CONTENTS AND FOREWORD TO RESULTS OF THE NUMERICAL SOLUTION OF THE INTEGRAL EQUATION ENCOUNTERED IN THE THEORY OF LIGHT SCATTERING IN THE ATMOSPHERE.

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200170036-3
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 5
• Document Creation Date: December 22, 2016
• Document Release Date: April 23, 2012
• Sequence Number: 36
• Publication Date: August 13, 1952
• Content Type: REPORT

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Conttrnts a~'1d ~{'oreword to "Results of the Nu~neI.~.ea1
Solution of tk~e ]:nte xa1.+' ua,a.o~a {' c;oun~ed ~n Lh(
Theol7 of Light Scattering in the Atmos here'.
Ye. S. Kuznetsov and B. V. Qvchinsktiy
Source: Trudy' Q ofizicheskogc Instituta, iN SSS,R, No ).~ (131)
Moscow/Leningrad s 19L9
STAT
STAT
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Cl
Y
1,CONTI!I'.fs AND ORLw9Pj1O 1L. !ULTS 0~~ T~iE NUME~C~
SOLUTION OF TIfE 1NTBQRAL 1~~,~TA` lOPd C UNTI ED xN THE THEOi ~>! LIGIITwSCA''~G'EIxNG 1N rr'ijE ATMOS1'IEfE' n
Ye. S. Kuznetsov,
B. V. Ovchinskiy.
The following represents the foreword and,contcnts of Trudy Geofizi-
rnote:
Cl1 ealCe s k y~ a Instituta 9 AN SSSR, No. ).i. (131), published 19h9, at Moscow and Leninw
c
g radj
Foreword.
The present investigation represents part of the greet computational work on
the application of the theory of scattering of light in the atmosphere, under
taken in the Mathematical nepartment of the Geophysical Institute, Academy of
e
Sciences USSR on the basis of the theory' works out in the Department during 19 3s'
,
(Note: See the works of Ye. S. lcuznetsov n lzvestiya Akademii Nauk SS4 R,
eofizicheskaya Volume ?VII, pages 27-336, 19i3; Volume
,~r~ruta ~.;e;o~raf~.ckeskaya i G
Ix, pages 63..72, l9; ' Volume , pages 2-223, l9L~ . )
The entire is divided into 2 parts each of which is
.material of
formulated ,separately, the present first part includes in ;the main the results of
the numerical the integral equation encountered in the theory of
numerical solution of tr , ~,
scattering in the atmosphere for various values of the physical parameters, and
also the auxiliary tables of various designations and tables of the 'haziness'
coefficients. All tables included in this part are of inciopendan interest, but
TR*cTED
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v! Ri
~ L o can serve As the basis ,for computations in solving; various practical rind
cal probloms connected with the scattering o1 light in the atosphero.
theoretical The tables are aecozn~ ~ anied bYtexts in the Form of six article, the anain aim
of' which is to give a TpoosiblY complete representation concerning the numerical
methods employed during construction of the tables. Most of the computational
methods and results obtained, as given in these articles were original and were
specially do veloped in connection with the corputatiofal work undertaken,
In the second part are included tables relating to various concrete applica-
lions of the theory of light scattering in the atmosphere.
is of eomputations in both the first and the second parts, refer
,~].1. the results
to thc, case of, spherical scattering. Non-spherical scattering is a subject of
special computational work, and the results relating this case will be foznulated
eiewhere.
She numerical cal methods employed during construction of the tables were developed
by Ye. S. Kuznetsov (Articles I, II, IV, VI) and by 13. V. Ovchinskiy (Articles TV,
v). General guidance of t1ie work wits exorcized by Ye. 5. Yuznetsov. The camputa
t -
was conducted by the computers of the Mathematical Department s~f the
~.onal work .
xnstalute :narel Yu. A. Gulin end Ye. V. Kuznetaova, under the direct guidance
?
., ~",
of B. V. Gvchinskiy.
The authors thank Professor I. A. Khvostikov for his organizational assistance
and unending attention.
Moscow
May l)t~6
TRLcTED
Ye
uzne is ov and
N. V. Ovchinskiy.
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Foreword
Contents
I. Table of the Functions En(x). Ye. S. I(uznotaov
II, Solution of the Integral Equation Encouriterc;d in thc~ Theory of Light
Scattering by the Method of Successive Approximations.
Yip. S. Kuznet$ov
III. Improvement of the Zero Approximation. ) . V. Ovchiris kiy
IV. Comparison of the Approximate Soluti mS of the Problem Concerning the
catter:Gng of Light in the Atmosphere UJith Solutions Obtained 4dth
12'2
2628
The Aid of Integral Equations, Ye. S. Kuznetsov 29.37
of Chandrasekhar's Approximate Method. B. V. Ovchinskiy 38~Li.3
The Accuracy
VI. Application of the Numerical Solution of the Integral Equation Ecountered
in the Theory of Light Scattering; in the Atmosphere to the Setting Up
of the Tables of the Coefficients of 'Haziness'
rxplanation of the Tables
gable I. Functions E (X) (n i,2,3,)1)
n
'fable II. Coefficients F and 4km
Table III. Solution of the Auxiliary Integra. Equation w(
Table IV. Solution of Integral Equation in the Theory of Light'
Table V. The Coefficients Hg
Table VI, rI%he Integrals II and M
Table VII. Solution , ()
y
Table VIII. Irradiation of the Earths Surface by Direct Radiation of
The Sun
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Table IX, Tot~1 Lumination of the Earth's ur '
A~?
Table X. APproxa mate Solution o L Sc
hwar7scllild and I''dcliton
'['able XI, ApproxlrSolution Accor'dins to ChFlndra$e~chsr
Table XSI, }iaGiness CUe'ficients cT (1"
9 Q) )
Appendix? T, Tables off' Trans:Ltion From O tica].
p Flaight; Above the
Earth's Surface to the Usual
xx, Graphs of Comparisons ox' Exact solutions with
Chandras ekh4 r, s olutions