Sci. Bull. Fac. Educ, Nagasaki Univ., No.19, pp,125‑139 (1968)
Radiational Flux due to primary Scattering falling on the Horizontal Plane
in the High Atmosphere.
By Shizuko UEMURA, Takao SATO,
(Nagasaki University)
Abstract
In the first paper (Ref.1 ) named by the same title (I) as the present the author has computed the intensity of scattering at 5Km level in four wave‑
length ranges, each of has the partial energy equal to 1/4 of the total solar energy falling on the upper limit of the earth's atmosphere. In the second paper (Ref.2) he has investigated the same problem at 75 levels from 1 Km to 38Km height, the interval between adjacent two levels being 500m. Moreover the total solar energy is divided into 12 wavelength ranges, each of which has the partial energy equal to 1/12 of the total. The study is restricted only to the primary in the plane normal to the vertical plane passing through the sun's centre in the sky dome. In the third paper (Ref.3) he has investigated the primary scattering intensity falling on the horizontal plane of 1 cm at the
above mentioned 75 level points in the case of the sun's altitude h=30°, 60°
90°, and found the next four laws, here q being connected with the height of level points by H=1/2(q+1), and λi′ the wavelength.
1. The intensity decreases with increasing q for each h and each λi'.
2. The intensity increases with increasing h for each q and each λi′.
3. The value of the wavelength in which the intensity becomes max. de‑
creases with increasing q for each h.
4. The values in the same meaning as 3 decreases with increasing h for each q.
In the paper just mentioned, the energy of the Sun outside the earth's at‑
mosphere for λi′ has been gained from the reserch of Abbot. Let θ1 be the angle between a line passing through Eg, which is hereafter named by θ1 line, and 0 Eq line. Let A be the azimuth of the vertical plane containing θ1 line relative to the Sun's side. Taking the following values of θ1 and A : θ1=90 +5n (n=1〜6), 150, 180;A=0, π/2, and 3π/2, we have computed the primary scattering intensities coming from (θ1 A1) directions by the combi‑
nation of all values of θ1 and A mentioned above. On the foundation on this
126 Shizuko Uemdra・Takao Sato
computation we have further computed the horizontal intensity by the primary scattering in each of 12 wavelength domain falling on the upper side of E
plane for the sun's altitude h=30°, 60° and 90°
In the fourth paper, i. e. this paper, he has investigated the same problem taking the next values of θ1 and A:
θ1=120, 150; A=0,π/2, and 3π/2, and compared the result of the 3rd
with that of the fourth. We have found that the former result is greater than
the latter for every combination of q, λi′ and h.
1. Introduction. In the preceding paper the author has researched the hori‑
zontal primary scattering intensity falling on the earth's surface (Ref. 1 ).
In this paper he has computed the values falling on the upper sides of the ho‑
nzontal planes at the level of (q+ 1 )/2Km, q‑ 1 ‑75.
2. The method of computation. Let 0 and O′ be the earth's centre and a
point on its surface. Take 75 points E,E2 Eg‑‑‑E75 on the prolonged line of OO', i. e. the vertical line at O'. Theelevation of E, from O'is lKm, and two adjacent points Eq and E帥are apart frcm each other by 500m. Hence,
o′Eq‑‡(Q+1) Km. Consider a horizontal plane of 1 cm2 area on Eg point,
which is vertical to OE9. It is named by Eg plane. This plane can receive the primary scattering intensity generated by the atmosphere in the sky por‑
tion bounded by a horizontal plane at E。 and the atmospheric upper limit.
The intensity is of course the horizontal primary scattering intensity falling on the upper side of Eg plane. Now, we divide the total energy of the Sun outside the earth's atmosphere into twelve domains. Let pォ, λl, λ/, k and I。 (λi') be respectively the mean transmission coefficient of each domain, the upper limit
of wavelength of the domain, the wavelength corresponding to pォ, extinction
coefficient corresponding to p* and the Sun's energy outside the earth s atmos‑
phere. We have the following table (Ref. 1 ).
The values of pォ,λi,λらt.(λ 0,kォ i 1 2 3 4
pi 0.600 0.795 0.867 0.912 λ̀ 0.409 0.466 0.519 0.577 λ i′ 0.3572 0.4364 0.4910 0.5445 I。(λ0 1655 2806 3109 2799 k̀ 0.4924‑10"3 0.2210‑10"3 0.1380‑1Q‑3 0.8915‑10"4
日b翌」^^^^HIL p* 0.973 0.985 0.991 0.995
λ 0.793 0.905 1.058 1.282 λ i′ 0.7456 0.8567 0.9850 1.1396 I。(λ0 1923 1405 1065 457
5 6 0.941 0.961 0.638 0.708 0.6088 0.6763
2643 2321 0.5836‑10‑* 0.3832‑10‑'
ll 12 0.998 1.000 1.738
1.4960 2.5356 352 74 kt 0.2595‑10‑4 0.1482‑10「 0.8519‑10"3 0.4753‑10 s 0.1601‑10"5 0.1940‑10'6
Io(λ O is gained from Abbot's research and Linke's Table. The unit and
Radiational Flux due to primary Scattering falling on the
Horizontal Plane in the High Atmosphere. 127 wavelength width are (cal/cm.min).10T6 and 0.001 p .
Let 6 , be the angle of a line passing through Eq, which is hereafter named by 6 t line, from O Eg line. Let A be the azimuth of the vertical plane con‑
taining 6 f line relative to the Sun's azimuth. Take the following values of O, and A : 6 1=120, 150, 180 in a degree unit, A= O , 7r/2, 5 /2.
In this case the atmosphere model is the same as in (Ref. I . ) and its upper limit amounts to 40Km height. Let O " be the intersecting point of 6 1 Iine by the atmospheric upper limit, and now let T. be a point on O I Iine which is apart from Eq by the distance of r. The amount of primary scattering dp, received at Eq Point from an air portion at T. exposed to the direct solar ray bounded by a cone of one steradian, with its axis at ( 6 1 A) direction and its vertex at Eq, and a shell of I m width with its centre at T. becomes in the unit of the incident direct solar ray.
dP* = (16 f: ) 5 k p(T )( I +cos p)p s(T.) ( I ) 1
cos (p =sin e I COSACOS h ‑cos 6 ,sin h ( 2 )
, here p(T.) being the atmospheric mass in I nf at T., (T.) is the sum of two traversed masses when the direct solar ray reaches T. from the upper at‑
mospheric limit and the scattered ray reaches Eq from T. in the unit of whole atmospheric mass penetrated by the vertical cylinder at O ' (Ref. 2 ).
Now put
p(T.)pi (T') = S'( i q 6 1 A r h ) ( 5 )
then
dp =( )5ki(1 +cos2 p)S'( i q OIA r h) (4) ' 167r 1
Let us denote
dHp. =dptsin( 6 1 ‑‑‑･It2 ) ( 5 )
Then we have only to execute multiple : integration to dHpS cos ( 6 t ‑=) *. 11
with respect to r from Eq to O " along 6 t line and 6 * from o I = 7c /2 to 1:: and A from A = O to A = 2 7r to find the horizontal scattering intensity Hv' (iqh) at Eq, i. e.
Hp,(1 q h) fdA fd6 fdr dHp, cos (O,‑‑) .* 7r 2 6)
Eq
The integrant in ( 6 ) is
( ) 5 ki( I +cosa p) S'( i q 6 aA r h)sm( a , ‑2‑̲ )cos( 6 ! l 2̲ )‑ ( 7) 167r
Hence
128. Shizuko UEM[7RA ･ Takao 'SATO
Hps(1qh) 5 ki 7c
= dA d6 ,( I +cos2 ) sin(O , ‑ )cos(6 1 ‑ )1611
f
drS'( i q 6 tA r h) (8)
Eq
To the calculation of ( 8 ) we will depend on the numdrical integration.
Let T1, T and T be three pomts on the line section Eq O " which devide EqO" into fonr equal parts and T0=Eq, T4= O ", and the value of S'(iq e 1 Arh) at T ( n = a ‑ 4 ) be S'( n ) and for brevity
S(iq 6 t Ah)= S'( O )+ 4 S'( I )+ 2 S'( 2 )+ 4 S'( 5 )+S'( 4 ) ( 9 ) Then we calculate as follows by Simpson's formula
f ･ ,‑dr S(1q6 Arh)=j̲ I . E C" S(iq6.Ah) (10)
J q 5 '
Now put
Eq O ".S(iq e , Ah)= z;1"(iq 6 1 Ah) (1 1 )
Substitute (11) and (10) in ( 8 ), we get
=
dAfdO ( I +cos (p) sm(6
Hp.(1qh) 5 ki 7r= cos 6 167r ' ) ( t )'
T ;L"(iq 6 Ah) (12)
1Moreover let us put
( I +cos p)2 "(lq6 Ah) 2 (iq6 *Ak) (15)
In the preceding calculation, Eq O " are expressed in the unit of the earth's radius 6570Km. Hereafter we will use C.G.S unit.
as I nf=10'cm', IKm=105cm, and
(1 1671)5ki. { 1 6570 105 10‑6‑5 16816k
‑. . . . ‑
S , (iq 6 , Ah)=5. 1 681 6ki2 '(iq 6 , Ah) (1 5)
is the amount of primary scattering intensity received at Eq POint from a cone of one steradian with its axis at ( 6 * A) and vertex at Eq We have calculated S1 for all combinations of i , q , 6 1 ,A, h .
Then we have
r f 1̲ )cos(6,L̲ 2) (16)
'*Hp.(iqh) =J dAJ. d6 , ･ S,( i q 6 Ah)sm(O ‑
Strictly speaking, (Tr) is dependent to A because the mass traversed by the direct solar ray is evidently dependent to A although that traversed. by the scattered ray is never dependent. But when the Sun's altitude h >=50' we can recognize (Tr) to be independent to A with negligible error in this research, then I +cos (p rs the only one exlstmg expressron m (i5) that Is dependent to
Radiational Flux due to primary Scattering falling on the
Horizontal Plane in the High Atmosphere. 129
A. Let us define F( i q 6 ,A h) by (17)
F(1 q e Ah) sm(6 )cos(6,‑ )S,(1 q e Ah) (17) 7t
To calculate the horizontal scattering intensity we must in general use the next procedure : we will at first integrate F with respect to 6 , and then in‑
tegrate thus obtained result with respect to A. This procedure demands us very much labour. But we can fortunately utilize the fact that the only exis‑
ting expression ( I +cos2(p) in (1 7) is dependent to A which is clear from the above explanation. This utilization enables us to save some extent of the la‑
bour.
A.s S( i q 6 , A h ) is independent to A in this case we can put S( i q 6 1 h ) instead of S( i q 6 , A h). From (15) we get
lr
S ( I q 6 Ah)sm(O ,‑ )cos(6 ,‑ )=5 16816ki( I +cos p)
7c
EqO" ･ S( i q 6 , h)sin( 6 t ‑‑ ) cos( 6 1 ‑I ) (18) When if we put
EqO".S(i q 61Ah)=S2( i q o h) (19)
(1 7) becomes
lr
S,( i q o A h)sm(O ,‑ r)cos(6 ,‑ )=5 16816k ( I +cos (p)
sm(6 , ‑ )cos(O , ‑ )S2( I q 6 h) (20)
Let us put
5.16816k ( I +cos=co)= f( I q 6 Ah) (21)
Then
Hp.( I q h) = "dAfd6 F( I q 6 Ah) = f dAfdO
7c 7r
f ( i q 6 a A h)S 2( i q 6 , h)sin(6 1 ‑ ) cos (e , ‑ ) (22)
It is clear that
'*
f f(i q 6 Ah)dA= {f(1 q6 o h)+ f(1 q c, h) 7c
+ f ( i q 6 , 7r h)+ f ( i q 6 I 7r h)} (25)
' Denote the blacket of the right hand side by f '( i q 6 , h ) in (25). Then
f t 7r
Hp*( i q h) = d6 ･ f'( i q 6lh)Sa( i q 61 h)sm(O,‑2‑)
l 50 Shizuko UEMURA ･ Takao SATO
Calculate f "( I q e * h) by
7T 7c
f '( i q e , h) sm( 6 , ‑ )cos( 6 ,‑ )=‑ f "( I q 6 h) (25)
Then
f
Hp.( i q h) d6 * f "( i q 6 1 h)S2( i q 6 * h) (26) = 7c
By putting
f"(i q6 h)S (1 qe h) S (1 q6 h) (27) f
Hp.( i q h) = d6 * ･ S3( i q 6, h) (28)
we have calculated S 3( i q 6 , h ) for the above mentioned values of i, q, O , and h. we have replaced the integration of S 3( i q 6 1 h ) with respect to 6 t by numerical integration. Hence the numerical formula of Hp, will be
71 5 71
Hp,( i q h)= ' ' {S3( I q 12C h)+s3( I q 150 h)} (29)
5. The result of computation.
The computations results for each wavelength domain Di are tabulated in Table I , 2 and 5. in ( I 112) ･ I*. 10‑" unit. Sum up these 12 values of each domain and divide by 1 2, then we can get the value for the total wave, Iength in I.. I O‑" unit given in the notation T in Table. In the Table q = O in the column of q means the earth's surface, q = I and q means the level of I Knl height and ( q + I )/ 2 Kin , so that the value for the level of 500m height is not calculated.
The attached mark * indicates the change of common unit. Let us denote Q as the value of q at which the value changes a unit. It should be noticed that the value of n in the array of the upper side is applied to the range from q= O to Q ‑1. However, n in the array of the lower side is applied to that from Q to 75.
The values tor A i' given in Table 4 , 5 and 6 are not introduced in the
pa per.
4. Some results. We can derive the folowing laws from the Tables as far as the primary scattering is concerned.
1 : The intensity decreases with increasing q for each h and each D,1' 2 : The intensity increases with increasing h for each q tand each Dt.
5 : The value of the wavelength in which the intensity becomes max.
decre ses with irlcre sing q for each h.
Radiational Flux due to primary Scattering falling on the
Horizontal Plane in the High Atmosphere. 151
4 : The value in the same meaning as 5. decreases with increasing h for each q.
The ratios of the values in Table I ,2 and 3 to the corresponding values in Ref. 5 ( i , e , Table I in Ref. 5 ) are tabulated in Table 7 . 8 . 9 .
We can find the next laws existing from this research :
1 : The value decreases with increasing wavelength for each h and q.
2 : It decreases with increasing q for each h and wavelength.
5 : It increases with increasing h for each q and wavelength.
(End) References
l ) Sato. T. 1955 : On the scattering of the sun's ray in the high atmosphere ( I ) ‑ Jour. met. Soc. Tapan, 63, 194‑204
2 ) Sato. T., 1964 : On the scattering of the sun's ray in the high atmosphere ( I ) . lbid 42, 165‑172
5 ) Sato. T, 1966. A numerical ̲P*esearch on the Primary Scattering of the Sun's Ray in the High Atmosphere ( I̲ ) .
Science Bnlletin of Fac, of Liberal Arts and Education, Nagasaki University, no, 18. 1967.
152 Sh玉zuko UEMuRA・Takao SATo
Table 1 h冨500
＼D乞
＼
＼n q＼
0 1 52
4 5 6 87
9
10 11
ユ2
］5
14 15 16 17 18 19 20
2］
22 25 24 25 26 27 28 29 50 51 52 55 54 55
ろ6
57 58 59 40 41 42 45 44 45 46 47 48 49 50 51 52 55 54 55 56
5ワ
58 59 60
工 2 5 4 5 6 7 8 9 10 ユ1 ユ2 T
（一5）（一5）（一5）（一5）（一5）（一5）（一5）ぐ一5）（一5）（一5）（一5）（一6）（一5）
80ワ9 ワ9547796 7649 7497 7514 7115 6915 6685 6455 6227 5998 5ワ725541 5509 5067 4845 4608 4569 4159 5917 5695 5468 5255 5051 2856 2662 2485 2516 2159 2014 1875 1741 1622 1506 1595 1296
］198 1111
】029954 882 8］6
755 691 640 590 545 501 46G 424 588 558 528 299 274 251 228 208
］88
171 60ワ85622 5579 5145 4918 4687 4462 4245 4024 581ワ 56］5 5452 5248 5G64 2895 2721 25ワ52419 2265 2122 1986 1856 1755 1612 1498 1587 1291 1196 1111 1027 952 888 822 ワ61 ワ05 65］
605 557 515 476 459 406 574 545 517 295 27G 247 228 2G9 192 176 161 148
ユ55
124
］ユ5 ユ02
9565＊
8545 ワ697
4447 4G59 5856 5640 5452 5267 5086 2915 2755 2597 2449 2505 2168 2045 1917
］ワ98
1687
］5801480 1580 1292 1205
］n6
］054962 891 805 765
ワ09 656 605 565 521 482 446 411 580 551 524 299 2ワ6
255 255 217 198 184 169 155 145
］51 120
UOlO1 9290＊
84ワ97724 7052 6595 5848 5545 4812
5157 2858 2680 2552 2593 2252 212］1996
］874
］765 ユ657 1557 1461
］5ワ5
1284 1205 1126 ユ052980
9］6
851
ワ91
755 682 652 584 556 500 462 428 597 567 559 514 29G 268 248 228 211
ユ94
］179
165 155 140
コ29
］］9
UO
］0］
9255＊
8490 7772 712ワ6529 6005 5481 4995 4570 4156 5778 5456
5］1工
2192 1956 1844 1757 1654 1555 1442 1554 12ワ11195 1118 1047 981 9］9 859 805
ワ50
701 654 609 567 524 488
45」
418 586 557 550 505 282 260 242 225 206 191 176 165 150
］58
］28
118 108 100
922］＊
8458 78コ2
ワ］86
6591 6074 5557 5088 4696 4274 5811 5588 5270 2992 2721 2475 2262 2057
1497 1529 1251
U75
1ユ051056 970 910 855 799 748 700 656 615 572 554 500 466 454 405 575 547 522 299 276 255 256 218 202 187 172
1058 920 864
8三フ ワ60
715 668 626 585 548 515 480 448 419 592 565 541 517 296
2ワ5
255
25ワ
218 205
］88
174 161 148 157 127
1］7
159 108
］47 9997＊
156 9224 126 8528
］16 7860 107 7261
9868＊6697
91076182 85985694
ワワ50 5249
ワ1444845
6568 4462
60544107 555］5775
5129 5482 4718 5205 4528 2945
59882701
5649 2478 5561 2276 5084 2806 2582 255ワ2158 1964 1ワ86
］6241476
］558 2088 1901 1748 1596 1461 1550 1210
UOO1000 906
606 555 502
4ワ1 441 415 586 561 558 516 295
2ワ6
258 241 225 210 196 182 170 158 146 156
⊃25 116 107 99 91 84
ワ8 ワ2
66 61 57 55 49 45 42 58 55 55
ろ0
28 26 24 22 20
］8
17 15 14 15
】2
11 998＊911 854 759 691 628 571 517
552 511 291 275 256 259 224 209 196
］85 171 160 149
1ろ9
150 121 115 1G5 98 90 84 78
ワ2
67 62
5ワ
55 48 45 41 58 55 52 50 28 25 24 22 20 18
］ワ
15 14 15 12
コ1
10 966＊886 815 747 685 625 574 524 479 456 597 56工 528 297
198 1ワ4 165
］55 145 154 125 117 109 102 95 89 85
ワ8
72 67 65 58 54 50 47 45 40 57 54 52 29 27 25 25 21 19 18 17 15 14 15 12 11 10
964＊
888
8］8
752 691 658 586 559 494 454
4賀
582 548 520 292 267 245 221 201 185 166
66 59 55 51 48 45 42 59
5ワ
54 52 50 28 26 24 22 21 19 18 17 15 14 15 12
］1
10
9 9 8 7 7
6620＊
572 528 487 450 414 582 552 525 299 276 255 255 215 198 182 ユ67 ユ55 140 129 117 108 98 go 82 74 67 61 55
8ユ ワ1
67 65 59 55 51 48 45 42 59 56 54 51 29 27 25 24 22 20 19
ユ7
16 15 14
〕5
12 11 10
9 8
2515 2145 2061 19ワ51892 18G8 1725 1644 1564 1487 1589 1545 1274 1207 1142 10ワ81010
961 905 848
ワ95
748 696 650 605 562 52G 485 451 418 588 8 561 75＊ 554 69 510 64 28ワ 59 266 54 246 50 22ワ 46 21G 42 194 59 180 56 55 50 28 26 24 22 20 18 17 15 14 15 11 10
9 9 8 ワ 6
166 155 142 150
】20
】11
102 9561＊
8586 7895 7144 6642 6087 5562 5091 4652 4222 5854 5505 5］70
Radiational F1ロx due to primary Scattering falling on Horizontal Plane in the High Atmosphere．
the
155
D乞
＼ q＼
61 62 65 64 65 66 67 68 69
ワ0
71
ワ2・
ワ5
74
ワ5
q／
／n
1 2 5 4 5 6 ワ 8 9 10 11 ］2 T
154 140 125
n29975＊
8876 7846 6882 5970 51ワ8 4412 5699 5045 245ワ
18ワ5 6955 6285 562ワ5046 4488 5996 5528 5095 2686 2525 1981 1659 1566 ユ094840
4545 5927 5516 5155 28052495 2202
」952
16ワワ
1451 1256 1056 855 685 525
2810 2557 2272 2058
】835 16】21425
】2481085 958 799 6ワ0 55］
441 559
］841 1661 148ワ1558
ユ18ワ
1055 951 817 ワ09
614 525 458 561 289 222
1209 1091
9ワ6
876 ワワ9 695 612 557 466 405 545 288257
」90
146 819 759 661 595 528 469 414 565 515 2ワ5 255 195
】60
128 99
46ワ
421 5ワ7 558 501 268 256 207 180 155 152 111 91
ワ5
56 268 242
21ワ 194 1ワ5 154 156
］19
105 89 76 64 52 42 52
150 155 121 108 96 85 75 66 57 50 42 55 29 25 18
50 45 40 56 52 28 25 22 19 16 14 12
9 7 6
65 44 55 52 22 11 10 0
2860 2591 2517 2077
】8481645 1455 12ワ41105
958 816 684 565 451 546
（一7）（一ワ）（一7）（一7）（一7）（一7）（一7）（一7）（一7）（一ワ・）（一7）（一ワ）（一ワ）
Table 2． h＝600
＼D6 ＼
＼n q＼
0 工 52
4 5 6 ワ 8 9
10 11 12 15 14 15 16
1ワ
18 19 20 21 22 25 24 25 26
2ワ
28 29 50
1 2 5 4 5 6 ワ 8 9 ユ0 旦 ユ2 T
（一4）（一5）（一5）（一5）（一5）（一5）（一5）（一5）（一5）（一5）（一5）（一5）（一5）
1094 1042 1012 980 946 915 879 846 810 776 ワ42 ワ10 6ワワ 646 614 581 555 525 495 467 459 411 584 560 556 515 291
2ワ1
252 254 218
ワ1ワワ
6549 6240 5955 5628 5542 5060 4ワ924524 4280 4045 581ワ5595 5588 5190 299ワ2815 2642 2475 25］02158 2008 1868 1ワ42 16コ51495 1586 1285 1187 1105 1025
5058 4556 4296 4065 5854 5621 5411 5215 5025 2846 2680 251ワ2566 2220 2082
］9491829
1ワ0ワ
1598 148ワ1586
1291 1198 11 1050
950 881 818 ワ56 ワ00
645 5488 51］92942 2ワ722609 2448 2506 216ワ2054
1910
］ワ98
1685 1575 1475 158」
1292 1208 112ワ1051
981 910 846 ワ85 ワ28 6ワ5
624 576 552 495 456 420
2585 2122 1997 1879 1ワ651657 1554 1458 1566 ユ2811200
］コ25
1050 984
9］9
858 802 ワ48 697 648 605 560
5］9 48ユ
445 411 580 551 524 299 277
1612 1429
］5451262 1185 1］101059
9ワ5 911 854
ワ99 ワ4ワ 699 654 610 569
55］
495
46］
428 599
5ワ］
542 51ワ
295 271 251 251 215 198 182
］112 985 925 866 811
ワ61
712 666 625 585 546 510
4ワ7
446 416 588 562
5ろ7
514 292
2ワ1
251 255 2］6 199 184 170 15ワ
］45
154 125
644 569 554 500 469 459 410 584 559 556 514 295
2ワ4
256 259 225 207 195 180 167 155 144 155 125
】］4
105 97 89 85 76 70
5ワ5 529 509 290 2ワ1
255 257 222 207
ヲ94
】81
169 158 147
15ワ
128
1ユ9 1］1
105 96 89 82 76 71 65 60 56 51
4ワ
44 40
20、g 185
1ワ5
162 152 142 155 124
］16
108 101一
94 88 82
ワ7 ワ1 6ワ
62 58 55 50 46 45 59 56 55 51 28 26 24 22
ワ0
62 58 54 51 48 44 42 59 56 54 51 29 27 26 24 22 21 19 18 16 15 14 15 12
］1
10
9 8 8 ワ
87
ワ6 65 55 44 4 55 55 22 22 22
2822 2526 2412 2500
2］8ワ
2080
］975
】、876
1ワ76 1682 1595 1507 1424 1546 1520 1192
ユ］25
105ワ992 929 869 1 811 1 755
］ 695 1 654 1 606
】 562 1 522 1 484 1 449 92＊416
154 Shizuko UEMσRA。Takao SATO
D
＼ q＼
5］
52 55 54 55 56 57 58 59 40 41 42 45 44 45 46
4ワ
48 49 50 51 52 55 54 55 56
5ワ
58 59 60 61 62 65 64 65 66
6ワ
68 69
ワ0
ワ1 ワ2 ワ5 ワ4 ワ5
q／
／n
1 2 5 4 5 6 ワ 8 9 10 11 12 T
205 187 1ワ4 162 149 159 129 119 110 101
9414＊
8685 8050 7400 6812 6297 5ワ925519 48ワ24495 4117 5782 5467 5165 2895 2665 2409 2196
］9901802 1654 1475 1521
11．84
1054 958 828
ワ26 651 546 465 589 522 256 197
949 878 811 752 694 642 595 54ワ
505 467 450 59ワ
565 557 510 286 265 241 222 204 186 171 157 145
15】
119 108
9866＊
8990 8109 ワ5626641 5947 5552 4744 421ワ5722 5265 2858 2450 2086 1748
】4461150 887
599 554 511 4ワ5 45ワ
404 575 544 518 275 270 249 229 211 194 179 165 151 159
12ワ
117
10ワ 981ワ＊
8962 8164 7470 6799 6】8G5616 5091 4599 4145 5715 5528 2965 2656 2527
204］，
17ワ21529
1502 1091 901 718 555
590 560 555 508 284 262 242 225 206
】90
1ワ5
】61
149 157 126
1］，6
〕06 g804＊
8971 8256 ワ5506899 6546 5795 52ワ84850 4595 5995 5629 5290 2971 2681 240］2155
19］6
］ワ05
1504
］5191145 988 842 705 582 464 558
256 257 219 202
］86
172 159 146 155 125 115 106
9744＊
8985 8255 7592 6982 6418 5872 5410 4944 4516 4154 580］
5472 5162 28ワ62614 2575 2155 1945 1755 1572 1410 1254
n15984 865 749 647 551 461 581 504 254
169 1］5 156 ユ06
］44 97 155 90
］25 85 1届 76
］，04 70
9654＊65 8886 60 8189 55 7550 6955 6598 5898 542G 4985 4595 4214 5856 5552 5259 2965 2729 2491 2280 2176 1888 1716 1560 1414 12ワ7 1152 1052 925 825 ワ52 646 567 492 425 562 505 250 199 154
5127＊
4ワ224555 4001 5671 5585 5112 2854 2618 2406 220ワ2008
］848 168ワ1544
］406
ユ2ワ9
1162 1056 958 865 780 698 627 558 496 458 584 552 288 245 205 169
］55
104 65 60 55 51 47 45 40
5ワ
54
5】
29 27 25 25 21 19
］8
16 15 14 15 12 11
882965＊
805 ワ50 664 605 547 494 445 599 558 518 285 250 2］9
］go
164 159
］］7 96 77 59
57 54 52 29 27 25 25 21 19 18
］7
16 14 15
］2
】1
10 956＊859 789
ワ24 659 606 555 506 461 419 581 546 514 284 256 229 205 185 162 145 126 1G9 94 80 67 55 44 54
2］
19 17 16 15 14 15 12 11
ユ0
959＊865
ワ96
752
6ワ5
619
5ワ0
522 479 440 404
56ワ
558 509 282 257 254 212 195 175 158
］42
］28
114 102 90 80 70 61 52 44 57 51 24 19
76 65 54 44 55
516＊291 268 247
22ワ
209 192 176 162 148 156
】24
］ユ4 104
95 86
ワ8
71 65 59 55 48 45 58 54 50 26 25 20 17 15 12 10
8 6
86 79
ワ5 6ワ
62 57 55 49 45 41 58 55 52 29
2ワ
25 25 21
コ9
】ワ
】6
15 15 12 11 10
9
8ワ ワ
65 54 45 52 22 11 11 0
587 557 551 507 285 262 245 224 207 190 176 165 150 158
12ワ 1，ワ
108 9914＊
909ワ8568 7665 7027 6450 5884 5579 4955 446ワ4069 5695 5545 5050 2ワ542448 2195
］9541758 1554 1545 1168 1010 860 1720
595
4ワ4
565
（一6）（一7）（一7）（・7）（一ワ）（一7）（一7）（一ワ）（一7）（一ワ）（一7）（一7）（一ワ）
