegraduatlons aEe indicated on it. The

metric rod ln Figute 1{-4 lE graduated in centimeters andnumerals are indicated for every fUIl meter and decimeternark. The single dot shown bel.ow each numeraL lndicatesthat readings taken on it'are ln the l-m range. Since mostrods extend to lengths'of either 3 or 4'meters, three orfour dots are used to correspondingly identify.each meterand declmeter graduation.

Each blackened graduatlon and each space between gra-.r.tuaa.a, e l4l

. taaftc.L ottiltctt

-

r v !J

-duation ls one centlmeter (0'01 n) hlgh' The fuII metermarksareidentifiedontherodby]'argenumeralswhichareusuallypainted in red' The decimeter marks are identifiedby snaller niicX"-painted numerals'In Figuge 1'l-5' the read-'ings for six difflrent positions qre glven as examples' ItyilL be notej-that r."ilngr to tliousandths of a meter are""1insggd ' as in

'd ana t wnf cn ate 2'155 n and 2'235 trlrespect ive 1Y.

fig. la-l. t'od gtailta'tioru. Fig. t{-5. Lztdit o luelhq r,od.

3 2.235 m

3 2.2oom

: 2.165 m

: 2. l3Om

: 2.O5Om

E 2.OOO m

once the instrument is set up and I'eveled' the fol'low-'ing steps are performed in taking a rod reading:

l.PositionTheRod.Theleve.lingrodisheldbytherodman on the designated point w!fuse elevation is to bedetermined. He staids beside or behind the rod' faces ittoward the instrumentman, and holds it as nearly pLumb aspossible. since directions and signals emanate from theinstrumentma'n, the rodman should a,Iways foius his attentlono"-nitn. : ]

2. Focus on The Rod. The instiumentman ains and focusesthe telescope on the rod at the same tlme seeing to it-thatthebubblecontinuestoremaininthecenteroftheleve].":ilf .-H"-;-Xr, "r;-at tfrr vertic4l

hair to check if the rodis held Plumb.3. Read The Rod. If the self-reading rod is used'- theinstrumentman observes directly from the telescope and re-

t

lc.a aaatu2caEtT 0F, I J?- Ja-iti.t nt.rttcrt

tcatuuEvac e I F.?tJtltrc.. gt srtnca,

-

| e:!

Fig. la-6. Tfu lzveling 4od oa {{:e, fr,to.ttlh the tzlz*ope..

VcrticolCrorc Hoir

cords the .reading indicated by the line of sight.'The read-lng is shown by the apparent position of the horizontal'cross hair on the rod. The view through the telescope isrlmilar to that shown ln Figure 14-6. Ifhen using a ta'rgettrod, the proeess of reading is identical except that thetarget is set (raised or lowered) so that the horizontalcross hair bisects it while the bubble is in the ceirter ofthe level via]. The instrumentman directs the setting ofthe target but the rcicl is read by the rodman. It. istxtremely important that a check is made on the centeringof the bubble before and after readings are taken on therod.I'-5. DBTBR}iIIIIIIG DIPFBRBXCB IN ELBVATIOII.Flgure I4-7 illustrates a typical set up for determiningdlfference ln elevation between two points, A and B, usingthe engineerrs level and leveling rod.The sequence of steps involved are as follows:

1. The instrument is set up and leveled at aabout halfway between A and B.

point2. Sight on the rod held, vertically at point A and

rccord the rod reading. fn the given illustration the rodreading at A is 2.00 meters. This means that point A on theground is 2.00 m below the horizontal plane of reference(or Iine of sight) established by the level.

3. Rotate the telesFope carefully about the verticalrxls and sight on a rod held vertically at B. Record theroo reading at B. To avoid instrumental etrors only one rodahould be used during the measurement. The illustrated rodraadlng at B is' 3.50 m which means that point B on theground la 3.50 m below the same horizontal plane of refe-

rence1. The difference ln elevatlon between polnts A and B

is determingd by noting the dlfference inr thetr. respecttverod readings or, 3.5O - 2.00 = 1.50 rn. This value correi-ponds to the vertical distance between the two lmaglnarylevel surfaces (assumed to be horizontal lines) passlngthrough points A and B.

Fig: l1-7. Utttrtitrittg difle,rcnce it cltvatiot.

Slght ot A Sighr ot B

From the given illustration, it can easily be seen tbatpoint B is lower in elevation than polnt A since its veE-tical distance measured downward from the established 1lneof sight is greater thaJr that take,n at point A. Also, lfthe elevation of point A is known, the elevation of point Bmay be determined by subtracting the computed dlfference inelevation frcm the elevation of A. The procedure justdescribed where the enginirer's level and a leveling rodrdere employed for measuring differences in elevation igcalled direct or spirlt leveling.1'-6. LEXGTHS OF SIGHT.It is always best to take sights at moderate lengths toattain speed and accuracy in leveling work. Ho*ever, veryshort or extremeJ.y long sights should be avoided. The mostsuitable sight lengths-wi11 depend upon the required degreeof precision, the surface of the terrain, the type of ins-trument used, and uPon the distance at which the rodrernains readable to the instrumentman. Under ordinary con-ditions the length of sight should not exceed about 90meters where elevations to the nearegt 0.001 m are desired.Beyond this length it is difficult to read the rodl accu-rately and

_the errors cause.d by curvature and refraction,-

^ tattuaEtEnf 0F

, I T- vinttcat otsrttcct

r.

f-^oo

have to be constdered.Irregular refraction during sutnmer months usually

causes rrbollingrr of the air. In such a condition, therefraction is quite large and precise results could not beexpected when very long sights.are taken. They should benade considerably shorter especially lf the Iine of sightclears the ground surface by only as much as one-ha1f me-ter. Extra long sights, however, may be taken where theterraln ls fairly level, only an ordlnary degree of accu-racy is required, and. completion time is of 'primary irnpor-tance. Very short sights cannot be avoided when the groundgurface rises or fa}Is rapidly such as in mountainous areasand where the terrain is significantly rough.1'-?. UAVIf,G THA ROD.By aligning the rod with the Vcrttcal cross hair, the ins-trumentrnan can determine if a rod is held in a verticalplane pas.sing through the instrument. 'He cannot, however,telI if the rod is tipped forward or backward in thisplane. This can.only be accomplished by waving th rod. Theprocedure is used to determine whether.the rod is plumbwhen a reading ig taken on it. It is accomplished by slowlyuavi.ng or tilting the top of the rod through an arc, firsttoward the'inetrument and then away from It (Fig. l4-g). TOthe instrumentman, it wiII appear that the.cross hair ismoving up and down the rod.

.*

Fig. l1-5. &'ving t\e a.od.

As the rod is waved, the instrumentman takes note ofthe rod readings which wirl alternatery increase anddecrease. The minimum reading observed is considered as thecorrect rod reading at the particular point sighted.when the long rod is used it is irr.y" idvisable to

wave the rod. rf the target rod is used, it must be raisedor lowered untiL there is found just one position when thetarget rises as high as the rine of sight wrrir. the rod isbeing waved.1I-8. CTNRYING THB INSTRUIIBXT.IThe level should always be h,qgt tn a lbox when it is not

'-'oi!?"f'11*Rod Tilled--*\Forwcrd \\

,, ifJiii';,'!il't' El.iO

15-1. sOURCBS OF ERROR IN LEI|ELIIIG.The accuracy of leveling work rnay be gffected by numerousfactors. However, it is not difficult to obtain accurateand preCise measurements in levgling aii theie.are differentsafeguards which could be taken agdinst expected erfors andmistakes. Accuracy in leveling operations is primarilyinfluenced by the type of instrument used. A great dealwill also depend on the skills of the members of a levelparty and the degree of refinement with which the wholeoperation is performed. If correct leveling procedures andcare are adapted in leveling work, systematic errors couldbe significantly reduced or eliminated. The remainingerrors expected to oicur would onty then be random errors'

The principal sources of error in leveling work nayemanate from either instrumental, personal, or naturalerrors. These sources of error are each discussed be10w asto their nature, .magnituder and how they may be minimizedor eliminated.

,1. lnstruental Errors. These errors are attributed toimper f ect ions in the instruments e ither f rom :fcul'ts inthelr manufacture or from improper adjustment. In levellngwork instrumental errorb ire usually dqq to a defectivetripod, a levellng rod not of standard length, or when theinstrument used is out of adjustment.

a) In*truEnt ''Orat ,.of Adjustrent. Tbe most commoninstrumerital error is caused by the level being out of ad-justment. Particularly significant is when the line ofsight of the telescope is hot parallel to-!h. axis of thelevd1 vial. The line of sight witl be inclined either up-ward or downward when the bubble is brought to the centerof the tube. lfhen a reading is taken on a rod, the resultis an error consistently either plus or minus, and with amagnitude which is proportional to the distance between theinstrument and the rod. This source of error can be elima-nated or kept at a minimum by frequently testing'the ins-trument and keeping it always in good adjustment. The errotwitl. also be greatly minimized or eliminated if the back-sisht and foresight distances are kept nearly equal. Sinceit would be difficult to predict when an instrument goesout of adjustment, thF latte'r method is the mo,re certainand should always be used for careful .Ieveling.

b) Ro4: Not Standatd Lengttr. It is possible to haveinaccurate graduations or divisions on a rod. This isusually due !o imperfections in their manufacture. In'accu-rate rod graduations can cause errors in measured verticaldistances similar to those resulting from incorrect mar-kings on a tape. In any case, a rod of, incorrect lengthwill introduce a systematic error in lev-e1ing work

It is important that rod lengtfrs dYe compared perlodi-cally with a standardized steel tape. Any error in length

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ahould be determlned and necessary correctlons applled totII measurements nade wlth the rod. ALso, the rod must al-UayB be handled carefully. A Philadelphia rod is easilydamaged when the upper part of the rod is alloued to stiaedovn so rapidly that the blocks on the two sections areerushed. Its bottom should be kept clean when used in muddytreas or where the ground is relatlvely sof,t. If the rodmanla not careful, he nay easily have some amount of soil,clay, dirt or mud sticking to the bottom of the rod. Thisgln cause severe errors in leveling.

c) Dcfoctlve ?rtgod. tne movement of the ievel dueIto Eettling of the tripod legs can cause possible errors inilcvel!,ng work. lhe trlpod usuaLly settleE in soft ground ordue to vibrations caused by passinE ve'hicular traffic. Itimportant to always set up the tripod r,igidly as this

n lead to erroneous measurements and waste of time. Boltstnd nutstat hinged joints of the tripod should be checkedle.gularly and tightened. To avoid sliding of tripod legsdue to vibrations, the instrument should be set up oply attlrn and stable. ground. Smooth surfaces such as concretepavements and steel plates should be avoided.

2. $$tlobal Brrors. Although personal errors occurlargely' du to' the llmitattons of the sences of toueh,rlght, or hbaring of individuals, the aki1Is, training, and'tearnvork of ,the members of a leveling party are also majorlactors to be considered. Personal errors are usuallycaused by er'roneous manipulations'and careless handling of

' tnstruments when making observations. Such errors includethe foll.owing:al Ertrblc 'No-t Cairtered. Rod readings will be in

crror when the bubble is not centered in the level viaI.lhe magnitude of the error depends on how sensibive thevial has bebn designed. Thefe are various conditions in thefieLd which nny cause the bubble not to remain centered. Itcould be caused by a tripod leg settling in soft ground,the instrument may not be level.ed properly or it may be outof adjustment. These are factors which could all be attri-buted to carelessness on the part of the instrumentman.

the instrument should not be handled unnecessarilyafter it is set up and leveled. Its tripod should not begrasped when taking a sight, and vertical pressure exertedon any part of the instrument shor.lld be avoided. The.errorintroduced by a bubble which is not centered varies as thedistance fron instrument to the rod. It is therefore impor-tant to exercise great care in leveling the instrument whenextra long sights are taken

.' b)-Parillax. If a pressure gauge or any graduatedcircular meter is viewed from different angles, one willnotice that. a number of sliqhtly divergent values could beread. This is due to the effect of parallax. Howeve!, ifthe pointir and scale of the gauge nere posit-ioned at

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exactly the same plane, parallax woulQ be totally ellmlna-ted. A similar condltlon occurs when sightlng through thetelescope to read a'levelIng rod. The effect of parallax lato cause relative displacirnent betieen the frnage of thecross hairs and the inage formed by the focuslng lens. Pa-iallax cbn be elimlnated by careful focuslng of the teles-"cope untll no apparerit movement of the horizontal hair re-Lative.to the rod can be detected when the eye ls moved up,and down while sightlng, c) Fral,til 1fi{d,.t*rilin{tl. The instrumentrnan at times

nay misread the number of meters,and decimals when taklng arod reading. An-incorrect rod reading is'usually the resultof the hngth"of cight', po(lr ueather condltions, and theskill of the lnstrumentman and the rodrnan. In ordinary Ie-veling work it is advisable that the length of sight shouldnot exceed 90 meters. The number of reading errors iEslrgnificantly reduced when short sights are taken. Uhenlong sights could not be avolded, a series of readingsshould be taken on the distant rod and only the mean rea-ding..should be used. Extra long sights are common such aswhen. levellng across a wide rtver or a deep ravine.

In precise leveling work, instruments used are equippedwith three horizontal hairs. Threi readings are usuallyrecorded at each sighting. Since the two extra halrs (orstadia halrs ) are equally spaced from the center rqlddlelralr, the dif ferenc'e between the readings of the middle andlower halr should be equal to the dlfference between thereadings' of the. middle and upper hair. The instrumentnanshould take ttm-,-to compare these two quantities beforetransferring to another set up sinbe it is an effectiveprecaution against faulty rod readings.

dl li$"f,ot llild Plurb,. Aslde froJn holding the rod ona flrm and definite polnt, lt should also be held as nearlyvef,tical as possible. If it is held off the verticaf itslll be intersected by the line of sight farther from the.bage and the reading will be much greater than what itshould reall.y be. The reading on the rod sill be lowestwhen it is held plunb

Appreciable lncllnatlons of the rod should be avoidedparticularly when a hlgh rod is used. In differential leve-ling, er.rors due to non'verticality of the rod tend to com-pensate at turning polnts, however, if the foresight read-tngs are consistently greater than the backsights, theerror becomes cumulative. It is easy to determine if therod is held pl.umb or not since it can be checked if it isheld parallel to the vertical cross hair. However, the ins-,trumentman cannot check lf the rod is leaning toward oraway from the instrument. Thls type of error'can be avoidedlelther by waving the rod or attaching a rod level. to it tofacllitate holding it plumb. The use of a rod level allowsthe rodman to plumb the rod,by sinply centering the bubble.Its use is preferable to swinging or waving the rod

e) Irecrcet 8:ttlng OI lergict. It is important to)C., tEputEattr oF

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always handle the lcvellng rod,carefully. The rodnan attlmes fails to set properly the target when a high rod rea-dlng ls rnade wlth lt. During use, the target nay slip down-uard because it is not clamped firmly at the exact positionslgnated by.thr instrumentman. To avoid this type of error,the lnstrumentman sh"oulil always take a second sight on thetarget after 'it is"clamped by the rodman in order to besure that it has not slipped

f ) ,Unrqprl lac}llght and Porcslght Dlatalrcs*i Inleveling rrork it is usually good practice to make backsightand corresponding foresight distances nearly equaI. In sucha practice, errors due to imperfect adjustment of the ins-trument and also those due to curvature and refraction arereduced or totally elimlnated s.ince the error " in the bach-sight is equal to'that in the foresight.

It ls sufficient to approximate only by eye foresightand backsight distances in ordinary leveling work. For moreprecise uork, pacing, direct taping, or stadia measurementsare employed in determining sight distances. Balancingforesight and backsight distances, however, nay not alwaysbe practical or possible. Thls situatio.n may occur when theterrain is extremely rugged or when Leveling across widerlvers. For example, in levellng up a steep slope the dis-tance to the foresight wlll be about one-half the distanceto the backsight. The two distances could still be heptnearly equal by properly posltioning the level a certalndlstance from the straight Iine between the turninE points.The whole length of the level.route is traversed by a zLg-zagging nanner in order to eliminate this source of error.

3. Irtural Erzors. These are errors which are due tonatural sources and could not be totally removed but theireffects can be reduced by applying corrections and usinggood judgment. Such 'errors include the effects of theJarthts curvature', atmospheric reqraction, variations intemperature, wind, and etc

a) &rveturc of thc lrrth. The ef fect of curvatureof the earth is to lncreaSe the rod reading. From thissource the error afiounts to .about 0.0? cm per J'00 meters.This error is introduced even tf the instrument used is inperfect adjustment. It, however, only occurs in extra longsights and when backsight and foresight distances are notmade equal. Since sight distaneeE in ordinary leveling do'not vary significantly, the resul.tant error arising fromthis. source is so small and ls considered a, negligiblen""";i:I'rong

sights courd not be avoided, the error may beellminated

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by appLying a correctlon to the computed diffe-rence in elevation or by employing the method of reciprocalIeveling. In other situations, the error due to curvaturecan be eliminated by'keepin{ the backsight and foreslghtdlstances from the same set up nearly equal.

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b) AibfDrpherlc lgfractlon. The pregence of heatwaves on a hot day is a sign of rapldly fluctuating refrac-tlon in the atmosphere. Reading drrors are Iike1y to occurwhen heat waves are present since it makes the rod appearunsteady when a sight iE taken on it. Sincqthe refractionls usually larger when sights are taken close to the groundsurface, the line of sight shoul,d be established at leastone meter above the ground. Because it may be impossible toread the rod when heat uaves are particularly intense,leveling work" should only be resumed when heat waves sub-side.

To reduce the effects of atmospheric refraction onlyshort sights should be taken. Balancing the lengths ofbacksights and foresights.aLso elirninates errors due torefraction. Its effect is negligible in ordinary leveling,but in precise leveling, combined corrections for curvatureand refraction are applied to observed rod readings.

cl Tcqrerature Variatlons. Changes in temperaturecauses leveling rods to either expand or contract and thesecould introduce errors uhen taking rod readings. To guardagainst such effects, invar or nllvar gr'aduated strips areused on rods for precise leveling work. Heat also cauEes

.w4rping or twistlng of the parts of a level. The liquid inthe level, vial expands and the bubble shortens when it isheattid. This temporar'ily disturbs the adjustment of theinEtrument and may affect the accuracy of rod readings. It

. is prefetable to use a surveying umbrella since this willprevent the rays of the sun from falling directly on theLevel and thus reduce the effects of heat.dl,flnal. A strong wind can shake a leveling instru-ment making it d,ifficult to center the bubble in the levelvlal,. It can also exert a suf f icient amount of force tocause an extended rod to vibrate making it stand unsteadyand hard to read or plurnb. If leveling has to be perforroedduring windy days, the instrumentman should either exertefforts to shelter the instrument or wait for a tull in thewirrd. Setting up the level behind a building or close to alarge tree trunk shouLd reduce the effects of wind. In an'open field, long sights should be avoided to limit the useof a high rod.

e) StttlGDnt.of the Inrtrum{rt. In soft or thawlngground, mudr Bnd swamps the instrument may settle in thelnterval of .time betfeen rod readings. This source of errorris cqmulative since every settLement of the instrument in-creases the computed elevations of all other observedpolnts by the amount of the spttlement. Errors due to set-tlement can be avoided if the instrumentman takes thenecessary precautions to insure that the level is alwaysset up on firm and stable ground. It is also important thatas ]ittle time as possible should be taken between rodreadingsi

.rtrrav Turnrng pornts. rn differential revelingwork, a poorly chosen turning point may be a source ofIAA tEAtutcuEtr oF

error. Thls condttion is slmlrar to that resulting 'fromsettlement of the lnstrument. rt is a cumulative type oferlor. since two rod readings are arways taken at a Lurningpoint from different set ups of the revel, it is importanito select firm*and sbrid turning points. They must also beeasily identified. care should be taken not to strike therod against the turning point or to exert any.pressure onit. rn soft and unstable ground, it is adviiable to use apeg or a steel plate as a suppor,t to prevent settrement ota turnlng point. The. instrumentman shourd guard againstmovement of the turning point and the rod should be h;ld atexactly the same point when another reading is to be takenon it

\5-2. @xl{oN l{rsTtKEs Ir{ LByBLrtrc.The folrowing are some of the most comrnonry nbde mistakesint leveling work:

1. l{isreading The Rod. During leveling the instrument-nan may occaFionally read the rod incorrectly; for example,he nay read 2.?5 m instead of 1.?5 m. This mistake mostfreguently occurs when the line of sight to the rod is par-tially obstructed by vegetation or other objects in thefield. It is lmportant that the instrumentman always care-fully note the fu1l meter marks above and below the ob-serve rod reading. Also, it is preferable to call out read-lngs as they are taken or to use a target, and lie-re the ins-trumentman and the rgdnan take and compare their respectiveread ings

2. Incorrect Recording. The pecorder should always callout the readings as he records them in order to prevent therecording of incorrect varuesl, To detect mistakes in recor-ding rod readings, the best method is to read the rod,record the reading, ,and then