University of Nebraska - Lincoln
DigitalCommons@University of Nebraska - Lincoln
DOD Military Intelligence
US Department of Defense
4-1-1944
Photographic Interpretation Handbook, United
States Forces: Section 04 Tables
Robert L. Bolin Depositor
University of Nebraska-Lincoln, [email protected]
Follow this and additional works at: http://digitalcommons.unl.edu/dodmilintel
Bolin, Robert L. Depositor, "Photographic Interpretation Handbook, United States Forces: Section 04 Tables" (1944). DOD Military
Intelligence. Paper 7.
http://digitalcommons.unl.edu/dodmilintel/7
This Article is brought to you for free and open access by the US Department of Defense at DigitalCommons@University of Nebraska - Lincoln. It has
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SECTION
TABLES
4.01 -
4.99
3
RESTRICTED
TABLES
UNITS OF MEASURE
UNITS OF LENGTH. ENGLISH
Statute
Mile
1
& METRIC
Cen timeters
Inches
Kilometers
Meters
Yards
Feet
1·6093
1
1609.3
1000
1
1760
1093·6
1·0936
1
5280
3280·8
3.281
3
1
fi33f)O
39370
39·37
36
12
1
160934
100000
100
91.44
30.48
2·54
I~
1 link
1 rod
1 cha in
1 furlong
1 mile
1 lea gue
7.92 inches
25 links
16th feet
100 links
4 rods
10 chains
40 rods
8 furlongs
3 miles
1 fathom = 6 feet
1 nautical mile = approx.
1
Centimeter
Decimeter
Meter
Decameter
Hectometer
Kilometer
Myriameter
1.15 statue miles
UNITS OF LENGTH. ENGLISH & RUSSIAN
Sta tu te
Mile
1
1
1
1
1
1
1
10
10
10
10
10
10
10
Millimeters
Centimeters
Decimeters
Meters
Decameters
Hectometers
Kilometers
'\1
l' of arc at the equator
METRIC
Verst
Kilometer
Sajenyam
Meters
Yards
Feet
Futam
Inches
Dyn'LIimam
Centimeters
1.-5086
1
1. 6093
754.29
500
468·7
1
1,609.3
1,066.8
1,000
2.1336
1,760
1,156.67
1,093·6
2·333
5,280
3,500
3,280.8
7
63,360
42,000
39,370
84
160,934
106,680
100,000
213.36
1.0668
1
\
I
1:1
OTHER
RUSSIAN MEASURES
1 marine
1 arshin
1 stopa
sajen
1 fathom
28 inches
14 inches
1 vershok
1 paletz
The Russian foot and inch are the exact equivalents of
1.75 inches
5 inches
the English units.
INTERNATIONAL MILE MEASUREMENTS
The
The
The
The
The
The
The
RESTRICTED
En gl i sh statute mi Ie
Italian mile
Spanish mile
Austrian mile
'geographical or nautical mile
Ru s sian verst
kilometer
1,760
1,467
5,028
8,296
2,026
1, 168
1,093
yards
yards
yards
yards
2/3 yards
yards
yards
4.01
RESTRICTED
TABLES
L
RESTRICTED
DEGREES & GRADES
UNITS OF MEASURE (CONT"
[
GRADES AND DEGREES
UNITS OF AREA
1
1
1
1
1
sq. inch
sq. foot
sq. yard
acre
sq. mile
1 Centare
1 Are
1 Hectare
6.452 sq. centimete~s
.093 sq. meters
144 sq. inches
9 sq. feet
.836 sq. meters
4,840 sq. yards
4,.047 sq. meters
640 acres
259 Hectares
1 sq. meter
100 sq. meters
10,000 sq. meters
On American and British maps, and those of several other countries,
the geographic coordinates used are based on the 360 degree circle.
On
many French and certain other continental maps, however, the coordinate
system userl is based on a 400 grade circle.
The units are subdivided
as follow s :
[.
[.
1,550 sq. inches
11 9 • 6- sq. ya r d s
2.471 acres
Degrees
'r-
degr.:>e
minu te
UN ITS OF VOLUME
16.39 cubic centimeters
1728 cubic inches
27 cubic feet
1 pint liquid
4 g~lls
1 quart liquid
2 pints
1 gallon
4 quarts = 231 cu.
1 bnrrel
31.5 gallons
1 hogshead
2 barrels
1 Imperial gallon (Great Britain)
liter
I
1000 cu. centimeters
.908 quarts (dry)
hectoliter' = 100 liters
26.417 gallons
kiloleter
1000 liters
2 6 4. :1 7 gal Ion s
.0164 liters
28.339 liters
765.16 liters
=
277.274 cu.
61. 02 cu. inches
1.0567 quarts (liquid)
.1 CU, meter
Complete circle
1 grade
1 minute
400 grades
100 minutes
100 seconds
An anglp or coordinate in degrees is written as follows: 25 0 10'
An ang12 or coordinate in grades is written as follows: 65 G 45'
may b", 2xpr,~ssed rlecimally 65.4570 G.
30 n
7 011,
In changing grades to degrees, first the number of grades is
x pre sse d d p c i mal 1 y a sap:] r t 0 f a r i g h tan g 1 e, i. e. 6 5 G· 45' 7 0 fI
0
0
1 S
• 6 5 4 57 0 f a r i g h t
an g 1 p 0 r 0 f 90 •
Then. I) 54 5 7 X 90 = 58. 9 11 3 ,
which is the equivalent number of degreps expressed rlecimally.
The
fractional portion of the numbpf of degrees, .9113, is changed to
minutes by multiplying by 60, giving 54.678'.
Again, the fractional
portion of thp number of minutes, .678, is changed to seconds by
multiplying by 60 • • 678 X 60 = 40.68 11 , which may be simplifiP8 to
4 1" •
Th e an g I e may now bee x pre sse din d e g r e e s a s 58 0 54' 4 1 " ,
e
L
CONVERSION OF DEGREES TO GRADES
L
28.3495 grams
16 ounces
2000 pounds
2240 pounds
360 degrees
60 minutes
60 seconds
Grades (Centesimal)
CONVERSION OF GRADES TO DEGREES
I cu. meter
1.308 cu. yards
453.59 grams
• 9072 metric tons
1.016 metric tons
gram
.03527 Ounces (av.) = weight of 1 cu. centimeter of water
1 kilogram
1000 grams = 2.~046 pounds = 1 liter of water
metric ton (rr.illier)
1000 kilograms = 2204.6 pounds
weight of 1 cu. meter of water
4.02
Or
inches
U NITS OF WEIGHT
ounce (av.)
1 pound
short ton
1 long ton
[
4732 liters
9463 liters
3.785 liters
4. 21 cu. fee t
inch.
(Sexagesimal)
Complete circle
:r-
1 cubic inch
1 cubic foot
1 cubic yard
TABLES
RESTRICTED
In changing degrees to gradps, first the number of seconds 1S
converted to decimal parts of a minute by dividing by 60, i.e.
25 0 10' 30 11 becorr.es 25 0 10.5'.
Minutes are n?xt changed to deCImal
0
parts of degrpPs by dividing by 60.
10.560 = .175, then 25
10.5'
0
becomes 25.175 •
The number of degrees must now be divi~ed by 90 to
change to a decimal part of a right angle.
25.175/90 = .279722 .
Since there are 100 grades in a right angle, the angle may be written
as 27 G 97' 22".
RESTRICTED
4.03
RESTRICTED
TABLES
RESTRICTED
TABLES
DEGREES & GRADES ICONT.)
DEGREES & GRADES (cONTJ
CONVERSION
CONVERSION TABLE
DEGREES TO GRADES
TABLE
GRADES TO DEGREES
Whole Numbers
-0
;
l-
eg- I e'!ilJJ s
'!il S
Q.~
.£;:;:1
!
=~rn
S
~
1
2
3
Q.§
£::s
0
'CI
=rn
/If
~gs~
e
i~
~
"
0
,
I
I ....0
"C
.::
o
";i
._ al
<:.l_
<1) a:J
~~
ogf
te g
.§o
.a~
=rn
<:.l
<1)
0
IZI
-
I
- It
te
G;I
-0
<l>
cd
111
~a
'0 'j
if
..'!J~
cd Q;)
.§o
~
Q;)
.~rn
.~~
~
Q
Q
- - - - - -- n
,.
H
e
C!:i
,
- -- - 1 l·L.
2
2·2 ...
Q)
Q
Sexagesimal
to
Seconds
CenteRimal
Minutes
>Ll
Q;>
Sexagesimal
to Minutes
Centesimal
'0
~
'01
'02
·03
'04
'05
'031
'()62
'093
'123
'154
·61
'62
'63
'64
'65
1'88 3
1'91 4
1·945
1·97 5
2'00 6
6
ll·ll
III
7
8
9
10
12·96
14'81
16'66
18·51
296
481
667
852
18'519
21·60.')
24'691
27' 778
30'864
'06
·07
'08
'09
·10
'185
·216
·247
·278
·309
'66
'67
'68
·69
'70
2'03 7
2'06 8
2'09 9
2·13 o
2·16o
71
72
73
74
75
78'8 ...
80'l)
81' 1. ..
82·2 ...
83·3 ...
11
12
]3
14
15
20·37
22·22
24'07
25·92
27·77
037
222
407
593
778
33'951
37'037
40'123
"13' 210
46·296
'11
'12
'13
Hi
12'2 ...
13'3 ...
14'4 ...
15'5 ...
]6'6 ...
'15
·340
·370
·401
'432
'463
·71
·72
·73
·74
·75
2·19 I
2·22 2
2·25 3
2·28 4
2·31 5
16
17
18
19
20
17'7 ...
18'8 ...
20'0
21'1. ..
22·2 ...
76
77
78
79
80
84'4 ...
85'5 ...
86'6 ...
87'7 ...
88'8 ...
16
17
18
19
20
29·62
31·48
33·33
35·18
37·03
963
148
333
519
704
49·383
52·469
55·556
58·642
61·728
·16
·17
·18
·19
·20
'494
'525
'556
·586
·617
'76
·77
·78
·79
·80
2·a4 6
2·37 6
2'40 7
2·43 8
2·46 9
21
22
23
24
25
23'3 ...
24'4...
25'5 ...
26·6 ...
27'7 ...
81
82
83
84
85
90'0
91'1. ..
92·2 ...
93·3 ...
94·4-...
21
22
23
38·88
40·74
42·.'59
24-
44·44-
46·29
64·815
67·901
70·988
74·074
77·161
·21
·22
·23
·24
·25
'648
·679
·710
'741
·772
·81
25
889
074
259
444
630
·82
'83
·84
·85
2'50o
2·53 1
2'56 2
2'59 3
2·62 4
26
27
28
29
30
28'8 ...
30'0
31·1. ..
32·2 ...
33·3 ...
86
87
88
89
90
95'5 ...
96·6 ...
97·7 ...
98'8 ...
100·0
26
27
28
29
30
48·14
50·00
51·85
53·70
;35·55
815
80·247
000
83" 333
86·420
89'506
92'593
·26
·27
·28
·29
·30
·802
·833
·864
·895
·926
·86
·87
·88
·89
·90
2·65 5
2·68 5
2·71 6
2·74 7
2·77 8
31
32
33
34
35
34'4 ...
35'5 ...
36·6
37·7 .. :
38·8 ...
91
92
93
94
95
101'1. ..
102·2 ...
103·3 ...
104·4 ...
105·5 ...
31
32
33
34
35
57·40
59·25
61·11
62·96
64·81
741
926
95·679
98·765
lU 101·852
296 104·938
481 108·025
·31
·32
·33
·34
·35
·957
·988
1'019
1'049
1·080
·91
·92
·93
·94
·95
2'809
2·8 40
2·87 o
2·9 01
2·9 32
96 106'6 ...
36 40'0
37 41'1... 97 107'7 ...
38 42·2 ... 98 108'8 ...
39 43·3 ... 99 110'0
40 44'4 ... 100 Ill· I. ..
36
37
38
39
40
66·66
68·51
70·37
72·22
74·07
667
852
037
222
407
114·198
117·284
120·370
123·457
·36
·37
·38
·39
·40
1·111
1·142
1·173
1·204
1·234
·96
·97
·98
·99
2·9 63
2·9 94
3·0 25
3·0 55
45'5 ...
46·6 ...
47·7 ...
48·8 ...
45 50·0
41
42
43
44
45
75·92
77·77
79·62
81·48
83·33
593
778
963
148
333
126·543
129·630
132·716
135·802
138·889
·41
'42
·43
·44
·45
1·265
296
1'
1·327
1'358
1·389
51·1...
52'2 ...
53·3 ...
54'4 ...
55·5 ....
46
47
48
49
50
85 ·18
87'03
88'88
90'74
92'59
519
704
889
074
259
141·975
145·062
148·148
151·234
154'321
·46
51
52
53
54
55
94'44
96·29
98·14
100·00
444 157'407
160'494
163'580
166'667
169'753
'51
·52
·53
·54
·55
1'574
1·605
1·636
1·667
1·698
56
57
58
59
60
103· 70
105' Sf;
107·40
109·25
111·11
172'839
175·926
179'012
182·099
III 185·185
·56
'57
·58
·59
·60
1·728
1·759
1·790
1·821
1'852j
8
9
II
'51 0'165
'52 ·168
'53 '172
'54 '175
-55 -178
6
7
8
9
10
524
6 18
7 12
806
900
3 14·4
346·8
4 19·2
451'6
524·0
1'944
2-268
2'592
2'916
3'240
56
57
58
59
60
5024
51 18
52 12
5306
5400
30 14'4
3046'8
31 19·2
31 51· 6
32 24'0
18·144
18'468
18·792
19·116
19·440
'06
'07
'08
'09
·10
'019
'023
'026
'0291
' 032 1
'56 'ISI
'57 ' '185
·58 '188
'59 '191
'60 '194
II
12
13
14
15
954
1048
11 42
12 36
1330
556·4
628·8
701·2
7 33·6
806·0
3'564
3'888
4·212
4'536
4'860
61
62
63
64
65
5454
5548
5642
57 36
5830
32 56'4
33 28·8
3401·2
3433·6
3506'0
19·764
20·088
20·412
20·736
21·060
·11
·12
'13
·14
·15
'036[
'039
'0421
·045
'049
·61
'62
·63
·64
·65
·198
·201
'204
·207
'211
16
17
18
19
20
1424 838·415 18 9 10·8
16 12 943·2
1706 10 15·6
1800 10 48·0
5·1845·508
5·832
6·156
6'480
66
67
68
69
70
5924
60 18
61 12
6206
6300
35 38·4
36 10· 8
3643·2
37 15·6
3748'0
21·384
21·708
22·032
22·356
22·680
·16
·17
·18
·19
·20
·052
·055
·058
'062
·065
'66
·67
'68
·69
·70
·214
·217
·220
'224
·227
21
22
23
24
25
1854
1948
2042
21 36
2230
II 20·4
II 52·8
71
72
73
74
75
6354
6448
6542
6636
6730
3820'4
38 52· 8
3925'2
39 57'6
40 30'0
23·004
23·328
23·652
23·976
24·300
·21
'22
'23
·24
·25
'068
'071
'075
'078
'081
'71
12 25' 2
12 57·6
13 30·0
6'804
7·128
7'452
7'776
8'100
'230
'233
'237
'240
'243
26
27
28
29
30
2324
24 18
25 12
2606
2700
1402·4
14 34·8
15 07·2
15 39·6
16 12·0
8·424 76
8'748 77
9'072 78
9·396 79
9'720 80
6824
69 18
70 ]2
71 06
7200
41
41
42
42
43
02'4
34· 8
07·2
39· 6
12·0
24·624
24·948
25·272
25·596
25·920
·26
·27
·28
·29
·30
'084
'087
'0911
'094
·097
'78
'79
'80
·246
·249
'253
·256
'259
31
32
33
34
35
27 54
2848
2942
3036
31 30
16
17
17
18
18
44· 4
16·8
49· 2
21· 6
54· 0
10'044
10·368
10·692
11·016
11·340
81
82
.83
84
85
7254
7348
7442
7536
7630
4344·4
44 16'8
4449·2
45 21· 6
45 54·0
26·244
26·568
26·892
27·216
27·540
·31
'32
·33
·34
·35
·100
·104'
·107
·110
·1I3
'81
·82
·83
84
'
·85
·262
·266
·269
·272
·275
36
37
38
39
40
3224
33 18
34 12
3506
3600
1926·4
19 58·8
20 31· 2
2103·6
21 36·0
11·664
11'988
12·312
12'636
12'960
86
87
88
89
90
77 24
78 18
79 12
8006
8100
4626·4
46 58'8
47 31· 2
4803'6
48 36'0
27·864
28·188
28·512
28·836
29·160
·36
·37
'38
'39
'40
'117j
' 1201
'123
'126
'130
·86
·87
'88
'89
'90
·279
·282
'285
'288
'292
46
47
48
49
41
42
43
44
45
3654
37 48
3842
3936
4030
2208-4
2240'8
23 13·2
2345·6
24 18·0
13'284
13'608
13'932
14'256
14'580
91
92
93
94
95
81 54
8248
8342
8436
8530
49 08' 4
4940'8
50 13·2
5045·6
51 18·0
29'484
29-808
30·132
30·456
30·780
'41
'42
'43
·44
'45
'133
'136
'139
'143
'146
'91
·92
·93
·94
·95
'295
'298
'301
·305
·308
51
52
53
55
56·6 ...
57·7 ...
58·8
60·0
61·1. ..
46
47
48
49
50
41 24
42 18
43 12
4406
4500
12450'4
2522· 8
25 55·2
2627·6
2700'0
14-9(14
15-228
15'552
15·876
16-200
96
97
98
99
100
8624
87 18
88 12
8906
9000
51 50'4
52 22· 8
52 55·2
53 27· 6
5400·0
31·104
31·428
31·752
32·076
32·400
'46
·47
'48
'49
'50
·149 ·96
·152 ·97
·156 ·98
·159 ·99
·162 1·00
·311
·314
·318
·321
·324
56
67
58
59
60
62·2 ...
63·3 ...
64·4 ...
65'5 ...
66·6 ...
RESTRICTED
3'086
6·173
9'259
12'346
15·432
73'3 ...
74'4 ...
75'5 ...
76'6 ...
77 '7 ...
·01 0'003
'02 '006
·03 ·010
'04 ·013
'05 '016
1
]85
370
556
74]
926
66
67
68
69
70
16·524
16·848
17·172
17·496
17·820
1
1·85
3·70
6'6 ...
7'7 ...
8'8 ...
10·0
11'1. ..
7
27 32'4
28 04· 8
28 37·2
2909· 6
2942'0
'77
1
2
3
6
4554
4648
4742
4836
4930
'76
--~-I-- - - - - 1
67'7 ...
68'8 ...
70'0
71'1. ..
72·2 ...
5'5 ...
51
52
53
54
55
'72
'73
'74
'75
Decimals of a
Second Sexagesimal
to Decimals of a
Second Centesimal
3'3 ...
4'4 ...
0·324
0·648
0·972
1·296
1'620
1
""
bD
3
4
5
032·4
1 04·8
1 37·2
209·6
242·0
1
IlQ
Q)
Q)
61
62
63
64
65
054
1 48
242
336
430
,
4.04
<1)
0_
~.§
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11
12
13
14
41
42
43
44
4
5
5'55
7·40
9·25
185
370
556
I Ill·1ll
'U
I
1
1
50
54
RESTRICTED
101' 85
630
815
000
185
370
556
741
926
l'4201j
'47 I· 451 '
'48 1·481
'49 1·512
·50 1'543
1
4.05
RESTRICTED
TABLES
RESTRICTED
TABLES
CONVERSION OF TIME TO LONGTITUDE
REFERENCE MERIDIANS
Although the equator is generally used as zero latitude, not
all countries use the meridian at Greenwich, England, as a reference
for longitudinal coordinates.
Some have used the Ferro Islands and
several the capital of their respective country, or that of :rance
as the location of the zero meridian.
In utilizing maps h~vln~
.
. .
transferring Information
different reference meridians,
as f or examp le· n
I
.
from one to another, it is necessary to know the angular separat~on
of their reference meridians, preferably in degrees.
The following
table shows the reference meridians whic h h ave b een use d by various
.
coun t rles
an d
COUNTRY
the longitude of the meridian from Greenwich, England:
REFERENCE
MERIDIAN
LONGITUDE FROM
GREENWICH
Old Austro-Hungarian
staff maps, extending
over much of the
Balkans.
Austria
Ferro Islands
Belgium
Denmark
Brussels
Copenhagen
France
Germany
Paris
Greenwich
Ferro Islands
Italy
Netherlands
Norway
Rome
Amsterdam
Oslo
Ferro Islands
17 0 40' w.
12 0 28' E.
4 0 53' 02" E.
10 0 43' 20" E.
17 0 40' W.
Portugal
Roumania
Spain
Sweden
Switzerland
Lisbon
Paris
Madrid
Stockholm
Paris
9 0 11' w.
2 0 20' 14" E.
3 0 41' 15" W.
18 0 03' 29" E.
2 0 20' 14" E.
4.06
REMARKS
4 0 22' E.
12 0 34' 40" E.
20
20'
13.950" E.
Greenwich for Ferro
Islands and Iceland
2 G 59' 69"
For all general maps
For Amt. (1/200,000
Countries Map).
RESTRICTED
CONVERSION
h.m.
0
0:00 0
0:04 1
0:08 2
0:12 :3
0:16 4
0:20 5
0:24 6
0:28 7
0:32 8
0:36 9
0:40 10
0:44 11
0:48 12
0:52 13
0:56 14
1:00 15
1:04 16
1:08 17
1:12 18
1:16 19
1:20 20
1:24 21
1:28 22
1 :32 23
1:36 241:40 25
1:44 26
1:48 Z7
1:52 28
1:56 29
2:00 30
2 :04 31
2:08 32
2:12 33
2 :16 34
2 :20 35
2:24 36
2:28 37
2 :32 38
2 :36 39
2:40 40
2:44 41
2:48 42
2 =52 43
2:56 44
3 :00 45
h.m.
0
3:00
3:04
3:08
3 :12
3:16
3:20
3:24
3:28
3 :32
3 :36
3:40
3:44
3:48
3:52
3:56
4:00
4:04
4:08
4:12
4:16
4:20
4:24
h.m.
0
45 6:00 90
46 6:04 91
47 6:08 92
48 6:12 93
49 6:16 94
50 6:20 95
51 6:24 96
52 6:28 g]
53 6:32 98
54 6:36 99
55 6:40 100
56 6:44 101
57 6:48 102
58 6:52 103
59 6:56 104
60 7:00 105
61 7:04 106
62 7 :08 1m
63 7:12 108
64 7:16 109
65 7:20 no
66 7:24 III
4:2B 67 7:28 i l l
4:32 68 7 :32 113
4=36 69 7 :36 114
4:40 70 7:40 115
4:44 71 7:44 116
4:48 72 7:48 117
4:52 73 7 :52 ne
4:56 74 7:56 119
5:00 75 8:00 120
5:04 76 8:04 121
5:08 77 8:08 122
5:12 78 8:12 123
5 :16 79 8:16 124
5:20 80 8:20 125
5:24 81 8:24 126
5:28 82 8 :28 127
5 :32 83 8:32 128
5 ;36 84 8:36 129
5:40 85 8:40 130
5:44 86 8:44 131
5 :48 87 8:48 132
5:52 88 8 :52 133
5:56 89 8 :56 134
6:00 90 9:00 135
RESTRICTED
OF TIME INTO DEGREES OF LONGITUDE
h.m.
0
9:00
9:04
9:08
9:12
9:16
9:20
9:24
9 :28
9 :32
9:36
9:40
9:44
9:48
9:52
9 :56
10:00
10:04
10:08
10:12
10:16
10:20
10:24
10:28
10:32
10:36
10:40
10:44
10:48
10:52
10:56
11:00
11:04
11:08
11:12
11:16
11:20
11:24
11:28
11:32
11:36
11:40
11:44
11:48
11:5.2
11:56
12:00
135
136
137
138
1.39
140
141
11~2
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
h.m.
12:00
12:04
12:08
12:12
12:16
12:20
12:24
12:28
12:32
12:36
12 :40
12:44
12:48
12:52
12:56
13:00
13:04
13 :08
13:12
13:16
13:20
13:24
13:28
13:32
13:36
13:40
13:44
13:48
13:52
13:56
14:00
14:04
14:08
14:12
14:16
"14:20
14:24
14:28
14:32
14:36
14:40
14:44
14:48
14:52
14:56
15:00
0
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
h.m.
0
15:00 225
15:04 226
15 :08 227
15:12 228
15:16 229
15:20 230
15:24 231
15:28 232
15:32 233
15 :36 234
15:40 235
15:44 236
15:48 237
15:52 238
15:56 239
16:00 240
16:04 241
16:08 242
16:12 243
16:16 244
16:20 245
16:24 246
16:28 247
16:32248
16:36 249
16:40 250
16:44 251
16:48 252
16:52 253
16:56 254
17:00 255
17:04 256
17:08 257
17:12 258
17:16 259
17:20 260
17:24 261
17:28 262
17:32 263
17:36 264
17:40 265
17:44 266
17:48 267
17:52 268
17:56 269
18:00 270
h.m.
18:00
18:04
18:08
18:12
18:16
18:20
18:24
18 :28
18 :32
18 :36
18:40
18:44
18:48
18:52
18:56
19:00
19:04
19:08
19:12
19:16
19:20
19:24
19:28
19:32
19:36
19:40
19:44
19:48
19:52
19:56
20:00
20:04
20:08
20:12
20:16
20:20
20:24
20:28
20:32
20:36
20:40
20:44
20:48
20:52
20:56
21:00
0
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
h.m.
0
21:00
21:04
21,08
21:12
21:16
21:20
21124
21:28
21:32
21:36
21:40
21:44
21:48
21:52
21:56
22:00
22:04
22:08
22:12
22:16
22:20
22:24
22:28
22:32
22:36
22:40
22:44
22:48
22:52
22:53
2.3:00
23:04
23:08
23:12
23:16
23:20
23:24
23:28
23 :32
23:36
23:40
23:44
23:48
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
J36
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
23:52 35e
23:56 359
24:00 360
4.07
~
z-t
NATURAL TRIGONOMETRIC FUNCTIONS
NATURAL TRIGONOMETRIC FUNCTIONS
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0.0494:3 0.05234
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84
83
82
81
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0.87402
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0.35293
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0.40142
0.41734
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0.37191
0.38805
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69
68
67
66
65
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20
27
28
29
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0.45399
0.40947
0.48481
0.42[,25
0.44098
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0.47204
0.48735
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0.44359
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0.65166
0.66480
0.6777H
0.69046
0.70298
0.65386
0.66097
0.67987
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0.7X801
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0.81748
0 . .'107:30
0.7!J(ji-;1-l
0.78ti22
0.77531
0.81412
O.smSli
0.7!':{:{S
0.78201
0.77047 0.77162
0.76G04
0.75471
0.7431-1
0.7313;)
0.71934
0.76417
O.7.')ZSO
0.74120
0.72!,a7
0.717:32
0.76229
0.750HS
O. nfJ:24
0.727:l7
0.71529
0.1-11242
0.81580
O.S05.'i8
0.7!1S12
0.7.'1,142
0.760·11
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0.72:):)7
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I
40'
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I
~
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4
0.00582
0.02;)28
0.04075
0.05824
0.07578
0.0087:3
0.02H19
0.04:3uo
O.OOl1(j
0.07870
0.01104 0.01455
0.02910 0.0:1201
0.0465S, 0.04!'49
0.013408 0.00700
0.081G3 0.08450
0.017-16
0.m492
0.05241
0.0699:3
0.08749
89
88
87
86
85
1
2
3
4
5
o
7
8
9
0.08749
0.10.510
0.12278
0.14054
0.15838
0.09042
0.10805
0.12574
0.14351
0.16137
0.09335
0.110!J!J
0.128(j9
0.14ti48
0.10435
0.0962D
0.09923
0.11688
0.13461
0.1524:3
0.17033
0.10216
0.11983
0.13758
0.15540
0.17333
0.10510
0.12278
0.14054
0.158;)g
0.17633
84
83
g2
81
80
6
7
8
9
10
11
12
1:3
14
0.17633
0.19438
0.21256
0.23087
0.24933
0.17933
0.19740
0.215tiO
0.23393
0.25242
0.18233
0.20042
0.21804
0.23700
0.25552
0.18835
0.2m45 0.20fi,18
0.22W9 0.22475
0.24008 0.24:HG
0.25862 0.2G172
0.1913U
0.20%2
0.22781
0.2..1li2·1'
0.2048:3
0.19438
0.21256
0.23087
0.24933
0.26795
79
78
77
76
75
10
11
12
13
15
16
17
18
19
0.26795
0.28675
0.30573
0.32492
0.34433
0.27107
0.28990
0.308!Jl
0.32814
0.34758
0.27419 0.277a2 0.28046 0.28360
0.299:38 0.:30255
0.31210 0.:315:30 0.:31850 0.:{2171
0.331:3() 0.33400 0.3;{783 0.34108
0.35085 0.35412 0.35740 0.360G8
0.28675
0.30573
0.32492
0.34433
0.30397
20
21
22
23
:,H
0.36397
0.38386
0.40403
0.42447
0.44523
[email protected]
0.38721
0.40741
0.42791
0.44872
0.37057
0.39055
0.41081
0.43136
0.45222
0.37388
0.39:391
0.41421
0.43481
0.45573
0.37720
0.39727
0.41763
0.4:3828
0.45924
0.38053
0.400G5
0.42105
0.44175
0.46277
25
2G
27
28
29
0.46631
0.48773
0.50053
0.53171
0.55431
0.46985
0.491a4
0.51320
0.53545
0.55812
0.47341
0.49495
p.5Hi88
0.5:H)20
0.56194
0.47698
0.408.58
0.52057
0.54296
0.50577
0.48055
0.50222
0.52427
0.54674
0.569G2
0.48414
0.50587
0.52708
0.55051
0.57348
ao
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32
3:3
34
0 . .')7735
O.OOO;:';G
0.024;:';7
0.fi4941
0.07451
0.58124
0.6048:3
0.{)2S02
0.6.'):355
0.67875
0.58513
0.00881
0.63299
0.()5771
0.68301
0.58905
0.01280
0.{):3707
0.(jG189
0.68728
0.59297
O.GIGSI
0.64117
0.6G608
0.69157
0.59691
0.u2mn
0.G4528
0.67028
0.G95gl:)
a5
0.70021
0.72G54
0.75355
0.78129
0.80978
0.70455
0.73100
0.75812
0.78598
0.81461
0.70891
0.7:3547
0.7{)272
0.79070
0.8194G
0.71329 o.7lnw 0.72211
0.739!lG 0.74447 0.74!J00
0.7/in:.; 0.7719G O.770Hl
0.79.')44 0.80020 0.1.;0-198
0.82434 0.82923 0.83415
2
3
0.831)10
0.8ti929
0.90040
0.93252
0.96569
0.11:W4
O.la1(j;j
0.14945
0.16734
0.185~34
0.29:305 0.29G21
I
0.84407 0.849060.H5408 0.85912
0.87441 0.87955 0.8847:3 0.88992
0.90509 0.91OB!) 0.!lW3:3 0.92170
0.~n797 0.94:1·15 0.!J48HG 0.!).')4.')1
0.97133 0.97700 0.91:)270 0.98843
~
m
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i;
GO'
I
50'
40'
30'
III
~
I:
~
COTANGENTS
20'
1
10'
5
10'
I~I
l~l~I_~o_'_I~~_~
:W'
11.43005 11.0.')943 10.71191
9.514:36 9.25530 9.009l:tl
8.144a5 7.95:302 7.7703S
7.115:37 {).!/682:3 6.826(J.i
6.31375 6.19703 0.08444
10.38.')401O.0iHO:~
.').48451
4.98940
4 ..5736:3
8.770S9
7.59.')7;)
0.fi!1l16
5.97576
9.78817 9.51430
8.555:)[; 8.34496 8.14435
7.42H71 7.2(iH7:~ 7.115:37
6.5G055 G.434H4 (;.:n375
5.87080, 5.7(j!)a7 5.67128
84
sa
3.01364
74
7:3
72
71
70
15
IS
17
18
19
3.73205
3.48741
3.27085
3.07768
2.90421
3.68909
3.44951
3.23714
3.04749
2.87700
3.64705
3.41236
3.2040()
3.0178:3
2.8502:3
3.60!)88
3.37504
3.1715!l
2.988(1)
2.823Ul
3.5u.'>57 3.52609
:C~402a 3.30521
3. i:W72 3.10842
2.0(l004 2.93189
2.79802 2.77254
3.48741
3.27085
3.07708
2.90421
2.74748
74
73
72
71
70
0.38386
0.40403
0.42447
0.44523
0.46631
69
08
67
06
05
20
21
22
23
24
2.74748
2.60509
2.4 75091
2.35585
2.24604
2.72281
2.58261
2.45451 1
2.336931
2.22857
2.698£)3
2.50046
2.43422
2.31826
2,21132
2.67402
2.538G5
2.41421
2.29984
2.19430
2.651O!l
2.51715
2.:30449
2.28167
2.17749
2.62791
2.4!l597
2.37504
2.26374
2.1{)090
2.60.')00
2.47509
2.:3558.')
2.24604
2.14451
69
68
67
66
65
0.48773
0.50953
0.53171
0.55431
0.57735
64
63
62
61
60
25
26
2.09654
2.005G9
1.92098
1.Sil77
1.76749,
2.08094
1.9\HlG
1.00741
1.i'2907
1.75550
2.0651;3
1.97680
1.89400
1.8l()4!l
1.74375
1.8040.')
1.73205
64
63
62
61
60
0.60086
0.62487
0.H4941
0.(j7451
0.70021
59
58
57
30
31
32
33
34
1.73205
1.66428
1.60033
1.53987
1.48256
1.6976G
I.G:nS5
1.5{iOt)!J
l.ii1084
1.45501
1.68643 1.67530
I.fi2125 1.61074
1.!j5!Hi611.54!)72
UiOl:3:~ 1.4!ll!lO
1.44598 1.437o:l
1.60428
1.6003:1
59
.58
1.5:mk7
57
1.4k2f>li
1.42815
56
5S
0.72654
0.75a55
0.78129
0.80!l7g
0.83910
54
5a
35
36
37
38
39
1.42815
1.37638
] .32704
1.27994
1.23490
2.12832 1 2.11233
2.035261 2.02039
1.94858 1.·J:3470!
1.86700 1.85462
1.791741 1.77955
1.72047 1.70901
1 ()5337 1.64256 '
1.590021 1.57981
1.53010 1.5204:31
1.473301 1.4U4UI
1.41934: 1.410Gl
1.3m.wol 1.35068
1.31004 1.31110
1.2723011.26471
1.22758 1.22031
2.05030
Ul6261
28
29
2.14451 1
2.05030
1.96261
1.88073
1.80405
.0
4"1
42
43
44
1.19175j
1.15037
1.11061
1.07237
1.03553 _
&6
55
52
51
50
49
48
47
46
45
-1---'-0'
~
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27
i
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1
1
1.18474
1.14303
1.10414
1.0661 3 1
1.02952
50'
1
I.:~514:2 1.;34:~2:~11.:~:~5
1.401D5 1.3D336 1.38484 1.37638
79
78
77
76
75
54
11 1.327041 5:3
l.:H):~~:n 1.2~);)41 1.2871.4 1.27!,!,4 52
1.25717 1.24!,(j!) 1.24227 1.2:WIO 51
1.21:UO 1.205!J:i 1.19882 I.H1l75 50
1
z
»
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C
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rVl
1
1.17777 1.17085 1.1 oaDsi1.l5715
1. 13u04
1.1:302!l 1.12:~()!l 1.1171:3
1.0!,770 1.091:31 1.0S49fl 1.07i'f~4
1.0[i!l94i 1.05:118 1.047(iGI1.041Gi'
1.02:355' _ 1.017: ~1~0051-l:1
1
40'
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82
81
80
14
1.8~On
m
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87
86
85
5.3055215.30028
4.!H510 4.84:300
4 ..')L071 4.44942
4,165:30, 4.11256
3.86671 ;~.82083
5.2256015.14455
4.77280 4.7046:i
4.:m9tl9 4.:33148
4.0fi107 4.01078
3.7759[; 3.73205
()
89
5.57638
5.06584
4.6:3825
4.27471
3.961G5
1
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1343.77371171.88.'J401l4.588658.').H397f)f,8.7fi009.'i7.2S9f)1l
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28.G:H,25 26.1:3lGO 24.54176 22.90:37721.47040:W.20555l!'.08114
19.08114 18.07498 17.1(j!):~4 l{).349S(i 15.60478 14.!J244214.30067
14.30067 1:3.72G74 13.1!J688 12.7062112.2505111.8201711.43005
4.21!J:1:~
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.sII
COTANGENTS
0'
~
I
5.67128
5.14455
4.7046:3
4.3:3148
4.01078
0.86410 0.86929
0.89515 0.90040
0.~)2700 0.93252
0.96008 0.9G569
0.99420 1.00000
----1---1---1---1
--,
~
~
NATURAL TRIGONOMETRIC FUNCTIONS
0.00291
0.020;3()
0.0378:3
0.05533
0.07285
40
41
42
4:3
44
o
:~8
0.00000
0.0174()
0.03492
0.05241
0.06993
I
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37
0.9G:{63 0.96285
0.95S8~ 0.v;)7\'!J
0.9[);)72 0.. \)5284
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0.942G4 O.!J11H7
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0.95[){j-l
0.95459
0.!/4924
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54
53
52
51
50
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0.58779
0.00182
0.61500
0.62932
0.64279
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0.5050:~
0.li2002
0.573liBI 0.57596 0.5783:3 0.58070 0.58307
3[,
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0.005R5
0.11:120
0.I:W5;)
0.14781
0.lU505
30'
TANGENTS
20'
10'
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1.l50:l7
1.11061
1.07237
1.0a.'>53 1
49
48
47
46
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0'
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8.-zm
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RESTRICTED
TABLES
RESTRICTED
TABLES
LOGARITHMS ICONT.)
LOGARITHMS
LOGARITHMS OF NUMBERS kONT.1
LOGARITHMS OF NUMBERS
N
N
1'0
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
'Zl
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
4.10
o
1
2
3
4
5
6
02938
06819
10380
13672
16732
19590
22272
24797
27184
29447
8
9
00000
04139
07918
11394
14613
17609
20412
23045
25527
27875
00432
04532
08279
11727
14922
17898
20683
23300
25768
28103
00860
04922
08636
12057
15229
18184
20952
23553
26007
28330
01284
05308
08991
12385
15534
18469
21219
23805
26245
28556
01703
05690
09342
12710
15836
18752
21484
24055
26482
28780
02119
06070
09691
13033
16137
19033
2174S
24304
26717
29003
03342
07188
10721
13988
17026
19866
22531
25042
27416
29667
03743
07555
11059
14301
17319
20140
22789
25285
27646
29885
30103
32222
34242
.36173
38021
30/194
414Cf7
43136
44716
46240
30320
32428
34439
36361
38202
39967
41664
43297
44871
46389
30535
326.34
34635
36549
.38.382
40140
43457
45025
46538
30750
32838
34830
36736
38561
40312
41996
43616
45179
46687
30963
33041
35025
36922
38739
40483
42160
43775
45332
46835
31175 31387 31597 31806
33244 33445 33646 33846
35218 35411 35603 35793
3710'7 37291 37475 37658
38917 39094 39270 39445
40654 40824 40993 41162
42325 42488 42651 42813
43933 44091 44248 44404
45484 45637 45788 45939
46982 47129 47276 47422
32015
34044
35984
37840
39620
41330
42975
44560
46090
47567
47712
49136
50515
51851
53148
54407
55630
56820
57978
59106
47857
49276
50651
51983
53275
54531
55751
56937
58092
59218
48001
49415
50786
52114
53403
54654
55871
57054
58206
59329
48144
49554
50920
52244
53529
54777
55991
57171
58320
59439
48287
49693
51055
52375
53656
54900
56110
57287
58433
59550
48430
49831
51188
52504
53782
55023
56229
57403
58546
59660
48572
49969
51322
52634
53908
55145
56348
57519
58659
59770
48714
50106
51455
52763
54033
55267
56467
57634
58771
59879
48855
50243
51587
52892
54158
55388
56585
57749
58883
59988
48996
50379
51720
53020
54283
55509
56703
57864
58995
60097
60206
61278
62325
63347
64345
65321
66276
67210
68124
69020
60314
61384
62428
63448
64444
65418
66370
67302
68215
69108
60423
61490
62531
63548
64542
65514
66464
67394
68305
69197
60531
61595
62634
63649
64640
65610
66558
67486
683.95
69285
(~638
61700
62737
63749
64738
65706
66652
67578
68485
69373
60746
61805
62839
63849
64836
65801
66745
67669
68574
69461
60853
61909
62941
63949
64933
65896
66839
67761
68664
69548
60959
62014
63043
64048
65031
65992
66932
67852
68753
69636
61066
62118
63144
64147
65128
66087
67025
67943
68842
69723
61172
62221
63246
64246
65225
66181
67117
68034
68931
69810
69897
70757
71600.
72428
73239
69984
70842
71684
72509
73320
70070
70927
71767
72591
73400
70157
71012
71850
72673
73480
70243
71096
71933
72754
73560
70329
71181
72016
72835
73640
70i15
71265
72Q99
72916
73719
70501
71349
72181
72997
73799
70586
71433
72263
73078
73878
70672
71517
72346
73159
73957
41830
02531
06446
10037
13354
16435
19312
22011
2455r
26951
29226
7
RESTRICTED
o
1
2
3
4
5
6
7
8
9
55
74D36 74115 74194 74Z73 74351 74429 74507 74586 74663 74741
56
57
58
59
74819 74896 74974 75051
75587 75664 75740 75815
76343 76418 76492 76567
77085 77159 71232 77)05
75128
75891
76641
77379
75205
75967
76716
77452
75282
76042
76790
77525
75358
76118
76864
71597
60
61
62
63
64
65
66
67
68
69
77815
78533
79239
79934
80618
81291
81954
82607
83251
8)885
71887
781:iJ4
79309
8000,3
80686
81358
82020
78032
7a?46
79449
80140
80821
81491
82151
82802
83442
84073
78104
78817
79518
80209
80889
81558
82217
82866
83506
84136
78176
78888
79588
80m
80956
81624
82282
82930
8J569
84198
78247
78958
79657
80346
81023
81690
82347
82995
83632
84261
78)19
79029
79727
80414
81090
81757
82413
?O
71
72
73
74
75
76
77
78
79
84510
85126
85733
86332
86923
87506
88081
88649
89209
89763
84572 846)4 8.4696
8'187 85248 85309
8~4 85854 85914
86392 86451 86510
86982 87040 87099
87564 87622 87679
88138 88195 88252
88705 88762 88818
89265 89321 89376
89818 89873 89927
84757
85370
85974
86570
87157
87737
88309
88874
89432
89982
84819
85431
86034
86629
87216
87795
88366
88930
89487
90037
80
81
82
8)
84
85
86
87
88
89
90309
90849
91381
91908
92428
92942
93450
93952
94448
94939
90363
90902
91434
91960
92480
92993
93500
94002
94498
94988
90417
90956
91487
92012
92531
93044
93551
94052
94547
95036
90472
91009
91540
92065
92583
93095
93601
94101
94596
95085
90526
91062
9159.3
92117
92634
93146
93651
94151
94645
95134
90
91
92
93
94
95
96
97
98
99
95424
95904
96379
96848
97313
97772
98227
98677
99123
99564
95472
95952
96426
96895
97359
97818
98272
98722
99167
99607
95521
95999
96473
96942
97405
97864
98318
98767
99211
99651
95569
96047
96520
96988
97451
97909
98363
98811
99255
99695
95617
96095
96567
97035
97497
97955
98408
98856
99300
99739
RESTRICTED
779«J
78675
79379
80072
80754
81425
82086
82~2 827)7
83315 8)J78
83948 84011
75435
76193
76938
71670
75511
76268
77012
77743
78390
7g;J99
79796
80482
81158
81823
82478
83059 83123
83696 83759
84323 84386
78462
79169
79865
80550
81224
81889
82543
83187
83822
84448
8J.880
85491
86094
866S8
87'Z14
87852
88423
88986
89542
90091
84942
85552
86153
86747
87332
87910
88480
89042
89597
90146
85003
85612
86213
86806
87.390
87967
88536
89098
89653
90200
85065
85673
86273
86864
87448
88024
88593
89154
89708
90255
90580
91116
91645
92169
92686
93197
93702
94201
94694
95182
90634
91169
91698
92221
92737
93247
93752
94250
94743
95231
90681
91222
91751
92273
92788
93298
93802
94300
94792
95279
90741
91275
91803
92324
92840
93349
93852
94349
94841
95328
90795
91328
91855
92376
92891
93399
93902
94399
94890
95376
95665
96142
96614
97081
97543
98000
98453
98900
99344
99782
95713
96190
96661
97128
97598
98046
98498
98945
99388
99826
95761
96237
96708
97174
97635
98091
98543
98989
99432
99870
95809
96284
96755
Cf7220
97681
98137
98588
99034
99476
99913
95856
96332
96802
97267
m27
98182
98632
99078
99520
99957
4. II