PHYSICS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600200436-7
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 17
• Document Creation Date: December 22, 2016
• Document Release Date: June 29, 2011
• Sequence Number: 436
• Publication Date: December 10, 1948
• Content Type: REPORT

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COUNTRY 'J3S'R
SUBJECT t'hyoics
HOW
PUBLISHED Periodical
WHERE
PUBLISHED i
DATE
Fobramrg 1
PUBLISHED
LANGUAGE Russian
ff1I100f.9v1gT00TI HlI I1t0Rtla90R 0U Cg10 TB1 INIIOILV. IITTNt1
q' 701 01rt,D' 176110 ilumil 771[ ^111101 0T CzRIuOa.u A1T 51
c. 0. n. FI i1,11,A 4 ?511015 ITS Tu11M,110R 01 T0111T11A910P
OP ITS COY110T, 11 SIT 0A1115 T'..! N1101f1010t1P P1?OA 1$ Pill-
U*110 0T WT. w*1*0? 5555 05 7011 wrto'p ve e*no. 00*
1P,L.MP010A1101 ,101TM111 10 505? OP M6 5555 T *1 BT113[10
THIS IS UNEVALUATED INFORMATION FOR THE RESECRCH
USE OF TRAINED INTELLIGENCE ANALYSTS
The fol coring p6por exebiAea tIle problem of the construction of
g no1vl naoravoopio equations of bbdrodynamd.os for "normal" fluids, derived
from the quashmsoheaioal a uatiofn of the noleouler system. Fundamental
attention is given to such ocmetruotiona sat to the nnalyais of the physical
pa+em~isea in the eiMmu&I g method, vhich, particularly, appears an a
quantnn amalo? Omroeponiing to the Bogolyubov'o method in claseloal
p~yeaos. Considering the definite restate, it ears that the origine+l
guano .e ohanioal picture flute its reflection in various foulaleti for the
cceffielents of hydrodyamnio equations.,
oreatiag stops to their approair~ations vmd limits o2 tsir applicaL_1.St.-i'.
be created a Corepum&IM ecadition of relationships for all demoted
operators. To`tevrer, since Leudau'a oqucticne vote not fermed? from
generally ui$erietood end a of quartiaa-meoheaical oguatiens, there L an
S.ntureet to further roeearoh on these equations for the garpooe of
ape=+ntora-af the dameitios and relooities axd, to cca plete these ogaations,
formulated by- L. D.JoAnAan Leagau fe-mid, mmloe=sl.B:nL o-L
. The problcas of the derivation of hydrodyne?ie equations of clasaioal
"leg, oc?irg from the molecnler-kinotic picture, lane lately received
much attention, an in ebova for ozm+la, in the ionggra~a ca Cbalsman
1] affi II. Ii. Bc~o]7sbC'! a25 the iatt of Kx voou. jj aM others.
A nonber of authors have noticed that an analogous problem o be
made by quaantum-theoretical exqmcinatians.
Operator emsmiaatione of qutnuhvm hydred9aemioe have already been
CONFIDENTlR!
STATE NAVY x nsRD 1 UIST'RtBUT1Cn ~
ARR1T .1^ ](J_f~.IC IA RnB Ix ----------
'-r-~
'
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9ha
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oRn' -VwA;ots dim stiom ; boweVerc, ;tttat yrobleaa was on3 the oolution
f o r ome D a r t o f t h e aeAe 124 1 at tbie time wu have nO 34nttationg.
beie yrob1 t yaegtmt* berg eTpesae as a 4 4DOWMI xation
t h i a a e bcoa t o O b t a in bydxvkvmAc e q u a t l o 1 w f o r " a1" (unw-
g eo *te) fintda. 1 also, in a sow reach, lee rill" mention the mmtYma
rhioh ]sods to the oalcu:tm#1on, frc*n the 4 kcal molecular
Pis of basic tinemstic oooffi$Xemrte?(1eooeit7, etc.). We vil.l leave
the estst.sd investdgaticn as a eab,Wt of futan'e was.
Me deaelopsent is the ) eonb year of the moued of solving the
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MI be W oma veer c asa4n auxeo1voe tbo Pronls3 of cec tructing
Oestsre1 maoroeooplo h442Aodymsmio ognatiws vhiob we derised fzes the
!o?al abec's a p+mAcrIetio a?t c will. be given below. We will
fully deter the ieg eaunibritmn condition (ys=+meetrio
ebaeuna daaeifff, ENNO ty, ; dffi boav ems. In afiatia eIuiUbrium
MUM three. '(two acelo W d o venter) a pear opmstantt =a
s of seals fl.uidg, the foii.ovimg p in ocsaitaone were
dgeeriptiion in file s9*tta equilI o .I . As in BW]$bov"a Mw in ioh
we c:ivuld hews trod two sas1 and two 4eotor dimensiotoa i.e., west
gealars) et a in this osae there arb two msaro7ele4tiee3
ememtnetion cuts of Imm mal" fluids Etch' the oTmoging meter ee:diticros
thsae am be selected fie soal8r d3s bicros ss in the classical case.
(If we mahe get oargelvt a the jiEdNbm of etoy'1ng a 1.Qiditt, -- flu
thee. o stops ran given is the pt o of I, U, Bogoi amd K. P.
Oamw Deere X. Qabv M7 The oo vg mstbeaaticel list n van
distnibntica fmoatioss detrsmitlin~ the mole onlar piofamo is olagerioal
am c a o chain dle hbatiaa cimto" 0042171M
y twe 1211
with 'WO d tiomom
opasntome cagttY ostAblia ed.
Ob tooo4, br this se t- I Owe am be oatabliabed a step for the
basis of ebb ring r ml o equation in tboao cease vharo the
molecular model am be described tv .
-P -
CONFIDFNTIA1.
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I
of patt#a7,oa 19i . (9) , 9j 1?) qt-' f ; ,d c; -- d?'djac 3 J
!' aostigatsan at ?a Seeds to +A* ecpa~totio a atZom
',, ,.. , but 4~sre. - OWFA),
an @=ov 1 ohweotdriebib$ of ba:
1. B,axtsitSan
F,jq~, ' (F*0~
to.. a oa.tt'at (bi=y) 1*v axd mVrJft to va3. a V. o
mmamtft
to tbq dexerlybim of sob a me9iei t
aeeei , dith the aft at the, d ti+om operators =ts1ce i)
To (8 _ 1, a,, ...):
F3 (Ir 2' ..., S) Vs 5pdr (r, .. ,, NJ, ] (2, i)
(s+l, ...,!) ?,}
or sat O matrlac raga (ia oaandsnata es at3oo)
01
+~e i)Is the kwm do dtiy Mb M of 3933aa Q" ~a 1 drL tio4 as the
Lmct:km of three c~rtesi n ooae+ab*tee in a tiao, at the sea's a
Ve a&oot ma 7ao1 ci 1 mcdale GV1vUW ;partto]?e of the eyatem N, ieaotdmg
tel m; is tho tomisn efor of the'laced eyesteva s reidat3ng w ith
*~? , (as oil) de V* operator Of the ,potantlal e~tffi+-
I. AqgptotU ognatian Yew Pat
des M ENS.) FsJ+ (s j) Lj( ~, s+,~F~+
JA 3t 819atie W. I right.
w6ea~ 1Q IS Is "M oyes+atak od Mw staled i and 4 4oordlnatee acting on
Um obmqp of4, it it utods as the ]+eft of BA,' aed on the abange of 9
Bij Fs (l,#...s)=Fs
at the bdaeW s'e'dan of the j and e+1 pnttiolae.
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vMMOENTIAL
5. Opewecbate (mat ico) ra, a1 to th caMitiai o the
z o oamaalatto, as tuwtm nodlfloatloa9 of Ibe axaoeioal
trrau st -Aiah states {hat at a sufficient vithdtaval. Of a nalwaisg
eaQh a gm ft 4iat dbution tmotfta ae fan be app>rax?matell, vith
thy a* the larammt* at the f Lion Si.
'meoc~tu of the aeoveeaiag oc e1at m boa a U Per val m
for the full aolnUan of ti-a daft of s 6 tive2y cabWot eel. opeetoza
c the egmatiam (2, 6).
6. Poor Ow Pasica1 @imeeaaian bating the ohecaoteaCiatic operator
ram
.. L
% j:((js c // (l-,?? ~fs~,
f ~"~ 44` `~ ~Nt \~Yj k N +g YX)~~2~ -'`j+d~Ql _x f ~JY'~ ~}
jci N J J
(p JA the 1Wu1ie oparato r. )
~'s tide, acoouamtiag for the wait Iampera iaem at the ooeratara P
WA `r ttm. 1Mt pch+lakiaa ct tho b1i y reeot2o ve vi1I Sail it, by
(1L1); wti iVe a41 1e tiwi latwvaa betmwm the two reacting psrtio1ae)
eooordl>Rg to txe Yaooaula (2, 7) we get the average Alaeosiamo:
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COM AL
/,q(X) (~,) j P (x) (2, 14)
nature of "parameter conditions" (introducing new agmbala at the eases time):
Having in 10.9.Il U. file 1.7Lsouea3on ;LD e6cn .Wl L, u.u11 tiJUGiiaz z pi; ' L ;lc, general pbyaical treatment ae operators (2, 9) - (2, 10) and avezage
Mate (2, 31) - (2, 13), me arm telm the foLlowing dimensions is the
ik= an abase-mentioned paper N it was noticed that cases of
Iunitone-spade distribution" are oMraatemisea by the luveriaaoe of the
operates (m&Wlz) Pe to space tamer, so that the sstheaatical
Arm the arremgeoent (3, 1) four the unifom-specs `diatrLbut it
fasiars that
i(q,,q,')zf, (t~* )).. (3, 2)
Ea the general arse of "noaaanifairm space distribution," by conversion
of ; aoordiaates, it am have the fora
(3, 3)
Fs=
2 GJ GS C, ~(~ S
uaifinltil, the sbeags of Is during the space transfers is saaoectsd
also faith o" of the first item in all tau aromonts. with the
oDea-gs of ig~ ), i.e., in the general came s9 1 , space n~ounitorrniity
eluaste ied b the presedae of the dependence of ?s on the argmeeat
sa that it can bo written
., ~... i _"r-
the iffispendeme, of fi , fret the first argosent .
PUrther, ,r9 have 9inilarlf ,
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for this a laaeien7 case ere fnUtn ed and applied to the VwQI aritiee of
method of introducing this parameter and o IIPWGICML aapedincy' of suoh
It is ccavcnient to introC parameter ./u . The
It is not difficult to be oeaavinoed, in taking into account (3, 1),
that the fanotiene uu p) g, vbioh ware not too wel by egaati o
(2, 11) - (2, 14) In the case of apace wnifaraity,appeatr "natant in
ties and space dime~oaime. :tear follming neorosoopio treatment of these
functions pxedstan nes the factual neutralization of the right-hand
parts or the forwela (2, Il) - (2, 14) slow the apace volass. phase
diseacietis are large in eeae ison with the radius of cotton o of
the oelecuier fro", and the ties interval is 1a?g In oo iaen to
the "unit at moleomlar time"/o fyiP~C_p*~t,e,~ eIPIop is the mathe*tloal
expeotatien of the absolute value of the molecular iesulae..
The vary eoleotign of the mstdd of "variation eoaetents" specifies
that we wjll be dealing with f,u tioas which a1ovl7 oaaugo in time and
space and with the calculatian of co that which is indicated. This
will indigate that e,4?ip, eappear as functions whiob elcoly change in
relation to the. indicated areas of the "moleouler scale."
3h the S at of the abome indications, it to neoansaz'S to sasamine
the ri;at. band parts of the fad (2 U) - (2, 13), which leas um
to a aerPTiots aadution for the fcameof is. The soluticm of the ion
(2, 6) ftw Iga, thick eatutios the oamditiona in (2, l1) - (2, 714
should di!"teoo spiv a little from the ootreeperAft rpaoa-uaifanettV
soszttiaal, evhioh is osturall for the eguatian (2, b)) .
and JA f .
Thee, introducing the spool = )A (i 4-7 GG .
F5 = i3
The last athiuitioal uanolnsian will correapand to tre introduction
of the M U pa>!aestor J4 , which aim be written
Fsa h(lu(Qr+T1)4) 21,1 ,,, ?J)AA)
with She idea that, as),(y 0, the s02utioa of is Boom cur to the cor-
respoaing apac.aailaaedt, sciatica. It lswdiata33 toilers that
the pae'eneter aWditioss in the general owe appear as t'amotscoe of
sOik fs = fsJVP'/,' M.6 ',k,1
zA.
~OfF1?ifl I
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I
Few (3,6) =a (2,6) it IS not diitioult to oaostruet an, squatioa
tai' Is ehUh we abed trite out here in a ?dsveloyed.? Poem (in vhiob the
O ft! alaog 9 and 4 are alreagy aooamted for an indepeadeat)
at % i~J4 (41
+1 fs + (3 l1)
Mai Oaree of rpaoa itnfaraiV P1 , in the fleeibed lpuirw, it Ss
o theoaf- the g .ral lbmtim a! the iy-nlse 41atr1batiaoo Wf)),
lP, )P,)a Jt'pr'','~~~'Z -pt) (3, 12)
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oalcala, a the arragumt 1n the ab?enae at degaaeratia I&M
l? l-W -.
OkMw:fc,.&, for brevity we will designate ? - fay '
TIAL
Pdd (3. l )
8m eft)mo "lee itian" airgaotearistias, i.e., At). l(y%ns. NV (P)
is tie awbw4a r'anotion. Ml Owe oaesols+uias, ae can be ily abaisn,
ravsla ID full lom ma are Valid In weds of 4,49 m 4to aita it 1,
is ra 'ded as a peareae6ar. It in fMailas (3, 18) -
M,30) to a'k??e'tL) andwtp)te )andw ,,p').
m eaoeinding tisia beatian it ati1X rasalnu tar us to a iso'(2,U)
(2. 13) wlth the aid 4"(' )&4 paIoh in easily done by calculating
3, 5) a 4 (3, 1) (bees' ~,i ~~;. - %; )~: = q; ) a
' LGi (~,~~_~"Y_ ?& ~ l ri)1~''a yr ?ru('cp) ;; (3, i7)
/?~~,) ?~' ~+ n S y r ~ My A At f, (~' &) AU~ f (-?)jj G +
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f
A study of the right-bead pats of the fW-MISS (3, 17) - (3, 20) Shows
that if we eliminate the fire:. ocuponent in (3, 19) which bas a definite
gstcn'F; dot. iratiou (as Wc; :; .EZ ll coo, an our valid approach to thin).
then we will oom to a full analogy with the classical theory In the
reacefti form. This leads to important eoaolusioass first, it E is
to be regarded an a parameter, theaw( ,p)oan be treated in the claaasicel
vay, as a "function of the c?eneity of the distributed ii,ulses in the space
point ?,0" ". Second, the analogy in the recorded form and indioatioaa of
the trestmant pfW(i l1g indicate in use the correctness of the selection
ofPV0-J?`'and U In the nature of parameter conditions used in Bogolyubor'a
aathod, the composition of which, with alterations for our problwla vs
shall now study.
$ conformance with the, examination of the problem here, Bcgolyubov's
method can be for ai1ated in the following way .
The abewe mentioned dupe Ior0P,/'a? ndp l9 introduced In the
eiuilibrium one aanser as constant dimeaaioas which are taken as t
"pau%w tar oaditions," i.e., the farce at operator chains (me'trix),Ice
in cuw case is fully dletiagxiahed by time pa matdre. At deviations
Prow tie ,g9,ni$ibrIM case we find as before that these five disMNiowe
ram eft in parameter condition, i.e., is every aaaaeat of tins t ,
for the t ee Of the abMa, s fully diaatingsishes the task ofp,11144?1- and/P49
vary aamct of time at which these five al 14608 are now
rs dad he slo Viy oheaging tuneticne of tim and apace . The form of
the last function is determined by the solutim of five differential
eq=tiem -- bydrodyasmie equations -- determining the behavior of
these five dim eeicas.
The basin ps'ob3.om ino3. den the construction of these equations in a
chow waAy. Tie will, notice at the outset that the darivutives of f,PkKandFO
in time mould satmttioal'ly return to zero when the equilibrium
caaditian ooanrs; formal t of this appears eaM - 0 . Because
Of this? we will present the desired equations in the ferns
"-A,
GJ, ;L ... (!?, r)
~,IP u?`/fits Al
t f0 /dt 01 ~- /C2- - , (413)
AM the apparent form of A,) A >... must yet be
foamd
We will rot= now to to chains watch, for asq moment of time,
iz fully determined by the five pmsramatara for tact Moment or tins.
This mesas that ammg the solutions of the agwtims (3, 1.) for fs
we shell choose aalr those solutions in which t e dependaoe otf on
tins is not direct but it s.lresit -- through the fore of dapendrmoe of the
fnoatima
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I
ca T TTAL
',vllr IVtN IIHL
c
et
ntes
ert Y - u thus equations, i o., the series of
dz iva'tive s1isenaions in rs deflate ealculaticru will be determined by
a series of P d * eaiaas mhiah, as we showad, Should be sia'sll . Thus
it aen 'Oars spill t2le a of fs in time is oy oztisedrith tSL9 ch,smga
of the Siva peg a; for a an U)..; , the same thing ocours.far
pane of the equatidaa (.4, 1) - (h, 3) in which the Solut3C?s Yor i~/'~
end f Q ra
e b
lt
d
on he ima / a w vxiv uv)1W34V114'V
rTnction
!n- n P~u, !~9'`J, thecl irclm this th? eXpren?ions for the
A e..d...,at....... . _ _
as tslov4 changing fund .onr rf rr r - ,- nnQ 4i.^g t f -,1 t -,o P^a (4, J-N
_
There M-~1 1e a deop physical nsa.i3ii in pitch a selection. First of all,
HA 7t;17 ,,And +7.n+ n?nne - .. y.-. ~.. __ -1-i _-..
From this vs., conclude that, "ersoaFhina cn t?P of ~ - i . A - - +x.,
521ua,. we i va or to the asoreeoo ,ic trestr t of p , LL
Q
,
.
We
oen nov call those aimensicu s,analogous to the c .aweical theory, that
oj-. asaaa-gy an a up=.
point mm egvatianu 11) pan be +7.....+-A ...4-'1 -___
!3s ~~s~s.",~ gs'1 {!sl~)+ s~~C~'/gd1?..,c~5~/",k?~Blf(4,w)
uymaaapei ax 5 (YjT Tarmo the t of these pelra,aeterq, The erpresoi
,4, ahoald eat1ef+8'+ by eo7,,.+1.,., 'it 771 >,..a a_ ea L31_ ..
:NS La) 1 O-'Jist~~ 54-+1= O
4m oz. VI ?' ,7;- -, fn
LHSs (a)
.7+ 4 J- ~ TO; , str ~9 i ~ y
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Em k alaz1flea the Hcmiltanian operator of the closed system 8
of the raeottng doles, which does not ocazeapcad to the operation
algag
Thise equations have a ooeaplets erreogownt. V. intr?~ o? than in
the ocnstruction of the possible unidenrioel breakdoean of into a
series (4,4). These a gaaents can be obtained simply by the aubatitution
of (4,4) In (3,16) - (3,ao).
CONFIDENTIAL
50X1-HUM
fw 10
0
rV JO)
fw =a 2, - 0
I t w e ranwaly pswsnt do/dti da 4f-Id tavid dt~Idt, as
derived frar (3 - (3si8), ti n us saea..diat ly can aotiee that the
goat torn of Ae, H , Cj is dtamia.d the solution at equation
( ,4 5) with the oaieuIatScaa of additional oawditiooe. It ve could soave
the agdatiowe (4,1) - X4,3) in the first apprdZinatIca thin by the now
tokis we could fully d.t.rrdae the farm of functions, obtained
to the reed'. of the oasraticn o A 67?/110417 l7A Co . $aveeer
the meta' (not detail.d) tarn ooA2, a2, t:2 can be fond without solving
the aquatics (4,6), with the additional conditions of (4,u) - (4,1.3),
at iioa the Amaral gwelttativi =81 19 of the op rat'osa Just mentioned
am be mad. Bach Is Bogolyubov'e sohe?e.
C tIAL
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I
At first, as we mantic sd previously, as will unMortako the formal
eanetrnotion from (3,16) - (3,18):
?'-~-~-- - -X f'; ~' (4 ?)4~o 1, J
(
z-v e,
d
r qq tt;; ,
V* dw
V. oospot. further from (3,11). Theo for (5,1) by va of several
omrayiaoo w ?.t:
d a cJ (:) d
;7t-- AA
The ocav rsiaas for (5,2) and (5,3) are :r-re a p1ex. In thm we
tUid quanta ulmaroot~rietioe of riantr7 f,,. at vhioh it is obvicue that
3W mp rate. ALL this Is of definite inte2vst eon tbsns a= c mvoreiams
fart (5,2) war. led also to the oaav reii,os for (5,3), whiah are
baetoaly anslo one but even mro cumbrous, and so for thaa. w will
writ. cut hers only the definite results:
Thus for
(5,2) w. 6A. !'ti am (3,11):
m An (Tu 1c, 01
: (3j
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tp' / (((c7 j t7v', lL''}G, ate -~'G, lz'r..,?zu'>Z,?dx't?" tV11
-rtJa ddt a~C~$~IganL y~'q??//~~jr~~I?~~o,
Haase h r,~ t ~ t, ` 1.)m T~ Vj~ i, - 9: I I `~ 3 \^UI) e.p.+. 1Oa
the derivastive for vh b we obtaln.d,, aoaomt for the fact that
Rheum, frft (3'13) ve find:
2: _L V
;L f
Bat In ooaNSianoe vita the g3 etry arraws ent (3,9) we have:
q (,5-)7)
a
-
frais vhiob
.l 419.1 c,%0 a___... L k (91, q) d.j
(' Z r) 8~ ~i, (, )-h dti ^.d,
COMMMUTINAll.
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Whioh is tht a., strioni tenor of the eeoagd aegree. A beeioaliy
ai?i].er ooaveialcn f'or (5,10 leado to the following result.
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Sol st )&
-f- J () q,) 26t (t, q1 eq ~-
spa w will notice coat acain tact cfaeivm sr a1 in (5,7.0) and
(5,12), not being ena1.6o06 to the oleseioal theory, are responsible
few only the tam of the eerieo no laver then the third degree of u. .
Tts aamp+wieaaa or (514), (5,10), and (5,22) With (4,1), (4,2),
and (4,3) rsupeotive]y Vault tai 1 sdiato writing at:
VAK~
C,~~IaN~~+T'~d .+a a 171
~ aS? 01 /0
~x
d
CAM' 'r.W
VC-1 -8
dire rats IS determiD$d tbio 4 (5,11) end
-1h-
CohP?AL
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COAL
f (e Uee 0- q) -I- ~0 j +,,-- -1 - - -.. (x? M)
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whereTlt 3s determined by the expression (5,].l.) in which ur and Ia
are placed Instead of ,rVerd (-+a),? In siailarly determined. j-,aUa,
we have came to the problem Of finding k? ?) and $L to) and fully determining
the hydrodynamic equations of the first approximation (ideal fluid), of
finding the ways of salving for I& rr)and h (rand, consequently, the possibility
of oonstructing hydrodynamic equations of the second approximation (vi ec a
fluidity).
VI. OBTAIPIf THE BYDEODYNAMIC EQUATIo$ OF THE FIRST APPROXIA(ATIc1
As is known from the general theory of equilibrium conditions. In cases
or the absence of motion of the system as a whole, i.e., the absence of
macroveloolty, and in the case of space uniformity, the function of the
distributed Impulses will bear even (/pl) en$, due to our basic
asoumptiona, will be delandent only, on two 'parameter conditions" - p and 99
If the system moves with the velocity Zd, , then the function of dietribution
v51' be Ur even (l r-.nuj); this remains true even in the pecrametric
depandenos of Zv on 4
Mu s, our f mottoni,.-(O)+hen7t=0 appoa.-a as
MA l'deae 7rtQs yv~p~,Lyaven~'p_i?}i pf)s?' . ~' IPi'cm (3,13) we
We will i itrcAwe a aeparate value for '%,-o
then
P.P, 9"t-1704 e(P, W)eV/)?/' dp, t6,11
Pzui (6,1) it is not difficult to ace that
lh OMMMI ones (no)
4y" P
,,,a'Vr %e(( Ae )? (6,3)
trAsie at the (4,5) eI stun sbava that they app rain ovations for
equ1li 'ie ocailItiums. Oar problem new as the solving of the (4,5)
egnatton v..th eedittomal mzs*Se?ents t,8) - (4,10). It is not difficult to
ebov that the solution of egmtiam, (4,D) in aatisflring the arrangements
(4,20), ri11 ear as (6,3)
1j) so
WsW
teris ' as in , (~.10
in 1610h r* i fle 1
MtUally. It f fq,.??, rolved by (4,5), thus satbdVng the amanamants
ni'o also be eolaed by these solutions,
end bcosm[e of a s1mi1k solution, it should be:
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the apparent ford ofTae1 and .S 0 does not present any epocdel ditfioealty;
it to oply necessary to aoooant at all times for the evenness 9runevewnaaa
of the integral functions anainue, the expression. For we get.
7"?$ x Sip ML ~' 1p -m-c1Z2. Op-mar/o P??'dp..a..
oil1(/q/)19'lea(q,Pad)dg)= , b b~
where Is Sroneker's egenbol, and the function P according to the known
'v4-y l" theory is the pressure.. As for jut , it is not difficult to
show that S sp.
Mtually, wheawe.WB?e? (1p - oaf), it is easy to notice that the
integral ezpreeaioo of the first cosWonest in the right-hand side of
(5,3) will be an odd-neabered function and,, actually, the integral is
equal to zero. ldnrther, fad (5,L4) and the calculation of (6)) and
(6,5) we get
jq .)r
f. 11-111 (( ---0- d ' qip, q, ` 0ltap1q yq, o, (6, 7)
~
N J ay
~ z) 4zegra U ?9r.%
and, oonsequentk, the second and thud o:mposenta in (5,3) will also be
equal to two, vhe ae ,,Se s0?
Thus, we get the bydrodynasic equations of the first app-ination
aP (gig 34 at ?0 64-'k- w 0, (ba p~
e) e) a
i.e., we obtained the general b$rodposaic equations of ideal fluids, raa
which we have oompLnted the problea of this paper. Tice analysis of the
squettoae (6,8) - (6,19) .howee that queotum-aeohenioal (end not the
olasutoal) doeoription, cowing from the molecular nodal, appears in the
computation of the flmation P. Al.thoa& the furauia (6,6) determines P,
it IN stellar to the classical, however, and the change of the classical
function of distribution is clatter to the quantum. The apparent form
of these eualogier is connected with the further devoioprw t of the
moleeuler ao6e1: 'eons, for axsaaple, in The de:ercaioetiou of Za 9"0 we may
have the known function of distribution of Bose.
it xaesiu for w to consider the emeral perspectives c8 oalculating
the ]cistlo poeffieiante. La hts var.
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Zgnation (4,6) is distinguished from (4,5) only by the presenoe of
a noni~aii'bra term. In the Calculation of our reeo.lte it to easy to be
ocavinoed that t$2enonnniform terra will appear an a 11neer,oombination of
primary derivatives for from the functions ,2 Y and 9
coefficients of these derivatives rema_n un1nown.. It follows from this that,
in accordance with the general theory of nonuniform linear equations, the
solution of (4,6), i.e., 1 , v ill depend linearly on the donated hi r
derivatives. If we Ln e j' and$?g`) ehero the solution ofd[
is substituted in subs Ming the itional arrangements of (4,11) - (4,13),
then we will arrive at espreesione, by my of the determined eathematitical
operations, t!bioh we similar to the classical. fuller comparisons
will sheer as the true physical interpretation of the coefficients of
derivatives, and older expressions of these coefficients throuoee
will give as a solution for the calculation of the kinetic coefficients
(' 57 and thsrwal coaductirrity) coming from the quantaa-mechanical
molecular pieta".
The isaediata ree9.ization of the aobsme put forth here
requires greater devdlopmat': of the molecular ploturs, I.e., the
seleotiee-..of seas concrete meal. In.partioular, suoba selection will
tally detereindie-97012 (lpl) and also rl s The determin?tioo of, r3 needs
oooeptttstioo 'od? a aerbpa. o! additional Considerations 1 for exeAvLe,
as ec utation "of a condition of decreasing correlation" for the
meth Ye, etc,.
The solution of the indicated problems will serve as a subject for
future study.
1.. Chspasn awl CowUng, ]fatheaatlltsal Theory of lionualf am Glass
New ink, 1934
2. 11. I. 8egolynbev, .bMema of L?hs_ iwemio Theory in ststiatieal
Pbyuo,s X, 7946
3. mirkwood, iTgml e! Qyea raaL Phsa. 14, ldd1, 19 ; 0, 72, 1947
4. L. D. 1andaa,l s 11, 592, 1941
E. P. lotus Disertat m. MM, 1946
6. a. H. ZogD'Fabor end E. F. (horny, , 17, 61$, 1947.
7. 8. P.; Ysateik 1W. Se 1, 135, 1947
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