levelling full chapter with examples and questions
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L e-/€L Lit/c
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e-/. va h an Q: ! /en Taot
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f*t. Hr /.-/ac'r| ,1cc
/tc'r.ts at 9tr'cfl
b .ga>ne cla turn And Ak'o )'t
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/Dot nb '2"1 P.r/)e,1a(/cul4f to Z4e
3 ect n a tc<ral e x4/4p Le /o. o 1. u
6ny <u//a-ce P4rLrh-l to t4e rn
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/.eVeL .farface,
Levet ltrte t Anl .l;ne ly;a-1 c'te leL/el 'g
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/lozi Za,a ta-L totane'. fb l3 t4e f'laae la,tjen6a( to /eveL s L/J/ac-. a'
an/ /9at4'c-u-La7' Vt ar 4 | uznler can
ha) zaq tal (t n€- : Jt iJ the- ,/t ,te
26 2v 2et7e'edi c+(ar to he 7/a'u5
Veqhc*t LUte': /t'ae normal e'o
4.L64m C4'4 6e acttza nd 4)' r'
cbc'
ttuo /'t ''
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a foi'lt' /no'. d'l
a6ave dr be/;d 4ct/u m Lze-
ruo ? r1t41'J ectiu? /iner /4 cteftzu<L
fhs a29h- t'J 3tn""o/f
r?i c-a'sl
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" ryhb .ol ltcJes af ce a- y'ar at
geA-Jo'lJmoasan<oo)e'/a'/oYP&4iodot'move"htan/?)'ca'i'-i
2. /a //ed ?7te ar? 'te.L /z?'ec (r/?. s- I ).
( noa z tt pakis t4e 4) al as c DKidercd
fndiq. ouJ vte44 sea .lev<-/ 7/1
(Qale u"/ / Jn/;a),
llat/)tn 2-71ea/t re4 ,/c lel
ld zlcte,rztt ne {eva h,
!qdia y's ca ns ider.d a.7
/Oa r'4 er' / 4
:%m6-7,
6ea"l rrl" rk ( e.2 A 7>o'tot of kzaun e/evahon L)it| .refe/eytee 1o
do/un 7J c4//e4 a 5e nc4 /ra7'< , 7ho
ith ,teference +o A ( -6encl rna.4,.
a/eun/>?v e/ P.tiEeJ are dalernttd
/4e hoJs 0t6crene tret4odc t>r/ deternt,ti,T
P oro t-, a,Te -Y^a,4e/ft a Zeuetl inj,
,} '77)J ,, o ,4afr/ a oy Znditeet ./eo.e/h,"Ur
r,) Dt r"ct 6/ spi'.ib /euc/linr
) 8 A'roytl ekic /cue//in .: Sarometer tj an , r(tyurrpne used Xo Treasuve,
AtmotDle,r'i L /Jr'cr,r u'r'e . E a,ted On Ltmos7/leziL /precsare /'ffu"'.rre- ie,Ftlteen
Varloa! /Oat
/, ts the e/eua6ans 4.te o tet-,a)ned , ,9i rae tee. ae,4 a.roh efl'a
/9/eJcu/e c'5atytcs /torn (i''t e lo i'me at a gi r'e. //a.2, /4u' met4. d i,s
nAL 44 a-Czu,Yaee mettod, jt can 6e z<-scal )n case tf .r"eca,r4ir-j,lsarce
-<4/ve/s plefe accuv4crt zt zot re,llrd
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'rr&no n elrta ^/e reltan,'l -7hiJ ti t4e Ar6.est of de-/zr',1taio7 e.leuahu,l
Oy' ?d.1ts 4/ T4casurl2 'loli 2aafal di,ltdnlec (tnd y'eyllc.l a nj'te,t '
zflakin3 Lrle of trrg,t o me€trc c-elah'ons e./eua.Ao+t Can be dcfermrnet,
1r) E/feee /ewe/t;aJ t -fr1 e4 /.r mectiol a- l07i?4nea.L s,u rira.:e is eclabltJ Acj
by' a 'gpi rfb /eveL e.nd lotdi^t o- V.iet.aL ,.SzaLe (.etaff) at p/ac c.
OU iCr'E o.fcqafi64
"/ 4 /Aoivtb iJ ,y.e?ai/e a and a.t g. t4. the d,72. -.n.c r,"t
e./e Lr'ar|'ofl 6efU142a /ao;tUt 1.r defe.rmi'ae{.
7 Al€ r4U.4 E^rr U€€O Fo4 LCUFLL| 44
' ot,ect /"u"@ 6y u-rrn7 /a/hary
.inttr umeq bc : ) Lcve I
ii) ttYa|1"'nf €dof f
i) Zet.Z ! .rr? aia atjeoe a7 uc/ 't1' e /e ve( t'€ fu c1eae an ,4or/ zatt e"L
:/rne t/ .e(thb. 7t/ov'm a/17 a &vel e ant/rec el f o//a tti46' 7ar€<
e) Aub$te €ute to 74ak<- ,:,.t r .Liae .'/ t)S 4a 4drt)aaeaa .
.) Le we //ia3 lce4 (tr;botd ) /o 6rt n1 6ub b Ct- 2'72 s?s ceqlte
O/ ru'n '
a) 'zw7"a <band
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a tx1 afe zl;ff e1'en? ac//e of /eu"/+
" iS Du^?Y /evaL t) wYe (v; /"u'l-
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t) hunpy leuef,: p*n77 fete( 464shfJ of
^a
telcacoPe 4)htL4 c'qh be
.roto-bed abou& rre-rtlcqt a-xls 1'r) g6od. Zt 2'r moante-.l ovcl
6ase tri6abch uJht'ci Cln<tsb of /hr.e 4r' fd.Lr +oat<.'r'cu)g
t)hrch ate- e4aed flr leLre/lfny, 7e kscafe ls aetach ecl uriti
a 6+66b Cq6e 9d €Aa? a(xi.r csl ce/escope aad a'x f'l Of 6a'6bte'
4ub e 4,/e Pa-ra ll el to e.a-c,5 o t/tet/,
e/euahor (
3. I -3
bepne
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eakl n5. ahy ./e: a<li nf , '7)ey are as
{z),eei+y up t4e. leue.L
Itt) Le we//ia1
[ttD E/im inatz dn d/ PELTa //ax
d ) s eht n:l t+p t4e /evel : zht'c )ne/udzt //xt49 zhe
qd1'uttm en€
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U) L:e!:!intj
level the
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a-b e,ve-,,/ ,re t <.27 o7 t nstru
/r-cteA ba/oaJ:
lev-t la trtVed and
4r-e ea ardl'us Ee-d
o/ /eJc 7$'r a.V2ro,<i mate y'evefnng
" Aag-r
t7i6al<h ?'! >'/1 ho ''t 2aA ea-L /oosi4oa
A7ee.r .eefil'ng +p of l<ve!, next ove.ralt o4 ?6 Xo Pe,rect?
2'n€t rur4e4e 4!in? /@oe ge-fca)s. Z,4e- fa //eui o3 Pre.-?d4fe
S c7'ze .1e4d :
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tr>
/37/nS A-// erfee fa't se-r-c &tJ to the ccnlre at'.fu4
Rotatc the eele6c6/oe and 6.ri,g tle 6abble Lube- pana/te,t La any /"-'a
of th+ foob 'lcneut < ,
tl) 7kr n ehc- eL,Jo fdot < c'r'cu)s e't'ihcr ln onuard 4/; rec*'on ol due'/hr4
d.lrechbn /il/ thc 6u-b&e edmes b 14e a-enter'"
- r '4eaeat
4h e a-bate
ZL,e leo+/e /o/ e//
leue//24 /aosihbrl '
Fd{ /ouf ,t C/eaJ 4 e4d :
gCep.( Zui.e or thr)oe tz?/ t4te b-bbl4' 't'ctta' 4c
a Joo pac;h'o,s: ' ludd 64a 2'a<t>'<uete 7t '4
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, 7u/a Cln €e/c-sctF oJ
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to Taot <: c icrtlJ @ a.l @
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,
2o ba,€e t4e le/escdf e 4/td 6r;nJ tne bLLbbLe t cz^be- V't2c'1/ic4/af
td P/e/i,.t" ',/"a
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4. t,) 7*.n the t6: /e5 aa2"- y':ill bhL bu66tz tctbe ?'e P4"a//c'/ ae> f eot screus@
tv) -Vurn €he /oat €c'Tc./Js '1'r12,.1ar/ clr a&t uard €/'mulC4neousE €l// tae
brzbble eom4t to 4he cenftL.
,) ReTeot eirc /oaoce<S Au;Cc al Xhflee €o ehac t/te bu66Le /e'qairs
a€ e/te c e>ttwe /aa J6o" f e-rr h oo f 4e/YscaPe.
Nocu ine y'nsETumcnb rc t'n /evet Pdsit'/a4 '
6tl E/r'mt'nat t'ort of foroto, : P 4'ra-n e< )'.s Ene coad,t;oa ar)ti 43 u;ien
not 1'n f4e P/aae ! the caoss
a.cc.L/aee- €ftAhaj ' -ft can 6e
*4e 2rTtajc f,rfned br, t4e O6,/'cc,4/e /3
har'7g, para//,2< .sla,// 6e 4e '/n
oted fd'r
done ln /a(o.,ias tu o €bef 'e .
7u1,4 t4e /e/e sccoTe
tD1ite //cr o"n ftant and fbeus Che eye- pieee
di.r+/ n c t, a4) a:tg-^ary' Y)stblc -
Fa cu's siaj tlt< 1)7 telescope 'rao34
*u'rn the adj4,(tt 43 €creu t1// &v recz,,l ia2s
10 'cky o{ Ao td a'
t/'tl tie c-1-aJg hatfs
etre poJihra * €toA
a.te cl eanQ rJt stbLe''
an de f u"/'f oJe lloa' dh t'c4
?! a /a 'c,t/'/ cd z'rt xa "7b //'r'''/'ut
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In 3 eodlehc suttlcf 4 leveL /t're ?"J a- c"t'r,'t-d s urface'
7.ru t <Ve-a& a1 e4e d,'ff erence z''t e/euah att etf tato f 4tc u 1:4 a' a(iffcr
in e/e,/aa'on %, ta.to ..'.T 'te! /4sst43 1,4''a414 taose Toi,ttc'
' l/etoeULt,/ 2'n Vola4e lcuelltAX t-4 e ior"/2a,rb-al.2/ar- /Aa'sJt
t4'1
*l1.raq3th a- ,ooint lJ eansiLered a< /eveL ,/.''ae t 't
q9/ecflaf c47'va/1a'7'e
an d ,tef rach ou e77eet<) 4J 2 t ?"9 qatrh aaltc f ^'' 't,"7 'L/) ta'ear' ' ,
74e 4drts^a4eal ,0laoe 't,t i?o'r n t'd 67 a' leve-led znc/r4me4a
AJhichiJc4//edflaneo/'ca//i*lat?on'7he'rta6'z'e'az/;zttr^satetaAen
At potnts 6,.tlto@'t d,'17etenc'-
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e'/eua6 o'1 t'€ r
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and /' 7V "'t€
na- t 4
e,t'euan'ort ea,1 6e dzZern ined
EA: ," * f2 t3 v'cn"t'i t' d lo clelet'mt ae d'
- 19in".6ot ;./1 a /. t,12 Aon !er5"e44 4 d'-l '
;,,inu 5ot in ek)osu, leL,,eea 4 ad /3 '
lo*')rrir
vrnor+ /4e <f,aff reodiV "" :'-';:
- -=- - - - +- ana 'ltaff o'eadti at'6: 'z "t
elrt ,,'*'jlt'";
-1"- - J-
- -5=-- - - +- ana .tcarr T ea&g az-B'-zn)
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/ €,=2nl EhL'-a"ho4.dl :': = i -":i;^'
/ .- =t"v'a4/a la = t'2='lm
6
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b')3 /m ae'/oat A '
,?e eAa als
l,sve I[r'n3
eyf e 's .
D/,/-. ce /ete///nJ : Oe?<. dig
)egr,"ed 44e d i rea a' le ve/h''7
Ot77e'ren tr z'C /eue //in+
f 7df"te le,/u t/' n7
C.r"o,sS - sech^<t't ,/Lzue-/t in t
,Re ciTra cal /e't o //''2
pYe c-;s e Leue/li'a7
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a,) Fa c ct < sing
5. 7E<.//15 AlVt /+eA R€VA 7/aM'q
S;Eattd4 ! €tati 0,1 is t/te Tsot
rtt 4)hele
r'aeai,/e d 4" 5e aleter'r1ine 11 ' tt
(,t) f rt t'cr- mediaae {Uh€ ( f 's') A// -f&ntc laken
in be?vseen 6aaL ctg4b c<a"l f"re <Qhe frou
Ca //e-d ?'nbct' m e cl, a,ee suh tG ,
P/"1 ' t<, Lze/ad4.a/.J ha
,/l , Crr/) S;y'//
tne €tahL 7J he/.] z4Jhoe,t ztle,,ru6o4
?:s not t4e /2ar at hl )e-re leueL
on fei[ ts af utkn o rt e/euaha't
u'et,V a7 2'4 s lrLtmeq e Afe'
)nar/ b c
ts ke-7t,
fnltl.uynene (r'f) | At evety ,rct cf o7 1natru,ncltt. thp-
he.,g4e' ort /43trur/tcnb ls determiaed Q/tt lefelenae ld 'J:2 '4e- dctt'tm
Jb z ndicatec the 7l,ano a/- c?/i;*t4C1dn aboue ?'ef el 4/'ce dz'tzLm .
(i,D
'r'r'= '<L -/
12:;f * <tzv,t )-e,,di! an a,vt,
Oack S,J,tt (C,s-.; : .ft zc t)e ,t€^ff rea.d,a3 Ca.ke4 Orl ?a/4t ay'
<n0LD,1 e/euaAon " /go,
o/. 6/ 4attu4 e/evaho') z< 8eoc4 mark.Th let.lt t44/
is taken 4a delermt4e the 4erytt a7 7',tstzt<ntzne.
Qv) f are eghe (F'.9) i 7t t t4e k..st |-ead;n3 Lakn f'tom cL €tzt cr
61 7 43tlt)ttlent o/2 /otot y unknod't eleuoi<tn - . 7-4tv /coitt 6 ezoacz t:h e'
/tet ytt oy' 4nouq e'/eua6'on for ne^t ,seL 4 d/ instlltucaE.
(Vt) Chan4e ?.))nb (c'P') at '7-urni!! /3d:4t! i2 P') ':' A 'rct o7 Ves st b/'"- rez'd' "7s
(Q.s, r,e, F3) a.re xaKvn f'am " ,l"tn^fr,T i'"7,7"if,;^7r."r;.7
? ''t'
/ok"' o n /4r t F' S '7-4 tt
f"r,t t ,
Dif/ c'rcnttat leueJtiqtr
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7he //J 1^o c< '99 6f
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Ex:
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leduzhon o/ leuc|a 6St 4eigae f Jn'c|'Tam<aL- (//-2.) rtze/,ltol ,
J /o/so n B,s, I z.s' I n's" /.-z I R. L' .4-e,n or4s
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t'+ /ol ,1o
s 2"1 lot-2oo
s 4,oo I O6 .3 o
2 E.s= ,9'1 tF,s--+'t
fiit64meh'e e^ec* ! 2 65,.'' lFs = l <'L'a FRL = O'3o
prdcedure : t) a#e' eae f/"'"c 'fea4iU La/(cn an En i,t 8'S' .>al/'n 4
- €'ber'at'
oC er leadi,Lt! 4a4e tt fiom set L?-l irt I'S ' .alan4 'toePt
latf reaJi'tV
En te.r la.ct' r' e-a.dia? 1r'6r4 t ef uf - |
z/ sh;Vr 9Ae- lcvel te
Q ro ea-teo'cete R'L' of Por oa'c de-fez'"ti 't'e Aeig'6t' oy letruu ctt u-
of' /r,r"" €ecu/,, //.r = R,L. ts 8'4 + sta'++ '/ca^itf on 6'n'
=
/O'aoo 'l- r'2 ' /Ot'2oofl
/o eo-Lzc+Labe 4.'L' uf 1D 9laha* '5 u't e' ,ai$ ls rtFs
R.L' = 4' r ' s
'*ff
/cu'd'E a'b +4'a't I
Reloe-a,t e./i'?- pr'o L4du{e
Atubhnabio c'leek;
28,f ,.-'' tF< =
4"t ,9 ez>orrd <et u/ '
la( e- RL La FRL
,Q ts€ & F$LL .nEToD o'< A€oucr^'/a LEt/€Ls
jq t4 rC r'nc t4od d- 67.-e,tce ol /eue1 6 et".t een Ct^lec.th'Ue Po)4 rs
is fd u"ld 6y cowytariaXt tae ,eca-l/. a'ea-d inXtc on At e- 'la2o pa)rtk far
'ftle .3a- e get-u? o7 tne z'nctrum enE, '74e dilScren.e, 2r7 €t.lt 'rcaAa'r6
,.lqeadia!, d a nexe '7'ea.1i4lL z',t 's
ma-lle'r ar /aryet
he vise Ccnd 1a// 1'{ eqcted t4 'lL*-{ leveoh ue
ol 4.t71 t"o 'reduced /eutec d/ nctr Poin,r tt
in nex t Fre 6/eu .
7. P
Qt le aaA fa// znethad 4r"f R , Le.'/Ld/1a/.s44
/4 aiJ,/ c /u , .t t/f
st.A.n ,t1.3 .
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r<, L. 4e ma rks
8k /'z /OO, O ao 6. n.
()"6 9 ? 260
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+ t.8 o,8 I9,r00
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t 2,2
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g 2,i 4'7 /0/ '200
s 3'O 0 0'9 /00 300
t 6.s. 4' + Fs'- t'i LR,sc= 3'3 5F^u =3'
o o
AqiQtt maA'c Checl. i f6S - tF3 -- t4ae € t€all = '-<L
>1 7'4/. = o'3m
p.rocedure : ) staeton I lt /ad<t 6'1a't €taAot 6 m 6cca'tte st'24 read'aV
ae .gtn. I ti m6/e tt'an cbaff readint ab a m iy (z'"'/'>) = 0'8 Fo4
Fi,td eat- 4L ae' 'rl | 6f 4'duc6at
^
<-L o/ a'/l q 4/4ou't 7l*
,'. R L u/ <e"'r '= /od- d'9 --?1'zom-
, conToare /4e staff reod' aX's cta stahon'c O ^d @' K"^a'U
a.e 6 t< > 7ea-diY :' O ' '4.".fo'"
?'
.', RL etl seto-rz o) @ = '€c o7 < aoa:ov A -
. o) C a mlo a'v'' ttt e 's lof f '/^a ad ia?"s ae
,read,'ttr 13 3'"?"1 tia't ',.t^fl "oa'^l
ae @ 4 f:! -'t's)-='o' ''-'
,'. RL of rta,,bvl @-- 'e'
ol '<t4^o"' @-o'i ,=.'-1 Ao^r'69,.n-
1) conror" dqe ,st^rc n.o'' nFt
r.:.,u -r'3n"ri
-rrorTo,,.onu )-/Je-. -
cta fl .-.oainy at (Q is l '/b&f/ rea-cl'^t ot v '' '-
hrn.)u</tl, et1 rrce = 2 - v,"e 1
?g',e +o'g= q1'q'n'
,., R. C . tt1 s €aA' o,t, @ od@
6) e. @ i4/oa''e o t @ ,', -Ze )r' 'r/J e
-rC a-ff 'feadiY? ot @
J'Fa rr "*
fu,:;,.g^-"li|--= l7;;',;n:::,b I d.7 -- I s. ? +a,7 = //' / 4
n -74e''e '7! chau'1e' "t. '"!u-"'tt
ak stahoz@'
79 c 6'4/44re xhe '9
e''ft {ea'diy n"* "efe//
I's ta'tc4 a-t '!7 z'J
j S ' at @ &yvat ea>' /o ra cess tz't/ a-// Ctt< /<-<zh t"- *<
CorV/oled . Ai'/e 4{/ eh'4 a'bc <z4o'P '
t 49 '-
'FS " {<tre'-'n t FaZA -
LR'L ''' F<U
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/,526, Z'zto) J'/o , 3'r,zg Ente'" tze-
4nd dct<tr7i4e- 44e R' L' df r'P/'
t
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6 een zzl ovel aAev" th rd., ,E i xtlt
2.?fo,3'tot, 2,sso, 6'76a, /,/6s-
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,.. &.L ol 4 = tLr'sc-e-o'd6t
- ,/l
18. /l/^eri th. leue( d)as aC P , A|e afry'r.4 t alifferena, t,.t e/evz, b o4
-- d.s2? n
-/h. 4iSTctence d, eltv.rlot -- Ot g|D t m
{,rrar ,'n @a<ezuq.-io,t
= o,?2+ -d,go.t = o./2dm
-//re Lbove en-a'' zs do<'. y'o ) cz-vrzolt'z'e ancl r eftachan
t) A//iYL'4h.4 <'r"/v'/'
&at en Ar d4e 1" caiu4/L. lt a4l rf,.7chua = + O, 6 4 ? m
Ca //i.ua A ob e'rloT = a. /23 - d" dl , -- A, 05* m
Ca //ina t fu't e'r'"d r 1 r' €a
-j's sO ?r1ol/ned tlaC- 7C
44/ehc/ fai'1t X4et'e 5ir
"
/Lhon dhae 2b ? s - //e /1cc
b7 an a,r'?o4ne- O '4f1 m 'tn a dtJfa
&n 4 = 2'ot?iro = a'oaoo63'!'
SrLe ta-n 6o"= 4'o0029O1 ,,
{= 59!j99 =r/" faTctod)
2to 7
..'/e /anKs a/
' ^.;nh-s A au'1 B on d//aJt "'
-,?- in ,/eo'e//rn' le/aven tato paink A aul 6 o7t '/ /
4^
-,-,",- l,he /euet t<)a' '!et Lf neal rt'.onl *:^-":::-,3*t::
ra /iuer , l,h e ,{.uec to4" '"' "7 - lttrl
'
'n'^' ">n
|and A
e te,tTech ve rea)taX's fl /
e '/
;flerfl ee aV /etre( delueen & 43 '
I
Co/uho'a :
"frVpa-rent
zl lf ,.cfet4oe ,fn elcva62, 6e.1'aee"r A a"4 O fzeu"l 't"ar n)
: 2'860 -/,2a5 = /'575 n (A i';'? h'gaar)
ht'len t4 - leuel t's set n e4r O
A,op4'.c,4t dith'cre4@- 5ctateel 4 a'nd 4 2i
= 2.22a -d'640 = /'340 m (4 3u2 2,?/i./ )
19. 74. dfV erc n c e 6elu.e n e/eua Aort
/'576+) 3co
2-
,/7r/' <. Cce/4dttra-art a
ltoD ,t C tt/,, <:i Y/7
a/ A atnzl A
= /4(tn (,+ 6 ti"6' h'3iet)
2 -/ttto Tointc
74e /ar/ou tx7
LcvcL ee
P
7le eTlor i4
it| /OO tt . a al cu [a te
ar)d t/Le ref'racfi'o4
.<o la t't4 1
Gut t'e
,Q a.nd 8 are /53o m f{rt' a ctaJs
lccf racaL le,tek ale taken u it,
'l eadi'tt't dn
A"B
2' //5 3' E lo
d ,f/o 2't5s
a di.le li vel ,
one I eueE,
tt) 7/a. d;ff ''re4zz' i't eleuaAo't 'lehtetn 4 a44 d
e @=/'545m
2
(tt) Error duz ti Cotrva-lttte- = A '
,'- l/v4e4 ?4e /eoel z's a't 4 ,
cor
' lat|.re C"l latte cnl ot ottz' /o cutua/u're = 0 '/ &4 n
C,r: Mr,cch'|, &/'z'e|+dctb, o,oo*_ rezo.0,o(lL m
ct: . co*,e',5bt du-e lo ca llimaA'on = -7; n'-
-
c.'r,te cf.d 'r4o+/ teaditV a71 B= 3'tl0 -(0'/?+ -6'a)7d'oilZ
= 3'(872 f C'r
Tvuc at.fFcrenLe' la 'leuel 6 e/a*eo hanl O =(3'<ttz+ct'2'69)
- /t"fz>7 *c'r)
tAe Ca/lit14hort a-4/u'ee''en kr a/ tne /euel '7'S -d'90+n
t4e /zae d;fference a/ /zue[ 6 e'4^teea tt anl B
e.qaal h /'5|5n
/"62.vL *Cne/'516
cr- 0'023 n
OALAi/c/$e A,e tro<5,9/efl7 a1d 44c< "I9HT O/s7n,uc€6
I, Coue f
y'eue/'i'4f 6y b a.a-ncin7 6ack: €gaL- and fitec<St4b
dtGbances CAP /oltour7 ?//'a/c J?et€ U/miaa"e*I 4?y' c'2' *u'e'
di/felenct- t'n ele tah'ou lelalee n tato 4oa/n
tc ok db b-/4zzl
i) e,tnor alcte lo q)ot) ?Vratl e't'|J'n g1 /i4e a/ co//iaah'o>1 an<l
4(rk ol 6uAle 1qbz.
;) Ev'ro7 aba- h earuatule o7 earh
', 6rro'r du-e h -/ef'7'achbt a7 almo<p4e"e'
20. i) /*ro, due $ '1o'1
' la r'^//e//3 4 E //'e F
''
I"r"ran t'44 @l €tJht
"r
t rtc/toed 4zuta'td
")'J, e , 2'd^ n on f '/a't t/LLe ha''Jza4cal
tU Ae- et"l
a3 6laut4
LxG al 6ab5O' l<54
in'fu.
.J
'Dt
Tlue dilfcvence 7'4 e/e uah'on '5el"teen A
H'- (-s) -tzz-/2)
= ( zz,-lr)+(.vr-g)
gut 9r= D, ta't e a4a
'.r=
O:'1" O
rA 6act arjttc o* f '94it at' c tan'et arc be'lanccl
'tf Dt lo, = o
,', H = 6tt,-zzt)+ (at4ng -2tane)
.'' lt =(*, -l') "'
ca'l/i'4al'o' e/'7'2'' 9e8 au'tozzafi-cally caace/'/e4'
.t €rror alue to ^/efa c+7'o/1 62nd e*"@/7fu'>a'sb1. '!i^2 E r/sne
./ -.
. --
Acu.aaa 1i..2 q A/tne
dee h e"nl'
a
,r 44e dl rle 4 ceJ
1te*aet>'o,1
are -zal e- €nzz4
4zcnncz;.tae -/eH
Let rat 6 nz : 4arre cA'o'vt to 'le aV7e'.d 1fur' m eaJk'r'eal 4eadiu'22
'' due rb Oombitled 2'e//4cA'04 and lotrvalune
,1 et eutaA uzt 6Jl-"'n 4 aul 4
7he dY4 eren ee .i
H= (ho-2,)-(nt-zr)
/,
-- ltta' h 6 ) - ( o't tzze o",' o' e672sDr)
4 4 =oz
ll = /4o -46)
€&4t aal frYe.
at.zz lo Cortlbtqc.d
4a f,saa h?a l/y .
fi
-If Baek
XAe e'/""N
14fl Ce //e4
,r-ey'q'L4h'a4 and
21. m"
c u.<uAru4E t+ND RE'<'aa 7/a'1t:
f-./, <' 4:ealadia.-r.c{ 4 L
/)6D, c/v , .9 t//7
,]t any /zrh'cu./at' /coitt , Aal zenbL
lr,te e P €anje,thal b tt. 'l-y"l Li*
Qnd 6 enee art a-naunt ol elrdl - Bc
aceu.$ i4 /e*//igr - -748 el'mf $ dLe
& c../vatuae al eotlbA atd it
lcX,uz'reg 4y Cut va/r..'1/c. Cd4'rechb4 '
ft t3 gr'urrt 6y ;
C.= dtd-/f,17,d n ---r3;^
(- '/e )
d)her'e c": 10rtaa60n /or c.1, u e/1/4e
d. : D'ctartce b e/at e en 74 q nusurcl
tn kmc,
Far't,er due eo /fe'a"chbr1 df aemaftele 4orizorbo! tin'"-
q eUhL deviateg z'4 dowrt uar/ ditechbn 4nd
/
er"To y =. DC aAWnu-bh
74k errdl 2's Ca/led ,/e/v.ach'on eTTol, CaY-recbb4 ,/or reTrach,on
hili
2":t""
:--
liat of
,43h 6
?',f gt/e,1 bY
7he f t nal
ety'o tb,r.sect
Cr= 0'
d: Odarce
eoz^re c.Abn
o//2t d: C+rt)
6elAc.deen P 4lQ
and "ref ra./t'o ,t ca n 6'
F/nd er, e eot/c.h'un
dua*e. aA a Lzao m
'r/
/ay' 4uyvaA,e/e
c= 406728d2 ^@
/-ot cr,(Tualu4e-
b) 3 '€4 knr .
A
a eorfe c66tt fbr ct't tualt"re '-
,/
5
4 orre c 4'o,a /at ruf'rac6'an =
b> Ca'r'r c.CA'ot *t c c'vualv're -- O'O7gt/t x3t'f
= O'18O m
ea,r,reeA'ott /ot 4e/'raett'o't = Q' Qll2t (o'+ra)-
= 0 ' /4o+ o
and r/ra-eh'on /trr a-
o , ozeq< d
z (d ;c ;n *-t)
o, d7e +q O' z)- = o'3-7 I ? 'm
o.utzt JL = 0.6//2t x6z'Z)L
= a .5+25 17)
a
'{o
I
...V
%' ,) o'6!erv e r .rtartdinT an ttie de"'t f a' 'sry iusc "ees
a
It4tb louse . zhe bf 'f dte li6ud Aou-se' rc 4 zn a6oue *he
S7.a lcueL and the ,t"7ac f ef
" obge-ueti e7e tk a m a-5ove /he-
tea Levet , fr,ul 4e d4ba'1 ce of dte a4'seruor -futw eb- 4)g; ttz'Qause.
.s,o/a6'or1 !
'-
let A: 4o'ct'hou
Q,: /at;ho"t
,f bP d/ a36? taac
ol cf e o/ o6,te. vq7
lee 46 6e eaA'al lo (4dkr/' JcLr./4C2- a.t O
22. 7a(n<4 '/'</'r4ci oa en/ callahte
c*c.t dltlzna- 9J trw, +
ot = 3 'g€,t&JlVt in ktla
= s,ett3 Ji4;
= 2.4. q g€ kr,u
//4Y oz t 3. gtsselz-
DVfa-nc''
= 7, *44 w
Aetutee't h$3= dr+do
e $zS. rt)-J l1rtu '
!
23. 2n letc//r1rbt lre acr'dcs V4/)ot)s ti u'toLk-g
p.r.oblcm't, ?o otter'Co,ne l4ese 2nltbm.t €he /dIodt'nJ ,/Oro.ed4rc'| nn9'5e fa
tlhoe€ e/euah'o| 2g eo &
4. L. o/ <7lcn f otte = AL 'f H f -('w 'fCLfic'rcaliu)
b Lr".xtT "" "rr"A..4 P : a)4"'7 Ae foi'.e
de/t>"mi,1zd r'c a'iove l;ne o7 €U'6.
€&Ff ,natt A"- 4 e'td 2' 'y'' v'r'te 04
4'h e po/at a nl .scnff 't"eadi''V. ha/
Oe *ea a'r neiaAt-
P/< O 8 L 6,+t.s /N ZZUE LU)JG
= R,c'tset + f n ue-f,J.'4f l- - -
,l/eqdin?,
e/euafi'oa a7 c4htjja-,
f*l 4' le-z/ c^& qr<'t/t"-
tldO, ctv ,3Vtf
aJb;clt rrz,/ 4L Ca'llcol as
),2
,19
'.$'
E<: 'm
0r) Levet/'
t) leve/r"al Jolcc 4 n,3! _tt)o!!_:
R1 .t
6rh
lv) L e,/e //i Aey'dJJ a .>.i.tez' ,!
) levc/t; o "v1 f u4m;ar ead
&n
.< ec,,7 /. aal /c/t //indl
holloz.t:
70 carry .ta/ vet' (/e ue
acTaC{ e t;/ t t'.ta ter l;'<e
eaKc^f 6r Pend , u)h.tes
e44t 44c v<.r7 /atz' f'ram
eaeh a Ctrcn, 6let."'Ahe .< ' L' d/
alalcr vu rf a.za f'ro,rtl oae ea4, '
bqe, dtte/ e-rd aia ed'hi4e- t
lal1iag a)a. tc'r ,/ut7ae e a.g 6'm-
t-aa* €iandiy €b/'/l tJatet' sLL//a'c)
7o lantr44e /e ye/haj Patr a4 .544
ua( hake ,'r|././ted -fafF /e4d;r'
Aololi*7 /a,ob clf ebafl in /ct'p/ at) tut
e d/ f
ara//. Oete'rmiq<' I'L' ol c'o/
f *,1, = ,tt ! f 6,
cintt,,,ai leuellill a, de4er erUe'
,D/+4 lo/
"/
ut// aJ 6'n'
H. t -2'= .? tqc 67 V uztt/ - €t
znry ,le /e//o and ,
f'a1
e.
muve 6o
2b {c &sed on *o" /ttl::il"
'is 4 71a Cua'ac ,level li c.
ss
s,
luotnl;b /
Nh;Le /e ve/l''i' t)T1 tuqm;t
3e I e cte/ .s4./1 cAue a'il {e aai nfs 4a71
zocibbn ej level t't 'ra
/l
be a4 tarh eA 7y'a>u c'17 t's
Aa //tu
''reacli n7
Po'si l'o4 ?^.1""?
afO Vttlbh- /L7du'l
'Cor4rr1 au di tt7 Pa'titi24
26. @ tzt' ca
blha t are t4e ter'fcyar', a-dJ'.as ? / ent€ o7 a /eteL 2 €zVlar a
U) t Ch nCa e s ke/ e/t e-,s .
@ €zgohi,t fe//otli7 mec'lads f -/eue-//tzt7, O/ve ','?eat 'skebctea
td, Cte evot' d€'t'614
z) OtTVe.re n Aal leve/I?
u) 2raVz e Zeu et/,'n7
,D crP-ls -Seeh'ott /eve///g"
t,) 4e.Vracoz /euel/t',V
,D 'Fy' /eue/t'7
@ Nirr, e /ar/t/ /e< c*7/ai tt hQ'itlt d/L '''/1rf'1 neta a'<zl fte an4 fazL
rne hdz/1 of 'Aooktg a^il 'red.uei g' levol- '
@ Wt,ot a/e k" c u'rv att+re 4fl4 '"/l'4 cA^o4 c'o rfeeho't't
f?::, -.rA o -/a//r 4/ 4+ 5'ta4/ "'eaAi
4+'t i'e{c o 6-rerue) 'sl'L
c'eJrt u+ clitt
V ' ^^- ^--,,') 't./tetr xhtrol dxLtt
,yeoloeed lettel c/ eh c /oe/,nt6 9/ n't". an/
-/ae
" m ef'tzl an/ a(:o
'Xhe
7e'adietr af C&e lia'a-
"sotn
i7 ttz- /rr.t? ^nd /a-ct ?o/4 t,
i, o 44n4hru e *on 7-v-af
eet- c4e /d//ad/"/r a'ea-/i<V 1^1"1^a t&en -
,p,C. o/ /t r'se Potrzt 4,4J ,/ao, odo /4, Enter C*z- rea-/t z?u in a-
/pai e d/ /euel 6ook a. nl detzr mtr-z' tdo R, 1' y p"t itr
/ ,,
6ee't 'rtaved o/""n Xhtrol' c)xL/t
-
' 23t o ' 83E i' ztc 2'(?a, 3'/25
artd Caleadate' Hte A't' f
Lot taken a)t'ti a 'tto/tf n
6) 7rJ e /o//tur',rd, cans:ecuhve feud;rr .'t)ct'e takea atilT o /eu'/
!..
arld 6 m te/e/h? 'f toll 6n 4 co'11/ nudas2 c/o7:u?t' Vraunl
"f,, o 4omrnon ioleruat ts 2" mete'r'g : o''en /' <J30t /'q2{,
. (69 J . // A
/ +, +95 , 74 e re d.tc.ed
g,/2{ n, Qu-/e aub'a- VUre o/ a-
e a)oue ,r-ealt W, e alzt, btc_ Cdt-
';5,<eoal/ufP on //tor
t) 4eoarn6' on zoad /eucl
t) Zrtucrkd o'ea-d/f oT
v) ae*at'7 dr) g t'o u'1)
Veae €ke leh ezf tatt Cre fdl/d it eeTm.t
Leve/tinj b) Lev"r caVa.ce- ) ziuet t;ne a() rla rt'za n baLPla na-
Har/ 2,atttz| //.t4e /) vertic-al ,/.,ne *) Daeam ,l) E/evoh<.,,t
2 a4a -tea /zttel i) 4 enc| m arks a-4 d efat
cYz6: &a-.tt c grLa-tr?i,tt,
A,ggt d'trme* r - /
Aa6,17./a'V,C
p ."/ . Q, Ze e/al4are5fi
//oD, a: rU, €v /7
a)
e)
2>
cnayp of Idrurteat
t/) &eadi*i on S -au4t! lcu{ 3m*n/ = o'75om
27. @
V) "(eo.ar7 ", qA/aor ./evel f e4n teen = /.taa m
V) ?nvcrd T .4/i'? Dn e'aod/t/ f eanhecfl6u;U'7='/'68-Sm
v> .<eadi? an 'ra a4 /eue/ )o
l-o'e/' a// 144cce4 = '/"26r-"
vtD .(eadinX> an //aar /euel / I a'dr e'r 4attl = / "f t a zt '
Ent^cr l4e o'eaattyts t'4 4- lFll L 7/ /eu cL Jaak
and 'redaZ a tie level o7 a// e44 /Oo/'n?'e '
e x tra' etel f'ro'n a' /evc/ 7''et4
T d/+gib Le aarlfl h e//d!c1 re'
fUuT*! and c!4cck j.o un /c^rz.t al-'r
Re 6ook a/// 44e 79/6t'4re.t 6/ t4e ,tzce a,td fazz rzte caz4.
!ta6on I's'. 2'€ <tSe Fo // '4.'1.
m 4enar4s
2'2s{ 232'4,60 B.n'i
2 /,85o >< 6'02 0
q 2'105 X
4 x /,r66 x
2'o,d t,?zt /t,Joo
6 X x 232,295 e ,/r2' 2-
7 ,/.4ro X 0'Jro
g 2't65 2./Oa X
ot
X X 2J3''/2t 4"m'3
-t
-'1)
f,l
" /a//oatiV notes rfel ta r'ec?Tocat /zuek taken ati4 ane-
leueC !
Zn,!er.,tmellt 4e .ftay'f readir €n
m
Rerlarkc
* & O^ian a 6ezt teer fu4.
A /,62? 2'74e
a 0.926 /" do6 RL 6I P = /24,386
Ftrrd i) 7.rue R'1, y A
,> 7he corab$aal 467'v24A'an far curualqre ad '''f 7 L'A'd"
lD -7/?e a nJu.laa e"'ra/ 2'4 C.l e ca/h'ttal on a d1'uL l'm ea 2
$ ttl e- zrtctrumeab
A 7le /o //" ai,4t o'eadtnTt dere o6cervld ,n a- TTof ;6" /eu o//'aft,
et an regulatr /4 hcYual 9/ zam.
O.5oO., ,/'26O/ 2'220/ 2'?6a., e,?gU, e,fagre V r'n,rtrunezt
/,21ct,2.6,50. 2,6do, 3'/zt, ,/'€oot 2'd.fo,./.965. Enter tA e
rc a.4;;t4 trt o' ?gte o7- levay' Jook and 4ey' ermtxz t'4. t<'l , Ora'd td'-
f-i+Lr" o7 grinl', DLae r rt iuz- a-l.r o grd/etc' d/ /,ne jq1u.r,t fg/-t7.,
28. 3:aI | &aete €urug/i.gr 4s3,,Sorrt.tt A./a -,1 P-"/' 4' lze/al)qaesfia
zaDl crv ) ,e/ tT
uJha t are E4e te rlpa raty a clj u.ctm e -c
P/ttt zte4t 'ske
l'crle
at a Heodah'be- Ez4at-o
/-
.et/Lat are /-le y'u.nlan entaZ a.Y/,t 9/ a I'lga/al|l-e t y''t P outs
tle deJlred qelar5 a,tei,p .4e/otecn ttlem.
6z7la, n ,ncagutenen,
"l
tlarr'zatbal a237a
lLst ene errar-s eO,ninaCe:d * aZ,t rze Lztod
6y .reyre.6t'h ari ,ret4t4
Ezvla io me4.rarc,ze4t
f 4or) zanta.L aryte ! dtre e{z.on or
7e fkrazl'o,a meehtd , z,/,fa ,/7d e e"^ra/€ e]>tnat.4 -
y'tll4 neet,s,Ae/c.{e,t e7/aia 2'rahy,'g gr a .c/rars4/- t'* I
Usttr t4e ac/a/,/e ,