Syllabus Methods Electromagnetic Distance Measuring · PDF fileECE Surveying Unit 2.2 Linear...
38
Linear Measurements ECE Surveying Unit 2.2 Syllabus • Linear measurements: Methods, Instruments used in chaining; Chain surveying, Ranging, Errors in chaining, Conventional symbols. Introduction • The determination of the distance between two points on the surface of the earth is one of the basic operations of surveying. Measurements of horizontal distances or measuring linear measurements is required in chain surveying, traverse surveying and other types of surveying. In surveying the distance between two points means a horizontal distance. As the map is potted on a horizontal plane, the distance are measured in surveying, these are always reduced to the equivalent horizontal distances for mapping purposes. Methods • There are three methods of making linear measurements. • Direct method • Optical methods • EDM methods • In direct method the distance is actually measured during field work using a chain or a tape. This is most commonly used method for linear measurements. • In the optical methods, principles of optics are used. The distance is not actually measured in field but it is computed indirectly. The instruments used for making observations is called tacheometer. • Electromagnetic Distance Measuring (E.D.M) instruments have been quite recently. • These are practically replacing the measurement of distances using chains or tapes. There is a large variety of such instruments and depending upon the precision required, a particular EDM instrument should be used.
Transcript of Syllabus Methods Electromagnetic Distance Measuring · PDF fileECE Surveying Unit 2.2 Linear...
Line
ar M
easu
rem
ents
EC
ESu
rvey
ing
Uni
t 2.2
Sylla
bus
•L
inea
rm
easu
rem
ents
:M
etho
ds,I
nstru
men
tsus
edin
chai
ning
;Cha
insu
rvey
ing,
Ran
ging
,Er
rors
inch
aini
ng,
Con
vent
iona
lsym
bols
.
Intro
duct
ion
•Th
ede
term
inat
ion
ofth
edi
stan
cebe
twee
ntw
opo
ints
onth
esu
rfac
eof
the
earth
ison
eof
the
basi
cop
erat
ions
ofsu
rvey
ing.
Mea
sure
men
tsof
horiz
onta
ldi
stan
ces
orm
easu
ring
linea
rm
easu
rem
ents
isre
quire
din
chai
nsu
rvey
ing,
trave
rse
surv
eyin
gan
dot
her
type
sof
surv
eyin
g.In
surv
eyin
gth
edi
stan
cebe
twee
ntw
opo
ints
mea
nsa
horiz
onta
ldis
tanc
e.A
sth
em
apis
potte
don
aho
rizon
tal
plan
e,th
edi
stan
cear
em
easu
red
insu
rvey
ing,
thes
ear
eal
way
sre
duce
dto
the
equi
vale
ntho
rizon
tal
dist
ance
sfo
rm
appi
ngpu
rpos
es.
Met
hods
•Th
ere
are
thre
em
etho
dsof
mak
ing
linea
rmea
sure
men
ts.
•D
irec
tmet
hod
•O
ptic
alm
etho
ds•
ED
Mm
etho
ds•
Indi
rect
met
hod
the
dist
ance
isac
tual
lym
easu
red
durin
gfie
ldw
ork
usin
ga
chai
nor
ata
pe.
This
ism
ost
com
mon
lyus
edm
etho
dfo
rlin
ear
mea
sure
men
ts.
•In
the
optic
alm
etho
ds,p
rinci
ples
ofop
tics
are
used
.The
dist
ance
isno
tac
tual
lym
easu
red
infie
ldbu
tit
isco
mpu
ted
indi
rect
ly.
The
inst
rum
ents
used
form
akin
gob
serv
atio
nsis
calle
dta
cheo
met
er.
•E
lect
rom
agne
ticD
istan
ceM
easu
ring
(E.D
.M)
inst
rum
ents
have
been
quite
rece
ntly
.•
Thes
ear
epr
actic
ally
repl
acin
gth
em
easu
rem
ento
fdi
stan
ces
usin
gch
ains
orta
pes.
Ther
eis
ala
rge
varie
tyof
such
inst
rum
ents
and
depe
ndin
gup
onth
epr
ecis
ion
requ
ired,
apa
rticu
larE
DM
inst
rum
ents
houl
dbe
used
.
Dire
ct M
etho
dO
ptic
al M
etho
dTa
cheo
met
er
EDM
EDM
App
roxi
mat
e m
etho
ds•
The
met
hods
give
nbe
low
may
beus
edin
reco
nnai
ssan
ceor
for
dete
ctin
gm
ajor
mis
take
sin
linea
rmea
sure
men
tsob
tain
edw
itha
chai
nor
tape
.•
Paci
ng:
Adi
stanc
ebe
twee
ntw
opo
ints
can
appr
oxim
atel
ybe
dete
rmin
edby
coun
ting
num
bero
fpac
esan
dm
ultip
lyin
git
with
aver
age
leng
thof
the
pace
.•
Pass
omet
er:I
tiss
mal
lins
trum
ents
whi
chco
unts
the
num
bero
fpac
es.
•Pe
dom
eter
:Thi
sin
stru
men
tdire
ctly
give
sth
edi
stan
ceby
mul
tiply
ing
the
num
ber
ofpa
ces
with
the
aver
age
pace
leng
thof
the
pers
onca
rryi
ngth
ein
stru
men
t.•
Odo
met
er:
An
odom
eter
isa
sim
ple
devi
cew
hich
can
beat
tach
edto
the
whe
elof
abi
cycl
eor
any
such
vehi
cle.
The
odom
eter
regi
ster
sth
enu
mbe
rof
revo
lutio
nsm
ade
byth
ew
heel
.Th
edi
stan
ceco
vere
dis
equa
lto
the
prod
ucto
fthe
num
bero
frev
olut
ions
and
the
perim
eter
ofth
ew
heel
.•
Spee
dom
eter
:Thi
sisu
sed
inau
tom
obile
sfor
mea
surin
gdi
stan
ces.
•M
easu
ring
whe
el:I
tis
aw
heel
fitte
dw
itha
fork
and
hand
le.T
hew
heel
isgr
adua
ted
and
show
sa
dist
ance
per
revo
lutio
n.Th
ere
isa
dial
whi
chre
cord
sthe
num
bero
frev
olut
ions
.Thu
sthe
dist
ance
can
beco
mpu
ted.
App
roxi
mat
e M
etho
ds
Pass
omet
er
(Ste
p co
unte
r)O
dom
eter
Mea
surin
g
Whe
el
Inst
rum
ents
Use
d in
Cha
inin
g
•Th
efo
llow
ing
inst
rum
ents
are
used
whi
lech
aini
ng:
•C
hain
•Ta
pes
•A
rrow
s•
Ran
ging
rods
and
offs
etro
ds•
Pegs
•Pl
umb-
bob
etc.
Cha
ins
•Va
rious
type
s of c
hain
s use
d in
surv
eyin
g ar
e:•
Met
ric c
hain
•G
unte
r’s c
hain
or S
urve
yor’s
cha
in•
Engi
neer
’s c
hain
•R
even
ue c
hain
•St
eel b
and
or b
and
chai
n
Met
ric C
hain
•N
orm
ally
,th
isch
ain
cons
ists
ofga
lvan
ized
mild
stee
lw
ireof
4mm
diam
eter
know
nas
link.
The
ends
ofth
elin
ksar
ebe
ntin
tolo
opan
dco
nnec
ted
toge
ther
bym
eans
ofth
ree
oval
circ
ular
rings
whi
chpr
ovid
efle
xibi
lity
toth
ech
ain
and
mak
eit
less
liabl
eto
kink
ing.
Bot
hen
dsof
the
chai
nha
vebr
ass
hand
les
with
swiv
eljo
ints
oth
atth
ech
ain
can
betu
rned
arou
ndw
ithou
ttw
istin
g.Th
ele
ngth
ofth
ech
ain
isco
nsid
ered
from
outs
ide
surf
ace
ofon
eha
ndle
toth
eou
tsid
esu
rfac
eof
the
othe
rha
ndle
atth
een
ds.S
imila
rlyth
ele
ngth
oflin
kis
the
leng
thbe
twee
nth
ece
ntre
sof
the
two
cent
ral
rings
prov
ided
atbo
then
dsof
the
chai
n.In
met
ricch
ain
leng
thof
one
link
is20
cm.A
teve
ryon
em
eter
leng
thof
chai
n,a
smal
lbra
ssrin
gis
prov
ided
.Bra
ssta
llies
are
also
prov
ided
atev
ery
5mle
ngth
ofch
ain.
Each
tally
has
diffe
rent
shap
ew
hich
indi
cate
sei
ther
5m,1
0m
,or
15m
from
any
one
end
ofth
ech
ain.
Met
ricch
ain
are
also
avai
labl
ein
the
leng
thof
20m
and
30m
.As
the
leng
thof
one
link
is20
cm,a
20m
chai
nco
nsis
tsof
100
such
links
,whi
le30
cmch
ain
cons
ists
of15
0lin
ks.
Leng
thof
the
chai
nis
embo
ssed
onth
ebr
ass
hand
leso
fthe
chai
n.
Met
ric C
hain
Met
ric C
hain
Gun
ter’s
Cha
in o
r Sur
veyo
r’s c
hain
•A
66fe
etlo
ngch
ain
cons
ists
of10
0lin
ks,e
ach
of0.
66ft,
iskn
own
asG
unte
r’sch
ain.
•H
ere,
10ch
ains
are
equa
lto
1ac
re,
•10
chai
ns=
1fu
rlong
and
8fu
rlong
(80
chai
ns)=
1m
ile•
This
chai
nis
suita
ble
fort
akin
gle
ngth
inm
iles
and
area
sin
acre
.
Gun
ter’s
Cha
in o
r Sur
veyo
r’s C
hain
(66
ft. C
hain
)En
gine
er’s
Cha
in
•A
100
ftlo
ngch
ain
cons
ists
of10
0lin
ksea
chof
1fo
otis
know
nas
Engi
neer
’sch
ain.
Bra
ssta
gsar
efa
sten
edat
ever
y10
links
.Thi
sch
ain
isus
edto
mea
sure
leng
than
dar
eain
squa
reya
rds.
Engi
neer
’s C
hain
(100
ft.)
Rev
enue
Cha
in
•R
even
uech
ain
is33
ftlo
ngch
ain
cons
istin
gof
16lin
ks.
This
chai
nis
used
for
dist
ance
mea
sure
men
tsin
feet
s&
inch
esfo
rsm
alle
rar
eas.
Stee
l Ban
d or
Ban
d C
hain
•St
eel
band
are
pref
erre
dth
anch
ains
beca
use
they
are
mor
eac
cura
te,b
utth
edi
sadv
anta
geis
that
they
getb
roke
nea
sily
and
are
diffi
cult
tore
pair
inth
efie
ld.
They
are
20m
and
30m
long
,12
to16
mm
wid
ean
d0.
3to
0.6
mm
thic
k.Th
eyar
enu
mbe
red
atev
ery
met
rean
ddi
vide
dat
ever
y20
cm.
Stee
l Ban
d or
Ban
d C
hain
Test
ing
and
Adj
ustm
ent o
f Cha
in•
Dur
ing
cont
inuo
usus
e,th
ele
ngth
ofa
chai
nge
tsal
tere
d,its
leng
this
shor
tene
dch
iefly
due
tobe
ndin
gof
links
.Its
leng
this
elon
gate
dei
ther
due
tost
retc
hing
ofth
elin
ksan
djo
ints
and
open
ing
outo
fthe
smal
lrin
gs.F
orac
cura
tew
ork
itis
nece
ssar
yto
test
the
chai
ntim
eto
time.
The
chai
nca
nbe
thus
test
edby
ast
eel
tape
orby
ast
anda
rdch
ain.
Som
etim
es,i
tis
conv
enie
ntto
have
ape
rman
entt
estg
auge
esta
blis
hed
whe
reth
ech
ain
iste
sted
.•
Whe
nth
ele
ngth
ofa
chai
nis
mea
sure
dat
apu
llof
8kg
at20
0C
,the
leng
thof
the
chai
nsh
ould
mea
sure
20m
+5
mm
and
30m
+8m
mfo
r20
man
d30
mlo
ngch
ain
resp
ectiv
ely.
Inad
ditio
nto
this
,ev
ery
mle
ngth
ofth
ech
ain
shal
lbe
accu
rate
tow
ithin
2m
m.F
ollo
win
gm
easu
res
are
take
nto
adju
stth
ele
ngth
ofa
chai
n.
Test
ing
and
Adj
ustm
ent o
f Cha
in
If th
e ch
ain
is fo
und
to b
e to
o lo
ng
•C
losi
ngup
the
join
tsof
the
rings
iffo
und
tobe
open
out.
•R
esha
ping
the
elon
gate
drin
g.•
Rep
laci
ngel
onga
ted
rings
•R
emov
ing
one
orm
ore
smal
lrin
gs•
Adj
ustt
helin
ksat
the
ends
If th
e ch
ain
is fo
und
to b
e to
o sh
ort:
•It
can
bead
just
edby
:•
Stra
ight
enin
gth
ebe
ntlin
ks.
•O
peni
ngth
ejo
ints
ofth
elin
ks.
•R
epla
cing
one
orm
ore
smal
lerc
ircul
arrin
gsby
bigg
eron
es.
•In
serti
ngne
wrin
gsw
here
nece
ssar
y.•
Adj
ustin
gth
elin
ksat
the
ends
.•
The
adju
stm
ent
shou
ldas
far
aspo
ssib
lebe
sym
met
rical
inei
ther
side
ofth
em
iddl
epo
int
soth
atth
epo
sitio
nof
the
cent
reta
gre
mai
nsun
chan
ged.
Tape
s
•Ta
pes
are
used
for
mor
eac
cura
tem
easu
rem
ents
.Th
eta
pes
are
clas
sifie
dba
sed
onth
em
ater
ialo
fw
hich
they
are
mad
eof
such
as:
•C
loth
Tape
•Fi
berT
ape
•M
etal
licTa
pe•
Stee
lTap
e•
Inva
rTap
e
Tape
s•
Clo
thor
Lin
enta
pe:
•Li
nen
tape
sar
ecl
osel
yw
oven
linen
and
varn
ishe
dto
resi
stm
oist
ure.
They
are
gene
rally
10m
,20
m,2
5m
and
30m
long
leng
than
d12
to15
mm
wid
e.Th
eyar
ege
nera
llyus
edfo
roffs
etm
easu
rem
ents
.The
seta
pesa
relig
htan
dfle
xibl
e.•
Fibe
rta
pe:
•Th
ese
tape
sar
esi
mila
rto
linen
and
plas
ticco
ated
tape
sbu
tth
eyar
em
ade
ofgl
ass
fibre
.The
tape
sar
equ
itefle
xibl
e,st
rong
and
non-
cond
uctiv
e.Th
ese
can
even
beus
edin
the
vici
nity
ofel
ectri
cale
quip
men
t.Th
ese
tape
sdo
nots
tretc
hor
shrin
kdu
eto
chan
gein
tem
pera
ture
orm
oist
ure.
Thes
eta
pes
are
avai
labl
ein
leng
ths
of20
m,
30m
,an
d50
mle
ngth
s.
Tape
s
Line
n Ta
peF
iber
Tap
e
Tape
s•
Met
allic
tape
:•
Alin
enta
pere
info
rced
with
bras
sor
copp
erw
ires
topr
even
tstre
tchi
ngor
twis
ting
offib
res
isca
lled
am
etal
licta
pe.A
sth
ew
ires
are
inte
rwov
enan
dta
peis
varn
ishe
d.Th
ese
wire
sare
visi
ble
tona
ked
eyes
.Th
isis
supp
lied
ina
lath
erca
sew
itha
win
ding
devi
ce.E
ach
met
rele
ngth
isdi
vide
din
to10
parts
(dec
imet
res)
and
each
part
isfu
rther
sub-
divi
ded
into
10pa
rts(
cent
imet
res)
.It
isco
mm
only
used
for
taki
ngof
fset
sin
chai
nsu
rvey
ing.
Met
allic
tape
Tape
s•
Stee
lTap
e:•
The
stee
lta
peis
mad
eof
stee
lrib
bon
ofw
idth
vary
ing
from
6m
mto
16m
m.T
heco
mm
only
avai
labl
ele
ngth
are
10m
,15
m,
20m
,30
m,
and
50m
.It
isgr
adua
ted
inm
etre
s,de
cim
etre
s,an
dce
ntim
etre
s.St
eelt
apes
are
used
for
accu
rate
mea
sure
men
tsof
dist
ance
s.•
Inva
rTap
e:•
Inva
rtap
ear
em
ade
ofan
allo
yof
nick
le36
%an
dst
eel6
4%
havi
ngve
rylo
wco
-effi
cien
toft
herm
alex
pans
ion.
Thes
ear
e6
mm
wid
ean
dge
nera
llyav
aila
ble
inle
ngth
sof
30m
,50
m,a
nd10
0m.I
tis
nota
ffect
edby
chan
geof
tem
pera
ture
ther
efor
e,it
isus
edw
hen
high
degr
eeof
prec
isio
nis
requ
ired.
Stee
l Tap
eIn
var T
ape
Arr
ows
•A
rrow
sar
em
ade
ofte
mpe
red
stee
lwire
ofdi
a4
mm
.One
end
ofth
ear
row
isbe
ntin
toa
ring
ofdi
amet
er50
mm
and
othe
ren
dis
poin
ted.
Itsov
eral
llen
gth
is40
0m
m.A
rrow
sar
eus
edfo
rco
untin
gth
enu
mbe
rof
chai
nsw
hile
mea
surin
ga
chai
nlin
e.A
nar
row
isin
serte
din
toth
egr
ound
afte
rev
ery
chai
nle
ngth
mea
sure
don
the
grou
nd.
Arr
ows
Ran
ging
Rod
s and
Offs
et R
ods
•R
angi
ngro
dsar
eus
edfo
rra
ngin
gso
me
iner
med
iate
poin
tson
the
surv
eylin
e.R
angi
ngro
dsar
ege
nera
lly2
to3
min
leng
than
dar
epa
inte
dw
itth
alte
rnat
eco
lor
band
sof
blac
kan
dw
hite
orre
dan
dw
hite
colo
rsw
ithle
ngth
ofea
cheq
ualiz
ing
20cm
.The
loca
tion
ofan
ysu
rvey
stat
ion
can
bekn
own
from
long
dist
ance
son
lyby
mea
nsof
rang
ing
rods
.Ift
hedi
stan
ceis
too
long
,aro
dof
leng
th4.
0m
to6.
0m
isus
edca
lled
asra
ngin
gpo
les.
•Th
eof
fset
rod
issi
mila
rto
the
rang
ing
rod
with
the
exce
ptio
nth
atin
stea
dof
the
flag,
aho
okis
prov
ided
atth
eto
pfo
rpus
hing
and
pulli
ngth
ech
ain
orth
eta
pe.
Itis
also
used
form
easu
ring
smal
loffs
ets.
Ran
ging
Rod
s
Pegs
•Pe
gsar
em
ade
oftim
ber
orst
eela
ndth
eyar
eus
edto
mar
kth
epo
sitio
nof
the
stat
ions
orte
rmin
alpo
ints
ofa
surv
eylin
e.W
oode
npe
gsar
e15
cmlo
ngan
dar
edr
iven
into
the
grou
ndw
ithth
ehe
lpof
aha
mm
er.
Pegs
Plum
b-B
ob
•Pl
umb
–bob
isus
edto
trans
fer
poin
tson
the
grou
nd.
Itis
also
used
for
fixin
gin
stru
men
tsex
actly
over
the
stat
ion
poin
tm
arke
don
the
grou
ndby
chec
king
the
cent
reof
the
inst
rum
ent
whe
ther
coin
cide
sw
ithth
ece
ntre
ofth
epe
gor
stat
ion
orno
t,by
susp
endi
ngth
epl
umb-
bob
exac
tlyat
the
cent
reof
the
inst
rum
entu
nder
it.Pl
umb
bob
isth
usus
edas
cent
erin
gai
din
theo
dolit
esan
dpl
ane
tabl
e.
Plum
b-B
ob
Cha
in S
urve
ying
•C
hain
surv
eyin
gis
that
type
ofsu
rvey
ing
inw
hich
only
linea
rm
easu
rem
ents
are
take
nin
the
field
.Thi
sty
peof
surv
eyin
gis
done
for
surv
eys
ofsm
alle
xten
tto
desc
ribe
the
boun
darie
sof
plot
sof
land
and
tolo
cate
the
exis
ting
feat
ures
onth
em.
•It
isth
em
etho
dof
surv
eyin
gin
whi
char
eais
divi
ded
into
netw
ork
oftri
angl
esan
dth
esi
des
ofth
eva
rious
trian
gles
are
mea
sure
ddi
rect
lyin
the
field
with
ach
ain
orta
pean
dno
angu
lar
mea
sure
men
tsar
eta
ken.
Prin
cipl
e of
Cha
in S
urve
ying
•Th
epr
inci
ples
ofch
ain
surv
eyis
todi
vide
the
area
into
anu
mbe
rof
trian
gles
ofsu
itabl
esi
des.
As
trian
gle
isth
eon
lysi
mpl
epl
ane
geom
etric
figur
ew
hich
can
bepl
otte
dfr
omth
ele
ngth
sof
the
thre
esi
des
even
ifan
gles
are
not
know
n.A
netw
ork
oftri
angl
esis
pref
erre
dto
inch
ain
surv
eyin
g.Th
ustri
angu
latio
nis
the
prin
cipl
eof
chai
nsu
rvey
ing.
Ifth
ear
eato
besu
rvey
edis
trian
gle
insh
ape
and
ifth
ele
ngth
and
sequ
ence
ofits
side
sar
ere
cord
ed,t
hepl
anof
the
area
can
beea
sily
draw
n.
Prin
cipl
e of
Sur
veyi
ng(T
riang
ulat
ion)
Term
s re
late
d w
ith C
hain
Sur
veyi
ng
•Su
rvey
Stat
ions
:Su
rvey
stat
ions
are
the
poin
tsat
the
begi
nnin
gan
dat
the
end
ofa
chai
nlin
e.Th
eym
ayal
sooc
cur
atan
yco
nven
ient
posi
tion
onth
ech
ain
line.
Such
stat
ions
may
be:
•M
ain
Stat
ions
•Su
bsid
iary
Stat
ions
•Ti
eSt
atio
ns
Term
s re
late
d w
ith C
hain
Sur
veyi
ngTe
rms
rela
ted
with
Cha
in S
urve
ying
•M
ain
Stat
ions
:St
atio
nsta
ken
alon
gth
ebo
unda
ryof
anar
eaas
cont
rolli
ngpo
inta
rekn
own
as‘m
ain
stat
ions
’.Th
elin
esjo
inin
gth
em
ain
stat
ion
are
calle
d‘
mai
nsu
rvey
lines
’/Th
em
ain
surv
eylin
esh
ould
cove
rth
ew
hole
area
tobe
surv
eyed
.The
mai
nSt
atio
nsar
ede
note
dby
with
lette
rA,B
,C,D
,etc
.•
Subs
idia
rySt
atio
ns:S
tatio
nsw
hich
are
onth
em
ain
surv
eylin
esor
any
othe
rsu
rvey
lines
are
know
nas
‘su
bsid
iary
stat
ions
’.Th
ese
stat
ions
are
take
nto
run
subs
idia
rylin
esfo
rdi
vidi
ngar
eain
totri
angl
es.
For
chec
king
the
accu
racy
oftri
angl
esan
dfo
rlo
catin
gin
terio
rdet
ails
.The
sest
atio
nsar
ede
note
dby
‘O’w
ithle
tterS
1,S 2
,S 3
etc.
•Ti
eSt
atio
ns:
thes
ear
eal
sosu
bsid
iary
stat
ions
take
non
the
surv
eylin
es.L
ines
join
ing
the
tiest
atio
nar
ekn
own
as‘t
ielin
es’.
The
lines
are
take
nto
loca
tein
terio
rde
tails
.The
stat
ions
are
deno
ted
by‘
‘w
ithle
tterT
1,T 2
,T3,
etc.
Term
s re
late
d w
ith C
hain
Sur
veyi
ng•
Mai
nSu
rvey
lines
:•
The
line
join
ing
the
mai
nst
atio
nsar
eca
lled
‘m
ain
surv
eylin
es’o
rch
ain
lines
.In
figA
B,B
C,C
D,D
Aar
eth
em
ain
surv
eylin
es.
•B
ase
Lin
e:Th
elin
eon
whi
chth
efr
amew
ork
ofsu
rvey
isbu
iltis
know
nas
the’
base
line’
.Iti
sth
em
osti
mpo
rtant
line
ofth
esu
rvey
.Gen
eral
ly,t
helo
nges
tof
the
mai
nsu
rvey
lines
isco
nsid
ered
asth
eba
selin
e.Th
islin
esh
ould
beta
ken
thro
ugh
fairl
yle
velg
roun
d,an
dsh
ould
bem
easu
red
very
care
fully
and
accu
rate
ly.I
nfig
,Bis
the
base
line.
•C
heck
line:
The
line
join
ing
the
apex
poin
tof
atri
angl
eto
som
efix
edpo
ints
onits
base
iskn
own
asth
e‘
chec
klin
e’.I
tis
take
nto
chec
kth
eac
cura
cyof
trian
gles
.Som
etim
esth
islin
eshe
lps
tolo
cate
inte
riord
etai
ls.
Infig
CS 1
,AS 2
,are
the
chec
klin
es.
•Ti
eL
ine:
•A
line
join
ing
tiest
atio
nsis
term
edas
atie
line.
Itis
run
tota
keth
ein
terio
rde
tails
whi
char
efa
raw
ayfr
omth
em
ain
lines
and
also
toav
oid
long
offs
ets.
Itca
nal
sose
rve
asch
eck
line.
Infig
T 1T 2
isth
etie
line.
Term
s re
late
d w
ith C
hain
Sur
veyi
ng
Sele
ctio
n of
Sur
vey
Stat
ions
•Th
efo
llow
ing
poin
tssh
ould
beco
nsid
ered
whi
lese
lect
ing
surv
eyst
atio
ns•
The
stat
ions
shou
ldbe
inte
rvis
ible
.•
Surv
eylin
essh
ould
bem
inim
umas
fara
spos
sibl
e.•
Stat
ions
shou
ldfo
rmw
ellc
ondi
tione
dtri
angl
es.
•St
atio
nspo
ints
shou
ldbe
solo
cate
dth
attie
line,
chec
klin
e,ba
selin
e,et
c.ca
nbe
form
ed.
•St
atio
npo
ints
shou
ldbe
sele
cted
with
inth
ebo
unda
ryof
the
area
tobe
surv
eyed
.•
The
surv
eylin
essh
ould
beta
ken
thro
ugh
fairl
yle
vel
grou
ndas
fara
spra
ctic
able
.
Ope
ratio
ns in
Cha
inin
g
•Th
e fo
llow
ing
oper
atio
ns a
re in
volv
ed in
cha
in
surv
ey.
•C
hain
ing
•R
angi
ng•
Offs
ettin
g•
Thes
e th
ree
oper
atio
ns a
re d
one
sim
ulta
neou
sly
durin
g ch
ain
surv
eyin
g.
Cha
inin
g on
Lev
el G
roun
d•
The
met
hod
ofta
king
mea
sure
men
tsw
ithth
ehe
lpof
ach
ain
ora
tape
iste
rmed
asch
aini
ng.
•C
hain
ing
invo
lves
follo
win
gop
erat
ions
:•
Fixi
ngth
est
atio
ns•
Unf
oldi
ngth
ech
ain
•R
angi
ng•
Mea
surin
gth
edi
stan
ce(S
urve
yLi
nes)
•Fo
ldin
gth
ech
ain
•St
atio
nsar
efir
stof
allm
arke
dw
ithpe
gsan
dra
ngin
gro
dsto
mak
eth
emvi
sibl
e.Th
ere
isa
typi
cal
met
hod
offo
ldin
gan
dun
fold
ing
the
chai
nto
prev
ent
the
prob
lem
ofkn
otfo
rmed
whi
leun
fold
ing
the
chai
n,af
ter
unfo
ldin
gth
ech
ain
the
itis
laid
stra
ight
betw
een
the
stat
ion
tom
easu
reth
eco
rrec
tlen
gth
ofth
elin
e.If
the
leng
thof
the
surv
eylin
eis
grea
tert
han
one
chai
nle
ngth
,in
term
edia
tepo
ints
are
loca
ted,
inor
der
that
the
chai
nis
pulle
dal
ong
ast
raig
htlin
e.Th
isis
know
nas
rang
ing
alin
e.
Cha
inin
g on
Lev
el G
roun
d•
Afte
rfix
ing
the
stat
ion
poin
tsan
din
term
edia
tepo
ints
ifre
quire
d,a
chai
nis
stre
tche
dbe
twee
ntw
opo
ints
.The
follo
wer
hold
sth
eze
roen
dof
the
chai
nw
here
asth
ele
ader
fixes
upan
arro
wat
the
end
ofon
ech
ain
leng
th.
The
lead
erpu
llsth
ech
ain
for
mea
surin
gfu
rther
dist
ance
.Th
ele
ader
goes
onfix
ing
the
arro
ws
atth
eot
her
ends
ofea
chan
dev
ery
chai
nle
ngth
.Atl
ast,
the
follo
wer
colle
cts
allt
hear
row
fixed
byth
ele
ader
whi
lem
ovin
gfo
rwar
d.A
tthe
end
ofth
ew
ork
,asa
chec
kth
enu
mbe
rof
arro
ws
are
mul
tiplie
dby
the
chai
nle
ngth
whi
chis
tota
lle
ngth
mea
sure
dFi
nally
atth
een
dof
wor
k,th
ech
ain
isfo
lded
and
tied
upw
itha
coir
thre
ad.
Cha
inin
g on
Slo
ping
Gro
und
•Th
eob
ject
ofa
surv
eyis
topr
epar
ea
plan
orm
ap.
Inth
epl
anor
am
apth
edi
stan
ces
plot
ted
betw
een
any
two
poin
tsis
alw
ays
ast
raig
htho
rizon
tal
dist
ance
betw
een
them
.Ev
enif
the
chai
ning
isdo
neon
asl
opin
ggr
ound
,thi
ssl
opin
gdi
stan
ceis
conv
erte
din
toho
rizon
tald
ista
nce
whi
lepl
ottin
g.Th
ere
are
two
met
hods
offin
ding
out
horiz
onta
ldi
stan
cew
hile
chai
ning
ona
slop
ing
grou
nd.
•D
irect
met
hod
•In
dire
ctm
etho
d
Cha
inin
g on
Slo
ping
Gro
und
•D
irec
tmet
hod:
•Th
ism
etho
dis
also
calle
das
met
hod
ofst
eppi
ngin
this
met
hod,
the
dist
ance
ism
easu
red
insm
all
horiz
onta
lst
retc
hes.
Asu
itabl
ele
ngth
ofch
ain
orta
pesa
yl 1
ista
ken.
The
follo
wer
hold
sthe
rear
end
ofth
eta
peat
apo
into
nth
eto
pof
the
hill
orsl
oppi
nggr
ound
.i.e
.atp
oint
(A)T
heta
peis
stre
tche
dho
rizon
tally
from
(A)a
ndat
smal
lste
ple
ngth
(l 1)o
f3
to5
m,t
hepo
inta
tthe
end
ofl 1
isdr
oppe
dan
dm
arke
don
the
grou
ndas
a1.F
rom
a 1,
agai
nta
peis
stre
tche
dex
actly
ina
horiz
onta
lpla
neat
aco
nven
ient
step
l 2,an
ddr
open
dof
l 2on
the
grou
ndas
b 1.L
ikew
ise
entir
ele
ngth
oflin
eon
the
slop
ing
grou
ndis
mea
sure
d.•
Fina
lly,t
heto
tall
engt
hof
lineA
B,i
.e.D
isob
tain
ed.
•D
=l 1
+l 2
+……
.ln
•W
here
,ln=
the
last
step
fort
hegi
ven
surv
eylin
e.•
Her
e,it
shou
ldbe
notic
edth
at,s
tepp
ing
dow
nth
ehi
llis
conv
enie
ntth
anst
eppi
ngup
.
Cha
inin
g on
Slo
ping
Gro
und
Cha
inin
g on
Slo
ping
Gro
und
•In
dire
ctm
etho
d:•
Indi
rect
met
hods
invo
lve
calc
ulat
ion
from
the
dire
ctly
mea
sure
dle
ngth
s.Th
ese
met
hods
are
brie
flyex
plai
ned
here
.•
Met
hod
1:H
oriz
onta
ldi
stan
ceof
the
segm
ent
isca
lcul
ated
bykn
owin
gsl
opin
gle
ngth
ofth
ese
gmen
tand
angl
eof
incl
inat
ion
ofth
atw
ithth
eho
rizon
tal.
•Th
ean
gle
ofth
esl
opin
gsu
rfac
ew
ithho
rizon
talc
anbe
know
nby
asi
mpl
eha
ndy
inst
rum
entc
alle
dA
bney
’sLe
vel.
•To
talD
ista
nce
D=
∑d
•∑
d=d 1
+d 2
+…..d
n,an
d•
D=
lcos
Ө.(
ford
1=l 1
cosӨ
1)•
Whe
reӨ
=an
gle
ofsl
opin
gsu
rfac
ew
ithho
rizon
tal
•L=
slop
ing
leng
th•
Itsh
ould
appr
oach
from
base
toup
hill.
Cha
inin
g on
Slo
ping
Gro
und
Met
hod
2
•If
the
elev
atio
ndi
ffere
nce
betw
een
two
term
inal
poin
tsan
dth
esl
opin
gdi
stan
cebe
twee
nth
etw
ote
rmin
alpo
ints
iskn
own,
the
horiz
onta
ldis
tanc
eD
can
beca
lcul
ated
as,
•D
=√
l2–h
2
•W
here
l=sl
opin
gle
ngth
•H
=he
ight
orel
evat
ion
diffe
renc
ebe
twee
nth
etw
opo
ints
.
Met
hod
2M
etho
d 3
•Th
ism
etho
dis
also
calle
dth
ehy
pote
nusa
lallo
wan
cem
etho
d.Th
ech
aini
ngis
done
onth
esl
opin
ggr
ound
,but
inst
ead
ofpu
tting
the
end
arro
wat
actu
alen
dof
chai
n,it
Iput
atso
me
adva
nced
dist
ance
and
that
poin
tis
cons
ider
edas
the
end
ofon
ech
ain
leng
thas
show
nin
fig•
Inth
ism
etho
d,th
ech
ain
of20
mle
ngth
ends
atpo
intB
,The
refo
re,
slop
ing
leng
thl=
20m
,but
the
actu
alho
rizon
tall
engt
h(D
)is
less
than
20m
and
calc
ulat
ion
isre
quire
dto
calc
ulat
eho
rizon
tald
ista
nce
base
don
Ө,a
nan
gle
ofin
clin
atio
nof
grou
nd.
•In
stea
dof
that
prac
tice,
inth
em
etho
dof
hypo
tenu
sala
llow
ance
,the
allo
wan
cein
adva
nce
ofen
dof
the
chai
nis
mad
ein
such
aw
ayth
atth
eto
tal
dist
ance
,i.e
.th
ele
ngth
ofch
ain
onsl
opin
ggr
ound
plus
allo
wan
ce,
isdi
rect
lyeq
ual
to20
mho
rizon
tal
dist
ance
betw
een
thos
etw
opo
ints
assh
own
infig
Met
hod
3•
From
figur
e,th
eho
rizon
tald
ista
nce
D=
(l+a)
cosӨ
•W
here
Dis
inte
nded
tom
ake
equa
lto
one
chai
nle
ngth
•Th
eref
ore
,D=
(l+a)
cosӨ
,•
Her
e,A
B=
one
chai
nle
ngth
=l=
D=
20m
•Th
eref
ore
putD
=l=
20m
•Th
eref
ore
20=
(20
+a)c
osӨ
•Th
eref
ore
20se
cӨ
=20
+a
•a=
20se
cӨ
-20
•=
20(s
ecӨ
-1)
•O
r•
a=10
0(s
ecӨ
-1)l
inks
,as2
0m=
100
links
•W
here
,a=
hypo
tenu
sala
llow
ance
for2
0m
long
chai
n•
Fort
hech
ain
othe
rtha
n20
m,l
engt
h.•
A=
l(sec
Ө-1
)whe
re,l
=le
ngth
ofch
ain
inm
•Th
us,t
hear
row
isin
serte
dat
(l+a)
dist
ance
onth
egr
ound
inst
ead
ofat
the
end
ofth
ech
ain.
Thus
,the
horiz
onta
ldis
tanc
efo
rthi
ssl
opin
gdi
stan
ceon
grou
ndis
equa
lto
one
chai
nle
ngth
(l)
Met
hod
3
Ran
ging
•W
hen
the
leng
thof
alin
eex
ceed
sth
ele
ngth
ofth
ech
ain
assh
own
infig
topr
ocee
din
ast
raig
htlin
e,in
term
edia
tepo
ints
are
need
edto
bees
tabl
ishe
dbe
twee
nth
etw
ost
atio
ns.T
hepr
oces
sof
esta
blis
hing
inte
rmed
iate
poin
tson
ast
raig
htlin
ebe
twee
ntw
oen
dpo
ints
iskn
own
asra
ngin
g.•
Ran
ging
mus
tbe
done
befo
rea
surv
eylin
eis
chai
ned.
Ran
ging
may
bedo
neby
dire
ctob
serv
atio
nof
nake
dey
eor
bylin
era
nger
orby
theo
dolit
e.G
ener
ally
,ran
ging
isdo
neby
the
nake
dey
ew
ithth
ehe
lpof
thre
era
ngin
gro
ds.
•Th
ere
are
two
met
hods
ofra
ngin
g:•
Dire
ctR
angi
ng•
Indi
rect
Ran
ging
orR
ecip
roca
lRan
ging
.
Dire
ct R
angi
ng•
Whe
nin
term
edia
tera
ngin
gro
dsar
efix
edon
ast
raig
htlin
eby
dire
ctob
serv
atio
nfr
omen
dst
atio
ns,t
hepr
oces
sis
know
nas
dire
ctra
ngin
g.D
irect
rang
ing
ispo
ssib
lew
hen
the
end
stat
ions
are
inte
rvis
ible
.Th
efo
llow
ing
proc
edur
eis
adop
ted
ford
irect
rang
ing.
•A
ssum
eth
atA
and
Bar
etw
oen
dst
atio
nsof
ach
ain
line,
whe
retw
ora
ngin
gro
dsar
edi
rect
lyfix
ed.
Supp
ose
itis
requ
ired
tofix
ara
ngin
gro
dat
the
inte
rmed
iate
poin
tMon
the
chai
nlin
ein
such
aw
ayth
atth
epo
ints
A,M
,Bar
ein
sam
est
raig
htlin
e.Th
esu
rvey
orst
ands
half
am
eter
behi
ndth
era
ngin
gro
dat
Aby
look
ing
tow
ards
the
line
AB
.The
assi
stan
thol
dsa
rang
ing
rod
atM
verti
cally
atar
m’s
leng
th.T
hero
dsh
ould
behe
ldlig
htly
byth
umb
and
for-f
inge
r.N
ow,t
hesu
rvey
ordi
rect
sth
eas
sist
antt
om
ove
the
rang
ing
rod
toth
ele
ftor
right
until
the
thre
era
ngin
gro
dsco
mes
exac
tlyin
the
sam
est
raig
htlin
e.To
chec
kth
eve
rtica
lity
ofth
ero
ds,t
hesu
rvey
orlo
oks
thro
ugh
the
botto
mof
the
rods
.The
rang
ing
ispe
rfec
t,w
hen
the
thre
era
ngin
gro
dsco
inci
dean
dap
pear
asa
sing
lero
d.W
hen
the
surv
eyor
issa
tisfie
dth
atth
era
ngin
gis
perf
ect,
hesi
gnal
sth
eas
sist
ant
tofix
the
rang
ing
rod
onth
egr
ound
byw
avin
gbo
thhi
sha
nds
upan
ddo
wn.
Follo
win
gth
esa
me
proc
edur
e,th
eot
herr
angi
ngro
dsm
aybe
fixed
onth
elin
e.Th
esi
gnal
give
nby
the
surv
eyor
are
show
nin
fig
Dire
ct R
angi
ngD
irect
Ran
ging
Dire
ct R
angi
ng w
ith a
line
rang
er
•A
line
rang
erco
nsis
tsof
two
right
angl
edis
osce
les
trian
gula
rpr
ism
spl
aced
one
abov
eth
eot
her.
The
diag
onal
sof
the
two
pris
mar
esi
lver
edso
asto
form
the
refle
ctin
gsu
rfac
es.
Ther
eis
aha
ndle
atth
ebo
ttom
ofth
ein
stru
men
tto
hold
the
inst
rum
enti
non
eha
nd.
Aho
okis
prov
ided
belo
wth
eha
ndle
for
atta
chin
gth
epl
umb
bob
totra
nsfe
rth
epo
int
onth
egr
ound
.
Dire
ct R
angi
ng W
ith A
Lin
e R
ange
r•
The
follo
win
gpr
oced
ure
isus
edto
esta
blis
ha
poin
tMon
the
lineA
Bw
itha
line
rang
er.
•H
old
the
line
rang
erin
hand
leat
the
leve
lon
the
eye
and
stan
dat
Mve
ryne
arth
elin
eA
B,a
sju
dged
byey
e.•
Obs
erve
the
rang
ing
rod
atA
thro
ugh
the
uppe
rpris
m,A
BC
.The
ray
oflig
htfro
mA
ente
rsth
eup
perp
rism
,get
sre
flect
edfr
omth
esi
lver
eddi
agon
alac
and
ente
rsth
eey
eat
right
angl
eto
the
lineA
B,a
sthe
inci
dent
ray
mak
esan
angl
eof
450
with
the
refle
ctin
gsu
rfac
e.•
Als
oob
serv
eth
era
ngin
gro
dat
Bth
roug
hth
elo
wer
pris
mdb
c.Th
era
yof
light
from
Ben
ters
the
pris
m,g
oes
refle
cted
from
the
silv
ered
diag
onal
dban
den
ters
the
eye
atrig
htan
gle
toth
elin
eAB
.•
Che
ckw
heth
erth
eim
age
ofth
era
ngin
gro
dsat
Aan
db
are
seen
inon
eve
rtica
llin
eor
not.
Ifth
epo
inta
twhi
chth
elin
era
nger
ishe
ldis
note
xact
lyon
the
line
AB
,the
two
imag
esap
pear
sepa
rate
d.•
Mov
eth
ein
stru
men
tslig
htly
back
war
dsor
forw
ards
,atr
ight
angl
esto
the
line
AB
until
the
two
imag
esap
pear
exac
tlyon
eov
erth
ean
othe
r.•
Tran
sfer
the
poin
tto
the
grou
ndby
hang
ing
apl
umb
bob
from
the
hook
onth
eha
ndle
.The
poin
tMso
trans
ferr
edis
exac
tlybe
low
the
inte
rsec
tion
ofth
etw
odi
agon
als
•Li
kew
ise
othe
rpoi
ntsc
anbe
esta
blis
hed.
Dire
ct R
angi
ng w
ith a
line
Ran
ger
Indi
rect
or R
ecip
roca
l Ran
ging
•W
hen
the
end
stat
ions
are
noti
nter
visi
ble
due
toth
ere
bein
ghi
ghgr
ound
betw
een
them
,in
term
edia
tera
ngin
gro
dsar
efix
edon
the
line
inan
indi
rect
way
.Th
em
etho
dis
know
nas
indi
rect
rang
ing
orre
cipr
ocal
rang
ing.
The
follo
win
gpr
oced
ure
isad
opte
dfo
rin
dire
ctra
ngin
g.
Indi
rect
or R
ecip
roca
l Ran
ging
•Su
ppos
eA
and
Bar
etw
oen
dst
atio
nsw
hich
are
not
inte
rvis
ible
due
tohi
ghgr
ound
exis
ting
betw
een
them
.Su
ppos
eit
isre
quire
dto
fixin
term
edia
tepo
ints
betw
een
Aan
dB
,tw
och
ain
men
take
uppo
sitio
nsas
M1
and
N1
with
rang
ing
rods
inth
eir
hand
s,Th
ech
ainm
enat
M1
stan
dsw
ithhi
sfa
ceto
war
dsB
soth
athe
can
see
the
rang
ing
rod
atM
1an
dA
.Th
enth
ech
ainm
enpr
ocee
dto
rang
ing
the
line
bydi
rect
ing
each
othe
ral
tern
atel
y.Th
ech
ainm
enat
M1
dire
cts
the
chai
nmen
atN
1to
com
eto
the
posi
tion
N2
soth
atM
1,N
1an
dB
are
inth
esa
me
stra
ight
line.
Aga
in,
the
chai
rmen
atN
2di
rect
sth
ech
ainm
enat
M1
tom
ove
toth
epo
sitio
nat
M2
soth
atN
2,M
2an
dA
are
inth
esa
me
stra
ight
line.
Indi
rect
or R
ecip
roca
l Ran
ging
•Th
etw
och
ainm
enar
eno
wat
M2
and
N2
whi
char
ene
arer
toth
ech
ain
line
than
the
posi
tion
M1a
ndN
1.Th
epr
oces
sis
repe
ated
till
the
othe
rpoi
nts
Man
dN
are
loca
ted
insu
cha
way
that
the
chai
nmen
atM
finds
the
chai
nman
atN
inlin
ew
ithM
Ban
dth
ech
ainm
enat
Nfin
dsth
ech
ainm
enat
Min
line
with
NA
,Thu
sthe
poin
tsA
,M,N
and
Bar
ein
the
sam
est
raig
htlin
e.
Indi
rect
or R
ecip
roca
l Ran
ging
Indi
rect
or R
ecip
roca
l Ran
ging
Offs
ettin
g
•Th
em
etho
dof
taki
ngpe
rpen
dicu
lard
ista
nce
from
the
chai
nlin
eto
the
obje
cts
whi
char
eto
bepl
otte
dis
know
nas
offs
ettin
g.Th
us,
the
dist
ance
mea
sure
dfr
omob
ject
toch
ain
line
iste
rmed
asan
offs
et.
•It
isdo
neto
loca
teob
ject
sfro
mch
ain
line.
Offs
etsa
reei
ther
take
non
one
side
ofth
ech
ain
orbo
thsi
des
ofth
ech
ain.
Ther
e ar
e tw
o ty
pes o
f offs
ets
•Pe
rpen
dicu
laro
ffset
s•
Obl
ique
'sof
fset
s:•
Perp
endi
cula
rO
ffse
ts:
•Th
eof
fset
sw
hich
are
take
npe
rpen
dicu
lar
toth
ech
ain
line
are
term
edas
perp
endi
cula
rof
fset
s.Th
ese
offs
ets
are
take
nby
hold
ing
zero
ends
ofth
eta
peat
the
obje
ctan
dsw
ingi
ngth
eta
peon
the
chai
nlin
e.Th
esh
orte
stdi
stan
cew
hats
oeve
rm
easu
red
from
obje
ctto
the
chai
nlin
eis
alw
aysa
perp
endi
cula
roffs
et.
•O
bliq
ueO
ffse
ts:
Obl
ique
dist
ance
isal
way
sgr
eate
rth
anth
epe
rpen
dicu
lar
dist
ance
.All
the
offs
ets
whi
char
eno
ttak
enat
right
angl
eto
chai
nlin
ear
ekn
owas
obliq
ue's
offs
ets.
•Th
edi
stan
ceto
the
chai
nlin
eat
whi
chth
efo
otof
the
offs
etis
take
nis
know
nas
ach
aina
ge.
•A
ccor
ding
tole
ngth
,the
offs
etha
ving
leng
thgr
eate
rtha
nor
equa
lto
15m
are
term
edas
long
offs
etsa
ndth
eof
fset
sofl
engt
hle
ssth
an15
mar
ekn
own
assh
orto
ffset
s.Sh
orto
ffset
sar
em
ore
accu
rate
than
long
offs
ets.
Obl
ique
Off
sets
Perp
endi
cula
r Offs
ets
Inst
rum
ents
for l
ayin
g of
fset
s
•O
ffset
s are
set o
f ins
trum
ents
such
as
•O
ptic
al S
quar
e•
Indi
an O
ptic
al sq
uare
•O
pen
Cro
ss st
aff
•Pr
ism
Squ
are
Opt
ical
Squ
are
•Th
isin
stru
men
tisu
sed
forp
erpe
ndic
ular
offs
eton
ly.
•Pr
inci
ple
ofO
ptic
alSq
uare
•Th
ean
gle
betw
een
the
inci
dent
ray
and
the
refle
cted
ray
istw
ice
the
angl
ebe
twee
nth
em
irror
s.•
Con
stru
ctio
nan
dw
orki
ngof
optic
alsq
uare
•Th
eop
tical
squa
reco
nsis
tsof
aci
rcul
arbo
x50
mm
indi
amet
eran
d12
.5m
min
dept
h.Th
ebo
xha
sth
ree
slits
atE,
F,an
dC
.in
line
with
the
open
ing
atE,
and
f,a
glas
sHsi
lver
edat
top
and
plai
nat
botto
m,
isfix
ed.
Itfa
ces
tow
ards
E.op
posi
teof
open
ing
C,
asi
lver
edpa
inte
dgl
assI
calle
din
dex
glas
sisf
ixed
soth
atth
ein
clin
eded
geof
glas
sI
and
incl
ined
face
ofgl
ass
Hm
akes
angl
eof
450 .
Whe
nop
enin
gC
face
tow
ards
obje
ctfo
roffs
et,t
heim
age
will
strik
eto
the
inde
xgl
ass
Ian
dre
flect
edto
horiz
ongl
ass
H.
from
this
horiz
ongl
ass
H,
the
imag
ere
ceiv
edfr
omgl
ass
Iw
illbe
refle
cted
and
rece
ived
bya
surv
eyor
hold
ing
the
inst
rum
enta
ndlo
okin
gth
roug
hop
enin
gE.
Setti
ng u
p th
e pe
rpen
dicu
lar b
y op
tical
Sq
uare
•Th
eob
serv
ersh
ould
stan
don
the
chai
nlin
ean
dap
prox
imat
ely
atth
epo
sitio
nw
here
the
perp
endi
cula
ris
tobe
setu
p.•
The
optic
alsq
uare
ishe
ldby
the
arm
atth
eey
ele
vel.
The
rod
atth
efo
rwar
dse
ctio
nB
isob
serv
edth
roug
hth
eun
silv
ered
porti
onon
thee
low
erpa
rtof
the
horiz
ongl
ass.
•Th
enth
eob
serv
erlo
oks
thro
ugh
the
uppe
rsi
lver
edpo
rtion
ofth
eho
rizon
glas
sto
see
the
imag
eof
the
obje
ctP
•Su
ppos
eth
eob
serv
erfin
dsth
atth
era
ngin
gro
dB
and
the
imag
eof
obje
ctP
does
notc
oinc
ide,
then
hesh
ould
mov
efo
rwar
dor
back
war
dal
ong
the
chai
nlin
eun
tilth
era
ngin
gro
dB
and
the
imag
eP
exac
tlyco
inci
de.
•A
tthi
spo
sitio
nth
eob
serv
erm
arks
apo
into
nth
egr
ound
tolo
cate
the
foot
ofth
eof
fset
fort
hegi
ven
obje
ct.
Opt
ical
Squ
are
Indi
an O
ptic
al S
quar
e•
Itis
bras
sw
edge
shap
edho
llow
box
ofab
out
5cm
side
san
d3
cmde
epw
itha
hand
le8
cmlo
ngfix
edun
dern
eath
.•
M1
and
M2
are
two
mirr
ors
fixed
toth
ein
clin
edsi
des
ofth
ebo
xat
anan
gle
of45
0 ;ab
san
dco
dar
etw
ore
ctan
gles
open
ings
abov
em
irror
s.PQ
RS
isth
eop
enfa
cew
hich
isto
betu
rned
tow
ards
the
obje
ctto
whi
chth
eof
fset
isto
beta
ken.
•Pr
inci
ple
ofw
orki
ngan
dm
etho
dis
sam
eas
optic
alsq
uare
.
Indi
an O
ptic
al S
quar
e
Indi
an O
ptic
al S
quar
eO
pen
Cro
ss S
taff
•Th
isIn
stru
men
tis
the
sim
ples
tfo
rmam
ong
all
and
cons
ists
offo
urm
etal
arm
sw
ithve
rtica
lsl
itsfo
rsi
ghtin
gth
roug
hat
right
angl
esto
each
othe
r•
Two
pers
ons
are
requ
ired
for
this
inst
rum
ent.
One
pair
ofve
rtica
lslit
isto
bebi
sect
rang
ing
rod
atth
een
dof
the
give
nch
ain
line
byst
andi
ngon
the
chai
nlin
ean
dot
her
pair
ofve
rtica
lslit
isre
quire
dto
bein
line
with
ara
ngin
gro
dat
obje
ctfo
rpe
rpen
dicu
lar
offs
et.
Ifth
isha
ppen
s.Th
epo
into
nth
ech
ain
line
isth
eba
seof
the
perp
endi
cula
rof
fset
from
obje
ctto
chai
nlin
e.Th
eve
rtica
lpo
int
ism
arke
don
the
chai
nlin
eto
mea
sure
perp
endi
cula
roffs
etan
dch
ain
age.
Ope
n C
ross
Sta
ffPr
ism
Squ
are
•Th
isw
orks
onth
esa
me
prin
cipl
eof
optic
alsq
uare
.In
stea
dof
two
mirr
ors
orre
flect
ing
surf
ace,
apr
ism
isus
edw
hich
has
two
refle
ctin
gsu
rfac
esIa
ndH
fixed
at45
0 .Th
era
ngin
gro
dat
Bis
seen
dire
ctly
thro
ugh
ape
epho
leon
the
top
ofth
epr
ism
.The
rang
ing
rod
atP
ona
line
atrig
htan
gle
toth
elin
eA
Bis
seen
belo
wB
afte
rre
flect
ion
from
the
face
sI
and
H.
Ina
pris
msq
uare
,the
reis
nopr
ovis
ion
ofad
just
men
tofr
efle
ctin
gsu
rfac
es.H
owev
er,a
pris
msq
uare
ism
ore
prec
ise
than
anop
tical
squa
re.
•Th
epr
ism
squa
reis
used
for
taki
ngof
fset
san
dse
tting
outt
hepe
rpen
dicu
lar,
like
anop
tical
squa
re.
Pris
m S
quar
ePr
ism
Squ
are
Obs
tacl
es•
Obs
trucl
eslik
epo
nds,
build
ings
,riv
ers,
hedg
es,
etc,
prev
entt
hedi
rect
mea
sure
men
toft
hele
ngth
,w
idth
etc.
betw
een
two
stat
ions
orob
ject
s.In
thes
eca
ses
itis
nece
ssar
yto
over
com
esu
chob
stru
cles
toge
treq
uire
dle
ngth
/mea
sure
men
ts•
The
obst
rucl
esm
aybe
offo
llow
ing
type
s.•
Whe
nch
aini
ngis
free
butv
isio
nis
obst
ruct
ed•
Whe
nch
aini
ngis
obst
ruct
edbu
tvis
ion
isfr
ee•
Whe
nch
aini
ngan
dvi
sion
both
are
obst
ruct
ed.
Whe
n C
hain
ing
Is F
ree
But
Vis
ion
Is
Obs
truct
ed•
Such
apr
oble
mar
ise
whe
na
risin
ggr
ound
ora
jung
lear
eain
terr
upts
the
chai
nlin
e.H
ere
the
end
stat
ions
are
noti
nter
visi
ble.
Her
etw
oca
sesm
ayar
ise.
•B
oth
ends
may
bevi
sibl
efr
oman
yin
term
edia
tepo
intl
ying
onth
elin
esu
chas
inth
eca
seof
hill,
the
obst
acle
may
beov
erco
me
byth
em
etho
dof
reci
proc
alra
ngin
gas
expl
aine
dea
rlier
.•
Bot
hen
dsm
ayno
tbe
visi
ble
from
any
inte
rmed
iate
poin
tsuc
has
inth
eca
seof
aju
ngle
orde
nse
plan
tatio
n.Th
iski
ndof
obst
rucl
esm
aybe
cros
sed
over
by‘R
ando
mlin
em
etho
d’.
•Le
tAB
beth
elin
ew
hose
leng
this
requ
ired.
From
a,ru
na
line
AB
’ca
lled
ara
ndom
line,
inth
eap
prox
imat
eco
nven
ient
dire
ctio
nof
AB
and
cont
inue
itun
tilpo
intB
isvi
sibl
efr
omB
’.C
hain
the
line
BB
’,w
here
BB
’is
alw
ays
take
nas
perp
endi
cula
rto
AB
’.M
easu
reA
B’
and
BB
’•
Then
,AB
=(A
B’)
2+
(BB
’)2
Whe
n C
hain
ing
Is F
ree
But
Vis
ion
Is
Obs
truct
ed•
Any
Inte
rmed
iate
poi
nts c
an b
e lo
cate
d as
C
and
D o
n th
e ch
ain
line A
B b
y ta
king
pe
rpen
dicu
lar o
ffset
s fro
m th
e ch
ain
line A
B’.
•H
ere,
C’C
= B
’B x
AC
’ and
D’D
= B
’B x
AD
’A
B’
A
B’
Cha
inin
g Is
Fre
e B
ut V
isio
n Is
O
bstru
cted
Cas
e -2
Whe
n C
hain
ing
Is O
bstru
cted
But
Vis
ion
Is F
ree
•C
ase
(a) I
t is p
ossi
ble
to c
hain
roun
d th
e ob
stac
le•
In th
is c
ase
any
one
of th
e fo
llow
ing
met
hods
can
be
adop
ted.
•(a
) whe
n th
e po
nds i
nter
rupt
s the
cha
in li
ne, i
t is p
ossi
ble
to g
o ro
und
the
obst
ruct
ion.
•Su
ppos
e AB
is th
e ch
ain
line.
Tw
o po
ints
C a
nd D
are
sele
cted
on
it on
opp
osite
ban
ks o
f the
pon
d. E
qual
per
pend
icul
ars C
M a
nd D
N
are
erec
ted
at C
and
D. T
he d
ista
nce
MN
is m
easu
red.
•Th
e po
nd m
ay a
lso
be c
ross
ed b
y fo
rmin
g a
trian
gle
as sh
own
in fi
g.
•A
poi
nt C
is se
lect
ed o
n th
e ch
ain
line.
The
per
pend
icul
ar C
M is
set
out a
t C a
nd a
line
MD
is su
itabl
y ta
ken.
The
dis
tanc
e C
M a
nd M
D
are
mea
sure
d. S
o,
•C
D =
√(M
D)2 -
(CM
)2
Cas
e -2
Whe
n C
hain
ing
Is O
bstru
cted
But
Vis
ion
Is F
ree
Whe
n C
hain
ing
Is O
bstru
cted
But
V
isio
n Is
Fre
eW
hen
Cha
inin
g Is
Obs
truct
ed B
ut
Vis
ion
Is F
ree
Cas
e -2
Whe
n C
hain
ing
Is O
bstru
cted
But
Vis
ion
Is F
ree
•C
ase-
bW
hen,
it is
not
pos
sibl
e to
cha
in ro
und
the
obst
acle
, e.g
. in
case
of c
ontin
uous
long
obs
tacl
es li
ke ri
ver,
valle
y et
c.
•(a
) Sel
ect p
oint
C a
nd D
on
oppo
site
ban
ks o
f the
rive
r on
the
river
on
the
line A
B. A
s sho
wn
in fi
g, w
idth
of t
he ri
ver c
an b
e ca
lcul
ated
as
und
er.
•Fr
om C
dra
w a
per
pend
icul
ar C
E of
con
veni
ent l
engt
h. E
stab
lish
poin
t G in
line
with
DE
beyo
nd E
by
rang
ing
so th
at a
line
AG
is
perp
endi
cula
r to
AB
at A
. For
m a
line
EF
para
llel t
o C
A so
that
F is
on
line
AG
.•
Mea
sure
AC
, CE
and
FG. H
ere Δ
EFG
and
ΔD
CE
are
sim
ilar
trian
gles
•Th
eref
ore
CD
= E
F or
CD
= A
C•
CE
FG
CE
FG
Cas
e -2
Whe
n ch
aini
ng is
obs
truct
ed b
ut v
isio
n is
Fre
e
Cas
e -2
Whe
n C
hain
ing
is O
bstru
cted
but
Vis
ion
is F
ree
•W
here
CD
isth
ew
idth
ofriv
er.
•(b
)Sel
ectt
wo
poin
tsA
and
Bon
the
line
onei
ther
side
ofth
eriv
eras
show
nin
fig..
Set
ape
rpen
dicu
larA
Can
dm
ark
itsm
idpo
intD
.Fro
mC
,es
tabl
ish
Eto
form
CE
perp
endi
cula
rto
AC
such
that
E,D
and
Bar
ein
the
sam
elin
e.•
From
trian
gle
BA
Dan
dEC
D•
EC=
AB
•Th
edi
stan
ceEC
ism
easu
red
and
thus
the
dist
ance
isob
tain
edin
dire
ctly
.
Cas
e -2
Whe
n C
hain
ing
is O
bstru
cted
but
Vis
ion
is F
ree
Whe
n C
hain
ing
And
Vis
ion
Bot
h A
re
Obs
truct
ed:
•Su
cha
posi
tion
whe
na
build
ing
com
esac
ross
the
chai
nlin
e.It
isso
lved
inth
efo
llow
ing
man
ner.
•Su
ppos
eA
Bis
the
chai
nlin
e.Tw
opo
ints
man
dN
are
sele
cted
onit
aton
esi
deof
the
build
ing.
Equa
lpe
rpen
dicu
lars
MM
1an
dN
N1
are
erec
ted.
The
line
M1N
1is
exte
nded
until
the
build
ing
iscr
osse
d.O
nth
eex
tend
edlin
e,tw
opo
ints
O1
and
P 1ar
ese
lect
ed.T
hen
perp
endi
cula
rsO
1Oan
dP 1
Par
eso
erec
ted
that
•O
1O=
P 1P=
N1N
=M
1M•
Thus
,the
poin
tsM
,N,O
and
Pw
illbe
onth
esa
me
stra
ight
lineA
B.H
ere,
NO
=N
1O
1•
The
dist
ance
N1O
1is
mea
sure
dan
dis
equa
lto
the
requ
ired
dist
ance
NO
.
Whe
nC
hain
ing
And
Vis
ion
Bot
hA
reO
bstru
cted
Whe
n C
hain
ing
And
Vis
ion
Bot
h A
re
Obs
truct
edEr
rors
in C
hain
ing
Erro
rs in
Cha
inin
g•
The
natu
reof
erro
ris
eith
ercu
mul
ativ
eor
com
pens
atin
g.Th
us,
erro
rsar
ecl
assi
fied
asco
mpe
nsat
ing
erro
rsan
dcu
mul
ativ
eer
rors
.•
Cum
ulat
ive
Err
ors:
•Th
eer
rors
,whi
choc
curi
nth
esa
me
dire
ctio
nan
dte
ndto
accu
mul
ate
are
calle
dcu
mul
ativ
eer
rors
.Th
ese
erro
rsef
fect
son
accu
racy
ofsu
rvey
wor
ks.
•C
ompe
nsat
ing
Err
ors:
•Th
eer
rors
whi
choc
cur
inei
ther
dire
ctio
nan
dte
nds
toco
mpe
nsat
ear
eca
lled
com
pens
atin
ger
rors
.The
seha
vem
inor
final
effe
ctsa
tthe
end.
Erro
rs in
Cha
inin
g•
Sour
ceso
fErr
orsi
nC
hain
ing
are:
•A
)Ins
trum
enta
lErr
ors
•B
)Nat
ural
Err
ors
•C
)Per
sona
lErr
ors
•Er
rors
occu
rrin
gdu
eto
faul
tyad
just
men
tsor
impe
rfec
tions
ofth
ein
stru
men
tsor
devi
ces
such
asch
ains
orta
pes
are
calle
din
stru
men
tale
rror
s.It
may
beto
olo
ngor
too
shor
t.•
Erro
rsoc
curr
ing
due
tova
riatio
nin
phen
omen
onof
natu
resu
chas
tem
pera
ture
,moi
stur
e,na
ture
ofte
rrai
net
c.ar
eca
lled
natu
rale
rror
s.•
Erro
rsdu
eto
chai
nor
tape
notb
eing
stra
ight
orw
orki
ngw
ithfa
ulty
met
hods
orm
ista
kes
done
whi
lew
ritin
gm
easu
rem
ents
etc
are
term
edas
pers
onal
erro
rs.
•Th
eer
rors
inch
aini
ngar
ere
gard
edas
+ve
or–v
ew
hich
are
acco
rdin
gto
they
mak
eth
ere
sult
too
grea
tort
oosm
all.
Erro
rs d
ue to
Inco
rrec
t Cha
in•
Ifth
ele
ngth
ofth
ech
ain
used
for
mea
surin
gdi
stan
ceis
foun
din
corr
ect,
then
corr
ectio
nsha
sto
beap
plie
dto
the
mea
sure
ddi
stan
ceto
find
the
corr
ectd
ista
nce.
•If
the
chai
nis
too
long
mea
sure
ddi
stan
cew
illbe
less
and
the
corr
ectio
nto
beap
plie
dis
posi
tive.
But
ifth
ech
ain
isto
osm
all,
the
mea
sure
ddi
stan
cew
illbe
mor
ean
dco
rrec
tion
tobe
appl
ied
isne
gativ
eas
show
nin
figgi
ven
belo
w:
•If
the
leng
this
mea
sure
dw
ithto
olo
ngch
ain,
then
,the
end
ofth
ech
ain
whi
chm
easu
res2
0m
will
bein
adva
nce
ofac
tual
20.0
0di
stan
ceon
grou
ndan
dat
poin
ton
grou
ndw
hich
isex
actly
20.0
0m
from
star
ting
poin
twill
mea
sure
19.9
orso
fort
heto
olo
ngch
ain
and
give
stoo
shor
tdis
tanc
e.•
Cor
rect
ion
isap
plie
dto
geta
ctua
llen
gth
•Th
eref
ore,
Cor
rect
leng
thof
line=L’
xm
easu
red
leng
th•
L•
(Act
uall
engt
hon
the
field
)•
Whe
re•
L’=
Inco
rrec
tora
ctua
llen
gth
ofth
ech
ain
•L
=D
esig
nate
dor
stan
dard
leng
thof
the
chai
n
Erro
r Due
to In
corr
ect C
hain
ing
•Fo
r Are
a,•
True
Are
a of
fiel
d=
2
x m
easu
red
area
•Fo
r Vol
ume,
•Tr
ue v
olum
e of
fiel
d=3
x m
easu
red
area
an
d
2
Exam
ples
Exam
ples
Exam
ples
(Con
t..)
Exam
ple
Exam
ple
(Con
t…)
Exam
ple
Exam
ple
Exam
ples
Exam
ples
Tape
Cor
rect
ions
•Pr
ecis
elin
ear
mea
sure
men
tsar
em
ade
bym
eans
ofa
stee
lor
inva
rta
pe.
Bef
ore
use,
itis
desi
rabl
eto
asce
rtain
itsac
tual
leng
thby
com
parin
git
with
stan
dard
ofkn
own
leng
th.S
ince
the
tape
isno
tuse
don
the
field
unde
rst
anda
rdco
nditi
onof
tem
pera
ture
,pul
letc
.,it
isne
cess
ary
toap
ply
the
follo
win
gco
rrec
tion
toth
em
easu
red
leng
thof
alin
ein
orde
rto
obta
inits
true
leng
th.
•C
orre
ctio
nfo
rabs
olut
ele
ngth
•C
orre
ctio
nfo
rtem
pera
ture
•C
orre
ctio
nfo
rpul
l•
Cor
rect
ion
fors
ag•
Cor
rect
ion
fors
lope
Cor
rect
ion
for a
bsol
ute
(Act
ual)
Leng
th•
Nat
ure
ofco
rrec
tion
(+ve
or–v
ecu
mul
ativ
e)•
Ifth
eab
solu
tele
ngth
(or
actu
alle
ngth
)of
the
tape
isno
tequ
alto
itsno
min
alle
ngth
orde
sign
ated
leng
th,a
corr
ectio
nw
illha
veto
beap
plie
dto
the
mea
sure
dle
ngth
ofth
elin
e.If
the
abso
lute
leng
thof
the
tape
isgr
eate
rth
anth
eno
min
alor
desi
gnat
edle
ngth
,th
em
easu
red
dist
ance
will
beto
osh
orta
ndth
eco
rrec
tion
will
bead
ditiv
e.If
the
abso
lute
leng
thof
the
tape
isle
sser
than
the
nom
inal
leng
thth
em
easu
red
dist
ance
will
beto
ogr
eata
ndth
eco
rrec
tion
will
besu
bstra
ctiv
e•
Thus
,Ca
=L.
C l
Cor
rect
ion
for a
bsol
ute
(Act
ual)
Leng
th•
Whe
re, C
a= C
orre
ctio
n fo
r abs
olut
e le
ngth
•L=
Mea
sure
d le
ngth
of a
line
•C
= co
rrec
tion
per t
ape
leng
th•
L= D
esig
nate
d le
ngth
of a
tape
•C
a w
ill b
e of
the
sam
e si
gn a
s tha
t of C
Cor
rect
ion
for T
empe
ratu
re•
Nat
ure
ofC
orre
ctio
nis
+ve
or–v
e•
Itis
nece
ssar
yto
appl
yth
isco
rrec
tion
sice
mea
sure
men
tsar
eno
tm
ade
atth
esa
me
tem
pera
ture
atw
hich
the
tape
isst
anda
rdiz
ed.T
hele
ngth
ofa
tape
incr
ease
sor
decr
ease
sw
ithth
ein
crea
seor
decr
ease
inte
mpe
ratu
reth
anth
est
anda
rdte
mpe
ratu
re.
•If
Ct=
Cor
rect
ion
fort
empe
ratu
rein
m•
=C
o-ef
ficie
ntof
ther
mal
expa
nsio
n•
T m=
mea
nte
mpe
ratu
redu
ring
mea
sure
men
t•
T s=
Stan
dard
tem
pera
ture
fort
ape
•L=
Leng
thof
tape
inm
.•
Then
,Ct=
(Tm
-Ts)
L•
The
aver
age
valu
eof
co-e
ffici
ento
fthe
rmal
expa
nsio
nfo
rste
elan
din
vart
ape
are
take
nas
12x
10-6
and
0.9
x10
-6pe
rdeg
ree
Cel
sius
resp
ectiv
ely
•Th
eun
itof
Ct
will
beth
esa
me
asth
atof
L,C
tw
illbe
posi
tive
ifTm
�Ts
and
nega
tive
ifT m
�T
s
Cor
rect
ion
for P
ull
•N
atur
eof
corr
ectio
nis
+ve
or–v
ecu
mul
ativ
e•
The
corr
ectio
nfo
rpu
llis
nece
ssar
yw
hen
the
pull
appl
ied
durin
gm
easu
rem
entd
iffer
sfro
mth
atat
whi
chth
eta
peis
stan
dard
ized
.•
IfC
p=C
orre
ctio
nfo
rpul
l•
Pm=
Pull
appl
ied
durin
gm
easu
rem
enti
nN
•Ps
=Pu
llat
whi
chth
eta
peis
stan
dard
ized
inN
•L=
Leng
thof
Tape
inm
•A
=C
/sar
eaof
the
tape
inm
m2
orcm
2
•E=
mod
ulus
ofEl
astic
ityof
the
tape
mat
eria
l.•
Then
Cp=
(Pm
-Ps)
L•
AE
•W
here
,Em
aybe
take
nas
,•
E=2.
1x
107
N/c
m2
fors
teel
and
•E=
1.5
x10
7N
/cm
2fo
rinv
arta
pe
Cor
rect
ion
for S
ag
•N
atur
eof
corr
ectio
nis–v
ecu
mul
ativ
e.•
Whe
na
tape
isst
retc
hed
betw
een
two
supp
orts
,it
take
sth
efo
rmof
ace
nten
ary
(sag
)w
hich
isas
sum
edto
bea
para
bolic
curv
e.Th
eco
rrec
tion
fors
agis
the
diffe
renc
ein
leng
thbe
twee
nth
ear
can
dth
esu
bten
ding
chor
d.It
isre
quire
don
lyw
hen
the
tape
durin
gm
easu
rem
ent
iske
ptsu
spen
ded.
Sinc
eth
eef
fect
ofsa
gis
tom
ake
the
mea
sure
dle
ngth
too
grea
t,th
isco
rrec
tion
isal
way
s–ve
.
Cor
rect
ion
for S
ag
•If
Csg
= C
orre
ctio
n fo
r sag
in m
•l 1=
dis
tanc
e be
twee
n su
ppor
ts in
m•
W=
wei
ght o
f the
tape
in N
/m•
Pm=
Pull
appl
ied
in N
•C
sg=
l 1(w
l 1) 2
•24
(Pm
) 2
•(U
nits
of w
and
Pm
shou
ld b
e sa
me,
bot
h in
te
rms o
f N o
r Kg)
Cor
rect
ion
for S
agN
orm
al T
ensi
on
•Th
ete
nsio
nor
pull
atw
hich
effe
ctof
pull
and
sag
are
neut
raliz
edis
calle
dth
eno
rmal
tens
ion.
Itm
aybe
obta
ined
byeq
uatin
gth
eco
rrec
tion
forp
ulla
ndsa
g.
Cor
rect
ion
for s
lope
•Th
e co
rrec
tion
for s
lope
is re
quire
d w
hen
the
poin
ts o
f su
ppor
ts a
re n
ot a
t the
sam
e le
vel.
•If
=
angl
e of
slop
e•
h= h
eigh
t diff
eren
ce b
etw
een
two
ends
•Lm
= m
easu
red
leng
th o
n sl
ope
•C
sl=
Cor
rect
ion
for s
lope
•Th
en, C
s l=
h2
•2
Lm
•C
s l=
hm(1
-cos
)
•=
Lm V
ersi
ne
•Th
e C
orre
ctio
n is
alw
ays s
ubst
ract
ive
from
mea
sure
d le
ngth
.
Exam
ples
Exam
ples
Exam
ple
Exam
ple
Alin
ew
asm
easu
red
with
ast
eelt
ape
whi
chw
asex
actly
30m
at18
0C
and
apu
llof
50N
and
the
mea
sure
dle
ngth
was
459.
2m
.Tem
pera
ture
duri
ngm
easu
rem
entw
as28
0C
and
the
pull
appl
ied
was
100
N.T
heta
pew
asun
iform
lysu
ppor
ted
duri
ngth
em
easu
rem
ent.
Find
the
true
leng
thof
the
line
ifth
eC
ross
-Sec
tion
area
ofth
eta
pew
as0.
02cm
2 ,th
eco
effic
ient
ofex
pans
ion
per
0C
=0.
0000
117
and
mod
ulus
ofel
astic
ity=
21x
106
N/
cm2 .
Solu
tion:
Cor
rect
ion
tobe
appl
ied
are
(per
30m
tape
leng
th)
Cor
rect
ion
fort
empe
ratu
reC
t=α
(Tm
-Ts)
LW
here
α=0.
0000
117
/0C
Tm=
280
CTs
=18
0C
L=30
.00
m(L
engt
hof
Tape
)Th
eref
ore,
Ct=
0.00
0011
7(2
80
–18
0 )x
30=
0.00
351
m(+
ve)
ASt
eelt
ape
was
exac
tly30
.00
mlo
ngat
200 C
and
whe
nsu
ppor
ted
thro
ugho
utits
leng
thun
der
apu
llof
9kg
.A
line
was
mea
sure
dw
itha
tape
unde
ra
pull
of14
.00
kgan
dfo
und
tobe
1800
.mT
hem
ean
tem
pera
ture
duri
ngth
em
easu
rem
ent
was
360
C.A
ssum
ing
the
true
leng
thof
the
line,
give
nth
atcr
oss-
sect
ion
area
ofth
eta
pe=
0.05
cm2
.The
Wei
ghto
f1cm
3of
tape
is0.
0087
kg.
The
co-o
effic
ient
ofex
pans
ion=
0.00
0012
per
10
Can
dm
odul
usof
elas
ticity
=2.
1x
106
kg/c
m2 .
Find
the
corr
ecte
dm
easu
red
leng
th.
Solu
tion
:C
orre
ctio
nto
beap
plie
dar
e(p
er30
mta
pele
ngth
)C
orre
ctio
nfo
rTem
pera
ture
Ct=
α(T
m-T
s)L
Whe
re,α
=0.
0000
12pe
r0C
Tm=
360
CTs
=20
0C
L=30
.00
m(l
engt
hof
the
tape
)Th
eref
ore,
Ct=
0.00
0012
(36
0 C–
200 C
)x30
=0.
0057
6m
(+ve
)
Con
vent
iona
l Sym
bols
•In
am
apth
eob
ject
sare
show
nby
sym
bols
and
not
byna
mes
.So
the
surv
eyor
shou
ldkn
owth
eco
nven
tiona
lsy
mbo
lsof
som
eco
mm
onob
ject
s
Con
vent
iona
l Sym
bols
Con
vent
iona
l Sym
bols
Con
vent
iona
l Sym
bols
Con
vent
iona
l Sym
bols
Ref
eren
ces
•El
emen
ts o
f Civ
il En
gine
erin
g-B
y Pr
of R
.B.K
hasi
ya•
NPT
EL•
Inte
rnet
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site
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anks
