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TRANSCRIPT
Eindhoven University of Technology
MASTER
Enige aspecten van lange, lage watergolven
Bontekoe, I.
Award date:1981
Link to publication
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fd=O Of ~.=0
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1; =_Ldl( ;J,. ~ (r"\t;) T. uWuJt ma± "HJJr ~.... dt .w..1& ~J:tit ~"'" r :
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i, l".!f = I(lC, 11-t). Oe ; .. .-t.raJ aJt>o. ~ ·.., 1;. A,.,. cWJt l!rlt .. ,JJJJ "'Oik... nad}L
n~a.Jn.. va.. ~ : 00
l; = ~_[Jx [71 f.t+f;L-• + t {;;} /1.\ fa'J~.,+······]
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!XJ( + ~d~ : 0 Vco-t. 0 ~ d ~ 1
1d = 0 or d= 0
f = !, (x,t) or d = 1
D~ or.b"'J J,.w,"" ·.., (lt [~ J) , I !OD A Coo:t: f (x,~)= Vff_oc dj !, Ce) ~ -~(ijx)
" w~ !,(~) dt Toultt!l;rtu...f~ i. w... i, lx). h)Om ~ :
aO
M )~~ I = .Jm _l cl! i.lll.l. w !h) ~l;i.) Cl" "
= -_j__ j J ~At f,ll) +~1 ~~Jx} '{fit -oD Ä<
" Uoo\ (i~ )1 f,(~) ~UMnt.l w(. 1J~~ : 00 2f
(LltÎ.li) = ~ J dx ~ ~(-J.) -~
'l.odai lAlt tul ~ +J. ~ ~".. Vod'< ~)~si :
(u)
R ·\.t) ~ ·~ .. ·\t.y-a.Jor.01.afdl:
R {x-x') = -fi [~ i;j-~ ~ iJAx-x') -IlO
= ,'tr ~~ & U) ~ ;J (x-x') {11) -CO
At ~ ~ <MA ntJ:J ~,lx,t) uJ: li. ~ i. ~ lx,t). HWJot UJO'ld.t eh. ~A~.ruJ crrJ:wJJJJ Jt.and ~= J :
()C) I n [~IJ fl~,~l = 6 ;J (d-1) ~~=I
Uo~ i ~n~ ~ }.w..Wt :
lof J 1 2 11tf] ~- II = 7 ?fJ ~=I + 1 7 l~ :J=' + ....... .
I-kt I)Ö(>JJ ~ 1 .t-1 I I .lil t)c.n <1. ~clt t ~; •.
-8-
U;i (11) u.,l!~t Jat ~""" 1QIIr 3J.e.. dL T~jor..-J.. u~ R :
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A. Voot Ja.1 Ök., iA rt = T + Olê). Jn (13) uÎ.n~ Wf. .la.. UOö\ T. ~.hwlt .... f :
aQ
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~o) wcrtAt dam : aQ
1;= ~_[dx ?(fJ + Olev)
o~ H~tcmacL-n l.bO'l ,k F~ Wi~ i-n ~ .tn 7 Aw.dt nu :
(t')
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-ID-
~. B.ttt~r or.vw:to'L
O.t ~,ut. or~ Jä wt "' 3. ~J.t.. lJl. L+ ..1 To~~i~fO'LitlW\dt ;
R. ct) = ~ !1) (to)
~oO't k..'f. .~ , dat w'.i ~t' lkXYl h .JJ~ .,ä:,. , j..., R.Lt) o~w~ WO'l~ ·~ ..&n ma~
~ '} .L D .l ..!:... 'I n. {Ac = 1- 3A< + 16 J - . . . . . ....
n~ Gf_vwt~ f{ ltw~ Of Wl/.laJ.t. rruuW.".ttt
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i. d
Rb = I + ]' 5;i. (tt)
(u)
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m 'v" ..utt mtw., CL~ooA±, f- lx 1 tJ ·14 tk ~~fi.Wt 11Nv\c:t~ ulkl
.~ { lC jt) ,e.n V> (x 1t} = - V {>C1t). . r)~ Haw\J!o~ 0o.tii. oobl ~ :
liP
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f) r lW- )C ( rn ,t) rJ. ri. i..~ 1 ~dr4 ~O.:, ~r~lx. t) .e.t :
w (m~) = - v> (x {V)\,t),t) ~~)
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j., Ja [1 J ·lA (l(.k\~d dat rk ii~dtmo.k UONl m lx ,t) .ttt ./{x,t) ntlUJ\. x lm,t) ~ 14/{m,i} .un h01r\on1tk t..~1dlmttti i.o. 0 ..t H a.~ t onÀ.Cl.a.tl ·"" ( .-.-t) - c.ow c!lnc.i~ wdldt tw. :
rif)
}L i J drn.x,. [ w~w + (t -1) ,/+{*-l'J ~o) -011
-13-
fR
~ = ~ f dm [ w ~ w + Á1 + 13
-+ O[ E lf)J (.31) -~
i .1.0 d2. ~w'~.j \la. &> ~-x ~r~.J u.&IIIQ. ( kdtt r 1Jo wo.t"vt. ) DQ_ ~cA:tR. t~ J .en l .k) :
1+7 = .~) b2)
7 ~ ) ~ k<.b UQ.n JA. o'IJl,. I!. I-let 'ti.~ V""
l:~1) -~ d.u,. .k......k.J .,....Jan Jo~ & ~urul.&f ~ : 1 ~ )+)1+ J3+ ......
O.e. ~fut".~;t' ·m nuu.~cuoä.ok""ii.. ~· :
~ S&/ (J 1 o2) v.lt = - óm ~1 =- + lA m (~.3)
)t = - ?.; :~ = - R w,. (.3y)
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)tt == R {1 + i 11l)rn"' (3.;)
( 2.)
TU>U. k ·~ -. (1) o~clt,. ek. )oue.v;,iCJU~mrlR. IJO~W~ VOe'l 1 ri :
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) -1 (.3)
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k
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00
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t'~
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'1.
l) R-I ..L 1-. . . ) !l Oo"L ll. = I- 3 àz1 ,n .tt, c, :
P k 1. ~ ( .!.. Pt.) k 3..!f_ ( Lpt)2. A: E. CO) z ~ t ·l1k1 1+3/k Co'l1 Z+ f..,flciJ lf-.3/k ~3kz
2. 1 2. ~ 'I ty3 · ( J. 1 s\2. c = J+ !--'2. + e · Bl1 + e · s12j6 I+ .3/JC J
'l. d
Uedl. d.t .Bot.w:~- ormaidt. fiJ = I+ t d22 ~nJR.n we :
0 2. 3 (1- J~2) 0 S .ft ( ~ Ot\( Dt) { ) A-= e ~kz + E. -q )<t.. Cd;)2A<z + e 6~1c'f 1- 3/k} I-3A< cm3k:z. 12
c'- I~- ~J'l+ lä. L- :t.J%-H•J+ e. ~ s~~' !1- Jl•)(~- t.J•)ll-311 (13)
jn J.. ~?" o~m;to IMtllt ~jjJ"'VtJ : J~ EL .
T wO'Uit M . ~J uCAM .Stk. ~d, k rf .dl. ~~ Q.G.t\ llr.AN\ d.t ~ lJGk\ cL.. ~rbt&tA. .t.n clt nüt-~ne~tht.
o~ "r~~d \}(Am cJL ~ "f~ Y?~ uJov.~t cl.atn :
1= e~hz + (e. ~3T + &~ Y .... e~ i:) cmtkz
{ a .t 2JL 3 .!t) + e. ,,,.r:t + E.. t'fT + e. g0 coo..3kz.
1 ( r j_ m. ) 1. { sT1
3 ~) · C. = I+ t: - .3 + ~T + Sltt3 + E . ïf + 'f + 15, t 1
( 3 I ) , 1 = e ~kz. + f..· iif + E.~ Lj Ct»tkz
{ .!L t..!L .3 3) + e. ~'ft1 + e. . J.tT + e . ij C0!)3 k z
t ( T ..1. !.!i! ) 2. ( T1
81 ) C. = I+ E. - :i + 8T + Sl!t.S + l .., + 5'1!T2
-a" u,dL alt. .Bel~Ml·~-or~ RJ, = H· !' h 1 ~ Wt ~
p ( 3 t) ( !L l .!!l. 3 YJ 1 A=- E. c~kz + E.· ~T - & cmtkz. + E.· 6~t'- E. ·t11 -r + t· u c~.3k~ l18)
~ l L' ~ .!!!!. ) t ( IS' .f!1. ) e = l + E. - 3 + ~ + su? + E - ~ - 2s' r1
-18-
Vo.,.._ ~ r~ "r.-fO'L fil,._ lj~d wmcit W:
l 2.{ r ...L ~) 3 ( -r2
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f 1f. 2(li l'il 'st1 _\ 3(333 3J'M5" :3.9&3 ) + 1 E.· blft2 -t-E atr + IO~f~ +6ssJ6tGJ+E. ru + 32,:6ltJ. + I!I01Z.T'I c:w.lkz l21)
2. u~ VCA.t-1 dL. "rJ~·Wir
B~ kt J,rut_ - cl.. l.d.t ~-~ VQ,f\ 1 ~d.R.n ~ r1 u.Mt .u.n e.d.) ~ k z.-~ o .un coo t k z- "brn . UOdt.. ck .w:a.ct.e. Of.Dlc:J&L R~ .L/) ck utudt otck ~ ·.
'f(.!i:- ,.,.tt .11_ J-r-1:1 ) llf = e 1tJ fT. c~ttkz- 12! 7 c.a'ltÄz.
V t'l f {n) {11) (tt) J An = e o., ~nkz + C&.n-t ~(n-t)kz + ........ Cz W)tkz
. :
-2.0-
IJo-tcJ.t d.t ~ h 1 = eT ;". c1. cf{f:~Ck. )~ ~utt~ l-~,
dCA.v\ 4tt ck dJU~ J dt vJ?'d.t vO'tm : aD
J :=. L llnrA (t) E- m c~nkz. (23) l'l=•, rt\:1
GO •
t2. = I + ~ ~dT) f' ~5) t:l
-21-
3. OrJ~;...,j ·.,. x-i- cootdi.nu1a..
OL ~'f~t; ·.., x-i-eodl.l>....b.. d~ wt ;" tr.18} t.l (I~~) t' oncJi.. A ' kd.t... :
?t = - (Rv+ ?vt
V-t = - { T V 2. -t- 7 t
c1 = R v + 7" + J, .L 2. 0
Cv = 2. V + 7 + A>.t.
-12-
StJ ILLL v&.-ci) = d-r V{x~ct)"- w~ ~ wa.cu.ck VIM\ v l4 . t-n wa.a.J~; v lx- ct) .th
-tof,n { ..... ci.ti io ) d... r-""JdJJ nJ ;.. . (2j) ~ l~J WO't~ tut :
(c-d) 7 = RV' + 7 'V+ J
( d )' "" I _.t I 12 D \C.- V = I V + 1 + 2 q + At
-2.3-
-25-
~ ~-t)- c.owckr,~ .. Om ck or~~f: ·~ lrll-t)-towcL:na~ t. ~ mrt d~ 1-r\ (x-t)- coÖY~e1~. ~{O'ltriVtRm wc. tb. ~ta. nwu. ~x-1)- towdi.nct"tin. D.e. dJf-1~ oao.r~c!W: ~ ~ ~-1d\..lh.cJAR_ ~ > w~ :
.-va= x+ t-lx- c.t)
Ak Ir I ' I ~""' i. .tit. .tJ." f l mI t) ( 1011: J = f .. ) "Lo dat
x== m- S (rn;t) (3~)
Dan dJJt : ) J(m.t) = rltr.-ct- ){nt,t) ('{o)
0". 1 """"" (x- t)- tDHcl.:.,.."fi,. .... t. .oulw.. , ~ wt { l_,j :
1 (x- ct}= J (xlm1Ü- à)=]( th- f[tt.-ct)- ct)
na. o~w'J,Unj ~ .Un Ta~ t.lotdt 1 lx-c,tJ:
-Jlx-ct) = l(tn-ct)- !lrn-ctJ.i,{m-ct) l~1)
0 I "J::L~ rndctt ?-tl = 1-,l ut.Jl.nrwn we. 7
.i lx-c.t} = 1 + )2. + 13
-2b-
][ ~.&.t.. ·... u.. ~i.~
1. I< O'lftwta- dL \)Jiu.~
Jn kt ~b!J (T. ti), (T-•3)
?t = -(f?v+?v)x
V't =- ( Iv'+ 7Jx
V= l'"-S
:!... ( .L J._ 3 2) r-~ = - ~x .2. r + 2 fii> ,. + LJ ,..
(3)
(s)
-28-
(R)
na. ~ k ~r ~ (6) :
(J-e),. + I rll~ + ~ r'" = 1 (Jo)
w~ ~ = >' - c.t · k j ~ i.n 'tlFtû.C#IV.)ta,n\i. ~ ; StJ n.u. :
t' lx-ct) = 1 d + ~(x-ct) l"J
; Lx-ct) ~ & 1tatio- , p.vU.ocLJ.. 11NnctAi d;,_ f~ddJd ncJ ~. (1o) ·h\ ';; uit~ wtYldt :
f1- k- ~ J )]î: + 6 t:~J + t r'" = .-e- ~ c1\ [,_,J.J J (12J
Uoot. k r,J ~tJl... wt c- td = c) .et\ ~- 132 d2. +(t-e). ~d =~~
d 1..., wo\clin ~aJd ~ k C<>'IU<f'....W..dt ~ uoó'l 7bo'l.
o~ ~f4Lj
(1-c)) ~ + t r~J + ~ r1= )) (13)
• ~ := n~ o( 11 ~nk~
(15)
~3) ~ dcm ii ~~'*" a! :
[c'- ( 1- l n!J1] o(n = ~ fh l'')
!ct lh\ ~ dL lJ- c1tCk 1w.dt eh. or~·m~ tJtNn (t') ·.
"'" [) ( 13 'I ..!:L) 0 .l.!L.. ' r = f, c.oo AcJ + E. • ~jL - f · 11IJ' CO) lAtd + f · 6tJY ca:>JAI~
~E;_ + f. · uiJ' Cd.) y 1~
') I P.t 2. ..i. y 1L C = I - 7: /k + e. · J{,jl. + E. • lotyi'
O..t 1clt dldt i:v.m ilodt. r ktaat t.Ût .Ut\ ~31~-~ .en
~ ed.) s1 d- ttn.~. ~ ~rl.t rcd.xocm ont~to.at a! (Jr. 2 2.) UodL J 1~ fT ~~ ~ ~ c' :
> ( I j_ jl - ) e = I+ ET -1 + l't2. + 1o1~1Y
-30-
Qj)
r = t ~ r" ~ nk~ . lb
~t'l . ~ & Ctml)tcu\'ti. , r-1 ::. I .
OJ c>-1 ·ll) ~ ~ 'm T :
-31-
2. B.B.I11~~~
fe-n ~Llu.t ~"tL O'Uk dy~i~J~n3 ~kJ) a1 ~. ~ (t) ~ (i) ~ m~ VCM\. .Un ~ vwû.a.&A v Wo.~ :
?= ;-rr -V= r--a-
-32-
.en mcJo'd ~ w~ cltJJoc dt. B.B.m.-~~ f"ot.nJ. VaO'\. ~.vtWd~ ,1~ ~~ IICVrl (2~ ~ Î 4n 4tcd:i~, p..VU:oclttl tn ~ 1,lNI!c.t.i. UJ: C 17-) .f;f\ (18 J I)J.~t dat ek
~ ddJJ.. wc.w>.J.. """"' Î rJf V. eo.an I J 1 W ~· cl dL ~~dJJ~ wu.c.u.dt ~ v ~ . ~00\ ""tircWt w6ld.t {tj)
(_ ) J... 3 1 0 u-c f+ 6 c ~~~+ îfi :A. (.!o)
~ ·~ $n .W\7u.t:U.CUV\bt""1i. ~~ ~· di kcH1
- ~j ~~ wt Ml :
rdx- et)= F(~} = ~ J + r (~) F 1~\. ·~ ~ <~t..t;.ma.Î.IL I p~ 'toto. J .... diA dU. ?"'dddJ u IA). u~ \.Ut (.31) k\ (.3o) ~ ' dam 1~ a :
(I- (c- ~ J )) f + * e r3~ + t l::: )' (s2)
WQ.~ ~, = j_ ~{,-c)d- heiL. IT1d / = c/(11- ~ ~) ~ f =. f /(H· ;J) wo'Ult (3~) :
( >\ l ~ ) ) 3 )1 "~ ( ) J- c) f + 6 c ÎäJ + 7i f = ft 33
A~ ~ ~~~ ~>/{u·~ d)~. O.e. orki.n~ UCAm (3~) +ot ~ mtt cLe ~ ~ ~ :
r' = f. e<n k ~ + [ e ~ tr ( I+ t.& t) - ê \!IJ1 (I+ 6/t %+ T,~·v ~Jk~ 3 .!1:.. l .L f)t) 1 D 'I !i._ ( ..!.. 12)
3 ~ + E . 6~1'1 1+- 'AC ~ 3At~ + € • lti""' I+ 611< Cdl q d
-33-
) I
c = 1+- t ~1.
rfu h1:: E.T wotclr ck arl~in~ V~ (s.l) :
> o ( ( L 11-) 2.( ..L ..!l!. ) 3 ...!.!...) l == E. Cc!r.)At~ + lf. ~T - 12a1J + E. 8 - 2s6t1 - e · ,ozyr ~2.k~
( a.. 2. j_ 3 ..i.) + t · ~'(t2. + E • 6yT + ê · ts' CC)!lk~ +
( 3L.. t~ 3.-i._ y 1 \
+ 2. · 128-cJ + E • ltit.t +- ê · !12T + t. · tot~ ) Cl»~ k~
-35"-
- O.t. e~l UQ,t\ d..t "f~~j ~ m~cotN"cLlnci~ 1\CA.CUL
ptw±s COdldl" uoPrlott JSek.tt rv:wJLma.t. ctt 3~~ ~I\.QJ1. .\A ~ t\CUUI.m~ dJt aJ!Anat. rotvt ~.
_ U.tMJJ.l t~~ di. k'dV- ~ BBm-er~~j w~ Y:'~ r\CLOA m.ll.it. l r.o"tb. wO'lclt . BB vOI)it J. w~ dt uVt4ctL A-. Jo d.t ~~.JW nwWLt t.t 1 . B~~ r'w Ál io clt kJV-.k.n~n~ .JtJAJIL ~Qn cta. BB nl-~u.dvttn'.
- foi"t" om. k ~..ct.. roti.ii.Jr~ li.(1! kt~ ..u T('IJ) UOO'l ~dû1. 3~ Of t. )~ ~ twlt tot -Ut\
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7 r . 00072 ~
,QfJCJ24
.IJIHJ24 -
I
0 IJr:i 7 2 ~ I I
.IJO 12 (J 25 50 75 100 125
1 = o. 1 e == o. j<j 8 'f 7 ( 0) = /. 0 B . I; 3
~ /-:!.1-
0~~~ ·m (x-t)-co~rd.Lnc.t~ v~ UUöacb. of.vwlou.n,À=o.a
.03
.. o 1 a 1\ 1 i!
I !
.006
-.006 I I
- (l "j Q • t_.J I""; l
I
I I . I I
-.03 L_ 0 25 75
1=o.l . ) C = I.OOLJ5'8
Rt. : E = O.OOjj 5"
Ro. e = o.ot
Rb ; f.=O.CIIOt
, "L = I. 00 S" , 7 { o) -::. o. o 1 I S''f
, T= 1 , 7 {o) = 0.02162.
, T = o. j Bo'l 1 7 { o) = o. o 21 '"
100 125
.z
• 12
7 r .. 04
-.04
-. 12
-.2 0 5 10
Re. : E= o.o85,'t'=~,~~1 , 7lo)= O.I3S5
R--. : Ec:o.o~l} T:::2.1q~ 1 7 fo} ::0.1~33 ~b : e = 0.12.8 ) T.:: t.~S3 ) ? {o) == o. 18o3
15 . 20 25
.'1 5.10
.1 0.10
-:I .10
.1. ,JO
I -1 .o
f"!Co)
\
+ Re • Rq, GJ Rb X Re. 11Ïa. (m-t)
.g;
' .ss .gg c 1 ...
.04
-.04
- 1? -. '-
-.2 0
h=0.5'
5 1 0
c == 0. jg' ; ()'lek. = 8
E.. = 0.100) T = 1.5' , .ilo} = o.•y3 ! = o.lo' ) r = 2.3s-8 ~ J {o) = o.l'f~ E..:o.l5o, T:l.,,r, J[oJ:o.,,!
15 20 25
I -::,.... I
·" 20.10
· IS.IÓ\
ao.aö'
l 'Ij lol
·95 ·96
~= o.s
X 'Re ® ~«
0'Rb
I .,
·98 c .. ·' ·99 1
-. -i; .. :
.. ·-- ~·
'
I I
~\
. u 1 8 ~\ r/r 1 I \
I \
.006
.006
1·018 i I !
! - • 0 3 0 ')C
L .._; 50 75
kd V : e = O.Ol 012. ) T = e-jeN. • r-lo) = O.O'l.ILJJ
BBm: e.=.o.o1o1& 1 -r::o.,i'fJ, r-loJ :o.ot~~r5"
I
I
100 125
/ -~3-
~ 0r1~·""~ \1ow kclV- ~ BBm-~nj. h:o.5
.2
.04
-. 0 4
- . l 2 ...
-. 2 0 s 10 15 20
kd V : ~ = 0.110 > T = 2.213 , rlo) = o.l5lf'
B8l1): E = O.lo8 I T = 2.315' ' rlo) = 0.1~1,
ft -t "0.10
.t .15.10
1{CO)
·96
1=o.s
® l<dV
&. BBM ·
9 'Rb • Ra
·98 ·99 c l ----~-~
Ar r""c~;x : ~~..:., c""'l" .... tv..p""t'"'""' s H.u: f-'le~D\1'\Q wctt c1. or~~d JmlJ 'm l:<-t)- ~ l~-t}- c.on.t~&·"Cl~ ~taai ~r~ Or\du_ Jt nQ.Cln; "~dij. Hcl- f>lormlr\Cl wa..t
k kclV ~ _BBm- tn~"' ~ ~ ~f~t J+- no.aft\ . . , BClteû.Jk. . F~.w.,dl V..vt.614x. 1.1 "lo D'UQ.n~ ~ oM· Var\ ~~t t.t. ~n n\Û ~ CifNt\tJ idtut, tn r"--CQ.~ ckl kt~, ~ or k ~ md ~~.(~[11])
B J .. :·. . -r-o ... )4~"1 "~~~
\JO'lelt ck. or-fcW-l~d ~cl ~ lx-tJ -(:()or~ncJJ.. dcm d~~ dJ.
o~cU. tkofpJck otll~nt' ~w~ op~ :
[(e-d t- R]? = -i RV1 +-(c-d) 7 V d.:J
(e-d) 'V = i v1+ 7+ )'1
~ ·IA dt. ~~JclJdt IJ~ 1/()n dt diJJJJI)4~d V 1 ~ V= d tv lx-c-t)
3tJ M c.> =c-d. W.t ~t' rw: ·
11\:0
~ "' ~ ? = l Î Cn,m1 E, c~nhd tn V= ,6 v [n,m] ê "'c~r~kd M ~ I n'l ':i
Wt_ ~tCULt#..n _kt J~~tmt. dCJO'l u_ d : 7 [,,&]~I -l.f\ 7 (J,m]: 0 1100\. "'>1. IJ(lr\f\.WL l1) Or~ 1-"dld.t ·~ .wut. dlk .m € 1 ~~ Wf.:
e'1 [o} = ~ 1:,]
Om ck o~~~ +Gt ~ F .. l.r~.2} ia.~, ~cuJ.t ~ Yr\.b.v. ~ f'lOc.etlwtt. I)Oat, ~ C\ Rv-2. & c.·? o- ~=tt t1\ n\Q1 ~ p+l. ~.»LA.. ~rl\h ~ ~~ .• 0~~ ~:
~ ~
7 ("):: t, 7 [n,,.] e'" ; {t l'lV1 (.) <f.. (i RV~[.,,.] t."
-Wf.M.o \JOC'l (e)? V )l ~) ' v{ n). 7 { r.) .16 nu ~ ~ .h\ t .fA>tt,~ e1t a~dttt. ~ . ~V\ (I) ~ we. tw.l ~ md. n: 1. ~~ cWu. ~~~j ~ c,2
ii kraJ~:
(e' 1- tH,J) 7(,) = 11'? V1
{,) +(e',v)li]
~n dJ. ~~ VOO'L d2_ Jo~ l~n\ aMo~ Wdlcl.t: 1 Jero.J~. \JoO'l n > 1 wO'ldt 1 ( W\ l i:ot ~ mQ't <1tdt p :
7 ( n } == I R v1 {") + c)? v l rt}
c)2.- R["]
v w~ ~J~ tA.Ä.t~d ·~ lt) :
V(~)= i ~1 {n) + 7ln) e'
H~o. ~ctm k ~t1'itm.t. kJD.Jd w~ d.ofl u ~ f mat 1 t ~o~. nwtCJ.t c ', v- .en ~ tot rM. ~ ot~ ~~ ~Glalot ) htln d IJ~ J,e,pwJJ doe'l clt ol~ Î ~ V Mtt
~ ~ LM~dvJc4~ :
d [ rh] = -(? V l [0. rJ
HWt.no. ~O'ld:t " ~aJJ doO'L : 'i (o, ~J = d Cm] ~ V rn,m] =V [fl, .. a vo dl V\~ i . c ~ar\ t\4t. ..&rd ~~ u.it : e ["'] = d [n. ] + c) ( .-J.
H.et ~~t~ ~O<>'l ~'(t. ·lh ~m-t)-COdiClUtu'tt.. i.. ~ ":""\Joudi~. D.e. ~m~ J~ ~ dw ii w~ op~,~:
c21 = R (i t i i'") -J.
wwJ,~ J·L1t1 = 1 ~ /f [ 11 l'l] =O VOO'l m ~ 1.
Jn ~ <Ytdt. .·IJ) cl. [a] = R [,]. o~ JA. "ri~~~ tot dldt f lp~2.) ~ J~~) wtrtc!t- J tlL2t ~ ~~du::idi~d M ~ r+L Uod'L n =I ~ 1'\AA.:
c.1 [t"f\ 1 = R [a] ( 1 + t 11 [l 1 ~+l1)
B.f4~~r\d ., .B~ »
H~ ~c1Û±mi. OrY\ ck . kdV· en 13Bn1-~ •r t ~~ Îll
aru&e~ ~ ~ ~$tr1\1 uoov (r.-t)-~nct~ ... Om & er ~~'"l tJO(H dt kcLV- ~"'' ii. "'"~ J,.J~ we :
(t-c) r + i r~~ + ~ r 1
:: J
r ·~ Qh\4.·~ (la" 1 .$.. ~ : r = 1 ~ r .... ) E. .. CU).kd .t.n c. = 2: (. [ ~] E. ".. .., ... :,
StJ ~ r~:a] = l ~ r r.,~ 1 -0 uod\ ~,..I. t-t "'e-tdt ~o.JJ tot ovk f. \Jod\. n = t Î.6 e tc;t ~ F ii. ~aAn dOdl :
(e- L- ?11)) r(.) .. ~ t-
1 {.)
r(n) ~ ii. kr~ ~ stelt p ~ ·.
r(n)= %r1 (rt) C- ( 1- I n'1~
B~ c1a. BBn1-~~ 'dttttt ~ ~~tN. ~ ~ IJVt~~ "'~u . he. +~ ..,..u. !At. r.el~L.kt. .,.P.m "'f' uo..- 4 io l.u:
l•-c) [l ;-i e Î~~ + ' ft= __g.
tlld l [1 1a =I ~ 1.(1, h\] .:0 lJOdl rn71 Wdltlt k ~e'Û,i-mt ~tw.± . VoO'l n.: a Clr\ e w~ ~aJd :
(el I~ U•)- t) f' (t) = ~ / {,)
Uoe'L n>' ~&'leLt ((h) or~t :
p(h)= ~f1 lnJ . e { 1 t i n ~~ 2) - 1
-So-
:w B~~ ~ ~ HamJtoMt. ~r~
1 J~cL:n ·-=.:.:;.;::=-;~.0 . .. ----- ------
------ . -~d,."_. CCTY'J>VWcJ.1 -1 'j/'k ~ ~~rnaJ .!,.;. ~..Ut..,
J. J.«. \J~ö'!.. m~a. ) ~~ .t.t-. ~~U2.. lJ.t. if\ ?"~ ~ ~Jl w4 MJd ~ M()U.~ ~ hL11t1rti.n w&tcl.e.n.
r~~. ~n ~ptc.to! ~JA" ovJ~ . M~cUn rtJ~~cUn. ~ 11'<\~"ti -ó'tw.cJhw.t.. SotttO ~Ck\ r14 -d1wcJ~ ~!·~ ""~ ~cf'Jt Je>o-t. MÄ.dd \.ÎQm ~ JJ~ ~· (jW\~t®mh ~~ .1.0 ~k.nrl ~ J.it. [8]
LJ.R. ~J~ ~ '.\~~ ~~ JDdl .u-n Ha-mcl-tamCI(Nn \10m. rk vJ~ch \1~ ~ .
6f = j H ( r, 1.) d x ( 1)
[k laM~ ~ ~:
~t = Hp (t)
Fi: = l~j,Jx (~)
oJ..,r ~ r ~ ~J, 1 .u.. mco~~ ~j.,J .e.. jx .et-n eL:~. ~Îit?- {i) ~ (.3) ~n.k\ .h'\. ..et-n n\Wl
~~ .. ..e.t.N<.J.. J ~ :eJ n.iti ;_.,;J;. ~"""" ~~ t4.,...U...,
cloO'L IA.= jx ~ ~Je! t. ~. & 1mt cl~ :
Ut= (Hp)J( (~)
r~ = (H~)x (s)
-SJ-
t.tt = Hr~ ~ + Hp10 Px (6)
ft - Huu. Ux + Hwp Fx ~)
!J..e. ~ ~ct l~J ~ (5) ~ .. ~ ~t\ ·~ k u~ Va-n a.n M~wa. Twu. ~ A:Jcut.bwe:t~ etU. ~ ~F.ect~ elt x-~ ~ olt i-~ notmt, -\ijt\ :
(uFh = (p Hp +uH~- H)x (~)
(Ht) = lHr HLl )x (~)
(8) ~ ~). ~~ it·~J ~ ~ ck wet l7~ ~~
t ~wrt h- ·..,_ ,kt ~ ~~ "'~ ~:
~t + Afx = o (Jo)
Wû~ ck cLtJili.cl ~ (u)F) .tft k ~ ttlu,r) IJoO'I. \xl ~ f:$J ~ ())~. ~n ~ ~J ~dt. cLt a~ .. r{u,~) .ttt aU ~ !f{u,f) ~nW.Ut crna.f~ ~ ~" J ~~ we. (1o) tr\Rf ,UJr VCAin ( 6) % (r) tUt~ . &. Äumt dan :
(~p Huu. +~u. Hpc.t. + "YJ Ux +(~pHwp+ ~u H~p-t "(~) Px=O (u)
~u. -r Hu.IA. ~P + Hur ~t.t :: o ( t3)
OoO'l .. ~.itrtr t. ~~ w~ ~ ~n.wuJ. .tfl
Ubt.~~ --Ut\ a.r.JAJ ~ . wJ!. ~ Ml ~ hhvJfJU.Cii.r
+~ oou:
~u.u. Hpjo = ~PP H u.u. (''i)
M wt .un 'f (u,r) knr~~-n ~ okt_ ~ (,~) 11Jcl"a, d~ ·LO
~ vJr, l11) af (13) ~ ~ "Y(u,p) ~r.At .v.. -&n AJ.~w ·~ cJt lJo-t.tn v01n L1o) ~adt. lJQN\f\Wt. eh. .fLm~trnaJ f = f ~ dx .et-n J,w,ern~-~~ ·IA , ·«A c1.t. ?~ oJa.J m.oX elf twll wr.wtt :
fî,}f}=Jdx(!f~- ~~) ·= fJx [-~u). Hp+ 1PlH.). 1
Oo.". ra.d;;t ·.,.r .e-n. olo.n o1t · ~·Jiu ~M.t "k ~ ) l>tnckn wt : - -
{I )f} = J dx [ ~..(H,.)~ + 1,.(H "JJ = fJx [ f'x I Vu. HI'P + VP H.rl+ u. ( ~" H,.~.~. -tV,. H.J]
lJ~nWL ~ aa-n (,~) uJJoa , ~ a .22-n .fnr.Mi ~ ~ - uJdoet ~ ltt) .e.n l13) ~eet :
f ~ , }f J = - J Jx lf x = o {!5")
-53-
~t + Al'x = o
O:+.~ T at : T = f(H:-x~! dx . T lh .een "k;rr~~t-t. th tac1~~ .. =
~T .L i.( ) dt = dt ) I t "t - x f J x = o ( 2o)
O.e. P~cnJaJ ntá T ~~ ~~ ~ )o..dcl.ttoraatt1t \)o(}t ~r~CPr\J.)~k . Orn eLf t. 'L1:twtt.n ~ we. ~ ûooUJ H va..t elt. \}~:
H = ( G\ -r f ,J. % f" + Y (u) ( 21)
D.t ,yJoUmck lanc~dk '*AH•tn iJj• :
14 = (rxp+ f"r~ (u)
ft =(t fr}+- V'(u)}x (2~) b.t -fL:. lla... l.I. 'v; v1( ..ee., ~ rc~J' IJ41it:
(o(pT f~.~r)t= ( t ~ p~+ .1. oifp ~+ l u/+ V'( .. }+ fl.l. V '{u)- f v'(u~x \10'1. d.i1: .lj'ffu.rn nûVIn ~ T= - ]t (o(p+ ~~p) +X t.t. Jx . D~ P~oJ~ ua... T MRt .u.. .4-t?nfcunl.lt<Mili. I io da..:
fT.!)=- }dx [(ff)x.Vp T (frt ~J = } dll [(i(lfx"~-1). fp +f ~ Llx ~J
= f dx ff ( f'x ~p +- Ux vJ + J d X ~ p =; J Jx ~ p
-5S-
-56-
2.1d~<kykn
o.Q. ~uttattn uJ: 1. e~ ~ tot or J~toj d~ ma 1Cl~~ ~+.d~~-·<k3J"e..). rfu". 00\W~ ~ _rk wdvecJt j~ · .q , ~cl e1L uectJaA \Janiatu. \)Ck1.
ck ~~~ ~ .d {)U[~]) ITl.d ). k w~-1. .e-n r rk <J~ck~.a.J ~ k H~~: a
jf = f Jx ~ [J1; +U-~l] (t~l
OOC'l ~~f~ ·v. r'~'l dat tb. oh~ wail..~o~iL n lo ) elt ~rJ.t~ llb-r\ dt W~ d .tn cit ~chk.;.J uam 1.J. wail... (. ~ j. "'L<In .
0-t ~.P~? i~ : 0
it = - ~ 1x)x ~5)
~t = - ( 1 ~1t + ~-1)) (tb)
D.t J ..... ~ "tu-iotrnafu ~ j = "'x _g,. "= fx ,._8;t dat (ts) ~ (~') oot:td~ tn. :
r»lt = - v'mx (t1)
-st-
dm = m x d x + mt dt (31)
O.e ~~ V~ X ncuu. ck tiJd 4i ~"ti. m ~ da-n :
~~) mt t m =- mx =V (.3j)
('d)() I 'àtn + = Xm = mx
o~ (o.~fllllM.l.3o) 3Qf.it I'IM.. ~ 111 :
L~ J dm [ t x:- Hx .. - tlL jJ~Uxt- tt~- t.J(3f)
lfu Xt = V uinclt.n we. IIOO'l riL H~t~ :
~ = Id." [ t / + ~ I I - t)] ( 3S)
o.L ~""'0~ ~·?" ~· =
-si-
~ met Xrn = 1:
)t = Vm (~8)
Yt = - ~ = I(-i•)m (.3j)
Ha t!>Jl~ .ló ML qJ~J .m ~ IIO'Yn. J~ .),x 1110~ ~ Jt. -w..Jia!.. ua .1. to( t. ra.Mtll. j. GLit rJ ~ IIOdl .te.. ~ ~ r :
~vv H_u = ~ Hvv =: ~Jl (~o)
Omdcd: f.l1v = o ·16 ~~ ·.., 1... ~n , Jat .J 1 .ten
o~l~~j ~ Velin (roJ ~V, ~VV .de. ~ ~ (y~)_ v;,edoe,n . Omd~ ck {~c:fw 1 .en v v~~p~d JJ~ ., ' eviUo.a., 0144 tuit ~JA. ~ rJi.lit~ .J. :
I 2. I V> 1'1/- 21 , ........... ..
1, )v, y )v~+ ~ (1)) ...... ··
~U) j." 1 n~ ~a.Jol ..,.,.,u.. . ·,.. (yo) 11\tt JJJr o/a..
Hli; - )3 ·
1.9..e ~-EJ~J.. ~ "#'' w~ ~ :
l~) .. + (*)t = 0 (~t•) ~h h. (x-t)- cooldLn..it:" uAt ii ~ rnti ~f' Va-n :
. ~
lW)m =~)x + v. (~)t
lJan~ tW. (~1) IAlo'ld:t wur.t • .,;.OvJ&LaJ ...ct J.. ( ~~ = i-) w .... clt ~ vu~~ :
~ LR1) +~x Uv~+"~')-~~ -1 txUv) = o
boot r t. rnJ"., va... l u) ~ :
~U~~)+~ Uv~+-r)= o
V
J.. 1 I 2.'1- rr I 3 V
1v - iJ I V ·i I
2tt v - 2J + ii]t
tJl+l.,rf
T J\l + vlo! J V
V - 211
v1 1
- -;11. + lJ3 v3 v
- i211 + lP
-V
j_ I t
-J - r"
- 6o-
.~ lkl~ r qm ~ lil~ 1:t ~) L6 ~~ w.J.t er ii. k .t.. ~ f-i 1i tl[t Ua._ cftt..o~. fYkt H.li =-1.3 'l.oek.. W(.
Of '"!f' Va., ~ ~..J~:
yw )3 'fii llf3)
fYI.et J44. uk ..akclt. ~IJ<\ <l~d """' ~wUJJ...: i :: u { vJ · YUJ telt ( ~3) :
.it. -A3~ = JA (~~) u ~
\Jo."_ f == o ~ U .t.. ~ .Ja. v7-.lt. orlass·rn~ : U { v) ct1 v+ a1
-bi-
~~ Z ,;tr- 3~~~tnd~ \Jam di. -Wtöt.. .en "truucL.. «JfJft
';ît J = À~ .tn m = -.3 IAlaou:lt t1L o~;,.~ va.n ('{ 5') :
~ UL. VI Z_, ( -2IÀI f'11)
LJ.t ~ -UMt k ~J dcit z .& _e~IMirXct û~ da. .t.eMiL ~Odlt ÎA • ~l~) hun dQn ~ rnu.J..~ ~~~:
( fl) ~ t-d' ).. 'UI D-rj ~ X == {io tl ~(ru·•J! A ·
O.e. -WIJ)"tL v~ orJ~~?' vc;L;n ~~) ~n :
~ 1 == 1 ; ~2 = lv ; ~3 = ~ iv~+ )od .P ;
1~ = t lv3 +- vlo~ i.
IJ.R!A. ~ orl~~ ~~ ~ ~ ~ clA.
~ ~ erJ~~~ <k t'oncÛ. ~- ~ 1JJr ~a., ~ )cutcl.U.of .RJLtitet .
3. B.J~we;t~ .ût ~WU:amt. ~~ctt.m~
lJ.tL ~ Ja ~:r~
}f = ]{t 'fx~ + f u:+ i!A~Jx
V~ = UUx - t(u~
(so)
(s•)
Dt. Pcisso~kJ Va.. .... i~ad. T 111ft T Ï4
f-r: F} =-fJx[(~U*J+arJ.-lifJJ
J. ~F
:=. rv . dx = 0
-bs-
~ 1 V ·~ .tJ..h ~~t. ~atm~~ma~Ji .. J3.J.owJa.. ro~ 'd" ti 0\~ nau cla. ~a.cul j" 1 na.. f~a.M;"j ~~~ dw.. .. ik~jó'lrnif"-. fk tXVt u"w~rt. ~n : ~ = u. ~ J3 = v ; 15'" = u." j
k =~~~-~ .. arf Moet~ rliJtiAJ -~~m .etA. 1a ~ FH-'1~ f Ja Jx ._ «- aJc& : ...
w = 1~ = uv u, ;~ = "\~ -fd1 ..,.J dam Ik ~J.rnrh . ~~In . }.J[. ... ;
O(>~),r,E,W ~f\ n~ -fi ~ai, ~JAn. o~ d.t4 w.t '\ ~ d@m WQ cv& u~t t... wtd :
SF<f .L t. J .2 ~u. = .tv+ ~d. u -f Ur- !f UUxx + t X ~.ux +.t!") u +Lt.h'xu
&fl gv = u V- 'J'")(x - f! LLI~x- W Llxxx
ma .JJ.J I" I) a.. ( ó o) .(,n lól) ·!à . :J/- ,
t f f8 dx= jf ~ v\+ ~~-~"x·~-~ .. x v-fu::.-1f"~~v.-zyuuxVz.-uu..,v +.u: Vx
1LL+ 1X~.xx 1/x- 2yuXxx v'x- H:u\,-WllUx1Lxxx-2tlllirUrxx- wu:U] b
~:
2 V,t = UI Uoc - U.IXXK
I l
_,,_
U.tt == '~.tx
t \/st = t!s L!3x + U.3xrnx
-bB-
~· KO'liL4- ck V~- UVt~j
OJ. ko4.~- c!t. VJW..,_ ~"J "'o'Uif nwk.i ·.., rh. .Jf"J..L fd!lelmil ~ :
-r Î1 3 I t 1 '6 =J6 u.- Tux elX.
-r f..L f J. l _i_ "d I& = j~Y u. - t u. Llx + la Uxx x
'
T k S' J..~t l. 1 .i. t 1 to =J'~o U - ~ U 1.fx + lo U!.ixx - 'fO Uxu ctX
Ut+ IA.U~+ ~xu =O
.BJovk~»ttt&.. ~~ ~ ~ 'm Á ~ ~ ronk...
! .
-j-0-
s. ntrt--1~ .s.t;;~rF·d
10.~ .u-no4~J Ntt-kwivu. $J,.;;.J;.ruam k.lt ,
l Af't ~-~XX +.l"f~)t\f (s')
LV~ AJ-'(x,i) .u.. c-rku- 3Jf{-ctiL ·14.
stJ tUt -tlxttJ = 1 + lf rn.e1: f MI j 'Uilt Jr;c:ti.e6 l}fM\ J.t ]~ ~ ck r-faais. Hit >WA dtJ ~ *~ (56) .,11f4t
Ft = _ ~xX" ~ ( r2+~t) (51)
f1d ~arnw d.eJ oam (s') .14 na. ~~tii:u:t~ v""' AY= 1+ ~f' :
~t =- rxx+ p lp~~~) ls8)
O.t H~t~ ~ Jjj k ~tJJ (s1),(s8) 1o~ i4 :
~= J t ~'+i~\ ~ (p: +j;) Jx (s~)
f-hl »f J.t ck ~ V<:." 12 "J )eiouJJ.. "' :
'2 ~t { P~x-~PJ:: ~ [1 ( p;+j:) ..{pi+j2)':_ 1{ffxx 1-1jxx)J
Oii k,t..,W. J~ cl.. 1IMid.ianaJ T :
T -f 1t (fjlC-1PJ +x lp'+!t) dx
J ( fi lli) ::. 2X p 8 j - 1 ~ p J X
Ik jcuJ.:-~ ~a.at ar T, T. .t.. M k.Lt ,
f{ Ji,lj ;r.) + ffT.T. J,M} + {~ .JIJ,Tj.,. o
0~ fo~J u~ k fa dat Tb\~ ~nrCJ1Y\6t~ ~", oJt uit lbl) dat :
f fT)~ J , H) = o
fJ~ ~ tla.t fT,T.} a.. ~CDMW ~. lJ.t. .1J8t.. ~ ~ la.d~vwi~ nttt ~ ~~~ tk P~orvf.cuJ rr.it T F~ ck rk r-cJ ·"' Á< rntt 1 ~ad.
-r f ( lli ~) ln-1 = x p S!f - j Sp clx
of h\it Ai' .tt\ ~ ai V~ :
-r,;_, = ;J x { ~ ~ - 'I' i~) dx
o~ o~ kwtrrumto...ii.. btb.dt.. y--J... , -r; - ~~\j•) dx = J 'I'~ dx
l; = /( f'j• - jfx) J x = } f i { '1', At - A/' At.) dt
T.; = J ~(r~t)~ t(r:+;)Jx = [ t (.y'tt ~ f(.f-.AF.) dx
"Ts = J ~{li-j•)( Pj.-jr'.) ~ l { P. jn- _,."..) .J~
= J f i I .Y't){ '~'•*- 'I'~)- ft i {'I'. Af .. - *• "~-••) dx
-r I I { _1. 1)3 I ( !. .t )( 2 2) j {1.. I. ) I ( )t 1t = ~ \r T-j + 8 fx + jx P +j ;. 1~ rx~ +ju + ty fPx+ ~jJc rJ x
= J Y~(~~t+ f(A~XAFJI-r't)+ ~('f .. Äf.,)+ ~[1.;.-;;l]t Jx
~ a-ndvtt 1~~ IJrJ;n dL ~- ~~icmJt nui-k~ ~~*~ orikkat J, we ~""" op .k eoordinaf.t., ,~i mQ;t:
'i'= (t;}& ~[;1) D~ H~t~) UJ:!cbult · m dut co~diruitn wdltLt dan :
.2.
~ = }(;\ r; + r~:J dx
~ .ló h<l t.. 3aa.. ela.t rk ~10'llll<l1it 1/Q.n p, 1 ~Cillll e) 1 ~ ~~0~ .~io-tmat~ ·ló .
f:l.t. .--&a.nonák ~ 1<1~ :
jt = - t(;~J. ( t ~ t)
~t = - iF + t;1 - 2; + ~)(
Û.t. 1f-- uc..- F, Î~', ·"' -te.. k/owk.. ~d: l .
~ lrtt•) = - fx ( t;~x'"+ f'2 + ~)
O.t. 1t.tmrt;.n.J WO.QllmU.. olt ~~ Áa.. \.Û~ r....it IA :
T = f{ttf~•- x f) el x
-1~-
n'kt ~x = V w~t dL Ja.dclucfaa.tar :
!,;_, = [~T.) = J tyï Jx
. -;s-
~o.t~
· 1 f. J. F. ~) j.A.kJ~ Con~lon r ma±vu.J to "8,,J. Covf-
d4.na.'tu a.ö ~ ca.ncmcJ ~J~;an A~. Sc.:. ~.13 (':i1~) ~'j
2. t J. F. BJtoe:t H.d~ H~~ ~ fwt ~ fji.Wila'A6
êtrica. Vkmt 13A ('ji5") no.b 58.3-~b
.3.J.m.\J.Thw.~ ~rvc..t J"'r.~ ~~k.. Af ~ T~ .. 'j1'
~· k.J. F. BJWbl On -f1. H~ ~ a{ ~4ua ~ ArrJ . .Sci.. Ru. 3o l1jrV) IJ.3o.
5. C. J .F B)loeJt. Arf'Ox~ma~ ":twd.ianb -{0'1. ;,"3 ~ WGUJt-4
AnJ.SU. ~- 31 {,jrs) 371
'· r ·J· P B~oeJt On it. ~twu;~,;tM of nota-kmu:t~ ~ ~f.tMl~M ·"' 14JQ.Ut r-'Wr,ation ArrJ. S~. ~- 5€~ B) vk. u
1· tJ,F~,E.\J.C. """' ~' d. m .\J. -r; .. uniM .
.Stal_ moJJ ~IACAiifM -{ot ~ w~ w~ Arr:J· 3u:.. ~ . .32{,~1') ''j
8.E.J. F .BxoeJL) ~.c.m.Bculcvuw. Po~;J. w~ ·"" o~ d.è.~ian ArpR. Se4.. ~. 32. (~~r'} 'f~s
l~·B.lJ~u.m t~ ~ ntm~~c&Àn. w~ lJ~ 0McJ ~CIM 1 1\w ~eJ '''f3
t,._
.. . .
to. R.m. t11iWt.a. > C. F. ~wull\1.\) m.o.~J
u. E .jcJnk., F tmcU.
12. n. F. VJ)fl:)i:vt
I~.V.E. Z~, A.B:S2tJot
TA af {tHtctim) w·~ 1~ tLnJ CJ.VW(b •