ГРАВИМЕТРИЯ - tehcraft.narod.rutehcraft.narod.ru/Documents/gravimetrija-v.i-kuzmin-2011.pdf · 3.4.2. Графический способ ..... 58 3.5. Определение

..

-

2011

550.831 89

: - , , ..

, , ..

, .. 89 []: . / .. . :

, 2011. 193 . ISBN 978-5-87693-467-3 - ,

.. .

, , , , , , , , , .

.

, , ..

-

550.831

ISBN 978-5-87693-467-3 (), 2011

............................................................................................................... 5 1. ................................................................................ 7

1.1. ............................................................ 7 1.2.

................................................................................................................. 9 1.3. ..................................................................... 13 1.4. ................................................................................ 15 1.5. ........... 22

1.5.1. .............. 22 1.5.2. ................................................. 24 1.5.3. ............. 24 1.5.4.

.............................................. 25 1.5.5. .................................................. 26

2. ............................................................................. 28 2.1. ................................................................ 34 2.2. ...................................................................... 37 2.3. ....................................................................... 38 2.4. ............................................................................ 38 2.5. ...................................................................... 39 2.6. .......................................................................... 41 2.7. ........................................................................ 41 2.8. ......................................................... 42

3. ..................................................... 45 3.1.

................................................................................................ 46 3.1.1. ............................................. 48 3.1.2. ............................................. 52 3.1.3. .............................................. 52

3.2. ................... 53 3.3. ............................. 57 3.4. - .. 57

3.4.1. ................................................................. 58 3.4.2. ..................................................................... 58

3.5. ........................................................................................... 59

3.6. .................................................................................................. 61

3.7. .................................................. 62

3.8. ( ) ..................................................................................................... 62

3.9. .............. 63

3.10. .......... 63 4. ............................................................... 65

4.1. ...................................................... 65 4.2. ........................................................ 68 4.3. .................. 69 4.4. ...................................... 70

4.4.1. .................................................. 70 4.4.2. ................................................................................... 73

4.5. ............................................................................................... 76

....................................................................................... 78 1 ................................................................................. 78 2 ................................................................................. 89 3 ................................................................................. 94 4 ............................................................................... 101 5 ............................................................................... 107 6 ............................................................................... 111 7 ............................................................................... 121 8 ............................................................................... 127 ........................................................................... 134 1 .................................................................................................. 136 2 .................................................................................................. 137 3 .................................................................................................. 138 4 .................................................................................................. 139 5 .................................................................................................. 141 6 .................................................................................................. 142 7 .................................................................................................. 145 8 .................................................................................................. 152 9 .................................................................................................. 155 10 ................................................................................................ 157 11 ................................................................................................. 158 12 ................................................................................................ 190 13 ................................................................................................ 192

, , . , , .

, , , .

, .

, , . .

, . .

, , , , , , 6101 , , .

, . : , .

(, , .).

, , ,

, , , . .

- .

.. .. .

1.

1.1.

[12, 33, 35].

, : [4, 7, 8, 11, 12, 25, 27, 31, 38].

.

(15641642), 1590 . , , , 10 /.

(16421717), :

221

r

mmfF

= , , (1.1)

1m 2m , ; r , ; f ,

, /( ).

. f 1789 . . (17311810) . (17241793).

f (6,673 0,003) 10-11/( ). f (6,67259 0,00085) 10-11/( ).

, , , . , .

, . M R :

2R

fMF = . (1.2)

F . ,

(. 1.1), C nF . :

C 2=C , (1.3) N ; ;

G . (m = 1) . G . , , , . .

2dim = TMLG , L (),

(), (). 1 = 1 /. , ,

, g, . :

2dim = TLg , L (); (). /c. .

g = 9,81 /c. 1

. : 1 = 110-2 /c ; 1 = 110-5 /c ; 1 = 110-8 /c . g

: ZYX g,g,g , g , . . Xg, ; Yg, ; Zg, .

. 1.1. ,

1773 . . (17361813) W(x,y,z), g :

zyx gZ

Wg

Y

Wg

X

W ==

=

;; .

. (17771855), , :

W = f ( )222

2YX

w

r

dm ++ (1.4)

V, Q:

W = V + Q.

:

,,cos

=

SgSgW s 2/2. (1.5)

, : 0,90cos == dWdSgdW s , . . W = const. 1873 . , , (18081882) .

, ,

dSgdWdSgdW ss == ,0cos ,

sg

dWdhdS == .

dS . sg : sg ,

. =sg ,

dndS = , nW

= , . . ( )

.

1.2.

1743 . (17131765). :

( )Bgg e 2sin1 += , (1.6)

eg ; ;

= 90 pg ;

, ;

e

eP qg

gg

25 =

= ,

:

2

5 = q ; (1.7)

(1.8)

; ;

M ; , ;

e . (1.6) .

, , 1929 . . . [14]:

BbBa

BgbBgag Pe

2222

22

sincos

sincos

+

+= . (1.9)

(1.9) (1.8), :

( )BBgg e 2sinsin1 212 += , (1.10)

1417

25

= qq ,

qq =+ 1417

25

, (1.11)

( )

( ) ( ) ( ),cos

;,,

;2

,2

;31

;

2

222222

2

2

232

Ba

dmyxfCdmzxfBdmzyfA

MBA

CKa

Kn

qna

Mfg

g

ga

Mfa

q

e

e

e

e

e

=+=+=+=

+==

+

=

==

=

21 8

1

85

= q . (1.12)

(1.10) (1.11) . 1 .

eg , 1 1909 . (18431917). 1901 1909 . 1 603 0 :

( )BB 2sin0000071,0sin005302,01030978 220 += . (1.13) 2,5 0 == eP , 0,53 %

0 = 981 . a = 6,387 106 , = 7,292 10-5/c = 15,04 /c,

8,14,32,5 0 == eC 0,18 % 0 . (1.13)

, , , :

4,2961

25

=

=

eP

e

e

g

gg

g

C.

1930 . : K0 ( )BB 2sin0000059,0sin0052884,01049978 22 += , (1.14)

. . K0

0 :

( )BK 2sin2,130,19 200 = . (1.15) , (1.13) (1.14) 0

, +13,87 . , 14 .

1971 . XV :

( )BB 2sin1059sin10024,531031,85978 27240 += , (1.16) 1967 .

( ), :

23 603398 = Mf ; = 6 378 160 ;

2J = 10 82710-7 ;

= 5,9761024 ; = 7, 292115146710-5 /c ; 2J , :

.249,298/123

22

2 =+=MfaW

J (1.17)

)1930(0 )1971(0 :

B2)1930(0)1971(0 sin6,132,17 += . (1.18) 0 , 1971 .,

, . , 5,11018 .

1980 . 0 : ( )BB 2sin1059sin10024,53168,978032 27240 += . (1.19)

:

; ; ; ; . ,

. 1.2.

. 1.2.

,

(2 900 ) 0 .

1.3.

.

() g

= gg .

HH

+=

0 ,

0 , ;

3086,0

=H

/

;

15

10

5

0

, /

, ().

. 2 500

980 . 1 000 ,

0

(1.20)

:

(1.21)

,

/

, .

.

3 000 6 000

1 500

1 000

500

g,

3

H,

g

g

, ,

500 -

:

, , .

1. ( ..BCg ): Hgg BC += 3086,0 0.. , (1.22)

0,3086 . 2. ( g ):

))(0419,03086,0( 0 gHHgg += , (1.23) 0,0419 ()

= 2,67 /3, ( ).

g .

, : , , . , .. , .. , .. , , .. , .. .. [11, 18, 19, 30].

: [12, 25, 35], . . , , .

CBg . 0 .

, . CBg . CBg [12], , .

:

2HfdWdS

== . (1.24)

= 1 = 2,5 /3:

6980

105,21067,614,3 108 =

dS (5,7 ).

g .

0 . , .

2

2 aHfdWdS

== . (1.25)

= 1 R = 100 = 2,5 /3

10980

10105,21067,614,32 758 =

dS .

( , ). g . , , .

.

42,4 . +660 (. ), 380 - ( ).

1.4.

(. 1.3) , Ng . W = C, . (), [12, 28, 35]. W = C . nn . nNM , (

g ) . - () . 11nn -

N n1 n

g n1 n

M

vg

v v

W=C

. 1.3.

. 1NMn - ( ):

vvg = , v ( )

, ( B L ) -. , .

g () ( ). (. 1.4). . 1.4:

; g M; n ;

1n -; ;

Z ;

Z ;

1Z ;

PZ ;

PZ ;

2ZZ A ;

BPZ = 90 90; = 90PZ 90;

nBPZ = 901 90; B, , Bn : ,

; L= ;

ZZ1 , A ZZ ( g ) - ( ) , ;

21ZZ g B ;

2ZZ ,

2ZZ A g g .

. 1.4 , - g :

Bg += , BBB n = ;

( )BPZ 902 += .

PZZ A2 :

( ) ( ) ( )[ ] ( )( ) ( ) ( )

==+=+==

.sincossin90sinsin

;ctgtg90tg90ctgcoscos

LL

BBL

. , :

;

;

B

B ==

( ) .cos;sec

BL

L

==

(1.26)

3 . -. . -. g

ONg, NOg = g (. 1.5):

Sg

gtg = . (1.27)

Z

Z1 Z2

Z

v

v

vg

n1 n

g

. 1.4.

. 1.5.

g ( ), tg

, :

sg

g= , (1.28)

sg : S . , W :

S

Wgs

= . (1.29)

U :

TUW += . (1.30) (1.29) (1.30) (1.28) :

+

=

ST

SU

g 1

. (1.31)

, :

0=

S

U;

(1.32)

S

Tg

=

1 ;

=T , ST / .

(1.32), :

SSg

=

=

1

. (1.33)

.

:

=

0

2

0

4

gR

( ) sin dAdS , (1.34)

( )S ;

( )S = 1 + cosec

+2

2sin2

sinlncos3cos5

2

sin6

2

ec , (1.35)

( 00 , ) N ( , ) (. 1.6);

. 1.6.

N;

g . ( )

( ) (1.33) 0 0 .

=S R 0 , =S R 00 cos ,

0 0 , ;

R . :

.

cos

1;

1

000

=

=

RR (1.36)

(1.35) (1.36), :

( )

( )

=

=

0

2

0 0

0

0

2

0 0

sin

cos4

1

sin

4

1

dAdS

g

dAdS

g

. (1.37)

(. 1.6)sin,, d , (1.37) 0 0

, [12]:

g=

41

0

2

0

( )

dAdA

ASg

sinsin

cos

. (1.38)

, (1.38) :

( ) ( )sin

2

Q

S=

-. (1.39)

- , 0 = . Q :

( )

+++

=2

sin13

2

2sin322

sin12

2

cos

2

2cos2

ecQ

.2

2sin2

sinln

2

2sin12

+ (1.40)

( )Q .. [15]. ( )Q . 1.1, . 1.7.

1.1. -

0 1 10 20 30 72 80 180

( )Q +12,370 +1,591 +1,02 +0,79 0 0,15 0

. 1.7. -

. 1.1 . 1.7 , - 0 20, 20 180 .

: 0 10 .

0 10, Q , . , Q1 -:

++

= 3

1242

2

2

1Q . (1.41)

r :

3602

== RRr .

:

R

r

2

360 = . (1.42)

(1.42) (1.41), :

++

= 32

36012491

3604

2

1 r

RrR

Q .

, 626520 = , 000981 = , 3716=R , , , :

CrBr

AQ ++=1 , (1.43)

= 1 339,6; = 61066 , = 0,315. (1.43) r

. 0 r0 , Q1 :

rQ

13401 = .

, :

( )

+=

=

,2

1,

;sin

cos

2

1

sin

cos

2

1340

10

1

0

0

0

2

00

2

0

2

01

0

2

0

rr

r

r

r

dAdrrFgdAdrg

dAdrA

AgQ

RdAdr

A

A

r

g

R

(1.44)

.2B

r ln A F(r) 2 rcr ++= ,

g = g . . 23.

(1.44) ("). 0 20 ( 0 2 000 ).

1.5.

10-410-5 (1 100 ), . .

10-510-6 , , ( 1.8).

, . , .

, . , : W = C. .

, , 10-6 . Z ( ). (, , ) .

1.5.1.

, ( ) , ( ).

.1.8.

. 1.8.

(. 1.9), S , n . S Z. , g , gZ ; v ; MQ

Q. () QZg .

gZ , ZQ. 1

QZg .

gZ ZQ. v

v A = ZQ KZv gA =+90 .

. 1.9.

nQZ g :

( ) aZA ctgtgv90cos 901 = + , (1.45) aZ Q.

v, , :

aZv A ctg 901 = + . (1.46)

AAv sincos += , (1.47) :

AAv A sincos 90 =+ . (1.48)

Z

Q

K

S

M n

gZ

1 v

v

v+90

Za

Zg

(1.48) (1.46) 1 :

( )AA += cossin ctg aZ . (1.49) ,v

, , , Z - [4].

, 3040. ctgZ 0,580,84, : 4020 ,, .

1.5.2.

QKZg (. 1.9)

: ( ) QKvZ Aa coscoscos 90 = + .

v , ( ) 1cos 90 =+Av , QK Q: ( QZZ = ) Av : AvZQK = . :

Aa vZZ += . (1.50)

, , , Z v , . . Zm 1 .

1.5.3.

. 1.10 .

.1.10.

gg

B

Z Z

S

D

C b

h v

. 1.10: S ; hBC = ; g ; v , ().

= b. , , ( . 1.10 AZ BZ). - b , :

vhb tg = . (1.51) v

, : vhb = .

, , v . :

= ihvb , (1.52) ih i- .

1.5.4.

. 1.11.

. 1.11.

. 1.11: S M N; g

( ); MZ

L

N

M W=C

K

S

Z

n

b

h

H

g

v

v -v

M N (); LMN ,

. 1.11 , ( )vSH == sin

vSH cossin =

v ( :

cossin = vSH

H . bS = cos

bvhH = . ,

1.5.5.

MN = S. , 1.12).

. 1.12.

, W = C; H W =

, h ;b

MN; v Z

( )vtgb = tg( v ),

vS sincos . (1.53) ) vvv == sin,1cos .

cos Sv .

hS sin = , (1.54)

0, 5 .

M N, MN . H

. 1.12.

= C,

M N, S

; N.

(1.53) .

5 , 2 .

, H

MN (.

M N M0 N0, Mg Ng M2 N2 ().

22 NM A , . Mn Nn ,

S ( 00 NM ). 22 NM M1 N1 .

10MM 10 NN 1v 2v + 90:

( )( ) ,

;

19010

19010

HvNN

HvMM

NA

MA

=

=

+

+ (1.55)

+=+=

AAv

AAv

cossin

cossin

222

111 ;

tg( )

0

12

11

1010S

Hvv

NM

MMNNAtg

=

= . (1.56)

v , , :

( )0

cossinS

HAAA = . (1.57)

, M N , , M2 N2 .

2.

. , , , .

. ,

, .

. , .

. -3 1953 . , .. . -, -7, -7 . -7. 0,030,06 .

1301783 . 557886 [9], . 2.1.

2.1.

, -

,

,

,

,

,

,

,

-, -4,

1953 1958

0,05 0,030,05

0,050,4 0,050,2

100150 80120

3 000 3 000

200 200

488 465

188 175

8,5 7,5

- .

-,

1960 0,030,05

0,050,2

100150

5 000

250

480 180

7,5

- ,

-1, 1961 0,01

0,020,08 70100 3 000

800 390

133 4,2

. 1967 1973 . 1301767 -2; 1973 . 1301773 -2, -7 . 1973 . 1301773 -1

-7, -7, -7,

1963 1963 1963

0,02 0,030,05 0,010,05

0,030,06 0,040,05 0,030,06

80120 80120 80100 1 000

5 000 3 000

200 200 200

425470 425 425

210 210 210

5,0 5,0 5,0

-2, ,

1966 1971

0,005 0,01

0,10,15 0,06

5 000 80

5 000

15 600

450 550

350 250 250

25 5,0

--1, , ,

1972 1948

0,01 0,01 0,01

0,03 0,020,08 0,020,08

80

80100

5 000

400 600

425470 290 400

210 120 140

5,0 2,3 4,5

, . , .

- [11, 27, 28, 36].

. 4 0,03 , 0,006 . 4,5 .

. 2.1 . , , .

. 2.1. : ) ; ) ; )

,

(. 2.2) 1,

132 .

) ) )

. 2.2.

2,

3, 5. 4, . , , , .

, , 120, . , .

, . d , , 120 . , (. 2.3).

1 2

3 4 5

. 2.3.

16

27, .

43, 33 . . 10. : 20,

14

6

14

5

4

3

2 1

. 2.3.

. 2.4. ,

26.

.

. ,

31. 2 .

. ,

,

5 11 45

(. 2.4) ,

.

7

10

9

8

14

11

12

13

28,

29. .

(. 2.8), .

3

:

5 ,

44.

. 2.4.

(. . 2.3)

, , . 13 .

42 16

45

(. . 2.3). : 2, 3, 9, 12, 8, 7 10 11, 6 0,5 , 5.

: , , , , , , .

2.1.

, ( ), . 2.5. : , , ( 1, 2 3), 1015,17.

16, 29 30.

- 16 9, 8 25. 4 : 66 99.

, 9 1. 25, 5, 4, 26 (- ) 20. 5 24. 7. . 0,03 .

. 2.5. -

10 (

), ( ) 11 16. 10 12, 16. 10 17, 14, 13.

1 4 , 14.

: 5 , , 9, . , , . , 1 100 (, ). , ,

. . . , , . . , , . .

, , . ( ), . ( ) . ( ), . , , , , . 20 , ( 1015 ). 19, 23 18. , , . . , , . , , , . , () . , , . 9, 8. - 2 22, . , .

2.2.

(. . 2.3) 14 7 10, . , , 120. , , . , .

, , . . .

30. 11. , . , .

( . 3.3, ) 32 . 100 . , , 0,1 , 0,1,29. 1 , 0,01 .

0,75 . , , 20, . . 20. 0,01 , 0,2 12.

4 , 5 , 3 6 . 35:

= C tg 30 = 20 1,73 = 35. 0,01 ,

0,35 2 = 30.

, 3 , 1 . .

2.3.

, , .

-5 10 -, 4,5 . - , .

2,5 3,5 0,150,25 . ( ). . 8 (. . 2.4).

50100 .

2.4.

(. 2.6) 2, 1, 3, 180, 4 30 5 20 , 6 7.

2.6.

,

. 0,1 , , 20 , 2 . : 0, 10, 20, 30.

2.5.

.

11 (. 2.3), 38, 7. 14. 42.

2 (. 2.5) 20, 38.

. , (. 2.7).

. 2.7.

3- . 1 ,

. 5. , , 7 8, . 15 .

() 3, 4, 100 . . 0 90. . . , 2. . 10 . . 19 . -, . . , 90 91 , 90 . . 2.7: 7,909 .

( ) 0,5 . , , 10 (1 = 1 106 ).

, , 0,5 , 68 . 7,5 (15 ), 90120 .

2.6.

, 100 200 . 3 (. . 2.5), 26, 21. 5080 . , 0,5 ( ) 200300 . 57 . , 2 0003 000 . , . , () , , . . , .

30 (. . 2.4), , , , . . 12 .

2.7.

, , , . (. 2.8).

. 2.8.

. : 5, 3, , 6. , 10 , 1, 4 . 3. 13 . .

2.8.

, .

, .

(

: 4 3. 5 2

, 8. 3

7, . 9 3

4 5. 3

. 4 3.

. . (133,3399,9 ).

.

,

. .

(. 2.9) -2 , ,

.

)

,

4 1

8. 3 ,

. 3

3 5

,

.

, -,

,

, 2.10).

. 2.9.

1 , 4

, ,

5103 5101 . .,

-

0,8 .

. 2.9.

; 2 ; 3 , 5 ; 6

7

. 2.10.

,

.

. . ,

.

.

(.

; 3 ;

. 0,950,97.

.

,

, .

, , (. . 2.2). . . 0,5 .

3.

, , , . , .

, : , , , , , , .

: , -, , , .

, .

, - , , . 3.1 1301783 [9].

3.1. .

-

(I) (II) (III) , d 80

, D 6 000

, t 3 - , 0,5 2,0 2,0

q, ./, 7,0 5,0 2,5

bK , 10-5 /, 1,1 1,3 1,6

, (10-3 / . .),

1,5 1,7 2,1

C , /1, C 0,5

3.1.

() . 3.1 .

. 3.1. :

1 ; 2 ; 3, 4 ,

,

. , .

( , ).

( ) 221

iii gSCg == ; iSSiS = 0 , (3.1)

ig , , ;

0S , iS , = 0 0, , .;

g = 0,981106, ;

C , /; ,

.

(. 3.2, ), , .

2

3

4 1

. 3.2.

. 3.2, : 1 ; 2 ; 3

. . 3.2, . (3.1) :

( ) ( ) ( )2

2

00+

=+==g

SSCSSCg iii ;

000 SSS = , (3.2) 0S ,

= . (3.2) :

22 21

21

++= gggg i .

0SC 221 g ,

:

02

0 21

ggSC == . (3.3)

(3.3) (3.2), :

21

20 += gggg . (3.4)

(3.4) , , (. . 3.2, ).

: ( )

2

2

20

=g

gSC, . (3.5)

, (3.1) g = 0,01; g = 980 ; = , :

0

g

1

2

3

+

-

S0

S S0

0S S

S

- + 0 -

) )

98,0

02 ==

g

g

104,1 4 ==

,

3.1.1.

2 (. 3.3, ), 4 , ( 4

1.

. 2.

, .

)

. 3.3.

46

104,11098

02,0 =

.

03526206 = . , 30

= 30 0,010

.

, ), 11 3 1

(). 6.

9 . 6

11 : ,

)

: ) ;)

30, .

0,025 .

,

11, 7

10 5.

-

-

. 3.3, : 1,6 ; 2 ; 3

; 4 ; 5 ; 7 ; 8 ; 9 ; 10 11 : , .

. 3.3, :1 , 2 , 3 , 4 .

, - .

,

00 =Tn . 00

Tn .

.

1. (. 2) .

10 . 0,1 , 2 ( ).

(n = 6), n = 2 .

. 2 1 3 ( 4 . 3.3, ).

(+), ().

, () (. 2, . .2.1, 2):

9876543210;6,0;4,0;2,0;0;2,0;4,0;6,0;0 +++Tn .

2.

1S , 7. 1t 5 ..2.1, . 2.

3. 6,0+=Tn 2S 2t .

, 2 , ( 2 . .2.1, . 2).

4. 00 =Tn

.

5. ,0 =n -

)

0

0;

3,0

3,0;0

321

+

+Tn

.

6.

S

S t

. 3.4.

7.

= min2i , i 8.

iS :

(i

i SSS +=

9.

1 2

S,

S1

0

0,1

0,2

0,3

1, . .

( :

,0

,0;

2,0

2,0;

1,0

1,0;0;

1,0

1,0;

2,0

2,0876543

+

+

+

+

,

, (3.5).

- .

iS it , t (. 3.4).

- S

R

( )iS0 R. ( ) iS

) i . iS

-:

2 3 4 5 6 7 8 9 t,

R

S3

S2 6

9 1

2

3

0;3,

3,.

, ( ),

,

S :

00 =Tn ,

.

( iS ),

3

( ) ( )2

i

i

iSS

S+

= ,

.

(S), . , (. 3.5).

. 3.5. S - 44

n: 1) ; 2)

10. n , :

0 += nn . 11. .

00 =n -, n .

12. -. , .

13. . n

nS + nS . 14.

.,020,0 SSS nn = + .

S,

+n, -n,

S0

S0

+

1 2

0 -2 -4 -6 2 4 6

4,2

4,0

3,8

3,6

3,4

3.1.2.

1. () .

2. , . , (), , .

, .

, . , , .

3. (). , ( ) . , . , . , ( ) () .

4. . .

3.1.3.

. .

1. +1n

( +1S ).

2. ( 2n )

( 2S ), + = 21 nn .

3. ( +1S ) (2S ) 20 ,

.

4. : ( ) ( )

221+ += SSS .

5. S . 6. ,

, (0) . 7. -.

8. . ( +1S 2S )

20 .

3.2.

( .S )

C, / .

. . 3 .

1. :

S

gC

= , /., (3.6)

12 ggg = ; 12 SSS = ; 21 , gg 21, SS

, .

-, ( g ) 13017-83 [9] 80 . g

H : 3086,0

HH

Hg == ,

(5,2 /10 ), .

( gm )

0,01 . g

m g

=

(1,7; 2,6 5,0)10-4 A, B C, .

. ( g ).

:

=

=

=n

ii

n

iii

g

gC

C

10,

10,

, (3.7)

i , 0,ig (0) i- .

C :

( )

( )1

2

1

2

=

=

nnC

CCn

ii

C , (3.8)

n . 2. 1S ,

, (, 200 ) 2S ,

( )12200

SSC

= .

, GS 11.

3.

, (3.1):

221

gg = .

0S ( 0 = ) (. 3.6), iS 0 , :

0SCg = 0 = ; (3.9)

ii SCg = cos 0 . (3.10)

. 3.6. C

(3.10) (3.9), :

( ) ( )ii SSCg = 0cos1 . (3.11)

( )2

sin2cos1 2

ii = , (3.12)

(3.12) (3.11) :

( )ii

SSCg = 022

sin2 . (3.13)

i , (3.13) , :

( ) iii

SCSSCg 2

0

2

== . (3.14)

, , ii SSS = 0 , :

i

ii

S

gC

2

2= . (3.15)

. :

Ti n= ,

/ da= ; 75,0=a () ;

125=d -. (3.15) :

( ) 222

Tii n

g = .

Kd

ag =

2

2

2

1, :

g

( )i

Ti

iS

nKC

2

= . (3.16)

, . . , , . , .

() (-3), ( ) -02 5,0 =m .

, :

( )iiSi SfSCg += , (3.17) Sig , ; , /.

iS , .; ( )iSf ,

. -

: 1. . 2. . 3. . 4. . 5. . :

=

2

1

i

i

S

gC , /., (3.18)

SSii ggg 1 = ;

0009812

cos i

=

+iS

ig ;

1SSS ii = , ( ) ( ) iii laCSf = ;

ii SSa = ;

n

SS i

= ;

iii aCll = ; Si

S ggl = ; [ ][ ]aa

alC = ;

; n .

[23].

3.3.

. , (). . 12 , ( ). , , , . :

n

gC d

2= , /, (3.19)

g ; , ; n .

3.4. -

- g g , T, :

( )iT t

T

SCK

T

gg

== , (3.20)

TK -; Ki

Hi SSS =

HK TTT = () () ;

1TTt i = ;

C . TK :

.

3.4.1.

, :

111 v= TKS T ; 222 v= TKS T ;

(3.21)

------------------------

iiTi TKS v= : iv , ,

, .

[vv] = min:

( ) ( ) = = 2iTiT TKSKf + 222 2 iTiiTi TKTSKS . (3.22)

( )TKf TK , ( )( )

0=T

T

Kd

Kdf,

( ) =+= 022 2iTiiT TKTSKf . (3.23)

( )

( ) =

2i

iiT

T

TSK . (3.24)

1301783 - B C 2 [9].

3.4.2.

, - g .

. 1. . 2.

- , (. 3.7).

4'

3'

1

1' 1

1' 2 2

3 3

4 4

4'

3'

g.. 4 g.. 1

R

A

g2, 0 1 2 3 4 5 6 7 t,

. 3.7. -

3. t ,

- . 4. (A). 5. R [vv] = min, v

R. 6. - ( ) ig R

, .

3.5.

.

, . , . . .

, , -.

, : 0 0S , 10 0 10S , 10 0 10+S ,

0S . .

.

1. (.): 0101001010010100 ,,,,,,,,, SSSSSSSSSS +++ . 2. (h, m): 10987654321 ,,,,,,,,, tttttttttt . g ,

: ( ) ii tKg = , (3.25)

( )

( )

=

=

=n

ii

n

iii

T

TS

K

1

2

1 ;

( ) ( ) 100 += iii SSS ; ( ) ( )iii ttT 010 = + ; 1ttt ii = .

- , :

( ) ii

i gSS .. += . (3.26)

(+10) (10):

3

.. =

i SS . (3.27)

, , :

( ) /5,2

.10

.10

=+ SSC

nq ,

() , 2201,0 == , (0,1

; 20 ); n . .

15 % g 500 . ( )

() . :

2 312

SSSi

+= , (3.29)

321 ,, SSS ;

i . :

nC

n

ii

== 12

. (3.30)

3.6.

. (), . , . .

20 0,2 10 . , 20 1 . g :

ii SCg = , (), (3.31) 0SSS ii = (.). g t (. 3.8).

. 3.8.

1301783 [9]. g .

1, mt .

1 g , cmt . cmt 3 min.

cmt , .

3.7.

. , .

1. 0,000 .

2. ( ). 3. ( ,

) , 12 .

4. ( minS ).

5. 15 .

6. ( ). 7. ,

, 12 .

8. ( maxS ):

( ) 100minmax = CSSg . (3.32)

.

3.8. ( )

, . . . .

C

c

T

v

3.9.

( C ) (). 3- T = 10. , T = 10, 20, 30 . , - C . C, , T, (. 3.9).

Ci, /

C0 1C

2C

3C

0 10 20 30 T,C

. 3.9.

R iC -

[vv] = min. R C

0C T = 0 C. C , TC

C = tan

, /( ).

iT :

iCt TCC 0 += , (3.33) ( ) CTTT ii = 0 . 1301783 C 0,5 /1 C [9].

3.10.

(. 3.10). .

C R

. 3.10.

1. (2) 6 1

. 2.

1S 1P . .

3. 4, 3.

4. 7, 300400 . .

5. 8, P2 .

6. , , S2.

7. : ( )

..

21

21

PP

SSCK B

= . (3.34)

1301783 BK 1,6 / . . [9].

4.

, , , , .

.

4.1.

, : , , , , , ( ), , , . , .

(. 4.1).

, (g), (t), (0) (i). .

1. , :

2

2

00gt

tHH ++= . (4.1)

2. , () :

gl

T 2= , (4.2)

l . 3. ,

, , :

2

gmlf

= , (4.3)

f , ; l , ; m , ;

, /. ,

, . :

0=+ FMg , (4.4) Mg ; F . F ,

, . , .

(g) .

g [ -2], . mg = 110-8 /2 . 110-9.

(g) g:

ggg .. += . ,

.

. 4.1.

22

21

12T

Tgg =

-

,

ggg = 0

2

00

002

+=f

fg

f

fgg

ggg = 0

22

t

lg =

2

24

T

lg =

ag :

980 000, 00

gt

tlll2

2

00 ++=

gl

T 2=

21 mg

lf =

M g + F = 0

4.2.

, .

, .

1. 1 : 1 000 000 1 : 500 000. , , . , , .

2. , - . 1 : 200 000 1 : 50 000 , .

3. 1 : 25 000 , .

- : , , , (, , ), .

. 1. , ()

() 5. = , . .

2. , > 5. . ( ) .

3. , .

4. , .

, . , ( ), .

4.3.

.

. 1. . 2. ()

() . :

, . . , .

3. . - , , (. . 13).

. (1.23) . :

( ) 2222

0 23086,0

HBg mfmB

m +

= , (4.5)

B

0 , /;

f , 6.6710-11 3/2 ; , /3 ;

2Bm

2Hm

, ; = 2,67 /, R = 6,371 g = 5 200 :

( ) ( ) .2,000052,0 2222 HBBg mmm += (4.6) , , g 0,1

, 40 , 0,3 [16].

. , : , , , .

4.4.

, , , : () , , . 3, , . - (. . 3.4). , .

4.4.1.

, - , , .

1,52,0 , . , .

, , . [16].

.

, .

1. (. 4.1) , [16].

. 4.1.

:

N

= , (4.7)

;

nN

NN-n

== ;

2

, (4.8)

N ; n ;

i ig ; gg ii = ; (4.9)

k

gg i

= ; (4.10)

k g , . 2. (. 4.2) ()

(). . ().

. 4.2.

, , 1-2-3-4-1, g

1-2, 1-4, 1-3. 1-2-3-4-2-1 g 2-1, 2-3 2-4 , , 1-4-3-4-1, 4-1 4-3.

:

22

nn

n

++= , (4.11)

n , n , , , (4.1).

3. , --.

( g ) :

mM

= ,

m

SN =

2 ,

S ,

4

4. . (. 4.3)

. 4.3.

,

( ) ( )iIIiIi ggg = . ig

. id

(4.12)

;

g

(4.13)

g

--.

4 ,

. 4.3)

[8,11].

,

. ,

. ig (I, II, III) :

(4.14)

,

:

;

.

, [17,28].

-

-

-. .

. .

(I, II, III) i-

,

n

dn

ii

d 2 1

2== , (4.15)

n (). , -

- . - , . , - , , .

, , 2-3 , g .

4.4.2.

. , -, .

. . , , . , , .

. .

-, , .

. 1. 12

. .

2. .

3. : .

4. , , , , , , .

5. . .

6. .

7. . . . 5 . 8 /, 0,004 . .

8. 1 0,5 . , , , , (, . .).

. 1. ,

, (. 4.4).

. 4.4.

-

:

( ) ( )12

02010201

tt

ggggK

SS

= , (4.16)

Sg01 Sg02

-1 -2;

01g 02g -1 -2,

;

1t 2t -1 -2.

2. , (. 4.5).

. 4.5.

-

:

( ) ( )HK

KS

HS

tt

ggK

= 11 , (4.17)

( )H

Sg1 ( )KSg1 -1 , .

3. , (. 4.6). , .

. 4.6.

, ,

20 %. - :

( )

=

=

=m

ii

m

ii

Si

T

Tg

K

1

2

1 , (4.18)

3 1

4

1 2

Sig iT () () ;

( ) ( )

Si

Si

Si ggg = ;

( ) ( )iii

ttT = . (4.19)

4.5.

: () ().

.

1. . 2.

Si, . 3. ,

i .

4. ig .

5. - .

6. .

7. .

:

222 ug ++= , (4.20)

u ,

,

, .

510 % . 50.

,

0 ,

.

ng , g > 3.

ng = 2 023 , g . 2 % .

:

1. , ;

2. ;

3. ; 4.

; 5. .

1

- : -

. :

[28, . 4], [14, . 7,8], [33] [9], . 3.1 .

1. . . . .

2. .

3. . , . 2.

4. .

5. .

6. . 7. - . 8. .

1.

, . 2 , [7, 11, 14, 27, 28, 39].

: ; ; . 2.

, , . 1, . 3.1.1 .

.

:

1. , ;

2. () , . 2: nt n , , 2 3 ;

3. nt= 0 1S 1t 7 5 . 2, . .2.1;

4. ;

5. 2S 2t . .2.1., . 2;

6. 3S 3t ;

7. , n, ;

8. - (nt= 0) 9S 9t .

iS : nT= 0 0S , .

, .

, ( ).

, . 1. . 2. (.

. 2). 3. (nT= 0)

1S 1t 7 5 . 4. ,

. 5. ( 2S ) ( 2t )

. 6. ,

.

7. 3S ( 3t ). 8. , . 6 7

( ) . 9. 8S 8t 8 6

9S 9t , , , . .

10. , .

11. 10S 10t , 8 6 . . 2.1 (. 2).

12. , . 10 11 ( ) .

13. 15S 15t : n, nT= 0.

14. ( 16S ) ( 16t ). .

( )ii nfS = . , :

2

iii

SSS

+= . (5.1)

, .

.

n, . -. -.

, n .

( ) ( ) 20+ nSnS , .

( ) , . , . .

3. , . 2:

) nS n: n , nS ;

) , , = 00;

) n () n () n nnn = , Si :

,)(

0

2

ii

SS

nk

= (5.2)

S0 = 0; Si i ;

n ; k , ;

( ) 2dag5,0k = , (5.3) ; d ; g ; ) C

Ci, i :

n

CC i

= ,

n Ci. 4. g

: ) (0 )

(15 ) , . , . , S1 , S2 ;

) :

( ) ,21 SSd = (5.4)

S1 S2 .

80 [8]. 5. : ) ; ) ()

, +N N S+N S-N, N ;

) S +N S -N :

3

3

1,

=

+ =i

i

NN

s

S ; (5.5)

) ( , ) :

( )NN SSL

q+

=

, (5.6)

, ;2201,0 ==

L N+ N . :

nC

n

ii

==1

2

,

2

312SS

Si+

= ;

S1, S2,S3 ; n (n = 3).

1301783 [9]. 6. : ) ,

, ;

) 10 220 05,02,0 , ;

) 20 : , , , ;

) ig : ( ); 0SSg ii = (5.7)

Si ; ; ) ( )ii tfg = . c

, . c: , t = 20 ; , , :

)( 00 ddk += , (5.8) d

, ;

00 ,, d , . 1301783 [9, . 2].

( )ii tfg = , , t . 1301783 [9].

7. -: )

10 ;

) . c iT , . ;

) , - ;

) - : ( )

t

SSk n

1= , (5.9)

; Sn S1 ; t Sn S1;

1TTt n = . (5.10) -

, 1301783 [8].

.

- 474 1. . .

. , , . .

2. : .

. 5.1 . 5.1 - 474.

5.1.

n ,. n ,. s ,. n ,. n ,. s ,.

+0,6 0,3 7,828 -0,1 1,0 7,349 +0,5 0,4 7,702 -0,2 0,1 7,400 +0,4 0,5 7,608 -0,3 0,2 7,475 +0,3 0,6 7,502 -0,4 0,3 7,552 +0,2 0,7 7,408 -0,5 0,4 7,651 +0,1 0,8 7,367 -0,6 0,5 7,766 0,0 0,9 7,349

. 5.1. -

474

: - 474 . .

3. - 474. . 5.2 . 5.2.

5.2. - 474

n , n ,. /

s . ns ,

. nss 0

,.

, /.

+0,6 0,7/0,1 8,467 8,577 8,522 -0,746 -8,526 +0,4 0,6/0,2 8,121 8,115 8,118 -0,342 -8,265 +0,2 0,5/0,3 7,859 7,851 7,855 -0,079 -8,945 0,0 0,4/0,4 7,786 7,765 7,776 0 0 -0,2 0,3/0,5 7,880 7,849 7,864 -0,088 -8,030 -0,4 0,2/0,6 8,119 8,102 8,110 -0,334 -8,463 -0,6 0,1/0,7 8,534 8,534 8,534 -0,758 -8,391

437,8 = /.

. 5.2. -

474

- 474, , 8,437 /.

(5.2) (5.3). S0 = 7,776 , = 0,75 , d = 125 , g = 981 460 .

: - 474 . .

4. g :

S1 = 12,898 ., S2 = 0,065 ., = 8,437 /; ( ) 272,108 21 SSg == .

- 474 1301783 [9].

5. . (5.6), L = 20 , = 2 .

.NS +

.NS

8,736 6,908 8,735 6,910

8,737 6,909

S 8,736 6,909

q 595,2827,1437,8

40 =

= /.

- 474

1301783 [9]. 6. - 474. C =

8,437 /. ( . 5.3 . 5.3).

5.3.

smt , 10m00s 10m30s 11m00s 12m00s 13m00s 14m00s

s.

7,724 7,742 7,750 7,770 7,775 7,777

s 65,167 65,319 65,387 65,555 65,598 65,615

smt , 15m00s 17m00s 19m00s 21m00s 25m00s 30m00s

s.

7,777 7,777 7,777 7,777 7,777 7,777

s 65,615 65,615 65,615 65,615 65,615 65,615

. 5.3. - 474

(5.8), . 2 [9] :

( )[ ] 031,0100272,108101503,0 5 += . 2 , 13017

83 [9]. 7. - - 474: C = 8,437 /. ( . 5.4 . 5.4).

5.4.

h m

,. S ,

. gr,

1S 2S 3S

8 9 15 7,764 7,765 7,762 7,764 65,505 1998 . 10 15 7,758 7,760 7,756 7,758 65,454

11 15 7,743 7,748 7,745 7,745 65,345 12 15 7,737 7,732 7,730 7,733 65,243 13 15 7,721 7,724 7,720 7,722 65,151 14 15 7,715 7,712 7,710 7,712 65,066

15 15 7,709 7,705 7,702 7,705 65,007 16 15 7,693 7,695 7,691 7,693 64,906

17 15 7,680 7,676 7,682 7,679 64,788 18 15 7,668 7,665 7,668 7,667 64,686 19 15 7,652 7,656 7,651 7,653 64,568 20 15 7,640 7,643 7,639 7,641 64,467

. 5.4.

:

. 1301783 [9].

1. 2. 3.

. 4. 5. 6.

-

-65,5

-65,0

-64,5

-

- - 474 = 2,3 /,

.

-. g (t), (

. .

- 474

474

(),

-.

2

:

. :

[39, . 1, 7, 8], [28, . 1, 4, 7], [27, . 1, 6, 8], [9, 23, 17, 14].

ig , , (, , ), .

. 4. . . .4.1. . .4.2 f (s). . .4.3.4.5. , 13, . .4.3 ( ); 46 . .4.4 ( ); 710 . .4.5 ( ).

( ) , - .

- , , .

(), 0g .

ig :

ii ggg += 0 , (5.11) ig

, , . 5.11 ig :

( ) , 0 iii gggg ss += (5.12) sig

sg 0 , ;

( ) ig - , .

:

( ) ( )sisi sfgg ++= g (5.13) )( sig , .

sig

( ) iisi sg = , (5.14) iT

iT , /,

( )00 TTCC iT i += , (5.15) 0C 0 = 0 C,

/;

C , /( );

is i- , :

n

s

s

n

i

i

= 1 ; (5.16)

n si i- , ;

( )sf , , ;

g , , g = g + g. cC ,0 ( )sf

, [6]. . g , [1, 2, 7]. g .

- : ( ) ,; . 0iii ttttkg i == (5.17) k () -

, /;

it 0t , .

.

1. .

2. . 3. . 1. ,

, k :

k = ( ) ( )

,tt

gg

12

0201CSS

0201 (5.18)

01

S 02

S

-1 -2; ;

01g 02g -1 -2, ;

1t 2t -1 -2.

2. , ( ) ( )

,tt

ggk

ks1

s1

= (5.19)

( )sg1 ( )ksg1 ;

t t .

3. , , - :

,

1

2

1

=

=

=m

ii

m

ii

si

T

Tg

k (5.20)

sig iT () () ;

m sig iT , . . .)()(;)()( ' iii

si

si

si ttTggg == (5.21)

. 1. (. 2.1)

, it

iS .

2. sig (5.13) (5.15).

3. - (5.17) (5.18), (5.19) (5.20).

4. ig (5.12).

5. (5.11).

981 245,000 981 217,500 .

- 111 0001,70 =C / 41017,13 = /( ) (. . 4, . .4.1).

( iS it ( ), i- , ) 14 (. 5.1).

f (s) . .4.2. .

f (s) f (s) . . 5.5.

, . 5, . 5.1.

5.5.

.

,it

,T

,is.

( ) ,sig

( ),isf

, g

,sig

, it

,)( . ig

, ig

,ig

1 2 3 4 5 6 7 8 9 10 11 12 1 9,00 12,0 4,500 31,572 6 - 31,566 0,00 0,000 0,000 981 245,000

1 9,20 12,0 5,200 36,483 11 - 36,494 0,20 0,009 4,937 240,063 2 9,30 12,0 6,400 44,402 28 - 44,930 0,30 0,014 13,378 231,622 3 9,70 12,5 2,000 14,033 32 - 14,011 0,70 0,032 17,533 262,533 4 9,90 12,5 6,200 43,503 33 - 43,536 0,90 0,040 12,010 232,990 5 10,00 12,5 5,100 35,784 8 - 35,792 1,00 0,045 4,451 240,549

2 11,00 13,0 8,400 58,945 31 - 58,976 2,00 0,090 27,500 981 217,500

. 5.5. ( )sf - 111 ( . .4.2. . 4)

.

1. - ?

2. f(s) ?

3. .

4. ?

-50

-40

-30

-20

-10

0

10

20

30

40

2 3 4 5 6 7 8 9 10 11 12 13 14

f(s),

s,

3

: .

: [28, 9] [39, 6365], [27, . 6366]. 3 .

, g

nD .

- . 0,165 , 0,076 . 0,241 .

110-9 -2 (0,1 ) [5].

, , , -2, - , g.

g , [26, 25, 37, 26]:

g = (g + g)k, (5.22) g g

; k . 1,14,

1,16, 1,17, (-) 1,238.

,

,1031

2cos2

,1031

2cos2

5

5

+=

+=

czR

Dcg

z

R

D

g

c

(5.23)

z z ; R , R 0243716= ;

D D . :

,

,sin

43

,sin

43

23

34

23

34

=

=

a

pRgD

a

pRgD

ccc

(5.24)

, m m M , . .

,

=M

m ;

=M

m (5.25)

a , ; pC p , ; g .

:

, 22

=R

fMg , (5.26)

f , 23 . ,

, () [2].

:

cra

cp =sin , ,479,8

cR

p

= ,sin

ra

p = (5.27)

r r ;

R - , (. .). [2].

(, , ) [34]. , . 1.

:

,coscoscossinsincos tz += (5.28) ; t .

0 vh += , (5.29) 0 0

h () (TDT). , ;

v ; h .

( ) ,TDT TUTh h +== (5.30) UT ( );

T , . , .

UT : ( )knDUT n += , (5.31)

nD n ;

k . k = 2, k = 1.

v :

,48

0 h

h Dhvv

+= ,

01 vvD = (5.32)

0

v 1

v

. , . : t ,mE += (5.33) E 12 , . .

;12 hE += (5.34) m . E :

,0 EhvEE += (5.35) 0E

+ 12 ;

Ev . :

;480 h

Eh

EE

Dhvv += 01 EEE vvD = , (5.36)

0Ev 1Ev

. ( ).

: ,+= UTm (5.37)

. + , .

: t s = (5.38) s ; . :

,0 +++= UTUTSs (5.39) 0S .

, ;

, 0027379,0 = . ,

:

( ) ( ) ,0=

=n

iii xTAxf (5.40)

( )xf ( ); x . :

,12 = hx (5.41)

h (. (5.30)); 24h;

( )xTi . : ( ) ( ) ( )nixixTi ,,2,1,0,arccoscos == , (5.42)

iA . . .

, iA , . iA , , .

(5.28) z z, (5.24) D D (5.23) (5.22) g, g g.

5,240431 0 = smh 1,10189 =

g, g g smh

nD 4,36576= 13 1988 . (.

5.6)

1. g.

5.6.

( )

1 nD smh 4,36576 2 1+n h10 ,9=n n ( )f= 3 UT smh 4,365720 (5.31) 4 T s0,57 , 1988 ., . 609. 5 TDT smh 4,335820 UTD 6 ( )hh TDT= h97594,20 12 1988 .

( )

9 0v 844,23 , 1988 ., .10 ( 12.01)

8 1v 650,24 , 1988 ., .10 ( 13.01)

13 D 805,1 (5.32) 14 48 hD 246,0 8 0v 844,23

15 v 091,23 (5.32) 16 vh 23,218 9358,860:7534,501 =

7 0 30,2084210 , 1988 ., .10 ( 12.01)

17 17,5993210 (5.29) 25 0ct 0889696,271 ct 24 hct h12597972,18 ct 3 UT smh 4,365720 . 3

23 smh 1,10189 22 E smh 027,475111 (5.35)

10 0E smh 537,075211

, 1988 ., c. 10 ( 12.01)

21 evh s510,20 20 ev s9778,0 (5.36) 19 48hD E s0106,0 11

0Ev s9884,0

18 ED s0242,0 (5.36)

11 0E

v 0,9884 S , 1988 ., .10 ( 12.01)

12 1E

v 0,9642S

26 Z 99,6587790 (5.28)

18 ED s0242,0 (5.36) 27 D , D (5.24) 28 g 023,0 (5.23) 2. g. (5.41) x

( )xf :

747945,0124

97594,202=

=

h

hx .

(5.42) ( )xTi i = 0, 1, 2, ..., n; n = 5:

( )( )( )( )( )( ) .883643,0

;9716814,0

;5699827,0

;1189930,0

;747995,0

;1

5

4

3

2

1

0

===

===

xT

xT

xT

xT

xT

xT

(. 60) iA

12 1988 . f(x): c:

4669

3702160

697128785164

01883027,004833886,0

78101723,276290375,5

50206569,1121018570,201

5

4

3

2

1

0

00

00

00

A

A

A

A

A

A

(5.40), iA :

smhh 150,0642137017083,13525624,2050 === ;

77,504313580769,13 00 == . (5.39) ,

(. 6, ) 0S h0 TDT12 1988 .:

smhS 3050,522270 = ; s = 7h22m52,305s + 20h57m36,4s(1+0,0027379)+ 9h18m10,1s = = 7,381196h + 20,960111h1,0027379 + 9,32806h = 13,701500h = 13h42m05,4s.

(5.38): 099688,35925,59592315,0642134,054213 === smhsmhsmht

. (5.28) z: z= arccosz .2,155145254242,45 00 == (5.24, 5.23, 5.22) D g = 0,026

g = 0,003 : g = 1,16(0,026 0,023) = 0,003 .

1.

- . 2. ,

?

4

:

. :

: [28, 65], [39, 71], [3, 5]. 4 . 6. . 0 10.

nkg , n k .

. n k (), n 5, k 2, :

,1

1,1

2

=

==

nkm

nk

jiij

g (5.43)

ji jig g ( g );

n k jig .

g :

( ).

1

1,1

2

nk

m

nknkM

g

nk

jiij

g ==

==

(5.44)

n ( 5>n ) k (2>k ),

[5, 17].

, 321 ++++= gg nk (5.45) g ;

1 , 2 , 3 , : , .

g , n k . 5.7.

5.7. ig

, , j iog ,

0 i i 1 2 ... K

1 11g 12g ... kg 1 10g 10 2 21g 22g ... kg 2 20g 20 ... ... ... ... ... ... ...

n 1 ng 2 ng ... nkg 0 ng 0 i

goj 01

g 02g ... kg 0 00g -

,

oj 01 02 ... k0 - -

. 5.7: ;

12111 ,,, nggg , i = 1 n;

kggg 11211 ,,, , j = 1 k;

gio ig k :

k

g

g

k

ji

io

= =1 ; (5.46)

ojg jg n :

n

g

g

n

ij

oj

= =1 ; (5.47)

00g g :

nk

g

g

n

i

k

jij

= = =1 100 . (5.48)

g : ) n g

k :

,1

1

20

2

==

n

n

ii

n (5.49)

0i 0ig 00g , ;0000 ggii = (5.50)

) k

kg0 n :

,1

1

20

2

==

k

k

jj

k (5.51)

j0 jg0 00g , .0000 gg jj = (5.52)

, ;

) 1 :

( )

( )( );

11

1 1

20000

21

+

== =

kn

ggggn

i

k

jjiij

(5.53)

) :

kn

2122

2

= . (5.54)

:

nk

2122

3

= ; (5.55)

) ( ):

; 2322

21

2 ++=g (5.56)

) , n k :

.

23

22

212

knnknkg++= (5.57)

:

.

21

222 nkkn

kn

g nk+= (5.58)

(0 22 < 0

23 < ).

:

( ),

1

1 1

200

21

== =

nk

ggn

i

k

jij

(5.59)

nknkg

212

23

22

,0,0 === .

(0 23 < , 0

22 > ),

:

( )

( )

.

;0;

,1

22

2122

3

2122

2

1 10

21

2

nnkn

kn

gg

n

n

i

k

jiij

+===

== =

(5.60)

(0 22 < , 0

23 > ),

:

( )

( )

.

;

;0

;1

23

212

2122

322

2

1 121

knkn

nk

gg

k

n

i

k

jojij

+===

== =

(5.61)

( 3=n , 8=k ) (. 5.8).

5.8. g

k n

1 2 3 4 5 6 7 8 0ig 0i 1 248,84 248,70 248,69 249,07 248,92 248,77 248,90 248,83 248,84 0,02 2 248,90 249,05 248,83 249,10 248,87 248,88 248,76 248,91 248,91 0,05 3 248,83 249,00 248,68 248,97 248,69 248,79 248,76 248,88 248,82 0,04

jg 0 248,86 248,92 248,73 249,05 248,83 248,81 248,80 248,87 248,86

j0 0,00 0,06 0,13 0,19 0,03 0,05 0,06 0,01

1. (5.46), (5.47) (5.48) nkg

( 0 ig ) ( jg 0 ),

nkg ( 00g ), 248,86. jg 0

0 ig jg 0 0 ig 00g , . .

jg 0 000 igg == ,

k

g

g

k

jj

j

=

=1

0

0

, n

g

g

n

ii

i

== 1

0

0

. (5.62)

2. (5.47) (5.49) 0ig jg 0

00g : 0i j0 . 3. (5.49) (5.51)

0ng k kg0 n : n k :

.095,0,047,0 == kn 4. (5.53) 1

, 0,091 . 5. (5.54), (5.55)

034,0 2 = ( ) 079,0 3 = ( ).

6. g ( ) g , n k , (5.56) (5.57) :

,125,0 =g .039,0 =g

7. g , (5.58),

0,039 .

1. g

. 2.

, ? 3.

? 4. 1 , 2 3 ?

5

: .

: [26, 25, 37, 15, 16, 6, 32, 27]. 5 . 6.

.

, :

1. ; 2. ; 3. ; 4. ; 5. ; 6. .

g , ():

. = gg (5.63)

: ( )10.. ggg += ; (5.64)

( ) , 210 gggg ++= (5.65) 1g H , ,

( ) 1 2cos00071,0130855,0 HBg += , (5.66) H , ;

0 [14],

( ) ,142sin107sin10302,51030978 26230 += (5.67) . 0 , 14 , . 8.

(5.65) 2g , , , , ,

H . , , [16].

: 5

2 102 = Hfg (), (5.68) f , 1067,6 8 3 / ( 2); = 3,1416; = 2,67 /3 ( ). h

, .

, , , , , , , 3g , :

53 1022 = hfg (), (5.69)

, ;/c03,1 3

h (), .

g , , ch .

1 2, :

( ) .ggg 10.. += (5.70) 3 , 0 =H . ,

.. [21], : . 0.. = gg (5.71)

( 4) h , ..g :

( ) .gggg 310.. ++= (5.72) , 1g

H h .

5 H h , . .

hHH += . (5.73) ..g (5.8),

1g H H , (5.73).

6, ch , (5.72).

, 1g , :

chHH = . (5.74) 3g

, , ch .

ch . ..g . 5.9.

5.9. ..g

B ,0 ' H,

h**, ( )hH +

, g , , 0 , 1g

, , 3g

, ..g

1 52 13 5 0 5 981 274,8 981 248,6 1,5 981 247,4 27,7

2 36 48 384 0 384 979 851,0 979 870,4 118,5 979 751,9 99,1

3 4 22 0 0 0 978 072,8 978 045,9 0 979 045,9 26,9

4 25 45 0 125 125 979 069,3 978 990,5 38,6 979 029,1 10,8 51,0

5 67 17 143 500 643 982 192,2 982 424,7 198,2 982 226,3 34,3

6 48 50 125 40 85 980 924,7 980 947,9 26,2 980 921,4 8,9* 12,5 * 3g = 2,67 /

3. **

h . : 1. ; 2. . 1, 2, 5, 6, ,

: . 2ggg .. += (5.75)

3 4, , :

hfg = )(2 2 . (5.76)

(5.75)

2g , (5.76). g . 5.10.

5.10. g

H , h , .. g , , 2g , g

1 5 0 27,7 0,6 27,1 2 384 0 99,1 43,0 56,1 3 0 3 820 26,9 262,4 289,3 4 0 125 51,0 8,6 59,6 5 143 500 34,3 16,0 50,3 6 125 40 12,5 14,0 1,5

1. . 2. ? 3. . 4. H (5.66)

? 5. ?

6

: .

: [28, . VI, 47, 49, 50, 54], [27, . 2, 3], [14]. . 9.

25 , 2 2 03 , . 1 : 1 000 000 10 .

g :

, 00 == ggg (5.77) 0g

,

0 [15].

: ( ) ,142sin107sin10302,51030978 26230 += (5.78)

. : 1. :

( )10. ggg += ; (5.79) 2. :

( ) , 210 gggg ++= (5.80) 1g H , . :

( )2cos00071,0130855,0 1 Hg += ; (5.81) 2g , ,

H .

, ,0419,0 2 Hg = (5.82)

, 367,2 .

1. (5.78).

2. (5.79).

3. (5.80).

4. 1:1 000 000 10 .

. 5.115.14.

5.11. 1

103,0 103,5 104,0 104,5 105,0

44,0 g 980 301,5 980 312,4 980 292,9 980 289,1 980 231,0 H 630 600 750 820 1 080

43,5 g 980 219,9 980 217,0 980 203,5 980 205,5 980 175,0 H 800 850 1 000 1 000 1 130

43,0 g 980 174,1 980 141,4 980 131,6 980 113,8 980 093,0 H 930 1 010 1 070 1 150 1 200

42,5 g 980 116,2 980091,4 980 076,6 980 031,2 980 016,8 H 1 000 1 030 1 100 1 190 1 240

42,0 g 980 056,2 980 032,6 980 020,7 979 990,0 979 957,3 H 980 1 090 1 130 1 220 1 310

5.12.

42,0 42,5 43,0 43,5 44,0

, 980 511,4 980 465,2 980 421,1 980 376,0 980 331,0

5.13.

103,0 103,5 104,0 104,5 105,5

44,0 52,9 83,1 126,0 56,0 46,5 43,5 57,6 91,6 61,2 22,2 29,8 43,0 42,3 57,0 95,9 58,5 22,1 42,5 22,8 19,5 21,8 76,9 42,3 42,0 30,7 20,7 12,1 6,7 32,6

5.14.

103,0 103,5 104,0 104,5 105,5 44,0 67,9 85,9 97,8 102,9 118,0 43,5 68,8 72,9 80,9 128,9 138,1 43,0 92,0 82,9 66,4 106,0 148,0 42,5 116,0 126,0 126,0 91,0 120,0 42,0 115,9 135,9 147,9 149,9 133,0

1 : 1 000 000 10 SURFER CorelDraw.

1. Surfer. 2. New worksheet. .

3. GridData.

4. Sheet2. 5. X Column B, Y Column A.

6. , output grid fail

, . 7. , report ().

8. FileOpen

.

9. nodes.

10.

11. Print Screen.12. Paint 13. Paint 14. 15. CorelDraw.16. 17.

.

Print Screen.

Paint . Paint JPEG. CorelDraw.

( ). .

Show

.

18. ( ), .

19. 160

200 ( ).

20. .

() 0,8 , . 1 .

21. . ( ), . 4,5 , 3,5 .

. , , .

Paint ( Windos, ).

Paint (,

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.

Word,

, . . . (

), .

, .

. 5.6

.

1 : 1 000 000

10 .

: . . -41 : .. ..

. 5.6.

-90

-110

-130

-70

-140

-140

-70

42.0 42.0

43.0 43.0

44.0 44.0

1. . .

1 ? 2. . 3. . 4. , . 5. . .

7

(), ()

() :

. : [23,

. XI, 6469] [12, . 13, 18], . 1.4 .

( g ) 1 : 1 000 000, 1 (. 10, . .10.1) , . 11, . .11.1 .11.2.

. - , .

() 0=4300' 0=69

00' ", " ( ). 100 .

,

g . ( ) 100 , , , (), .

. , , , , .

g . 10.

: , 0 0r , 0r ir . 0r 5 , , , 5 100 . :

( )

+=

=

=

=

=

=mk

k

mk

k k

kk

gm

rg

r

A

Arg

1

00

00

10

2

2

sin

cos

8

, (5.83)

= 8 , : 2, 4, 6, 8, 10, 12, 14, 16;

kg g 0r ;

4= kAk 0r ;

k (1, 2, 3,, ); , 981 000 ,

0g . 4, 8, 12, 16 ( )= 270,180,90,0kA

0 0 :

=

=

4

11

0

0

sin

cos

k k

kk A

AgC , (5.84)

0263,08

1 =

=C .

2, 6, 10, 14 ( )= 315,225,135,45kA :

=

=

4

12

0

0

sin

cos

k k

kk A

AgC , (5.85)

0186,0707107,00263,0sin 112 === ACC . 0 :

=

=

=+=+=

8

10

1

00

00 .00032,000255,02

2

k

k

mk

kk gggm

rg

r (5.86)

5 100 :

drdAA

AQg

R

r

r

=

=

=

100

5

2

01

1005 0sin

cos

21

, (5.87)

1Q (1.43). 16 8

, 0,005. ( n= 16) 22,5.

, ,

A

Pr

A

Cr

A

Br

A

Cr

A

Brlrl kkkkknkn +++=

21

211 22

. (5.88)

( ) rCrBrArF ++= 22

ln , (5.89)

( ) ( )011 rFrFP = ; (5.90)

500,016

1 =

R

P. (5.91)

5.885.91 (5.87) :

= =

=

16

11005 sin

cos500,0

k

VIII

Ii i

iki A

Ag . (5.92)

5 100

( ) ( ) =

= =

100

5

2

01005

0

21

r

rM dAdrrFg . (5.93)

(5.93) :

( )

.1014910169

47322215

516

1

16

1

16

1

16

1

16

1

16

1

16

1

16

11005

++++

++++=

VIIIVIIVIV

IVIIIIIIIM

gggg

gggg

(5.94)

, 0100

, 1 : 1 000 000, , , . , , . 10, 11.

.

1. , ( . 12, 4 6).

2. , , , NS .

3. 0g ig , 2, 4, 6, 8, 10, 12, 14, 16 4 .12 . 0g 6 (. 12) 00255,04 =C .

4. ig 2, 6, 10, 14 ( ). + , (5.83), (5.87). g .

5. g 1 (. 12, 4, 2).

6. 1 0186,01 =C 1 14 (. 12, 1).

7. g 2, 6, 10, 14 ( ).

8. g 2 ( 2, . 12, 1).

9. 2 018601 ,C = , 14.

10. g , 16, 8, 4, 12.

11. , , . , g .

12. 2 2 , 12.

13. 1 2 , 1 2 , 0-5 50 5 (. 12):

.

;

2150

2150

+=+=

(5.95)

14. g

3 . 15. 00032,03 =C

50 . 16. 0-5 50

5, 0 50 . 6. , , 5100 . 1 (. 12).

17. , 1 (. 12).

i = I VIII. k = 0 16. . g .

: 1, 7, 9, 15; 2, 6, 10, 14; 3, 5, 11, 13; 16, 8, 4, 12. , : 22,5, 45,0, 67,5, : 16 360, 8 180, 4 90 5 270.

18. , g I-VIII. , 9 . . .

19. , ig ( ) 1 .

20. g ( ) 3 .

21. ( 0 ) ( 3 ). :

( ) ( )30 = . (5.96) . 22. , 49. ,

iC . 1, 7, 9, 15:

=

=

9001,0

6004,0

5,22sin

5,22cos500,0

1C .

2, 6, 10, 14:

=

=

5003,0

5003,0

45sin

45cos500,0

2C .

3, 5, 11, 13:

=

=

6004,0

9001,0

5,67sin

5,67cos500,0

3C .

16, 8 ,4, 12:

=

=

0005,0

0005,0

90sin

360cos500,0

4C .

i i 1005 1005 :

.

43211005

43211005

+++=+++=

(5.97)

23. 1005 1005 5 (. 12), 5100 .

24. i ( 0,01 ). ig

510iK . 25. i

4 ( 0,1 ). 26. 1005 6 (. 12),

5100. 27. , :

10055001000

1005501000

1005501000

++=+=+=

().

(5.98)

1. 4

(. 11). 2. ,

, , ( ). , . .

3. , . .

4. .

5. .

1. . 2. . 3. . 4. . 5. , ,

, . 6. ?

8

: .

: [28, . VI, 47, 48]. 5 . 8 . 7.

.

. NJ 00108,02 = ( N ).

1. 0 :

0 ( )BBe ,142sinsin1 212 += (5.99) e , , 1

; e ,978016 = ; 005302,0 = . 1 , . (8.1) 1 0,0000071. , (8.1) : e , . 0 . , e .

0

g : ( ) ( ) 14ggg14B2sinBsin1 1212e0 =+=

(5.100) ( )

,000978

B2sing000978gBsing 21e12e

++= e (5.101)

g ;

1g ; g . :

=

==

+=

==

.x

,000978x

,g

),B2sin000978g(l

,Bsinb

,1a

e2

e1

i

i2

1eiii

i2

i

i

1g (5.102)

iiii lxbxa ++= 21 , (5.103) i , i = 1, , n; n . :

,=+ LAx (5.104) (-)

,

2

1

=

n

,2

1

=

nl

l

l

L ,2

1

=x

xx (5.105)

.22

11

=

nn ba

ba

ba

A (5.106)

2. [ ] min = . :

,0=+ lNx (5.107)

[ ] [ ][ ] [ ] ,

==bbab

abaaAAN T ; (5.108)

,...

...

21

21

=n

nT

bbb

aaaA (5.109)

[ ][ ] .

==bl

alLAl T (5.110)

3. , :

,1 QllNx == (5.111) Q N ;

.2212

12111

== QQ

QQNQ (5.112)

4. :

.

;000),978(

e

2

1e

x

x

=

+= (5.113)

5. :

,25

= q (5.114)

e

2 aq

= ;

, = 7,29 10-5 /; a a = 6 378 245 . 6.

2J :

[ ]qJ += 2321

. (5.115)

7. :

[ ]

,

;;

;;

2

22

11

mm

m

mmQm

Qmkn

vv

e

e

e

e

=

==

=

=

(5.116)

11Q , 22Q QN =1 .

( ) . 5.15.

5.15.

/ B , ' ( 000978g ),

1 5213' 3 275 2 3648' 1 851 3 422' 73 4 2545' 1 069 5 6717' 4 193 6 4850' 2 925

1. . 1g , (5.66), .

5.9 5. ib , il , (5.1005.102), (. 5.16).

5.16. ib , il

/

B ,

( 000978g ),

1g ,

Be 2sin 21 ,

l ,

be ,

,

b ,

1 52 13 3 275 1,5 6 3 282 3 189 13 0,62463

2 36 48 1 851 118,5 6 1 976 1 832 62 0,35883

3 4 22 73 0 0 73 30 38 0,00580

4 25 45 1 069 38,6 4 1 034 964 0 0,18874

5 67 17 4 193 198,2 4 4 395 4 344 30 0,85087

6 48 50 2 925 26,2 7 2 958 2 894 8 0,56670

A :

,

56670,01

85087,01

18874,01

00580,01

35883,01

62463,01

=A

.

9582

3954

0341

73

9761

2823

=L

:

.

vxx

vxx

vxx

vxx

vxx

vxx

621

521

421

321

221

121

=+=+=+

=+=+=+

95820,56670

39540,85087

04510,18874

730,00580

97610,35883

28230,62463

(5.117)

2. :

=59967,159577,2

59557,26N ;

;3708

71813

=l

.0370859967,159557,2

07181359557,26

21

21

=+=+

xx

xx

3. , . :

MathCad; . D [27]:

[ ][ ] [ ]

[ ] [ ][ ] .86105,2=== bbbbnbbb

bnD

1x 2x , :

D

Dx ii = ,

iD . :

[ ] [ ][ ] [ ]

;59967,13788

59557,2738131

=

=bbbl

blD x

;7,7611 == D

Dx

x

[ ][ ] [ ]

;370859557,2

7181362

=

=blb

lnD x

108522 == D

Dx

x;

[ ][ ]

[ ] 1,599671 === bbbb0

bD

1xP;

;5599,01 ==

D

D

P1x

1

P

x

[ ];6

1

0=== n

b

nD

2xP

2,097.1 ==

D

D

P2

2

x

x

P

MathCad:

;10108,5

668,76

3708

71813

097,2907,0

907,0559,03

=

== Qlx

.1085

7,76=x

4. :

;077978000978 1 =+= xe

.005222,0

2 ==e

x

5. , 003468,0=q :

,25

= q

003448,0 = , 2901

= .

6. 2J :

.297

1;0033623,0;003468,0 ===q

7. :

[ ]40

==

kn,

n ( )6=n ; k ( )2=k .

;30

11

1

=== QP

mx

e

58

22

2

=== QP

mx

e;

000059,0

==

e

em

m ;

.5 2

==

mm

1. e , ,

. , [26, 16, 4648].

2. ? 3.

, ?

1. .. . .: - . .. , 1996. 188 .

2. 1988 . .:, 1988. 690 .

3. .. .. // . , . 1960. 6. . 4551.

4. .. . .: , 1983. 112 .

5. .. , // . . . . 1956. 7. . 755764.

6. .., .. , , 1981 // . . . . 1983. 3. . 4351.

7. .., .. . .: , 1968. 512 .

8. .. . .: , 1967. 320 .

9. 1301783. . . .: - , 1984. 36 .

10. 523342005. . . .: , 2005. 28 .

11. : / . .. , .. . 2- ., . . .: , 1990. 607 .

12. .. . .: , 1976. 512 . 13. .., .. . .: ,

1978. 176 . 14. .., .. : .

. 4- . .: , 1988. 364 . 15. ..

// . . . 121. ., 1935. . 4375.

16. . . . 5. .: , 1980. 80 .

17. ( I ). .: , 1988. 253 .

18. .., .. . : , 1981. 171 .

19. .. // . . 11. : , 2006. . 98100.

20. .., .. : . . : , 2000. 34 .

21. .., .. : . . : , 2001. 56 .

22. .., .. : . . : , 2005. 39 .

23. .. : . . : , 1996. 30 .

24. . / . . .: , 1983. 520 .

25. .. . .: , 1968. 408 . 26. . / . . .: ,

1975. . 1. 568 . 27. .. [] / .. .: ,

1972. 512 . 28. .., .., .. [] /

.: , 1978. 325 . 29. .., .. ,

1 [] / .: , 1983. 30 .

30. .. . . III. : . .: , 2006. 384 .

31. .. ( ). .: , 1978. 264 .

32. .. , , // . . . . 1980. 12. . 75 89.

33. .. . : , 1981. 33 .

34. .. : . . . .: , 1984. 239 .

35. . / . . .: , 1999. 429 . 36. .. . : , 1968. 332 . 37. . / . . .: , 1982. 288

. 38. .. . .: , 1973. 432 . 39. .., .. : . . .:

, 1980. 320 .

1

a = 6 378,245 b = 6 356,777 032,3716=R 25,298:1 = 2710973,5 =M 80665,9=g /2 111067,6 =f 3/ 2 1110496,1 =A 67,2 = /3 03,1 = /

3

251035,7 =m 623,1=g /2 1401384 =r 61,513 =D 350,3 = /

3

16,275 = 4,4743=D

( ) 3210002,09904,1 = = 1, 410 /

3 DC = 3159, 26'' gC = 273, 80 /

2 C = 8, 794'' r = 149 599 300 DC= 1 392 000

2

.2.1.

: ; - 1039

, .

h,m

S,

.

,

/. Tn n

n

iS iS ( )2Tin ( )2TnK iC

1 2 3 4 5 6 7 8 9 10 11 12 13

0 in 1t 1S

+0,6 6in 2t 2S

+0,4 4in 3t 3S

+0,2 2in 4t 4S

0 in 5t 5S

-0,2 2+in 6t 6S

-0,4 4+in 7t 7S

-0,6 6+in 8t 8S

0 9t 9S

0 in jn 1t 16t 1S 16S 1S 15 SS 0 +0,6 3+in 3jn 2t 15t 2S 15S 2S 25 SS 1C

+0,4 2+in 2jn 3t 14t 3S 14S 3S 35 SS 2C

+0,2 1+in 1jn 4t 13t 4S 13S 4S 45 SS 3C

0 in jn 5t 12t 5S 12S 5S 55 SS 0 -0,2 1in 1+jn 6t 11t 6S 11S 6S 65 SS 4C

-0,4 2in 2+jn 7t 10t 7S 10S 7S 75 SS 5C

-0,6 3in 3+jn 8t 9t 8S 9S 8S 85 SS 6C

:

( ),,

21

,,2

,

, 20

21

da

gKSSSSS

SS

nKC

n

C

C ii

i

i

ii

Ti

i

n

i

===+

=

==

.125,75,0,000981 === dag

4

2

.4.1.

0 ,

,10 4

,10 4

.

,10 4

.

2g ,

1 111 7,0001 16,74 13,17 1,97 981 448,420

2 401 7,6854 9,22 7,60 1,72 981 447,489

3 413 6,8691 11,12 10,42 1,45 981 448,716

4 44 7,8001 15,04 40,59 2,01 981 447,178

5 73 7,0956 16,53 12,30 1,63 981 448,259

6 76 7,1321 12,47 10,31 1,99 981 448,208

7 116 8,0758 7,43 24,17 1,43 981 446,868

8 650 8,1515 13,91 2,70 1,13 981 446,581

9 1 172 6,6769 4,90 1,45 0,82 981 449,018

10 (0) 375 7,1081 6,58 2,16 1,10 981 448,279

.4.2. f (s),

-

M (f), 2 3 4 5 6 7 8 9 10 11 12 13 14 15

111 32 22 17 5 37 15 39 18 36 2 0 36 36 20 27

401 16 6 6 7 2 21 18 30 13 22 0 44 24 5 24

413 1 1 0 4 1 1 0 6 2 5 5 10 0 3 17

44 0 11 20 31 17 18 8 51 95 79 5 13 0 6 31

73 0 5 3 13 10 27 3 22 0 17 12 14 24 10 13

76 0 21 10 7 10 18 26 17 19 37 17 0 43 15 16

116 2 12 2 0 13 8 18 2 22 8 6 14 36 0 10

650 28 6 0 4 17 16 7 18 17 10 13 20 23 5 13

1 172 0 3 2 0 0 2 1 2 3 1 1 0 2 2 7

375 13 3 2 0 4 7 8 3 2 5 0 7 1 3 8

,

.

.4.3. 1. -1 -2

, h

S , .

t,

T, h

S , .

t,

-1 9 15 6,589 20,0 8 1033 11,998 1 9 23 5,327 9 10 42 12,252 2 9 34 3,152 10 10 54 13,508 21,0 3 9 44 2,008 11 11 03 14,643 4 9 53 4,298 12 11 12 10,828 5 10 06 7,456 20,5 13 11 24 9,777 6 10 15 9,701 14 11 32 8,915 7 10 25 10,825 -2 11 51 8,125 21,5

.4.4. 2. -1

, h

S , .

t,

T, h

S , .

t,

-1 700 4,021 11,0 6 901 6,400 11,5 1 7 21 5,250 7 9 20 8,602 2 7 43 4,032 8 9 42 7,000 3 8 00 3,500 9 10 03 5,254 4 8 22 2,200 10 10 22 6,301 5 8 40 4,040 -1 10 41 4,109 12,0

.4.5. 3.

, h

S,.

t,

T, h

S , .

t,

-1 946 5,443 21,0 4 1301 9,532 20,5 1 10 32 6,265 3 13 40 10,168 2 10 55 7,850 6 14 14 4,100 3 11 35 10,032 2 14 51 8,111 4 12 18 9,453 1 15 16 6,636 5 12 37 3,574 20,5 -1 15 51 5,555 20,0

5

.5.1

____ ____________________________________ - ____111__ _ _______ , tC __7,001__ /. () _______________________________ ____ ..________________ () () ___08.08.2008_______________ ____ ..________________

() ()

Ti, Ti,

t, C

iS,.

Sig

Gi,

sif

,

gi,

ti, gi,

gi, ig

,

gi,

gi,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

:

gi igg += ; 1ggg ii = ; 2)()( ii

igg

g+

= ; is

ii

Sii gfggg +++= ; it

Si SCg = ; ii tkg = ;

1TTt ii = ;

=2

)(

i

ii

T

TGk ; )()( Si

Sii ggG = ;

iii TTT = . g

i = g + g

gi g , 3.

6

4

1

k n

1 2 3 4 5 6 7

1 248,78 248,62 248,84 248,69 248,88 248,60 248,91 2 248,56 248,72 248,68 248,91 248,59 248,59 248,84 3 249,02 249,00 248,85 248,78 248,59 248,59 249,10 4 249,07 248,92 248,77 248,90 248,89 248,89 249,03

2

k n

1 2 3 4 5 6 7 8

1 248,71 248,69 248,57 248,94 248,94 248,72 248,95 248,80 2 248,76 248,97 248,65 248,78 248,84 248,83 249,03 248,97 3 248,80 248,76 248,62 248,78 248,92 249,00 248,83 248,87

3

k n

1 2 3 4 5 6 7 8

1 248,94 248,78 248,78 248,90 248,84 248,92 248,72 248,72 2 249,00 248,95 249,03 248,83 248,80 248,97 248,97 248,87 3 248,91 248,95 248,96 248,72 248,68 248,71 248,