ON LONG-TERM FORECASTING OF THE CRITICAL FREQUENCIES OF THE IONOSPHERE AND OF CASES OF DISTURBANCES IN IT

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200170008-4
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 25
• Document Creation Date: December 22, 2016
• Document Release Date: April 23, 2012
• Sequence Number: 8
• Publication Date: August 13, 1952
• Content Type: REPORT

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Ionos h re and of Cases of D sturbances ~.n it
oft?
Akademii Nauk SSSR, Otdeleniye Tekhniche$kikh
Izvestiya
Nauk, No 9, pp 119-113, Russian Mo per, Sep 197
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:. STAT
 11
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ON LONQwTRN 11QCAiTxN
ION0~1'ii~ IND OF CAS OF DISTU t 3A C S IN IT
0. N9 a'ten4Y
Pxe~end by Aademi.ctalt? , Vvedenaki?Y
? ti.on ~~
'~ha gc~nexailY' known cirG,amst~nc~, that the ~,'~~ ntita
u1h the iana~ah3ze is :~c~as, the shaxtc~x
radio eaves on pas~za.ge thxo G
. reiect? an ~'ax ~~rair~te~xupted,
the wavy, aompe1~ si ,
~~ tx~ which, wr~i.~.e c~,osc to the cra.ta,Ca~. wave"
off' the shortest wa've~.erl ~
iength, is still capable pI being ref1.eced from thG ionized layers
o 'b is wave1e1th, texm,ed the aptamUm, is also
off' the atmosphere. ~
'1~h xe.~ ect to Gbtaa.nin~, the bes't possible
the most adv~,n'~a ~'eaua w~. p
transit off' the wavesa
have been est-a1a].a.shed between pl'~~enomerla
The c o~~xela,~,.G11a thy?,~ ~
the var].a.t'ions that take place in
on the sung on 'the one hand, and
the ? ' mabnet~.c field, an the othexhand,
i.c-nasphere and the earth
clicti eomaglet1C and jonasphCIblC disturbances,
make it pass~.b~.fa , t ~o pr ~
. ~ d working Wveiength5 for radio con
cx~~.ta.ca,l frequenc~.es n
that we are able to foretell the development a~
t1.GT~y t0 the extent ~'i that
solar activi.'by's
va.t ' is characterized by the follc~wM
The candi.,o~, o~ sa~.~.~ pcti ~
ing da. ? ,.~erent which correlate non i~unfor1~.1Y with the phen-
the wa1,f numbers, the areas occupied
~ ~ indices, omens, transpiring on the earth ;
by Eand ~r~,cu~,a,e, the ampuJ.ses of sol~x acw
?ivs9,unty and spots, he prom~.nonc relative a~ intensity in the su.nspqts and an the solar
L '
e a' the Baniex series of hydrogen lines m
su7f'~. ~.C
of.' correlation is due to the character
the xion~unifGXm degree
.,
STAT'
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, and ~,~fk,~~
?1t ax
o~ the x~f~~A'~`~tCn tx~
motion extib ted b
to the d~ac,t~,ax~ a C~ the sun.
'~~?,~' tQW~d8the ~C1G a or tati~c the ~a ~ gC~l~aUx
why a~.dr
.
Th ~r~bex ox ~pns ~;oxraed on tie ~--
d area off,' tk~ actiYS x ,
ax
cge nu .., ~'ab~.' e'x'am ye to
rs; onstant and ;uc uat oons~dp
c sa.ct~, '~y
,ux~aLf; not c u ,~ eax~~ ayC~,e off' so1s~,x
the ~'und~nenta,~ ~.~. Y
ye',esu1ta.ng ~,n ~x,atw Tl mnt ~,owc
Ve z~e~;~,ons ~'cam Yaighex to "a
~.an n~ the ;~ct~. rnant ' tY1e
Wha.Ch s due to the deve10P off
~.~udes on ~~-~ snlax` stiu
~vn ude caused by the
, d1$P1G.c,ement in 1.0rl
da~lental cycle t e h ~,~.na;~~nn off' the se's
?~a1e ~.nc
' tho hello splex'e, and a,.1sa
xo~,~~~~.an n~ ? ? sex` a:th at~~ex We1~.w~r~ptiin
the eciipta.C, togetr t,hf.
ac,~s to .~p~?anF~ n.~
ve cYc;~,es ovaxa.atiQZ~ a.n
. in the to ~~. G auseS ~ g1,vF; x~so~ ua~.~ aern,:~a,n,nu~~ (sprig
cnr~d,a.ta.on o~ the 100s~bexe; 11Myeax, ann
nal and'?7wdaY' GS'n1es~
au?tiflfl maxi-rnm) 3 Seaso
the oarx'eJ.at1?on be?
~a er, We shall prisidex
In ?~he present r P
and off' ~,nnos~k~ex'a.a
~~ .ta,ca~. ~~equerlca.~;s a
~,Ween the J.~.?~,eax C~yG1e at: c L~nlbGxe~
rye handy and tha Wok n
? is d~,stu.~^b~nGes, on t he o
end mag~aet
on the othcx hand.
'j,GNJTIC AND :CONOSPN~
IT :SON T0 TkI~ i1"' GIG L OF O? NB
o~ c;~c'~.t~.c;~~.~'?xequenc;y
e 1s i~ s usir g the dat a
~3erkn.e~' ad ~~. sltiingtran and ~ath~c~a
haxe stat1ols [iL Wa
n ~
mar~'emen~s by the ~.oc;s
f ~an between the nurabex
a la,neax xe1a.
hi shed
xom ~g3~ to 1937 a es~~.
annum
of sun5pots and tha square off' the mean a,,ue off 'the
fox the '2
'xequefc
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Judson, in his papor ''Comparison off' data, on ionoaphQrC, ~unM
pots terrestrial ma net:Lsm" 2) a ax.d also Smith) Gi11iiand
d
s an..
and Kirby using the cri:bica~w requenCY measurerltenta o the
~ 3~ ~
s h ra station from 1133 to 1937, established a good
aha,nrton onop
W~~ ~.
correlation
practically a strict one M between the WoJ$ numbers
and the critical frequencies L'or the k~, F, and F2 layers for noon,
and for their diurnal minma0
By now the ionosphere stations ox the world have accumulated
enough experimental material to draw conel.usions on the variation
of the cr ,ticai frequencie 3 :for the ionasp11er( during the enti.rc
11-year period. The Washington ionosphere station has the fullest
expexhimen*tal data (Table 1), and re ul&ly publishes the results o?
its measurements in the journal 'T'errestrial Mai netism end Atmo w
pheric Electric ity
Table 1
_
-
Year
F
? :
f
: h
2
1933
5.15
206
1098
3
13
509
1931
6025
3015
3075
3.08
11
901x.
1935
608
3.35
)4.23
3062
18
3605
1936
10
3.7
5096
108
20
7906
1937
i1a~15
3.8
602
5.68
3$
11302
1938
1102
3.75
6068
y?82
L0
102
1939
1O2
3.66
5,9L,
L.8
38
92
191.0
8Q6
3.5
5.22
L025
32
68
1911
7. 5
3.37
14.5
3.43
2L.
48
19L2
7
3
)kl4
3.L1
19
30
19L3
67
2.9L.
)..9
3~2
18
.~
:L9L1i4
7
2486
L..8
3429
16
10
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I~i~1ia1~UAs*u6k~+
61i YN61 ch'aMteriHtthe
?iura 1 thAW~ the C
flobserved at waDhiton end in
vax'tion in the Gx;i,jor~i exaqua
a.cc;ord~?~ to ?thu 5rd~,avsk, cctita,lc-~I
the n1umbux N o! magnetic s~oacm r7
n ss have been taken at. 100 percent. lha
The m~x~.mm valuo~ or ~ ~Y1~a
~ the m?an va-loos ~'or rho cx~.t~,na7. ?rcaquan-
curv(s o1 rdistribution ~ ~a,on o
w r o storms 1'1 are s~.ma.lr~' to the cu.rvc;
etas f and the number off' man.a~~ ~~
~ s mean values o,~ the Wca1~f` numlaaro W,
oi solaz' ac~-~.vt, ~ya exprs~~~~ac~ a
the c'$ in the pxe~maa~~m?Yl ~,'z'c~na ~.9 33 to
but ~tii~.s rr;srr~bl.ance of ?trlc
' n~;d a,~',ex the naaa-~.m.~am. r'ha.s rs~;ul~ts from
1937 is not .~u~.].y maa.n~-aa.
cause, be.lng the pxoce;ss o1 soa.ax`
the ~a,ct that besidcs the priniary
o'r~her cause that an~'~.uencee ~thc; oY~arc~a~tc:r
ou~tbux~~, ?tYlerc: is also r ~o an
C~ a ~
'h~.s second ca .u~,c , consa.s~t:~ in
of the a'tm,asphe1ic ~.on~.7 a,i~?i.ort curves. '
ase dGVe;l.t~p, the ar.~t,vc~ zones o:C the sun
the ;:act that as the ~~1^OG
in OOrlY1~C~1.aI1
the high solar laU.?tudes towards the equator,
move ~xc,~m
these a,ctivo arga.s towards ,thy plane
wa.?th which the radiation :Crorn
o ;C n?ta.y also towards the e arch is more
t,
' the ecliptic ( ~ ~nd c on,~egtia
each o~ doc]..i-ning aG?ta.va.Gythan during the
con;a:t.dsrrlbl.e during the p
epoch of its rise
fact should be noted that not all of the max-
~he remarkable
icna oi the U.?yoat' curve a1' critical frequencies coiri.cide with the
~ rjY~e ma~.i~am number of magnetic s?tarm-
maxima o the Wok' numbers. -S.
s about a yeax? 11ae curves of critical . frequencies also .,aa,.~ by .~
F ~.aya' and off' the frequencies for
o;C the noon va.)a~es for to 2
the E layer co e with to maximum o:L' so1aX' do ~iviy, ~~~b,~t the
~.nca.d rn
r frequencies and
m in~.m~um values of early morning critioal fr~,q ~1
(n
i ht ' lag by a year in their max.arna be-
also those at m~.dn ~
hand the '- solar it W, and. coincide instead ~ri?th the curve of
solar cux~rc the
number of . magnetic storms 'these facts, remarked by us as early as
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e uenol~ the mnA~~,c Q~s, arid 1a?ax~
~'or th e cx~,~~,aa
191t,l ~, fx~
car~irmQd
' ~ret~a ~ to'm, were
atr~~.n, ~r~ 1943, fox the rawn?r off ma
b ;by S. K. Vsal~svy y a5k~, C) an the bads of his study off` 1103 ma~
ncUc storms in the 31utsk catalog [8~ From 1878 to 19}Q
The emphiitic betwc err this maxima of thc~ daily val.
d~.scxeps.~r~oy ~
On tha ana hand,
ucs fax the criticai frequefcies F,~ sxrd E
and aninima (o, r1y morning) ~ra
and the ~.uct u o~
nactux naa. ~~
the cx cnc~.os a on the othex', may be explated by 'bhe
critic al fxa ~qu
exis cornponents in the so1azradiatlan~ both p1 r
~,stenet~ a~ two bas
:Lng a ubyt~t .z1tiai party ..n the ioniitiari off' the atnLaspheI, nanc;ly
~
the ultxava.olet component and that oi' corpuscular radiation o
i riri the dayt:ine a when the principal ionizer ( supplemsntin?;
D
the ca:rI)u,scu,lax and other radiation) is the ultraviolet radiation,
Gn the, maxima o the 1i.year.march of the
of the E layer and o;C the noon values oC the
rra.ta.t,al frequencies
critical frequencies for the F layer' with the maximum of the curve
~
o:f: the Volt' numbers (Fig, 1) o
41
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reMd:wfl how:6, whpm the dal~ ~ida
At fli~ht end dUX ~n~ tho p
pto 'the rad~.a"
a the torresksrial sphare is inac
iax, r~diatic)n p1ay~ a subs~en~~.~7.
'triqn q~ thq ~'U1"la the GQrpuscU,
tha 1layer, wYa~.c~~ is axcc~,lent.Ycon
role in the ~,ar~~,zat~an q~ . r;
?trmcd by the 11~ye max'c,h o~ he critical requpncles
(Flga i)
. vea and off' the curve a~
~Y~s lag ill the ln11urrq~ thaw cur
'
,
the awe x'eassan~ mn~aa.an to~r;axds the
mr~gnet~,c oxms a.s due to ? ~ a1' corpuscular x`adia~%a,can ha~n~ ~.aw
sa~,ar equator by the saurcr
as was e, tablishcd by Me Gnc,v~,ck'iev
solid t~n~les ~$ w) duress,
and !L? Ol '
se ax'a.t~.on bet-wecn the curves a~
~l'ize remax?l~ able c;Ef F.ct o~' a p
d thaw in in the nights as well
cx,a,ta.ca~. xec~uenaa.es duxx.n~ the d7,y
as tYic coaxicide.noe between. the mar Ch athe ..curve a~ 'the n>.ber o~
curves o~ the nocturncr~.t~.o~~l ~'xe~,ue"
ma.gnc~t~.c atax'm;~ with the
ex' car~irm the corpusaulax origin of magnetic
ca,es for thE, ~~ lay ~
st.tv.tas an additional argument in favor a~ the
,tr,~x~ns e This con
theory off' magnetic staxm5 18 , according to
Chapman which
~~'erx'aro ?r~ ~,l cox' ,uscu~.ar stream ejected by the sun,
they are c~ aus ed by a ~neut ~
4 ~.tr~~.~ra.olet
~ a,~,bin~ then to u
and against the theory of ~;~~ scr
? ' influence on corpuscles of terrestx'ial origino
acting aa d~.stuxb:~,n~ Thus, the physical d.ependc.nc
e a1 the ll~ye ar rrlarclrl. o.C the
~.onas here on the solar actin. ty o~ the.
cx~.t~.c I ~rec~uenc~.es ;far the p
But to forecaWt the l1-yep" march a
same period becomes obvious
. ~ we must have a qu.antita.tc;starnate o~
the critical l . ~'rcquenc~.es
values that characterize the ll~yeax'
the correlation between the Ae~t~'~~.
~~a.cteri~ G the off' ioniz ati.or~ a Kd
x?oc;ess an the sly. a.nd those that ch
p
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_ 08-4
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4rEr~
the *Yo:aneio torso
The signii'ic ant statistical constants in tha stU,dy o this
.,
quantitative rolatiol are the correlation coe~ffieient, in the
/:hear correlation, and the corre1Vtiorr ratio, . in the
CEl~e Af
case o,' non~1i.near correlation
After determination of the correlation coefficient, a
correlation equation is s et up, by means o1' which the critical rcam guenca.es or the number of magnetic storms are computed.
BeTre setting up the eorrelatlon equation, we must f.ir,3t
establish a criterion of lineax''ity together with its probable error.
The criterion of linearity makes it possible fox' us to judge whether
it is suffi.ctent to eonf in.e ourselves to a linear' carrea.ation equa'
Lion, to express the relation between the statistical values of the
Wolf numbers and those of the critical frequencies, or whether it
is necessary for us to pass to equcltions of higher degreeo
The correlation coefficient r and the correlation ratio
may df'fer only slightly iron each other far a distribution of i,
f and N. In such a case the question arises as to whether or not
such divergence is significant.
As a criterion o1' linearity, Blacianan 9) has proposed that
the correlation be considered linear if the ratio between the
J
mea,ur '~~ and the probable error of the measure of
C
~~~ of l~.nc~ar
linearity is less than 3, i. e. if
(1)
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Tha MAUV4 0 lif~axity i repx~+se1t6d b
bablo exxxor othe measure of 1ineaxit1 i$ approxi-
The pro
mately equal to
h
(z)
(2)Q .' (,,3)
where n is the ,r:u1i number of observations,
thus, to accomplish thcr task set, that is, to Coreeast the
critical axequenci.es j, we must :find the correlation coefficient x
between the curve osunspot distribution W and the curve of criti'"
and them i we are not co rlva.nc e d that
ca14xequency distribution ,
the xegres Asa, : on (he term IregreSSa.on" currently adopted in the
?
statistical literature i ?a.teratuxe wa , intx'oduced by Gallton. It i~ not entirely
~.cal l -
apt , It would be c:leaxer if we were to write, instead of the words'
'
o re .ression'' or "equation 01' regression", the words:
i1clarve ~
stcorr curve" or "correlation equationof the statistical
~?.at~.on
s et S (wh
, n) is linear, , we must determine the cox''
fi
nhi
ratio ?ta For this we construct correlation curves o:C the
aired distribution of the wo1 numbers W and the critical fx'quenw
ca.e of the 2 the noon va:Lue f (Fig ? 2 ) , the midlhight value
..
(Fig ? 3) , the diurnal m:Lnimum value ., Fx (Fig ?1~.), the noon
value for the F sayer (Fig ? ) , and the number o E magnetic
storms N (Figp. 6) b The absolute values have been plotted on these
curves, taking the maximum as unity.
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Fl5
rq,
F,
In contradistinction to the law of dull di,tribut .on o
sta ci 4 Fig. l), the concept of. paixcd distribu"
elements (
tian $ case, ; that is, in studying the distribution
'
is used ~.n i,h' ~. ~
~ etc. '" the diS"
of one statistical element' _wr in this r case F
a
M'a..bution of another statistical el rnerxt is considered, i.e. W
tx
(Figso 2m6)?
In making a combined study of two or more statistical ele-
menu, when only a small number oi' observations is involved, the
scx stributions is investigated, but with a fairly large
~,e s of di
number of observa a tions, distribution tables o1 the distribution of
values is studied instead, which makes it poesible to make a
those
complete study of their distribution and of the relation betowe+en the
~'
paired means W and a 1G h
F~h h
As is commonly known ~O, 11, l2 ~~ for a stns l number of obser-
vations the correlation coefficient r'r
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T5 4~ki' _ Q;e ?the~4 iaiitiai values, tra~be~ with t
(coo Table 2) in equatiafS (8) to (1Table
(a) the noon values of to cr .t cal ;Crequenciec or thc~ F2
i1ay er ;
Td ,77 1' O O W,
F 2W
(b) bhe mldnight values of the critical ~rec~uencic;s for to
1~yer
3,2 0,0237 W,
( c) the diurnal inLnunuxn values oI' he critical frrquencies
?ax the 1 2 :Layer
3,1 + (),O2Lt. W~
d) to noon va,1u.e$ or The critical ?requenci.es for the E
ayer~
f :x 2, 72. + 0,01 W',
E
(e ) the nwiaber a1 magnetic storms:
12 + 0,2)47 W
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1t e thin ab'trains
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Check vnlpu'Gati?f a were made by th a 'orm~l1a t, and on thi
basis theoretical ?orecasting graphs of the 11yaar course o the
ritica1 ?rf3quenaies and the nber o magnetic storms wexc~ prcpax d
c
(Fig 7"11), An the same grelphs the mean values o the xperimenta11y
deterniined critical frequencies wore also plotted.
As may be seen from these fox'eca ting gralplls, there is satis?
f aotox coizicidence between t he experirnentaJ,1y determined points and
'y
the theoretical curves, which enables us to make reliable ;forecasts
of: the critic tl ?requenciec and oL' the number olf magnetic storms L'or
any year oithe iiuwyeax' epoch, i the Woil' number is known.
gure 7 F~gUreB
rwr..
F~9ure 3
~"`,~"Irin,ulrY,
:ccjLr ?kO
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Such procnosae may be mudp'or any point on earth having ara
ionosphere 8bation that has assembied enough expeziarwent&L materiai
to Cori itz'a t the correlation equat;Lnns
0
.-
1933 193 1937 1939 19L.1 19LL3
L~.Lr!urt? 11,
_..w.w._,.___._,,.-.,
N0NM,LINEAR C0RR LiiION
~~
sfiiii
65,;yf
We now proceed to determine the non.iinear correlation equa~
tic~ns Except for the normal distribution of statistical elements
little work has been done to develop the theoretical basis for
solving this problem, In this case, there?'ore, various empirical
rules for finding curvilinear regressions are often used; and iC
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xec?vxss i~ then ac :O jttyng a p;rabal;l,o
these yiaid nQ rasu~s~.n~ Lo ~,~1abshev~
last squ'ps! or to using
curve by the me~had Q~
mr~th?dh
o; to curves show
d
t
y
s
u
xy
Pre1;lm,l.n?, s,11aws us to apP?~'
Cheby s1ev' s meta d 1a x aG~
e use o;E caxlta.nuad ~
1~t
a ~p1119 ?t11em! W ~.t~1 U th
a1S11p~~.t~d
me
Whev
f~he Cheai .. in the va~,uc off' the ~~ndep
t~?n that the ~,,r~.xa,a.cn ?
,
under the
~'0nd, ntc.rvals! cor~sa.ste in he yuc
cunt ~r en
. b1s ~la~. ~ ~
. ~x' ~.a l~l be ~ttan at egti~ sex~.es;
the tex"cns a:~ the ~0~.1.awzng
cam~utati~ans o~
Ge Sa~.V'~ w r J
r
A0(w)
ree in W bha~ s'ati$eY
arni als of. a.~th do r1'
3e the p?~n ? ~: ext
where 1L:
.~. R. I~uran~ end D.
(c . P . !
the CandL '~:i.ans a.~ a;rth?onala?tY
liL/)
th?d off: det~xmmn~.n the p
((Q, CPj ) (i = O 1, 2,
' a~.s equ:~v~~.ent to
the ~a~^st a~hpti~e canda.t~.
hexa
w
C k
~,nd t,rie -~ecand to
h the ?~
~~ c~tc~~n"J.X1a'~Lan (10J ?~ the cae~'~~:cien~,s A ~ and ' p
the d
lam ia ( 'an ~~.~) enable S us to abta:n
~') that enter a.nt? equai~i
;f.ax ca1culat10 n} in those arias
lner Coxxe1atior~ equati?ns
ncar,~..
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/23 : CIA-RDP82-00039R000200170008-4
itoxion off' nono~' oquatior~5
whex~a, arcoxding to the cx
hou:L be employado
A) branch off' the oyclc o~
`Wa thin obt~tn for tha ascQndtfl~ (
ion:L f~,tiO11 or the F 1a er, at nooiU
s
d d. E1 w
x
FW *T(~_ 'Q
i-cL
~F~ 2
(vJ2
Wz CCPoPo)
(XPa CP~)
1-AD' c
( L- )
)
!
descending (D) bxaoC of the cycle oC miri~.inum
For thE
of ion;iza'tj.on o: the F iayeZ',M ~e ave.
(pcWo~ ~{F,.w)
C~? ~0~)
n
(c~ cpa)
(c(c1:)
For the
Ccp04p05
,. \4o 0(
\t'J
((p0 Qe1
+ lb. (20)
values
?f\icp
\4-
so(w)-W-~'
(ccp)
I
,
/l)
`fin (@LM~,
~.-~a,~a
C
complete (A) and (D) 11 yet' march o nocturnal
ionizabien of the F2.ayer we had
~(~
w 1A\ d
FW
( ~ ~ yob
~ (v'J+
~
(c~o)
- -
p R N
+LCPlJ2
(fr)r/D)
'rz
w- W CPo(w)
(v%J:cQ:)
L
CWao)~?C(e~ cp,)
11
cQ01(v'J
~... ~~
(4:(;) 0 -i cpI
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/23 : CIA-RDP82-00039R000200170008-4
Fox the ascsend.tfl branch (A) oC the 1iMy~ax march of thQ
nwnbex of magnetic ~vbacros~ wo havoc
(%W~) ____
~W CAD ~;)
2 2
+ a (W) (w)- (j c)) +..
( o ) cp (p )
2.
( q: ;) L
(v) CP ) (' I L ('4 L o) ?II
1.
(oL P
(w)
1
(1WJ -/ (W)
_ _
q 1 1 ~~Y r l 1 ~~' ` I ~u
C)1, 2., ' t,
'or the numc;rieal expression o,t? the equations (20) to (23)
o o~~ l t,~ hied, we calculate the coei'fcients A and the poiyno~nials
Ira and guiding ourselves by correlation table 1, we set up Table .
8 , t') elow , which enables us to calculate 'the basic totals (ci. bottom
line of r2ble 8).
(See ollowing page for Table 8)
Such tables were set up fox each o:C the curves on Figures 2,
3, L1. and 6, the branches of which, or the sake of precision in es-
tablishing the regressions, it is convenient to express as a non-
linear function with the aid of the Chebyshev poiynomiala
~ad'c.7
Expressing the total through scalar
h M n (~ )
2
%W2 (w2)
h
-w L
2_ nhWhw (W)
w-w
nhxhwi,~
h
:;i nhf'h
n'W
huh
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hW3 (W3) = (w3 , ),
n
`~
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'c;:: ': :':
;rIil c'4
W
PH I CH r~1 ICf.+ N
$ p rN g c\J
cp'a r-I
Va
W
~;.I
~ r-1
.1
CV r-
p,.w
H
CVO N
C\i
I
IUaa~
tr1
W
cr.
.
1-4
Cs Ua ~
W
r1 ~ r
W
rq
W
H _N rrl
1
N
.S H
~H ~N
x; rti H cc'j
rc ~.. ~~
g :: N G
14?I
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/23 : CIA-RDP82-00039R000200170008-4
e oo6f 'iciant~ A ' the po:l r OYnia1 (i8) and of the
we ca,1cu1ate th
' W fox o 'mtl1aa (20) to (23).
po1ynorn;.a18 P FcL,kre t
Fi9ur.
r b.'.
010
_ -.M.
a~F~ M Cp(W)
Q 042. -, 1'0
cp(\4) w
As a result of this calcuiation we obtain, in place o,
rormulae (20) to (23), the following corplitationai equations for
non..linear corre1atio1aa s
d fi02W+U,268W2, (2k)
(B) ~ o,'76 ~" 2
o,6 + O, 38)4W + o,1o w2 , (2)
(B) = a, 4B4 + o,68 ~d - o, a94w` ,
r2~
(H) F2W 0, 647 + 0 3w w o, alsw2 ~
(B) 0,289 + 0,81W w a,20w
w
(26)
(28)
VeriiTifl calcuiabions were made on the basic of these formulae,
and from such calculations the theoretical graphs of the ll-year march of the e,x uencies and magnetic sttorms were then plotted
~,ta.c al fr~q
(cf. Fig. 12 values exper~imentallY found were also plotted
~ l) m The _
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q~ ~
M ~ 7 IM
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/23 : CIA-RDP82-00039R000200170008-4
on thaaa graph3. Js may ba s~~-fl
~ ital off` Va 9 with the th??~~ ~tio~
;CactoX'Y co;.ncidenca a~ tha axpax~
a1i~.b~,a oxa~a~~a athe critical
o~1a~, which anab1a8 ua to make ~'
magnetic d~,stuxb;jr~caa or a~" yak' ai , ~h~
~rvc~er~ca.as as~d n~~~~r~ ~~ mama.
liw yaax period
Fure 14 Fi
(W)
cP (W)
the su~.~~$ of the calCUlati0 obtained by
Compa~c~.so~1 o~ ~k~~ xa
usthg the lineal? cvrrC1a~iob aq a
cua.tions (cfM Figurea i2M:l.6) pr.oia the
superiority of the latter. But the accuracy is not so much increased
make us abandon the use aC the less curnbaxsoma
in the ~~~~~~ case ~o uationS in solVin the px`obiam of mkin?; Foxe
~,~.ri8a~' cr~~^ra~.a~a~; r tio.l w
' at tan, ht h is adegUato 1or pr o pur
sus in ffra b appr
oa
pose 3.
2O "
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 Declassified in Part - Sanitized Copy Approved for Release 2012/04/23 : CIA-RDP82-00039R000200170008-4
x..
!,~
As exper:th ntal maters 1 accumulates at tho Soviet ionaspx~eZ
station, the mothod of foreoasti we have sat Forth mray Cain t acAp'l~~
woe on the territory of the USSR; and it is proposed to devota one
of the subsequent Papers to its elucidations
Q4:: V4rLQ I
S'EGTION FOR SC1l;N'1'IFIG T1S REC1~IVED BY THE EDILORS
,NFker~lv,:? nwi~MinYeMMr:.p.M.Mrs~r11M11~V~~MIM~wIMMWYMIMy
OF ` 'TROD C'MS ' RADIO T? GYEI1 ItVR/$dL JUNE l9 70
OF TH1I ACEDEMY OF SCII NCES USSR
13IBLIOGRAPHY
1. 13erkner, Le and eils, H. Terr. Magn. and Atm. El., 13,
No 1. March
Judson, 1~. Ho P.T ,., 25, 38, i93'?e
3. Smith, N., Gilliland, T. R and Kirby, S. S. J. of Res. '
th.e 1'a 2 Bureau o1' St xidards, 21, Noe 6, Dec., x.938.
14. Kerblay, 'l'. S. and Fedorova, N. L. Ka"aloe I'int~akh l3ur'
-3Vc rdlovsko7 observaon. (Catalogue of Magnetic Storms of the
w,,._.~
Sverdkovsk Qbservatory) Tru nauchnowissll dov_ata1 agp~stit? t,a
remno~o ma . nc ti zina .~..~r.,_____d
tT ansactions of the Q~nstitute J r scientific Research Terre atra.al
Magnetism). Moscow and Leningrad, l9L 6m
. Vsslsarlrsk.y, S. K Kos s.'~ea obzor
No. 189 (Cosmcbc data, ten'?day survey No. 1$9) for 192.
6. Ben' kova, N. P. and Kalinin, Y@ U. Katalo ma ,nitnikh burl
Slut skoy magnitnoy observatorii. (Catalogue of Magnet;Lc Sterns at the
Slutskaya Magnetic Observatory) a Ko eskij dardekadn
- 21
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G ?iQr No, 12 , 126, 127 and 12$ Co? JanuarI and i~ebruary
Gnav;l,cheV, N N and Ql, A.. Terr. d aAtm. IL.,
7?
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,
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B1R~c1m1~tf, J. B~.ome k, V. IV.
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Statistics), Publications oi' GONT1, 1938.
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V. S. Tear' a matematiCh a~tistikl (Theory o;E
Ys~trernsk~.Y , - _ I - . ...~
Mathematical -Statistics). PLANKE!OZOIZ, Moscow, 1930.
12 ? M:~ 'ttropal.' skiY, A. K. Tekhnika stata ati eso?,ischislenia.
~....(ihe Technique of Statistical Computations) SEL' KOLKHOIGTZ, 1931?
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Cheb sheva (rjlhe General Theory oi: Chebyshev Polynorn1a1s) . NNaucllna e
iy e Po L. Cheb sheva (The Scientific Heritage o1 P. L. Chebyshev)
Ns._SIP _d .~--..'
VIP. 1 matematika (Mathematics). Publications of AN SSSEt (Acaderny
o:f Sciences ussa), 191.15p
1).. Kuront, H. and Gill Bert, 13. Meto matematichesko1 :'iz d.
(Methods of Mathematical Physics), vol. I, GTTI, 1932.
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