ITR-9
SOUTHWESTERN RADIOLOGICAL HEALTH LABORATORY
INTRALABORATORY TECHNICAL REPORT
January 19, 1966
A TABLE FOR DETERMINING
THE TRUE TIME REPRESENTING AN OBSERVED COUNT RATE
by
B. W. Hoffman and S. B. Van Camerik
Radiochemical Laboratory
Introduction to Tables
The accompanying tables were compiled as an aid in selecting a time
correction for the radioactive decay which occurs during countingo
For example, when a count is made,, neither the time at the start
nor the time at the end of counting is a true representation of the
disintegration rate calculated from the observed counts. Howevers
there is a time during the counting interval which is correct for
this rate of disintegration. A value,, ft, obtained from the table,
when added to the time at the start of the count produces the
desired true time.
The most obvious use for the time correction tables would be in
work concerned with short-lived radionuclides, as encountered
in reactors and activation analysis. In any instance, the tables
are useful whenever the counting time is appreciable as compared
to the half life of the radionuclide being counted. .
-------
Mathematical motivation
Definition of variables:
N = number of radioactive atoms at start of count*
N = number of radioactive atoms at end of count time^T*.
T = count time.
ti/a = half life of radionuclide in question.
X = lambda = InZ/tj/z
A t ~ time correction (tabulated results $
From the standard decay equations:
-dN/dt = AN and,,
N = NQe-At
then at time T;
N = N VAT
T ° AT
A N = (NQ - NTJ = CNQ - NQe" = 0 - e.
The DPM observed for count time T is:
-AT
DPM =A N/T = NJl - e )/T
but this observed DPM actually occurred after some At.
Therefores since:
DPM = -dN/dt = AN = AN e
and equating DPM's:
it follows that:
e~MtMi -e-XT}/AT or,
AT
-AAt = ln{(l - e" }/AT) .
Substituting InZ/tj/z for A :
-At ln2/ti/2 « ln
-------
Defining R for half lives counted) = T/tj/2
this relationship now becomes:
At = -t1/2 ln(U - e" )/(R In2))/ln2 .
For a constant R in the above expression, it is immediately apparent,,
as is borne out by the tabulated values for Ats that At is directly pro-
portional to ts/2 .
Use of the Tables
The physical structure of the tables includes the values of Rp half
lifei, and the time correction At, where:
R s Counting Time/Half Life - number of half lives counted c and
At s Time increment to be added to the chronological time
at the start of the count* The resulting time is the
true chronological time for the observed disintegration
rate-
A necessary restriction on the use of the tables is that the count time
and half life must have the same units of time. In the event that the
half life under consideration is greater than the largest tabulated
value of 60C the units may be changed to those of the next higher
time unit for both the half life and the counting time, or the R ratio
may be located and the value of At multiplied by the appropriate
factor to obtain the required correction (See sample problem below)
Sample problem
Say one has:
tj/2 = 120 min,
and T = 30 min.
Therefore:
R = T/tj/2 = 30 rain, /120 minu = 0, 25,
Since the half life scale (ti/2 ) is limited to 60 units,, the ti/z - 120 min,
can be reduced to tj/2 = 2 hrs while R remains = 0, 250 and T = 0, 5 hrs.
Therefore,, for a R = 0. 25 and a tj/2 = 2 hrs, the At may be read
directly from the table:
i. e. At = 0. 25 hrs. ;
-------
or working in minutes,, for R = 0, 25 and tj/2 r 60 min. the&t value s
7. 39 min. Since the tj/2 we are actually concerned with is 1ZO min, ,
or exactly twice (120 min<, /60 min. = 2} the 60 units limit of the t$/z
scale, for ts/2 - 120 min, , the value of &t = 2x7. 39 min. = 14,, 78 min»
ca= 0. 25
The slight discrepancy in the results of the alternative approaches is
due to the rounding incorporated in the computerized compilation. The
effect of this rounding process is most prominent when using the values
at the lower end of the ts /2 units scale.
-------
.05
. 10
. 15
.?o
.75
.30
. .35
.56
.60
.65
.7^
7 C.
' '
. 80
. 35
.00
.05
1 . on
1 . 0 5
1.10
1.15
1 .70
1 .75
1 . > 0
'1 .35
1 .40
1 .46
1.65
1 .60
1 .65
1 .70
1 .76
1 .80
1 .35
1 .90
1 .95
7 . oo
7.05
7.10
7.7S
? . 3 0
7.35
7.40
7.45
7.50
.6
.01
.07
.04
.06
.06
.07
.09
. 10
. 1 i
.1 ">
. 1 3
. 14
. 16
.I"7
. ^
. 1 9
. 7''1
.71
.?>
.74
.?S
.76
.77
.78
..''O
T.
. 31
. 37
.33
.34
. 3C
. 3. 6
.^7
"3 P
'
.*°
.40
.41
.6?
.43
.44
.4R
. 4 r-,
.67
.48
.40
.50
.R1
. 5 7
.61
.5 '4
1 .0
. n /
.OS"
.07
.10
.1?
.15
. 17
.70
. 77
.74
.77
.79
.^1
.74
.*6
. 3 8
.40
.43
.'»5
.67
.69
.67
.c./,
.56
.68
. 60
.6?
.64
.66
.69
.71
.77
.7C
.77
.70
.81
. 8 3
.85
.87
.89
.01
.0?
.94
.96
.98
1 .00
1 . o ?
1 . 04
1 .Oft
1 . 0 7
1 . c
.04
.07
. 1 1
. 16
.18
.7?
.76
.79
. 3 3
.""^
. A 0
.4?
.A 7
.en
.^4
.5 7
.61
.64
.67
.71
.74
. 77
.81
.Q4
.07
.0(1
.93
.97
i .r.Q
1 .03
1 .Of,
1 .00
1.1?
1 . 1K
1 . 1 p.
1.71
1 . 7 4
1 .77
1 . 3 0
1.^3
1 . '' 6
1 . >. Q
1 . 6 7
1 . A 4
1 . 4 7
1.50
1.6°
1 .6ft
1 ,5P
1.61
7.0
. 0 5
. 1 0
.1 5
. ? 0
.75
.79
.34
.39
. 4 4
.60
.^3
.58
.6^
.67
.7?
.76
.81
.85
.90
.°4
.09
1.03
1 .07
1.1?
1.16
1.20
1.25
1 .79
1 .3-3
1 .T?
1.41
1 . /. ^
} . 4 Q
1 .53
i . t
.80
.87
.04
1.01
1.0H
1.14
1.71
1 .78
1 ,-*s
1.41
1.48
1.56
1.61
1 .68
1 .76
1 .80
1.87
1.93
1.9°
?.r'6
2.12
7.18
2. 74
7 , 30
7.-^
7.42
7.48
2.64
2.60
7.66
7.7?
7.77
7.R3
7.3 O
7.04
7 .on
-5.06
3.11
'3. 17
>.??
3.S
.00
. 17
.76
T r,
. 4 3
.52
.60
.68
.7^
,pc
.0-5
1 .01
1 .00
1 .IP
1 .76
1 .36
1.41
1 .49
1 .57
1 ,6S
1.73
1 . 8 0
1 .88
1 .°6
7 . 0 3
2. 1 1
2. 18
? . 7 c-
7. 3^
7.40
7.47
7.^4
''.6?
7.69
7.7A
7 . P °
7.90
7.97
3.07
3.10
°.l7
T. 74
*.->o
->.37
5 . A 4
3 . r-, 0
3 . S 7
3.63
^.60
3. 7r,
4.0
. 1 o
. 7 ' ^
.30
.40
.49
.59
.69
. 7 R
,3P
.°7
1 .07
1.16
1 .7.5
1 .34
1.44
1.53
1 .6?
1.71
1 . 8 0
1 . 0 P
1 .07
7.06
7.16
7.73
7.3?
2.41
2.49
7.58
7.66
7.74
7 . P. "»
7.01
7.00
3.07
^. 1 ^
5.73
3.31
3.39
3.47
3.65
^.67
0.70
3.78
'3.85
5.03
4. on
4 . o 8
4.15
4.7?
4 . 3 0
6 .S
. 11
. 7?
.33
.44
.55
.66
.77
.88
.00
i no
'
1.70
1 .30
1.41
1 .^1
1 .61
1 .72
1 .82
1 .0?
? . C 7
7.1?
7.72
7.32
7.4?
7.61
7.61
7.71
2.80
. 7.90
0 . OO
i n o
3 . 1 P
-> . 7 7
3 . 3A
3.4^
T ,R4
3.63
3.72
3.81
3.00
3.99
4.08
4.16
4.75
4.33
4.47
4.50
4.59
4.67
4.7S
4.83
5.0
. 1 ?
.7<=,
.'57
.40
.62
. 74
.86
.OR
1. TO
1 .-1!
1 .3^
1.46
1.^6
1 . «.«
l.-'Q
1.01
2. 02
7.13
7.75
7.3ft
7.47
7.^3
7.«;o
7.79
7.0 5
3.01
3.11
3. 77
-5.-3?
>.A^
T. t7
3.0
3. il>.
3.04
-5.04
4.04
4.14'
4. 74
4.33
4.43
4.^
4 .6?
4.7?
4.81
4.01
5.00
5.oq
5.19
S.7R
S.37
PACE- 1
-------
6. o
7.0
R.o
o. o
n. n
.0K
I '
. 16
.70
. 75
. 30
.36
.40
.45
.60
.65
.60
.65
.70
.76
.80
. 85
.90
.96
1 .00
1.05
1.10
1.15
1 . 7 0
1 .76
1.3^
1.35
1 .40
1.45
1.60
1.-6
1 .60
1.66
1 .70
1.75
1.80
1.85
1.00
1 .95
7.00
7.05
2.10
7.16
7 . ? 0
7.75
7.30
7.76
2.40
7.45
7.60
. 14
.77
.41
.54
.6°
.81
.96.
1 . 0 7
' I
I.'*
1.46
1 .50
1.77
1 . R *
1 .97
2 . 1 0
£_' ' '
7 . 3 6
7 . ': 1
? . 6 0
7. 7
7.8 7
7 . 0 r.
7.0'7
3. 19
3.31
3.47
3.54
3.66
7.77
^ O Q
4.00
4.11
4.??
4 . 7 ^
4 . 44
4 . 5 r'
4 . 6 6
4.77
4.87
4.98
5 .09
5.10
6 . TO
5.40
5.50
^.60
5.71
6 . 8 ]
5.01
. 1 5
.3':
.45
.69
. 74
.88
i .07
1.17
1 . ° 1
1 .46
I . 6 0
1 .74
1 . ° 8
7.0?
7. 1 c
7.7°
7 . 4 3
7.66
^.69
.? . R 7
-.^6
7.00
7."??
7. -5 6
3.48
3.61
3.74
3.86
3.99
4.11
4 . 7 A
4 . 7 6
4 . 4 8
4 . 60
4.73
4 . 3 ')
4.06
5 . "! R
6 . ? 0
6.3?
5.43
6.65
6.66
5.78
5.89
6.00
6.11
6.7?
6 . 3 3
6 . 4 6
. 16
. ~* 7
.48
.64
.80
.06
I.I"1
1 .77
1.4?
1 .6°
i .7*
1 . R8
7. 07
7.18
7 . 7 -3
7.48
7 . 6 7
?.77
7 . 0 ?
3.06
^.71
7 . 7 6
3.4°
7.63
3. 77
3.01
A . 0 5
4 . 1 8
4 . 3 7
4 . 'i 6
4 . - °
4.77
4.96
4 . 0 9
r- . ' ?
5.7-
6 . 7 R
5.6]
6 . 6 3
^.76
6.R9
6.01
6.14
6. ">6
6.79
6 . 6 0
6.6?
6.74
6 . 8 6
6 . 0 p,
.17
.35
.6?
.6°
.86
i .0'
1 . 7 0
i.^7
i . r^
1.70
1.86
7 . 0 3
7.19
"'.76
7.^1
2.67
7 . 8 3
7.90
->. 1 4
T . 7 0
7 . 6. 6
"* 6 1
3.76
3.91
4 .06
A . ? 1
4 . 3 6
4 . r- 1
4 . 6 6
4 . 8 0
4 . ° 4
c, . [ ) 0
5.23
5.37
6.61
5.65
6.79
6 . 0 7
6.07
6.70
6. 34
6 . 4 7
6.61
6.74
6. ft /
7.00
7.13
7.26
7.39
7 . S 7
. 19
.37
.56
.76
°2
1 .1 i
1 .79
1.67
1 .64
i .R">
? , 0 0
7.17
.7.35
7.67
7.69
? . 8 6
7.07
7.70
^.37
"5.67
>.70
7.86
4. . ( i 7
4 . 1 9
4.36
4 . r- 1
4 .67
4 . 8 3
4 . 9 Q
^. . 1 A
= . 3 0
6.46
6.60
6 . 7 6
^ .0 I
6.06
6.21
6.36
6 . 5 0
6.66
6.79
6.94
7.09
7.27
7.36
7.50
7.64
7 . 7 8
7 . 9 7
o . r: ^
.?i)
.40
.59
.79
.00
1.18
1 .^7
1.^6
1 . 7 r->
1 Q/^
7. I"5
7.3?
7.60
7 . 6 9
7.87
3.05
3.?3
8 . 4 1
7 . 6 O
7.77
3.06
4.1?
4. 70
4.67
4.64
4.81
4 . 9 8
6 . ] 6
5.3?
5 . 4 P
5.66
6.01
5.9 R
6 . 1 4
6.70
6.46
6 . 6 7
6.78
6.97
7.09
7.74
7.40
7.66
7.70
7 . p =>
8. 00
8.16
8.30
8.45
R . 6 0
.71
. 4 7
67
.84
1.06
i . 7 c'
1.46
1 .66
1.86
7.06
7. 76
7.46
7.66
7 . 9 6
3 . 0 6
3.74
3 . 4 4
3.6°
"5.97
4 . 0 1
4 . 1 O
4 . 7 ,q
4 . * 6
4 . 7 r^
4.03
5. 1 1
5.29
5.47
5.66
S . DQ
6.0f
6 . 1 «
6. ^6
6 . 6 ?
6.6^
6 . 8 6
7.0?
7 . 7 0
7.37
7.6-5
7.70
7.86
8.0?
R.18
R. 34
8 . 5 0
0 . 66
8.8?
8.97
9.17
.7?
.46
.67
.80
1.11
1 . 33
1 . 6 4
1.76
1 . ° 7
7.1°
7.40
7.6J
7.P?
-5.0?
3.? 7
3.43
3.66
3.84
4 . "4.
6 . ? 6
6 . 4 4
4 .64
4 . P 3
6.07
5.22
6.41
5.60
6.70
5.98
6.17
6.36
6.^6
6.72
6 . 9 1
7.1,0
7.27
7.46
7.62
7 . 8 0
7.9,R
8 . 1. 6
8.32
R . 4 9
P. 6 7
8.87
9.00
9.17
9. ?4
9 . 5 :J
9.66
.24
.67
.71
.94
1.17
1.4-
i .67
1 .86
? ."Q
7.71
7.67
2.75
7.07
7.19
"* .4 ]
3.62
* .84
4.05
4.77
A . 6 q
4 . 6 o
4.89
r-. 10
6.^1
5.51
6.71
5.92
6. 1?
6.3?
6.61
6.71
6 . 0 -
7.1."
7.?o
7. 4R
7.67
7.86
8.05
8.73
8.42
8 . 60
8.79
q . 07
0.16
9.73
9.50
9.68
9 . 8 5
1 0 . 0 3
l o . ? o
. 76
.60
.74
.00
1 . 73
1.47
1 .71
1 .06
"'.TO
"'.4 7
7.66
7.00
7.13
->.36
-5. cq
3 . Q2
4 . 04.
4. ->7
6 . A 9
4.71
4.07
5.15
^.77
6.^9
5.80
6.0?
6.23
6.64
6.65
6. Q6
7.06
7. ^7
7. A 7
7.67
7 . R R
8.08
8. 77
8.47
8.67
R. 96
9.06
9.76
0.64
0.63
Q . Q ?
10.00
10. n
10.37
10.56
10.76
-------
1 1
17.^
l^.c
i 4
.OS
. 10
. 15
.. ?0
.75
.3^
.'5
.40
.46
.r>0
.55
.60
.65
.70
.75
BO
.85
.90
.95
1 .00
1 .05
1.10
1.15
1 .79
1.75
1.30
1 .35
1 . 4 o
1 .46
1 . RO
1 . r, r,
1 .60
1 .65
1 .70
1 .75
1.80
1.85
1.90
1 .95
7.00
7.05
7.10
7.15
7.70
7.75
7.70
7.75
7.40
7.45
^.50
.76
C, ~>
. '
.7R
1.04
1 . 79
1.5^
1 .80
?.0C.
7 . 7P
7 . 5 r-.
7.80
1 . 0 4
7.?3
?.«=*
7.77
4.01
4 . 7 4
4 . 4 8
4.71
4 . 9 r-
5 . 1 8
5 . 4 1
5.64
5 . R 7
6.0Q
6.77
6.54
6.76
6 . o R
7. 90
7.47
7.61
7 . 8 c.
8.06
R. 77
8.48
8.69
8.90
9. 10
9.71
".51
9.71
9.Q1
10.11
10.^1
10.5 0
10.70
10.89
1 1 .08
11.77
. 77
.5^
.8?
1 .09
1 . ''6
1.67
1.89
7 . 1 5
->.A 1
7.67
7 . °7
5. . 1 9
* . 4 4
5 . 6 9
3.95
4.70
4 . 4 ri
4.69
4.94
c . 1 8
* . 4 ->
5.67
^ . 9 1
6.1^
6 . 3 8
6 . 6 7
6. Rci
7 . 0 8
7.^1
7. R4
7.77
7.99
8.?7
8.44
8.66
8 . 8 R
9 . 1 0
0.37
9.53
o.7^
".96
10.17
1 o. 3R
1 o . K 9
10.80
n .00
11.71
1 1 . 4 ]
11.61
11.81
. 70
. 57
.«6
1.14
1 . 4 ?
1 .70
I .°7
7. 7^
7 . - 7
7.79
7.H6
'4 . 0 ->
^.60
^.86
4.1^
4.39
4.65
4 . "> 1
5.16
c . 4 ?
^ . 6 7
5.0?
6.18
6 . 4 7
6 . 6 7
6.97
7. 16
7.40
7.64
7.oo
o. i 7
8. ->6
P. . RQ
8.^3
0.06
0.79
9.67
9.74
9.97
10.10
1 0 . 4 1
1 0.64
1 0 . R "S
1 1 .07
11.7 Q
11.5 0
i ! . 7 7
11.93
17.14
1 2 . "> c-.
.T")
. 6 -' i
.89
1.19
1.^8
1 .77
7.06
7.^4
7. -3
7.0]
7 . 7 0
7 . /: 8
^ . 7 5
4 . 0 7
4.-M
4.58
4 . 8 5
^.17
^.70
5 . 6 5
^.07
6.18
6.44
6.70
6.^6
7.-V
7.47
7 . 7 3
7. Q8
P . 7 ~>
°. . 4 P
8.77
8.97
9.71
9.45
9.69
9.9?
10.17
1 0.4')
10.64
1 0 . R 7
11.10
i 1 .->-}
11.65
11.7 R
17.00
17.73
i 7.45
i 7 . 6 7
17.89
Q 1
. '
.67
.
1.74
1 .r-4
1 . P 4
7.14
7.44
7.7/,
7,r,-j,
? . ? ^
''.IS?
->. . q i
4 . 7 ri
4.48
4.77
5.06
r-. .**,
S.61
^ . RO
6.1.7
6.44
^.71
6.Q8
7.7S
7 . 5 7
7.78
8.06
8 . * 1
«.67
p t n i
9.09
9.34
0.59
9.R5
10.1 0
1 0.34
1 0.59
10.84
1 1 . H 8
1 1 .??
1 1 ,c^
i 1.80
1 7.n/t
17.7 7
1 7 .50
17.74
17.97
i Q . ? U
1 ^.47
.*?
. 6 r->
.97
1 . 7 P
1 .60
l .0?
7.7?
7 . => 4
7.R^.
7.16
7.46
-5.77
4 . 0 7
4.^7
4.66
4.96
6.25
5.^5
5 . R 4
6.1°
6.41
6.70
6.Q3
7.76
7.^4
7.«7
8 . 1 o
8.^7
8 .64
R . °1
o. TP
9.45
9.71
9 .98
1 0.?4
1 0. 60
10.76
11.01
11.77
11.5?
1 1 .77
1 7.07
17.77
17.=-?
1 7.76
1 3.00
17.75
13.4 9
13.7?
! 3. of,
.74
.A7
1 .0(.
1.7-5
1 .66
1 .00
7.7]
7.64
7.06
3. 7P
"5.60
^.91
A. ??
4 . ^ i
4 . R 4
5. 1 6
5.46
5.76
6.06
6. 76
6.66
6.96
7 . 7 !S
7.54
7.8^
8.1 ?
8.41
8.69
8.07
9. 76
o . q-3
9.81
1 O.OQ
10.76
1 0.6-3
1 0 . 9 0
11.17
11 .44
i 1 .70
i 1 .^6
17.7^
1 7 . A o
17.74
1 *. .00
!'..?=>
1 3.50
11.76
14.00
14. 7^
14.60
.36
.7:)
1 .04
1 . 1 8
1 .7?
7.^6
7.40
7.74
i n -r
- ' '
7 . 4 0
-5. 73
4 . 0 =,
4.38
4.70
5.02
5.34
5.66
^.97
6.79
6.60
6.91
7.71
7.5?
7.82
8.1 ?
R.42
8.7?
Q..-1
Q.71
0.6^
9.RO
1 0 . 1 8
r;.46
10.74
11.03
11.31
11.68
11.86
17.14
17.41
17.6°
17.0^
1^.71
13.48
n . 7 4
14.00
14.26
14.57
14.78
16.0 3
. Va
.7.7
1 . 0 R
1 .43
1 .79
7.14
7.49
7.87
''.I Q
1 . 6 .7
7.^6
4.70
4. 64
4.87
6.70
6.53
5.86
6.19
6.61
6.R1
7.1^
7.47
7.79
8 . 1 0
8.41
8.7?
9.0^
9. 34
0.64
o . OA
1 '"'.7 A
1 0.54
1 0.83
11.13
11.4?
11.71
17.00
17.78
1 7 . S 7
1 7.QK
1 *. 1 ^
1 ° . 4 1
1 -5.6°
1 7.06
14.73
14.50
14.77
16.04
1 S . 3 1
15.57
.^7
.76
1.1?
! .4fl
1 .8^
7.71
7.^7
7.07
7 . TO
7.64
'\ . oo
4 .34
4 .60
6.04
6 . TR
5.7?
6.06
6.4 ;;
6. 74
7,ny
7. A.O
7.73
8 . H6
8. -58
8. 70
Q . n 2
0 . T4
9.66
0.07
1 0 . -> «
10.^0
10.QO
11.71
1 1 . S 1
11."!
17.11
17.41
12.71
n.oo
n.7Q
1 7 . c .p
1 T.Q7
14. 1 6
14.44
14.7?
16.00
15.78
15.66
1 5 . R 7
16.11
p /\ r, r _ -2.
-------
.05
. 10
.15
.20
.25
.30
.35
.40
4.5
.50
.55
.60
.65
.70
.75
.80
.85
.90
.95
1 .00
1 .0-
1.10
1.15
1 ? 0
1 . ?c
1 .30
1.35
1 .40
1.45
1 .50
1 .65
1 .60
1 .65
1 .70
1 .75
1 .80
1 .35
1.90
1 .95
7.00
7.05
7.10
7.15
2.20
7.25
7.30
2.35
2.40
?.45
7.50
15. ft
.70
.77
1.15
1.53.
1 .91
7.78
7.66
3 . 0 3
3.40
3.76
4. 13
4.4°
4.8*
5.21
5.56
5.91
6. 76
6.61
6.96
7. 30
7.6^
7.99
8. 3?
8.66
8.9°
9.37
9.65
9.98
10.30
10.6°
10.9*
1 1.77
1 1.58
1 1 .90
17.71
17.5?
17.83
13.13
13.44
13.74
1 4 .04
14.33
1 4. . ft 7
14.9?
15.? ?
15.51
1 5.7°
16.08
1.6.36
1 6 . 6 4
16.0
.40
. 8 0
1.19
1 .58
1 .97
7.36
7.74
3.13
3 . ft 1
3.88
4. 7ft
4.63
5.0]
5.37
5.74
6.11
6 . /. 7
6.83
7.13
7.54
7.RO
8 . 7 4
8 . 5 9
8.94
0.78
9.62
9.96
10.30
10.64
10.97
1 1 .30
n . 6 3
n .96
12.78
1 .7.60
17.9?
1 3 . ? 4
13.56
13.87
14.18
1 4.49
14.80
1 * . 1 0
15.41
1 * . 7 1
16.0]
16.3, j
16.6'-'
1 6 . 8 °
1 7 . 1 8
16.*
.41
.8?
1 .73
1 .63
? . 0 3
2.43
7.33
'' . > ?
3 . ft ?
4 . 0 I
4.39
4.78
5 . 1 ft
5.54
5 . Q 2
6.3.0
6.67
7.0 4
7.41
7.7°
8.14
R . ft 0
8.36
9 . 7 7
0.57
0 , p 7
10.? 8
10.6?
1 0 . o 7
11.31
11.6*
11 .99
1 7.37
1 7.66
13.0 0
13.33
13.6 *
13.98
14.30
1 4 . ft ?
1^.94
1 5 . ^ ft
1 ^ . *> 7
15.80
16.30
1 6 . ft 1
16.8 1
] 7 . 1 ?
17.4?
17.77
17.0
.4?
.85
1.76
1 .68
7.09
?.51
2 . 9 1
3.3?
3.73
4.13
4.^3
4.9?
5.3?
5.71
6 . 1 0
6.49
6.87
7.75
7.6?
8 . 0 I
8 . ', 0
8.76
9 . 1 3
9.50
9.86
10.23
10.59
10.95
11.3 0
1 1 .66
1 2.01
1 7.36
1 7.70
1 3 . 0 5
1 3 . 7 Q
13.73
1 4 . 0 7
1 4 . 4 0
14.74
T:.07
15.40
15.72
1 ft . 0 5
! 6 . 3 7
16. ft 9
1 7 . 0 1
17.32
1 7.63
17.95
<8.?5
I 7 c;
.44
.87
i . "* n
1 . 73
7.16
7.58
3 . 00
3.47
7.P4
4 . ? *.
4.6ft
5.07
5.47
5.88
6.78
6.68
7 . o 7
7.47
7 . 8 6
8.7*
P. 67
9.0?
9.40
9 . 7 8
10.1*
10.53.
1 0.90
11.77
11 .63
1 7.00
n.36
17.7?
l 3 . i ; 8
1 3 . 4 7
13.78
14.13
14.48
1 4.83
15.17
1 * . 5 1
1 5 . P 5
16.18
1 6 . * 7
16.8 5
17.1 8
1 7 . c> 1
17.83
1 8 . 1 *
1 8 . 4 7
18.7 9
1 P. . o
.45
.80
1.3/4
1 .78
2 . 2 2
7.65
3 . o o
3.52
3.04
4.37
4. 79
5.71
5.63.
6.0-
6.46
6.R7
7 . ? ?
7 . 6 8
8.08
8.48
3.88
9.77
9.67
1 0.06
] 0.44
1 0 . 8 3
11.71
1 1.59
1 1 .97
1 7.34
12.71
' ' '
13.45
13.81
1 4 . 1 p
14.54
1 4 . P Q
15.75
15.60
i <-, . o 5
1 6.30
1 6.6^
i 6.09
17.33
17.67
1 8 . o 1
1 8. 34
1 8 . 6 7
19.00
I 0.33
18.*
.46
Q2
1 . 3P
1 ,R3
7.7P
2.73
3. 17
3.61
4 . 0 =.
4 . 4 0
4.03
5 . 3, ft
5.70
6.21
6.6^
7.06
7.48
7.8°
8.31
8.77
0.17
0.53
0.03
10.73
10.73
11.13
11.5?
n . 9 1
17.30
1 7 . 6 P
1 3. . 0 7
13. . 4 *
13.8?
14.? (j
] 4 r-. 7
14.94
1 5 . 1 1
15.67
16.04
16.4 0
16.75
17.11
1 7 . 4 ft
17.81
18.16
13.51
18. R*.
19.19
19.53.
19.87
I
.47
.94
1.41
1 .88
7.34
7.80
^.26
3.7]
4.16
4.61
5.v)6
5.50
5.94
6. 3«
6.8?
7.2C>
7.68
'8.11
8 . 5 3
8.Q*
0.37
9.79
1 o. 20
1 '.'.61
11.02
11.47
11.83
12.23
1 7 . 6 3
1 3 . 0 3
13.4?
13.81
14.? 0
14.58
1 4 . 0 ft
15.34
1^.7?
16.1 0
16.47
16.84
17.71
17.57
1 7.93
18.79
18.65'
19.01
19.36
19.71
2 0 . 0 6
? " . 4 ' J
10.*.
.40
.97
1 .45
1.93
7 . 4 0
2 . R 7
3. 34
3.81
4 . ? 7
4.77
*. 1 9
5.65
6.10
6.55
7.00
7.44
7 . R P,
8.3?
8. 76
0.10
".ft?
1 0.06
1 0 . 4 7
1 0.89
1 1 .3]
11.73
17.14
12.55
1 7.96
13.77
1^.77
14.17
14.57
1 4 . 9 7
1 * . 3ft
1 *..75
16.14
16.^2
16.90
17.70
1 7.66
18.^3
1 8 . 4 1
18.78
19.14
19.51
1 9 . 8 7
?-.? 3
20.58
7 i '.04
7 o . n
."^
.00
1 . 4 0
1 .OR
7.46
7 . O ft
7.4T
3..0]
4. 7R
4 . Pft
*.33
5. 70
6.76
6.7?
7. 1 R
7.ft3
P. OR
P. 53
P.oR
0.47
Q . R7
10.3 J
1.0.74
11.17
1 1.60
1 7.0,7
12.45
1 7 . P P
13. . 7 ()
13.71
14.13
1 4 . * 4
1 4.04
1 5 . 7 ft
1 * . 7 c
16. 1 5
16.**
16.04
]7.74
17.77
13.11
18.*')
1 3 . P R
19.76
1 9 . ft 3
70.01
70.7 8
70.7 5
21.11
7 1 . 4 P
-------
.05
.10
. 15
.20
.25
.30
.^5
.40
.45
.'SO
.55
'.60
.65
.70
.75
.80
.85
.90
.95
1.00
1.05
1.10
] . 1 5
1 .20
1 .25
1.30
1.^5
1 .40
] .45
1 .50
1 .55
1 .60
1 .65
] .70
1.75
1.80
1 .85
1.90
1.95
2.00
7.05
2. 10
2.15
7.20
7.75
2.30
7.35
2.40
7.45
7 . 5 0
70. s
.^1
1.0?
1.6?
2.03
2.53
3.07
3.5?
4.01
4.49
4 . 9 P
5.46
5.94
6.41
6.89
7.36
7.82
8.79
8.75
9.21
9.66
10.1 l
10.56
11.01
1 1 .45
1 1 .89
12.33
12.77
13.20
1 3 . 6 l
1 4 . 0 5
14.48
14.90
15.37
15.73
16. 15
16.56
16.96
17.37
17.77
18.17
18.56
18.96
19.35
19.74
70. 1 7
20.51
20.89
21.77
21 .64
22.01
21.0
.5?
1 .04
1 .^6
2.08
7.59
3.10
3.6 0
4.10
4.60
5.10
5.^9
6.08
6. ^7
7.05
7.53
8 . 0 1
8 . 4 9
8.06
9.4 '*
Q . o 0
10. ^6
10. p?
11.? 8
11.73
12.18
17.6 3
1~.08
1 3 . * ?
1 ?.06
14.4 0
14.8-
1 5. 76
1 5.69
16.1?
16.54
16.96
17.38
17.79
13.20
18.61
19.02
19.4?
1 9 . P 7
20.??
?0.6]
2 1 . 0 1
21.40
71 .78
72.17
2 7 . r- r>
21 . K
.54
1.07
1.60
2.13
2.65
3.17
'< . 6 o
4.7 0
4 . 7 1
r-. -% o
2 . /
5.7?
6.73
6.7-*
7.2?
7.71
R . ? v '
P. . f-. o
f-< . 1 7
9 . 6 5
1 0 . 1 ^
10.61
11.08
1 1 . 5 '-,
17.01.
17.47
1 2 . ° 3
1 3.^9
n . 8 4
14.79
14.74
1 5 . vq
1 5 . A. 3
16.07
16.5 0
1 6 . 9 3
17.36
17.79
18.71
1 8.64
19.05
10.47
1 c . q R
70.79
7 ''.70
71.11
71.51
7 1.91
??. 3u
22. 70
V3.MC!
7 7 . 0
.56
1 . 0 9
1 .64
2.17
? . 7 1
3.?4
*.77
4 .^0
4 . « 7
5. './f.
5 .86
6.37
ft . ^ 8
7.39
7.PO
8.3°
8 . 8 0
9.19
^ . P P.
10 . ' 7
10.8 r-
1 1 . °. 3
11.8]
17.79
1 7.76
1 ~ . 7 'J
1 T.70
14.16
14.6 3
1 5.0?.
T-'.^i
1 5.99
16.4 /,
1 6 . 8 8
17.53
17.77
18.7 (J
1 R . 6 4
1. v . 0 7
1 9 . 5 0
19.0?
70.35
70.77
71.18
7 1 . f '"'
? ? . 0 1
77.4?
2 7 . M 7
7 3.2?
7 "< . 6 7
77.6
.56
1 -1 ?
1 . 6 7
? . 2 ?
7.77
> . 3 7
3 . P 6
4.4'^
4 . 9 'I
"=. . /, <-
5 .QQ
6.5?
7.f'4
7.56
8.07
P . 5 °
Q. '.0
Q.60
10.1 "'
10.60
11.1°
11 .50
1 7 . ' ) °.
17.^7
1 3 . 0 5
1 ~ . 5 ^
1 4 . ^ ;
1. 4 . 4 9
14 .06
1^.4-J
1 R . P Q
16.35
16. P!
17.27
1 7 « 7 7
18.17
18.6?
lc'«06
1.9.5')
19.94
70.38
? 0 . 8 1
21 ,74
71 .65
7 7 . ' 9
77.51
77.93
73.34
? 3 . 7 5
74. 1 6
? 3 . 0
.57
1.14
1.71
2 . 2 7
2 . 8 3
^ o O
1 . 0 /,
4 . 4 o
5 . 0 4
C. . K 0
6 . i ?
6.66
7 . 1 «
7.73
8.?^
8 . 7 8
9. ?i>
9.81
1 0 . * 3
1 0 . 8 4
1 1 . ? t;
11 . R *
12.35
17.85
1 3.^4
13.8^
1 4 . > ?
14.81
15.? 9
15.77
1 6 . ? (\
15.7?
17.19
1 7 . 6 ^
1. 8.1?
18.58
19.03
19.4 9
1.9.94
70.^8
2 0 . P 3
71.77
21.71
27.15
72.5°
? 3 . 0 1
73.6 3
? 3 . M 6
? 4 . 7 8
' 74. 7 0
,?<*.^
.so
1.17
1.7^
? . 3 2
2.90
1 . 4 f,
4 . 0 ~
4 . c °
5. 1 r;
r, . 7 1
6. 76
6 . P 1
7 "* c
7 . P 9
8.43
8 . " 1
9.5-
10.0?
I 0 . ^ 5
11.07
1 1 . c °
17.11
17.6?
13. 1^
13.6^
1 4 . 1 4
1 4 . * >
15. 1 -»
15.67
16.11
16.60
17.00
17.^6
1 8 . 0 4
1 8 . r^ 1
18.°8
19.45
19."1
2 U . 3 7
7 n , p ->
71.78
71.7''
27.18
2 2.6^
2 3 . ^ 7
23.51
73.9/,
24.
74.81
75.73
7 /,."!
.60
1 . 1°
1 .73
7 . 2 7
2 . 9 5
3 . 5 '.
4.17
4.6"
5 . ? 6
H.PT
6.^0
6 . o "
7.^1
8.06
8.61
9 . 1 6
9.7-
1;'. 74
10.7 8
1 1 . ? 1
1 1 . P '4
17.37
17.8°
13.41
\"*.Q?
I 4 . 4 /4
1 4 . ° 5
1^.45
15.05
16.45
16.0^
17.44
17.°3
18.42
18.9 0
19.38
1 9 . H 6
70.3-3
? :> . 8
71 .?7
?1 . ?>
? 7 . ? -J
? 2 . 6 c-
2^.11
7 "J . K 6
?4.iJ'1
?4.46
74 .9-0
75.3 4
7^.7 7
7 4. 5
. 6 1
1 .??
1 .
5 . '; P.
6 . ° 7
6.66
7 . ? 4
7."?
8 . 4 0
8.97
9.54
10.1 '
i ^. t et~>
I 1 > 3
11.7 8
1 P . -53
i 7.88
13.43
1 3.07
14. ^0
15. ^4
15.^7
16.10
16.6?
17.14
1 7.66
18.17
M.63
19.10
19.6"
70. 10
20.^9
21.13
21.67
?2.i 6
??.64
- > 1 2
? -* . O
2 4 . ^ 7
? 4 . r- 4
75.0 1
76.47
7 5 . 0 3
26. 39
? '-. . P, 5
PAf.P- 6
-------
.05
.10
. 15
.20
.25
.30
.35.
.40
.45
.50
> .55
.60
.65
.70
.75
.80
.85
.90
.95
1 .00
1 .05
1 .10
1.16
1 .20
1 .25
1 .30
1.35
1 .40
1 .45
1 .50
1 .55
1 .60
1 .65
1 .70
1 .75
1.80
1 .85
1 .90
1.95
2.00
7.05
?. 1.0
2.15
2.20
7.76
?. "30
2.35
2.40
2.45
7.50
75.5
.64
1 .77
1.90
2.52
3.14
3.76
4.37
4.98
5.59
6. 19
6.79
7.39
7.98
8.56
9. 15
9.73
10.31
1 0 . 8 P
11.45
1 2 . 0 ?
17.58
13. 1A
1 8.60
14.75
14.79
1 5. 34
15.88
16.4?
16.95
1 7 . 4 3
18.01
18.5-3
10.05
19.57
70.08
70.59
21.10
21 .60
22. 10
22.60
7-3.09
73.58
74.07
74. 5 5
75.0 ->.
75.51
75.98
26. 4 p<
26.9?
27.38
76.0
.65
l.?9
1 .93
2.57
3 . 2 0
3.83
4 . 4 6
5.08
5.70
6.31
6.9?
7.53
8 . 1 3
8.73
9.33
9.9?
1 o . = 1
1 1 .09
11.67
17.7 5
17.8?
1 3 . A 0
1-3.96
1 4 . c. 2
1 5.08
1 5.64
16.19
16.74
1 7. 7H
17.33
IP. ^.6
18.90
19.4 3
19.95
70.48
?! .00
71.51
22.03
22.5^
?3.0A
7^.55
7 A . 0 c,
74.5 4
? 6 . 0 3
76. 6 7
76.01
76.49
76.97
2 7 . 4 5
77. 9 ?
76.5
.66
1.3?
1.97
2.6?
3 . ? 6
3.91
4 . 54
5. IP
5.31
6.47
7.06
7.67
8 . 7 0
8 . 9 0
9.51
10.11
10.71
1 1 . ° 1
11.90
17.40
1 3.07
1 3 . 6 r-
1-4.? 3
14.8 0
1 5 . 7. T
15.04
16.50
1 7.0A.
17.6?
18.17
13.77
1°.?6
10.3 0
7 0 . 3 4
70.87
71.4 3
71.93
22.45
22.97
?3.49
74.00
74.5 1
7 5. . 0 1
? 5 . M
76.01
? 6.51
? 7. on)
? 7 . 4 9
2 7 . 9 7
? 8 . 4. ,6
27.0
.67
1 .-4
2 . 0 1
2.67
3 . 3 3
3.98
4.63
5 . ? 8
5.9?
6 . 5 6
7. 19
7.82
8.45
9 . 0 7
9.69
10.30
10.91
1 1 . 5 ?
17.1?
17.7?
13.7-?
1 '> . 9 ]
1 A . 5 0
1 5.08
15.66
16.74
16.81
17.- 8
1 7 . 9 6
18.61
19.07
19.6?
70.17
20.7?
71.77
71.81
77.3 4
27.87
73.4 0
2^.9?
74. A ^
7 A . 9 7
? 5 . 4 8
7 6 . 0 0
7 6 . 5 1 1
77.01
? 7 . 5 1
7 8. '.'1
? 8 . 5 ' )
7P . o ?
1 1 .°5
1 ? . 5 7
13.19
13.81
1 4 . A 3
1 5.04
1 5.64
1 6. 24
16.8 4
1 7.4 4
I
18.61
1 9.-M,
1 0.7P
7 0 . -! c;
70. o?
7 .!. . 4 9
7 ? . 0 5
7 ? . 6 1
73.1 7
23.72
24.?7
? 4 . « ?
75. -36
?5.39
76.47
76.96
77.49
?8.0]
? 8 . 6 ->
29.04
79.56
3 > . 0 7
78.5
.71
1 A .'
7.1? .
2.8?
3.51
4 . ? 0
4.39
6.67
6 . ? 5
6.9?
7.5Q
3.75
8.9?
9.57
10.23
1 "!. 37
1 1 . c ?
17.16
1 ? . ° '
13.4-3
14.0^
14.6 P.
15.3 0
15.9?
16.57
17.1 4.
1 7 . 7 r.
18.^.
1 8 . 9 ^
1 9 . <= A
70. 17
2 o . 7 )
? 1 . 3 : *
?1 .87
? 7.46
23.0 ?
? 3 . 5 8
74. 15
74.7(1
75.? 6
? 5 . fl 1
76.^6
76.00
77.4 '4
77.98
73.61
79.04
79.56
30.00
3 0 . 6 o
?o.O
.7?
1 . 4 A
2 . 1 6
7 . H 7
3 . 5 7
4 . 2 7
4.97
5.67
6.86
7 . 0 4
7.7?
8 . 4 0
9.07
9.74
10.40
11.07
11.77
i 7. ^7
n.07
n . 6 7
14.3]
14.94
15.57
16.7 0
16.3?
1 7.44
1 8.06
18.', 7
1 0 . 7 0
1 0 . D R
7^.4 a
7 i . r .3
71.67
7 V . 7 A
77.3 4
?3.4?
24.00
74.57
2 5.14
? 5 . 7 0
7 6 . ? 6
76.8?
7 7 . 3 7
?7.9?
7 8 . 4 7
-> n o i
. i
79.55
30.08
3 ' ' . 6 1
31.14
79.5
.74
1.47
2.19
2.92
3.63
4 . 3 '}
5.06
5.75
6 . 4 7
7.16
7.86
3. 5 A
0.73
9.91
1 . 5 3
1 1 . ? 5
11.07
1 ? . c o
1 7 . ? 6
13.90
1^.56
15.70
15.R4
16.48
17.11
17. 7A
18.3 7
18.00
1 c . 6 1
. '.
> - . q T
71 .44
7 ? . 0 4
? 7 .64
? "3 . ? 3
? 3 . 8 ?
7 A . 4 1
74.99
25.57
76. 14
76.77
77. 73
? 7 . 8 4
78. VO
? 8 . 9 6
?°. C>1
'0.06
3 < i . 6 )
31.1 4
'' ! . 6 8
3 " . o
.75
1.40
2. ?3
2.97
3.70
4.4?
5.14
- . Q6
6 . 5 7
-*.->*
7 . 0 0
8.6Q
9.33
10.03
10.75
1 1.45
1 "> . 1 3
17.30
I'3 . 4 '
14.14
14.30
1 5.46
16.11
16. 76
17.4 j
18.05
18.63
. * 1
' Q . ^ A
->"!. r. -7
1 I . i O
7 1 . QP
^ 2.4?
i 3 . 0 7
? '< . 6 *.
24.73
24.32
2 5 . 4 2
26.00
26-59
7-7.74
?8.72
78.78
? 9 .4 6
^ f\ f-i I
3 0 . p-- 7
n . i 2
"J. 1.67
3 ? . " I
-------
70
71.0
79.0
13 A . 5
.05
. 10
. 15
.20
.25
.30
.35
.40
.45
.50
.55
.fin
.ft 5
.70
.75
.80
.85
."0
.95
1 .00
1 .05
1 .in
1.15
1 . ? 0
1.25
1.30
1.35
1 .40
1 .45
1 .50
1 ,5S
1 .60
1 .65
1.70
1.75
1.80
1.85
1.90
1 .95
2.00
7.05
2.10
2.15
2.2n
2.25
2.30
2.^5
2.40
2.45
2.50
.76
1 .57
2.27
3 . 0 .1
7.76
4.50
5.7?
5.96
6.6°,
7.40
8.12
8.87
9. "W(
10./4
10.94
1 1 .64
12.37
17.01
1 3.70
14.37
1 ^.os
15.71
16.78
17.04
17.69
18.35
18.9Q
19.64
70. ?8
20.91
71.54
22. 17
22.79
23.41
24.02
24.67
25.24
25.84
26.44
27.03
27.52
28.21
78.7Q
29.37
29.94
30.51
31. OR
31 .64
72.^0
32.75
.77
1.54
?.7(l
3.06
7.82
4.57
<=. . 7 ?
6.06
6.70
7.53
8.25
R.98
0.70
1 n . 4 1
11.12
11.87
17.^7
1 7 . 7 '>
1 ->.97
14.61
1 r^.?9
15.07
16.6 c>
1 7 . -> 7
17.08
18.65
19.3 1
lc>.96
70.61
21.2 r>
7 i . P 9
7 7 . =, 7
77.16
27.79
24.42
25.04
25.65
26.26
26.87
27.47
28.07
28.67
29. 76
2 9 . R «=
70.4^
71.01
3 I . 5 '3
37.16
37.77
37.79
.70
1 .^7
7 . * 4
3 . ] 1
3.88
4 . 6 4
^ . '. 0
6. 1 ci
6 . o o
7 . 6 5
8.70
9. 1 7
o . 7c;
1 0 . 5 8
11.7 0
12.0 7
1 ;- . ~> *
1 3.4.':.
14.i 4
1 4 . 8 4
15.^ 4
1 6 . "> '*
16.9 7
1 7.60
1 8 . > ?
18.95
19.6 7
70.73
70.94
21.60
2 2 . 7 ~<
77.8 9
2 3 . 5 4
24. 1 8
24.8 1
2 5. A 4
2 6 . 0 7
26.6°
27.70
27.07
78.57
79.13
29.7 7
70.70
30.9 2
71.51
72.1 0
7 ,? . ft ft
7 7 . o S
7 7 . H 7
.80
1 .59
2 . 7 a
7.16
7 . 9 4
4.77
5 . 4 9
6.75
7.01
7.77
8.57
9 . ? 7
1 0 . 0 1
1 0 . 7 5
1 1.48
12.71
17.07
1 3 . f, f,
14.77
1 5 . 0 8
1 5. 79
1 6 . 4 9
17.18
17.88
18.56
19.2 s
19.9 3
70.60
71.77
21 .04
77.60
77.76
27.91
24.56
25.70
25.84
26.48
27.11
77.74
78.36
28.08
79.59
70.70
70.81
31 .M
77.0 1
37.60
73.1 o
77.7 f*
74.3 6
.81
1 .67
2.4.7
3 . 2 !
4.-01;
4.79
r- . 5 7
6.^r<
7.17
7 . 8 o
P . 6 5
9.41
10.17
1 0 . 9 7
1 1 .66
1 ? . 4 0
1 7 . Vi
1 7 . 8 7
1 /. . ') 0
1 -i . 3 '.'
16.07
16.74
1 7 . 4 5
1 8 . 1 ft
18.85
1. 9 . 5 6
2 0 . 7 4
? o.o?
?1 .61
22.28
7 7 . QC
77.6 7
24.7 8
24.9 4
25 .60
26.2^
26.89
27.53
28.17
28.80
7^,47
70,; 06
70.68
71.79
31 .90
37.51.
3 7 . 1 1
> 'J . 7 1
3 4 ; 3 '!
74.°t<
.8?
1 .64
2.4=--,
3.76
4.07
4 . 8 6
5.66
6.45
7.?"'
8.^1
8.79
9 . 5 6
10. 77
1 I . n 8
1 1 .84
12.59
1 7 . 7 /,
1 4 . P 8
1 4 . « 7
15.5 S
16.78
1 7.00
17.77
1 5 . 4 4
1.9.1 5
19.85
70.55
2 1 . ~ 5
? ] .94
72.62
7 7 . 7 1
2 3 . 0 p,
24.66
25.3 3
25.09
26.6^
27.31
27.06
28.60
29.2 5
79. 89
7 0 . 5 2
7 1 . 1 *
7 1.77
72. ^9
33.01
33.62
34.?7
13 4 . 8 4
7 5 . 4 A
.°.4
1 .67
7. 40
3.31
4.17
4.9A
^.7'!
ft . ^
7.74
8. 1 =
8.97
o. 70
1 'i. V
11.2-
17.0 ?
1 ? . 7 P
n . 5 /.
14.? °
1 => . 0 4
15.7 9
16.57
17. ->ft
17.99
1 R.71
1°.44
20.15
2 0 . 8 6
2 1 . r! 7
27.2 7
77.0 -?
7°. 66
24 . 7«=
2 c . 0 7
2^.71
26.78
2 7 . 0 c,
27.72
28.38
29.04
29.6°
°0.7/4
3U.9R
31.62
^2. 2C-
37.89
37.51
34. 13
34.76
35. 7f,
7 S ^ c, -/
.«r->
1 .69
7.5^
3.36
4.10
5.') 1
^.33
ft . ft 4
7 . /. 5
8 . 7 5
9 . ( ' 5
9. 86
1'W*
11.4 ?
1?.2 0
12.07
1^.7 4
14.5!
i ^ . "> 7
16.02
16.77
1 7.52
18.76
1 ft . ° °
1 » . 7 7
2 0 . 4 5
21.1 ''
7 1 . P 0
7 > . 6 "'
27.71
?4 . 01
7/-.71
7^.41
?. 6 . 0 9
76.78
77.46
78.1.7
28.80
29.47
70.13
70.79
''I.. ^4
39.00
^2.74
7 7 . 3 p
7 4 . 0 1
74 .64
35. ?7
^5.89
36.51
.86
1 .7]
7.R-7
7 . 4 1
4 . ? 5
[T.O('
5.97
ft . 7 '<
7.^6
8.38
9.1°
9.0Q
T-.70
1 1.59
12.38
1 7 . 1. 6
17.04
1 ':- .77
1 =^ . 4 O
1 6 . 7 6
1 7 . 'V
1 7 . 1 H
18.53
1 o . 7 7
70.07
? '."' 5
2 1 .48
p 7 . - i
7 -1 . Q '-
2^.6=-
74.77
75.07
7^.78
26.48
2 7 . 1 7
27.8ft
28.55
29.2?
29.90
30.^8
71.74
^1 .o]
77.56
? ? . 2 2
, 7 7 . P 7
'34.51
^5. 15
35.79
76.4?
7 7 . 0 ^
. .T7
1. ''4
2.60
7.46
'* . ^ 1
5.16
6.00
fs . Q 4
7.6"'
Q . c,(>
0.7?
'0. 14
10.0=,
1 1 . 76
1 ? . 5 5
1 7.7^
1 4 . i ^
1 A . m
15.7 7
16.49
17.7?
1 8.07
1 «.8C
TO.CC^
7 0 . 7 1
2 1 . o c-
71 . QT
-1 7 . "- "
-> -3, f -,->
24. "(.'
74.7?
7 c, . 4 4
26. 1 *
2 6 . " 6
27.^7
28.77
2P.n6
2 9 . 4, 5
3 0 . > 4
31 .02
^1 .70
3 2 . 3 7
^7. ^4
7 7 . T
34. 75
36.01
35.66
36.3 1
36. OS
3 7 . c. 8
-------
35.5
36. 0
36.
37.0
37.5
3 ') .
.05
. in
. 15
.20
.25
.30
.35
.40
.45
.^0
.55
.60
..55
.70
.75
.80
.85
.90
.95
1 .on
1 .05
1.10
1 . 15
1 .20
1 .25
1 .30
1 .35
1.40
1 .45
1 .50
1 .55
1 .60
1.65
1.70
] .75
1 .80
1 .85
1.90
1 .95
2.00
2.05
2. 10
7.15
7.20
7.25
2.30
2.35
2.40
2.45
2.50
.RR
1 .76
7.64
3.M
4.37
5.73
6.09
6.° 4
7.7R
8.6?
9.45
1 0 . ? R
11.11
11.Q2
1 2.74
13.^5
14. 35
15. I*.
1 5 . o 4.
16.7?
17.51
18.79
19.06
19.8"
20.60
71.35
77.11
22.86
23.60
24.34
25.07
25. RO
26.5?
27.25
77.°6
28.67
29.38
30.08
30.77
31.46
32.15
3 2 . R 3
33. M
34. 18
34.85
35.51
36. 17
36.82
37.47
38.17
.90
1 .79
2.68
3.^6
4 . 4 4
5.?1
6. 17
7.03
7 . 8 9
R.7/<
9.^9
1 n . 43
1 i . ">6
12. 09
17.92
13.74
1 4 . c e-
15.36
16.17
16.96
17.76
1 8 . 5 c.
19.3?
2 0 . 1 1
70.89
71.65
77.4?
73. 18
73. 0^
74.68
75.4-5
76. 1 7
76.90
27.63
78.35
29.07
79.79
30.50
31 .70
31 .91
37.60
33.29
33.08
34.66
3 ^ . 3 4
36.01
36.68
37. ''4
38.00
58.66
.°1
1 .PI
2.7!
3.61
4 . K 0
5.38
6.76
7 . 1 '>
o.oo
R . P. 6
0.7?
10.^7
1 1 . /. 7
1 2.26
1 ? . 1 0
1 i. . 9 3
1 4 . 7 c
1 K.C7
16. '9
17.70
18.01
1, P . R 1
19.60
2 0 .30
21.18
71.96
?2.73
73.5 C
24.?6
7 5.02
75.78
7 6 . c 3
7 7 . 7 7
2 8.01
78.7*
29.48
30.20
30.92
31.64
32.35
?3. 05
33.76
? 4 . /. 5
? 5 . 1 4
?5.°3
36.51
37.19
3 7 . P 6
? 8 . c 3
30 . 1 o
.92
1 .84
2.75
3.66
4.56
5 . 4 5
6.34
7.23
P. 11
8. OR
o . 8 5
10.72
11.^7
1 7.4.3
13.78
14.1 2
14.96
1 S.79
1 6 . f 1
17.44
18.75
19.06
19. R7
70.67
71.47
72.26
73.04
73.8?
74.60
75.37
76. 1 3
76.89
77.65
28.40
79.14
29.88
30.62
31.35
37.07
37.79
3 ? . 5 1.
?4.7?
34.°?
35.6?
36.32
37.01
37.70
38.3 8
39.06
3 9 . 7 3
.93,
1.86
2.79
3.7]
4.67
=..53
6 . 4 ?
7.33
O 1 'v
1 ' / ,'
9 . 1 0
O . Q O
1 0 . P 6
1 1 .-*>
12.6'V
1 3.4-r.
14." ]
1 5 . 1 (-
1 A . P n
1 4. . P 4
17.67
IR.^o
19.3?
2 r . 1 4
20.95
21 .76
27.56
2 3 . 3 <,
24.1 4
24.0?
25.71
? 6 . 4 9
77.76
7 R.C.1 7
78 ,,78
29,^4
30.2 9
31.03
31.77
37.51
33,24
33.96
34.6 8
35.40
36.1 1
36. PI
37.51
38.71
3R.90
3 9 . 5 Q
4fi.27
.95
1 .89
2.8°
3.76
4 . 6 8
5.60
6.5?
7.4?
8.3^
° . P °
1 ' ; . 1 ?
11 . r> 1
1 1 . O Q
1?."76
1 ? . 6 3
1 4 . c. f
1 5.36
1 *>.?!
1 7. '"'6
! 7 . 9 1
18.75
1 0 . ^ R
70.41
2 1 . 2 3
22.05
22.86
73.66
? 4 . 4 7
7^.76
76.05
76.04
2 ^ . 6 2
28.3°
29.16
2 9 . o ?
30.6 9
31 .44
32.19
32 .04
3.3. ftR
34.41
35.14
35.87
36.^9
37. 3()
? 8.01
38.72
39.4?
4 0 . i l
4 0 . P 0
.CV,
1 .°1
7.86
3.81
4 .74
5.67
6.6'"'
7.^7
R . 4 4
q . TC
1 0 . ? R
11.1-
1 -1 . ^ 4
1 2 . ° 3
13.81
1 4 . 6 9
15.5 6
16.43
17.79
18.1 4
18.90
19.8 4
?o.ft7
2 1 . M
72.34
23.16
2 = . 9 R
24.70
"> t co
.... ... .
26.4 0
27.19
7 7 . 0 R
2R.77
29.55
3 0 . 3 7
31.09
31 .86
32.62
33.37
34. 12
34.87
35.61
36.34
37.07
37.79
38. cl
39.73
39.94
4 0 . 6 4
41.34
.'57
1.94
?.or
3.8^
4 . 8 0
5.75
6.69
7 . 6 ?
q . s ,-,
0.4/7
1 o . 3, a
11 "5 n
1 i
-,-..-> -,
1.3.] 0
13.00
1 4 . R 8
1 5 . 7 6
16.64
17. M
1 R. 3R
19.24
?:. 09
7 " . ° 4
21 ."'9
22.63
2 ? . 4 6
2 4 . 2 9
2 c . 1 1
-> C ^ O -3
26.74
?7.54
7 P. . ? 5
?9.1 4
29.93
30.7?
31 .50
37.27
33.04
3 3 . R 1
34.56
°5.3?
0 6 . o 7
36.81
37.^^.
38.78
3 o . ; .. i
? 9 . 7 4
4'.l . 46
41.17
41.8 R
. o o.
1 . " 6
7.94
3 . Q 0
4 . R 7
5.R?
6.77
7 . 7 2
8 . 6 6.
o . RO
1 > . s. ?
11.4 4
1 "5 . 3 f,
13.27
14.17
1 ^ . 0 7
1 5 . 9 7
16.°^
1 7. ^4
1 °. . 6 1
19.4°
7 -1 . ? 5
71.71
22.0 7
2 ? . 9 2
2 3 . 7 5
24.60
"": . 4- 3
2 6 . 7 6
27.08
27.9'!
? R . 7 1
29.51
3,,. 3 2
3 1.11
31 .90
32.69
33.46
34.24
35.01
TS.77
^6.C3
"> 7 . ? P.
3 R . n 3
3R.77
39.51
4 0 . 2 5
4 u . 9 7
41.7.-'
42.4?
1 .no
1 .OC!
2.0-7
?.°5
4.03,
5 .o,>
6 . P, 6
7.0".
q<--7
">.-'1
n . 6 c
i ' r o
- n . c 1
1 " . 4 4
1 4 . 3 . c
1 5. ?fc
16.17
1 "7. "7
17.o^
1 ° . ° c>
IQ.TO
? n . A, i
' i . 4 P
; 7.^5
2 ? . 7 1
24.06
74.01
?5.?5
7 6 . c 9
27.4 ?
7 P . 7 S
oo . "7
2 9 . R 9
30.70
31.^0
32.3 J
33.1 0
33.89
? 4 . 6 7
35.45
3 6 . ? 2
36. oo
37.76
38. cl
39. 27
40.0 1
40. 76
41 .4 c>
42.23
47.o f.
- R
-------
40.5
4i.o
47.0
47.5
L 4 . 0
4 . ^
45.0
.05
.10
. 15
.20
. 75
.30
.35
.40
.45
.50
.55
.60
.65
.70
.75
.80
.85
.90
.95
1 .00
1 .05
l.io
1.15
1 .20
1.25
1.30
1 .35
1 .40
1 .45
1 .50
1.55
1 .60
] .65
1 .70
1 .75
1 .80
1 .85
1 .90
1.95
?.oo
7.05
2. in
7.15
7.70
7.75
2.10
2.15
7.40
7.45
7.50
1.01
7.01
3.01
4.00
4.99
5.97
6.°4
7.91
8. PR
o . PI
10.78
1 1 .71
12.67
1 3.60
14.53
15.45
16.37
17.78
18. IP
19.08
19. Q8
70.87
71 .7^
? 2 . 6 3
23.50
24.36
25.27
26.08
26.07
27.77
78.60
79. 44
30.76
31.08
31.90
32.71
33. 51
34.31
15. n
15.89
36.68
37.45
18.7°.
38.99
39.76
40.51
41.77
42.01
42.75
43.49
1 . 0 7
7.04
3.05
4.05
5 . 0 5
6.04
7 . 0 ->,
8.0]
P.°9
O . oc,
10.97
11.87
17.81
1 i. 77
14.71
15.64
16.57
17.49
1 8 . 4 1
1 9 . i 2
20.71
71.17
7 2 . 0 2
22.90
23.7 9
24 .66
25.53
26.40
27. ?6
28.1 1
28.96
70. PO
10.64
31.47
32.29
33.11
33.93
34.74
35.^4
36.34
37.13
37.92
38. 70
1 0 . it 8
40.? 5
4 1 . 0 1
4 1 . 7 7
47.5 1
43.78
44.0 3
1 .03
7. Oft
3.00
4.10
5.11
6.17
7.17
8.11
o. no
10. OR
n .05
12.0?
1 7.98
1 "* . ° 4
1 4 . P 9
] 5 . P 3
16.77
17.71
18.63
19.56
70.^7
71.^8
77.70
7 i . 1 8
2 4. OB
24.96
75.8 4
76.7 7
77.5 9
7 8.45
79.11
30. if,
3 1 . 0 1
31.85
17.60
33.57
14.14
36.16
15.07
36.78
37.53
38.18
10.17
19.0 6
40.74
41.5 ]
.'. 7 . 7 F.
4 3 . n c,
4 3 . P, 1
4 4 . 5 *
1.05
7.09
3.17
4.15
5.17
6.19
7 . 7 0
8.71
9.70
10.70
11.18
17.16
13.1 4
14.11
15.07
1 6 . 0 3
16.98
1 7.07
18.86
19. 79
70.77
7 1 .64
7 2 . r- 5
73.4 6
2A.^7
75.76
76. 16
77.04
27.92
28.79
79.66
10.53
11 .38
37.71
13.08
11.92
14.75
35.58
36.41
37.7?
18.0 4
38.84
10.64
4 0 . 4 4
4 1.71
4 7 . 0 1
4 7 . 7 9
4 1 . 5 7
44.3 4
46.10
1
7
3
<4
R
6
7
8
0
1 o
1 1
1 7
13
14
1 5
16
1 7
18
10
70
70
2 1
77
?i
24
25
26
77
78
29
If)
10
31
17
11
14
3r>
36
3^
37
38
30
40
4f)
41
4 7
4 1
44
44
4c;
.06
.1 1
. 1 6
. ? :
.24
.76
.2°
.3!)
.°1
.1?
.37
.31
.79
.27
"> t;
'- j
.72
.1 8
.1 i
.08
.01
.07
.on
.87
.74
.66
.56
.47
.36
.2*
.14
.02
.89
. 76
.62
.47
.37
.1 1
. 0 1
.84
,67
.49
.30
.17
,,07
.7?
.'-I
.1C
.09
.86
.64
1.07
7.14
3.70
4.75
5 . 1 0
6. i4
7 . * 7
8.40
9.47
1 0 . i, 4
11 .45
17.45
1 3 . 4 5
14.4 4
15.4''
1 6 . M
1. 7 . 1 8
1 8 . * 5
1 9 . T 1
70.76
71.71
7 ? . 1 5
71.09
74.07
24.Q5
25.87
76.7 8
77.6 8
78.59
79.48
3 0.37
11 .75
37.13
33.00
13.87
14.73
15.58
36.43
37.27
38.11
33 .°4
19.77
40.59
4 1.40
4 7.71
4 1 . 0 1
4 3 . 8 1
4 4 . 6 0
4 'i . 3 9
46.1 7
1 .08
2.16
1.7 ^
4.^0
5.16
6.41
7.46
8 . * 0
O . c. 1
10.* 6
1 1 .^8
1 7.60
13.61
14.61
15.61
16.6 f
1 7 . c 8
1 8 . c 6
10. c^
20.* f>
71.4 6
77.41
73.16
24. i J
25.24
26.17
77.09
2«.0]
2 8 . 9 7
29. P 7
30.77
31.62
32.50
11.10
34.2 6
35. l^
36.00
36.85
37.71
38.55
39.19
40.71
4 1 . n 6
41.88
4->.70
4 i . * 1
44.3 ?
45.1 7
4 5 . 9 7
46.71
1.1"
'> . 1 °
1.77
4.36
5.42
6 . 4 o
7.54
8.60
Q.64
1 0 . f- P
11.77
1 7.76
13. 76
1 A . -7 °
15.70
16.79
17.78
18.77
1°.76
70. 71
71.71
27.67
73.63
74.58
25.53
26.47
7 7 . 4 0
28. J'3
79.75
1 0 . 1 7
31 .'08
11.98
37.88
11.77
14.6^
15.5 i
36.41
17.7 8
18.14
19 . ui'i
1 9 . 8 r>
4 ".6 9
4 1.51
4 2 . 3 6
43.1 9
44.01
4 4 . M 3
4 c> . h 4
4 6 . 4 6
47.2 f,
1.11
? . 2 1
i.il
4 . 4 .'I
5 . 4 3
6 . 5 6
7.61
8.6°
o.75
i-vao
11.85
1.7. 89
11.97,
14.05
1 * . o 7
16.98
1 7. 99
I8.oo
1".38
?c.o7
71.9 5
77.91
71.9')
74.86
2.5.82
26.77
77.71
78.65
29.58
-> 0 . 5 1
1 1.43
17.14
13.26
14. 1 5
15. n ^
15.04
16.5? 2
I"7. 70
18.57
19.44
40.3 0
41.15
47.00
42.8 5
4 3.68
4 4.51
4 5 . 3 4
46.1 6
4 6 . 9 8
4 7 . 7 M
1 . 1 7
2.^-4
3.^5
4.46
5 . c' 4
6 . 6 1
7. -»2
8. 79
0.06
1 0 . o i
1 1 . ° Q
1 i . "i
1 4 . ^ 8
15.11
16.15
17.17
1=1. 19
1 9 . 7 c
>-.? i
.? 1 . 7 1
?~> . 70
73.18
24. 1 7
25.14
26.1 1
27.07
28.02
7 8 . -? 7
2°. 92
3 0 . 3 5
3 1.78
17.7]
3 1 * ?
34.54
15.4 4
36.14
3 7 . ? 4
18.17
1Q.01
39.98
40.75
41.67
42.47
41.1 1
44.1 7
4 ^ . ") 1
46." 5
4 6 . 6 8
'! 7.50
4 R . 1 2
PAGE- 0
-------
45.6
46.
4 7.0
47.5
4 8 . 0
48.5
A 0 . '1
69.6
5 0 . <">
.05
.10
. 15
.20
.25
.30
.35
.40
.45
.50
.65
.60
.66
.70
.75
.80
.85
.90
.95
1 .00
1 .05
1 .10
1.15
1 .20
1 .25
1.30
1 .35
1.40
1.45
1 .50
1 .55
1 .60
1.66
1 .70
1 .75
1 .80
1 .85
1 .90
1 .95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
1.13
2.26
?. 38
4.50
6.61
6.71
7 . 8 0
8.89
9.P7
11.05
12.12
13. ]R
14.7?
15.78
16.37
17.36
18.39
19.41
70.43
71.44
77.45
73.44
74.4?
75.4?
76.40
27.37
28.33
29. 2P
3 0 . 2 6
31 .IP
?2.16
??.07
34.00
34.92
36.84
36.75
37.66
38.55
39.4 4
40.33
41 .21
42.08
42.95
43.81
44.66
45.5?
46.36
47. 20
48.03
48.86
1.15
2 . 2 9
3.47
4.56
6.67
6.78
7.89
8.99
10. OR
n.l7
I 2 . 2 *
1 ? . 3 7
1 4 . * P
1 5.45
16.50
17.55
18.59
1°. 6?
71"!. 66
?1.68
7 7 . A P
7?. 70
76.70
75.70
76.69
77.67
78.65
79.67
? 0 . 5 R
31.5 4
37.49
?? . 4 ?
34.37
36.30
36.7?
37. 15
38.06
38.97
39.87
40.77
41 .66
47.54
43.4 ?
44.7 9
45.16
46.0?
4 6 . 8 7
47.7?
48.66
4 P . 4 0
1.16
7.31
3.66
4 . 6 0
5.7?
6.85
7.97
9 . 0 9
1 0 . 1 P
1 1 . 70
1 7.?8
1 ? . 6 7
14.6 6
15.6?
16.68
17.74
18.79
1 P . 8 4
7 0 . fl R
71 .°1
7 7 . P 6
73.06
7 4 . P 7
7 5 . P R
76.98
77.97
2 8 . 9 6
2 P . P 4
3 0.01
si .RR
37.84
??. RO
34.75
35.6P
?6. 6 7
37.55
3 8 . 4 8
39.6 '.)
6 0 . ? 1
41.71
4 2.. 1 1
4?. 00
43.80
44.77
66.65
46.57
47.? 8
48.? 4
49. 0 P
6 9.93
1.17
2.34
3.49
4.65
6.79
6.93
8 . 0 6
9.13
1 0 . ? r
11.61
17.61
1 ? . 6 1
14.7 0
16.79
16.86
17.93
1 9 . 0 u
2 0 . 0 5
21.1 0
77.15
??. 1 8
? 4.7?
?5.74
76.76
7 7.77
28.27
29.27
30.?6
^1.74
37.77
??. 19
34.16
35.1?
^6.07
? 7.0?
37.06
? 8.89
? 9 . 8 7
60.74
4 1.65
67.5 6
6 3.47
4 4 . ? 6
46.76
46.14
6 7 . 0 ?
47.8 9
4 8 . 7 6
4 9 . 6 1
5U.47
1.18
7.36
-.57
4.70
£ .85
7.^1 )
8.14
P . 7 8
1 o . 4 1
1 1 . ' "3
1 7.66
1 > . 7 6
1 4 . R 6
15.96
17.04
18.1 7
1 P . ? ' !
7 0.77
7 1. . 7 3
7.7.? 8
7-5.4?
76.47
75.61
26.54
27.66
28.5 7
2 9 . 5 8
30.58
?1 .58
37,57
? ? . 5 5
^ 6 . 5 7
35.4 9
?6.46
? 7.41
? 8.36
? 9 . 3 1
40.2 4
41.17
47?10
4 ? . 0 7
43.97
4 4 . R ?
45.73
4 6 . 6 7
47.57
48 i -<-''
4 0.77
5 0 . 1 4
61 .01
1. .70
2.39
^.67
4.74
5.91
7.08
8.23
9.38
If1. ^7
n. ^
1 2 . '' 8
1 T.DO
1 5 . ~> 7
16. 1 2
17.??
\ 8 . 3 7
19.4')
2 ' > . 4 8
7 1. . * 5
? 2 . 6 2
7 7 . 6 R
? 4 . 7 ?
25.78
26.8 2
27.85
28.87
2 9 . 8 P
30.90
? 1 . P 1
77.01
3 T O , "i
? 4 . R P
35.87
36.84
? 7 . 8 1
38.77
^9.72
60.67
4 1 . 6 1
42.54
43.4 7
44. ->0
4 5 . > 1
46.2?
47.1 2
4 8 . 0 ?
4 8.91
49. 79
50.67
5 1. . 6 4
1.7]
2.41
"* . 61
4.79
5.97
7.15
8.32
P . 4 8
lO.f?
1 i . -">
l?.Pi
1 4 . 0 5
15.17
16.29
17.4 0
18.61
19.60
20.69
21.78
2 ? . R c
7 ° . P ?
76. 9 P
26.06
27.09
28.1 4
29. 17
30.? 0
31.??
3 ? . ? 4
3 ? 7 5
36.76
3 5 . 9 r,
36.?6
37.7?
3R.70
39. 1.7
60.13
6 1 . 0 9
4 7 . 0 6
47.9 8
4 ? . o 7
44. 86
46.78
46.70
47.61
48.6?
49.42
60.31
51.20
57.08
1.7?
7.44
0 . 64
4.84
6. .(-4
7.7?
S . 4 0
P . 5 7
1 ^ . 'V /i
M . o -
13.05
1 4 . 1 P
16.3?
16.46
17.5 R
18.7 0
1 P . R 1
*> r1 o i
7 7 . ° ^
7-5 . - IP
?6. 1 7
25.75
7 6 . ? 1
27. ?7
7 8 . H 3
29.47
3 f . 6 1
31.66
77.57
7-5.50
? 4 . 6 1
? 5 . 6 1
? 6 . 6 .1
37.61
3R.59
3 9 . r- 7
4 0 . c 5
4 1 "=> 1
6..7.47
4 3.63
6 6 . -> 7
4 5 . 'J ?
4 6 . 7 r>
47. 1R
4R. 10
4 9 . 0 ?
49.93
50.8 3
51.7 3
57.6?
1 .73
7.46
? . 6R
4.89
6 1 0
7.30
8.49
P. 67
1 n ^ q c.
1 -5 . ^ 7
1 ?. 1 8
1 6 . ? 4
1 r- . 4 8
16.63
17.76
n.S9
20.01
71.17.
"> "> 7 T
. .
? ° . 3 ^
76.4 2
75.6 0
76.^8
77.6 5
78.72
29.73
7 i.1 . 8 3
?] . R7
37.01
^.P4
''6.96
75.00
36. Q9
'} ~1 O O
.
13 8 . 0 P
3 9 . P 8
6 C . r> 6
61.94
6 2 . ^ 1
67.37
4 4 . ° Q
6 6.78
46.72
47.66
'48.59
69.5?
5 0 . 4 4
61.3 5
57.25
^ 3 . ! 6
1 . 7 6
2.49
3.72
4.P4
6.16
7.77
:J. 5 7
9.77
1 ^ . o A
> > . - /i
1 3 . 7 1
1 4 . 4 R
1 t; . 6 4
16.79
17.P4
I 9 . 0 R
2 0 . ? 1
0 1 * 3
^7.66
7-5 . =6
7 6 . A 6
? 5 . 7 6
26."5
27.9?
2 P. 01
3 O.OB
31.14
? ? . -"-5
? ' . "> 4
* 6 . 7 a
OQ . 3 1
0 6 . ? '+
37.? 6
? P . ? 7
3P. -3R
6 0 . -3 R
6 1 . ? 7
4 2.^6
'. -J . -5 4
4 4 . ? 1
66.7 8
66.7 4
4 7 . 1 P
48.1 4
4 9. OR
50.0.7
6 0 . '' 4
5 ! . R 7
57.7 8
L-3.69
p A r, F -1 o
-------
so.s
51 .
- 4. s
.05
. 10
. 15
. 2 0
.26
.30
.35
.40
.AS
.^O
.55
.60
.65
.70
.75
.80
.85
.90
.95
l.oo
1.05
1 .10
1.15
1 .20
1 .25
1.30
1 .35
1 .40
1 .45
1 .50
1 .55
1 .60
1 .65
1 .70
1 .75
1.80
1.85
1 .90
1 .95
7.00
2.05
7.10
?.15
2.20
7.75
7.30
7.35
7.40
2.45
2.50
1 .76
2.51
3.75
4.99
6.2?
7.44
8.66
9.87
1 1 .07
12.76
1 3 . 4 S
14.63
15.80
16.96
18.17
1.9.27
70.41
21 .55
72.68
73.80
74.91
26.0'
77. 1^
28. 2 :
29.30
30.38
31 .45
37.51
33.57
"44.67
"45.67
36.70
37.73
38.76
39.77
40.78
41 .79
47.78
4^.77
44.76
45.7-4
46.70
47.67
48.6''
49.. 57
50.57
5 1 . 4 S
52. 3 8
5^.31
5 4 . 2 3
1.77
2.54
3.79
5.04
6.78
7.5?
8 . 7 4
9.96
1 1 . l s
1 7 . -> 8
1 3.^8
14.77
15.95
17.13
18. -V)
19.46
70.61
21 .76
77.^0
?'f.03
7 s . 1 6
76. 7 8
?7.?o
78.49
79. 5 9
30.68
31.76
37.84
3^.90
34.97
36.07
37.07
38. 1 }
39. 14
40. 1 7
41.19
47.70
43.7]
44.71
45.7 0
46.1 9
47.1 7
4 P . 1 4
49.10
50. '"'6
S] . 07
51 .96
57.90
53.84
5 4 . 7 6
1 .78
2.56
3.H3
5.09
6.^4
7. 69
R.8-4
1 0.06
1 1 , 9O
1 7 . S 0
1 "4.71
14.9 2
16.11
17.30
1 8.i8
19.6 5
2 0 . 8 ?
71.97
73.' 7
74.?7
75.4 0
76.53
77.66
78.7 7
79.88
30.98
32.07
33.16
34.74
45. -M
3 6 . ? 7
^7.4. 3
? 8 . 4 R
39.53
40. Sf
41.59
47.61
43.63
4 4 . 6 4
45.64
46.6 4
47.63
48.61
49.59
5 0.55
s 1 . 5 ?
5 7 . 4 7
5 3 . 4 7
5 4 . 3 6
55.30
1 .30
2.58
4.37
5.14
6.M
7.66
8 . 9 7
10.16
1 1 . 4 0
17. A?
1^.85
1 5.06
16.77
17.47
18.66
19.84
71.i.) 2
77.19
7 3 . 3 5
7 4 . S 0
75.65
76.79
77.0 7
29.05
30.17
31 .78
3 2 . "4 3
33.43
34. 57
0 5 . 6 5
45.73
*7.79
38.85
'49.91
4 0 . 9 6
42.00
43.03
4 4 . 0 5
4 s . 0 7
46.00
47.09
48.09
49.08
5 0 . U 7
51.U5
=7.. 17
s 7 .98
c:, 3 . '; 4
54 . H9
5 5 . 8 4
1.31
7 . 6 1
4.90
S . 1 9
6.47
7.74
9.U<;
1 n. ?6
i i . s i
1 7 . 7 *
13 . 0 p
15.70
16.47
1 7.63
1 R . P '-t
7 0 . 0 3
71.2 7
77.4 0
7 3 . 5 7
?4.7 4
7 s . 9 0
7 7. OS
7 P . 1 9
29.^?
30.45
31. .58
3 7 . 6 9
3 '1 . 8 0
34.9 0
3S.99
'17.03
"">. 1 6
3 9.23
40.79
4 1 . 3 5
47,4 ' J
43.4 4
4 4 . 4 8
4 S . 5 l
46. 5'4
4 7.54
48.5 5
4 o , 5 5
S 0 . 5 5
SI . SA.
S ' . 5 7
S 3 . 4 '-3
5 /. . 4 6
5 5 . 4 7
56.3 f
1 . T?
2.63
3 . 04
5.74
6.ST
?.3i
' 9.09
}0. 36
1 1 . 6 ^
17.3 7
1 / . 1 1
1 5 . "4 s
1 6. S8
17.80
1 9 . 0 2
? 0 . 7 ?
21.4?
27.61
73.80
74 . 03
76.14
2 7 . -M
73.46
2 9.6i
3 'J . 7 5
31.88
33.01
34.1?
35.7?
36.^4
47.4^
5 8 . 5 ">
39.60
4 0 . 6 8
41.7 /f
42.80
4 3 . R A
44.00
45 . 94
46.97
48.0 0
4 o.Ol
5 0 . n a
5 1 . 0 ^
5 2. '13
6 3 . 0 ?
s 4 . o ; i
:-4. '>»
5 5 . 9 lr>
5 6.91
1 . i 7
2.66
3 . Q 8
5.29
6.^Q
7.80
9. 17
.1 0.45
1 1 . 7-?
1 '> . o o
1 4 . 7 5
15.4°
16.7 A.
17.97
10.7'.;
2 0 . 4 1
21.67
2 7 . R ^
2 '-» . 0 7
?^.?l
2 f- . "4 o
27.56
2 8 . 7 ?
2 9 . ? 9
3 1 . (V,
32.18
33.32
3 4 . 4 '<
35.57
Q 6 . 6 «
37.7°
3 S . 8 8
39.98
4 1 . 0 6
47. 14
43.71
4 4 . 7 7
45. T>
4 6.^7
47.4 7
48. 4 5
4 9 . '4 $
5 '"' . S n
51.51
5 7 . 'i 7
b 3 . 5 7
': 4 . r> 1
5 5 . 5 ' ''
'.i 6 . 4 8
") 7 . 4 5
1 .35
7.68
4 . 0 1
5. 34
6.66
7.06
9.26
1 r . 5 5
* 1 . P 7
T*.l 1
14.38
15.64
16.80
1 8 . 1 4
19.37
20.60
7 1 . 8 3
23.04
74. 7 s
7 S . 4 ^
7 6 . 6 4
'' 7 . ,q 2
70.0 )
3 0 . .1 7
31.33
3 7 . 4 8
33.63
^4.77
Q 5 . 9 0
3 7 . 0 7
'48.1 4
0 9 . 7 5
4 0 . 3 5
41.4 4
47.53
4 3.61
4 4.6?
45.75
4 6.81
47.3 6
48.90
49.Q4
50.07
51 .99
5 3 . U 1
5 4 . 0 7
SS.f, 7
5 6 . ( ! 7
57. >:)
5 7. '.'9
1.36
7.71
4 . 0 5
5.39
6 . 7 1
8 . 0 -4
9 . 3 4
1 ;:.6b
1 1 . 0 ',
!*.?*
1 * . * 1
1 5.7P
1 7 . 0 <-->
18.31
19.55
20.80
72.03
7 ° . 2 5
7 4 . 4 7
7^.6°
76. PP
7 S . 0 8
? 9 . 77
7^.45
3 1. .6?
?>. 78
33.94
35.09
*6.23
*7. 36
33.4°
^0.61
40.72
41.83
47.9 ?
4 4 . 0 1
45. 1.0
46.1 7
a 7 . ? 4
4 P . ^ >."'
40. -46
50. 40
51 .44
S 7 . 4 7
S'' . sn
64.57
6 S . 5 3
5 6 . 5 3
57.5 3
S M . ') 7
1 .37
7 . 73
4 . 0 9
5.44
6.78
8. 1 1
9.4?
. 10.76
1 - . ^ S
n . i =,
1 4 . ft S
1 5. "3
17. 71
1 8.47
10.73
20.99
22.23
7 3 . 4 7
74. 70
7 t; . 0 7
77.1-3
7 8 . * 4
7 9 . r- 4
30.7 3
"41.9 1
33.08
? 4 . 7 5
35.4!
36. 56
37. "^l
3 °. . ° 4
39 . 07
41 . 1!'.
47.2 1.
i. ~> . -\ ?
44.4?
45.5 1
46.60
4 7 . t 7
4 8 . 7 4
49.0 }
50.96
SI .01
5 7 . o 6
53.00
5 S . n ?
56.04
')''. 05
Li8 . fil>
'>9. 06
P A r, F -11
-------
55.5
56.0
57.0
57.5
5P.O
58.5
59.5
60. n
.05
. 10
. 15
.20
.75
.30
.35
.40
.45
.50
.55
.60
.65
.70
.75
.80
.85
.90
.95
1.00
'1 .05
1.10
1 .15
1.20
1.25
] .30
1 .35
1 .40
1 .45
1 .50
1 .55
1.60
1.65
1 .70
1.75
1 .80
1.85
1 .90
1 .95
2.00
2.05
2. 10
2. 15
2.20
2.25
2.30
2.35
2.40
2.45
2.5n
1 .^8
2.76
4.13
5.49
6.84
8. 18
9.52
10.84
17.16
1 ^.47
14.78
16.07
1. 7 . 3 6
18.64
19.91
21.18
22.43
23.68
24.97
26. 15
27.38
28.59
29.80
31.00
32.20
33.38
34.56
35.7?
36.90
38.05
"3. 9 . 20
40.34
41.47
42.60
43.71
44.87
45.97
4 7 . 0 2
48. 1 1
49. 1.Q
50.76
51.3-3
57. 30
5 3 . 4 A
5 4 . 4 8
55.57
56.5^
57.57
58.5Q
59.60
1.40
2.78
4.16
5.54
6. 90
8. 25
9.60
1 0.04
17.77
1 -3.60
14.91
16.77
17.5?
1 8.81
2 0 ,\j 9
7 1 . °. 7
77.63
2 ? . 8 Q
75.15
76.30
27.67
28.85
3 0.07
?! .28
32. 49
33.68
14.87
36.05
37.73
3 8 . ? 9
39.55
40.70
41.8 4.
47.98
44. 1 1
45.73
46.34
47.44
48.54
49.63
50.71
51.7°
57.86
53.9 7
54.97
56.07
57.06
58.00
59.1?
60. I ?
1.41
2.31
4.2 0
5.58
6.06
8.33
9.6°
11.04
1 2 . "3. °,
13.7-7
1 5.0/,
!6.°.6
17.6 7
1 8 . 9 P
70.77
71 . 56
77.8 4
74.1 1
25.37
76,ft 7
77.87
79.1]
3 0 . 3 4
31.5 6
32.78
33. 9 o
35.18
36.38
37.56
38.74
3 o . Q n
41 . 06
42.??
4 3.36
44.5 0
45.63
4 6.75
47. q?
48.97
* 0 . 0 7
51.17
5 7 . 7 c-
5 3 . -> 3
54. A 0
5 5 . A 6
5 6 . 5 7
5 7 . 5 -'
5 8.61
50.64
60.6 7
1 . 4 7
7.83
4 .24
5.63
7.07
8 . 4 0
0.77
11.14
1 ">. A 9
1?.84
15.18
1 6 . r- 1
1 7.83
19.1 4
2 1 ' . 4 5
7 i . 7 5
73.04
74.3 7
75.5C!
7 6 . 8 6
78.1?
29.37
30.6 1
31.84
?3.07
'< 4 . 7 9
? 5 . 5 0
36.70
37.89
39.08
40.76
41.43
42.50
4^.75
44.8°
4 6.03
4 7 . 1 7
48.7°
40.41.
50.5 7
51 .67
57.71
5 3 .80
5 A . 8 8
5 r^ . 9 5
5 7 . 0 ?
5 P. 08
5 9 . 13
6'-'. 17
61 .71
1 .43
7.86
4 .78
5.68
7.08
8,48
9 .86
n . 7 >.
1 "'.60
1 3.96
15.31
1 6 . 6 5
] 7. on
1 9 . 3 ]
2 0 . 6 3
7 1 . q 4
?. 3 . 7 4
74.53
25.8?
7 7 . 1 0
2 P , ^ 6
79. 6^
3 o . a 8
37.1 7
33.36
34.50
35.81
3 7 . (.; ?
3P.7?
3 ° . 4 7
4 0 6 1
41 07o
47.96
44.1-3
45.79
46.44
47,58
4 8 . 7 1
40.8 A.
50. "6
57.07
5-3.10
- 4 . ? ~>
5C ,,36
56.44
57.5?
58.50
5 9 . 6 c-
60. 70
61.7 ';-
1 .^
7.88
4 . 3 1
5.73
7. 15
8 . 5 5
9.04
1 1 . '< -3
17.71
14. OH
1 5. 44
1 6. 80
18.1 4
19.48
20.81
7 ? . 1 3
73.44
24.75
76.04
7 V . 3 -3
28.61
7 9 . o p,
31.15
37.40
33.6^
3 4 . 8 o
?6. 1 2
37. ^4
38.56
3 9 . 7 6
40.06
42.1 s
43. 34
44.5 1
4 5.68
46.84
47.9"
49.1 4
5 0 . ? 7
51.4 0
52.53
53.64
5 4 . 7 5
5 5 . p, /.
56.04
58.0?
5 9 . 1 n
6 J . 1 6
61.2"
6 ? . ? P
1 .4.6
7 . 9 1
4.35
5.78
7.21
8 . 6 7 '
1 o.cn
\\»l\ 1
T'.OT
14.711
15.^ 8
16.9 A
1 8 . 3 ('
1 9 . 6 ^
20.Q9
77.3?
23.6 5
24.96
26.? 1
'? ~f . 5 7
28.86
30.1 /i
3 1 . 4. 1
3-5.68
33.94
35.10
36. 413
37.66
38.89
40. 1 1
41.7?
4 -> . 5 ->
43.71
44.9 ('
4 6 . 0 ?
47.? 5
4 P . 4 1
4 ° . 5 6
50.71
5 1 . P 5
57.98
5 4 . 1 ' i
5 5.7-5
5 6 . '3. '',
57.4?
5 R . 5 7
59.61
60.68
61.7*
6 7 . n ?
1 .^
? . 9 3
4.39
5.83
7.7 7
8.7-.)
10.12
11.^
i -> . o ^
T, . 3 ?
15.71
l^.OO
18.4 6
1 9 . 8 2
71.17
77.^1
? "I . 8 5
75.17
76.40
7V. 0(1
?9.10
^ : ' . 4 '"!
''I .68
* 7 . 9 6
V, .23
? t, . 4 o
?6.?4
-^7.99
39.22
4 ;'i . 4. 5
41.6 7
4 7 . R 8
44.00
45.28
46.47
47.65
4 P . P 2
49.99
51.1 4
c> 2 . ? o
53.43
54.56
55.60
5 6 . 8 '
57.0?
5 o . ( : ?
60. 11
61.2 0
6 7 . 2 °
6 3 . 3 r'
1.4°
7 . 9 6
4 . 4 7
5.88
-'. '33
8.77
K'.?;.>
1 1.63
1 -'.'V,
1 '( . 4 5
1 r>.84
17.7?
18.61
19.98
?!.*??
22.70
74.05
75.30
76.72
7 « . 0 A.
79.^^
"* 0 . 6 6
31.95
''".24
'^4.52
3 5 . "' 0
-3 7 . 0 5
78.31
39.55
40.79
4 ? . 0 ?
4 3 . 7 c-
44.46
45.66
46.86
48.05
4 9 . ? -3
5 o . 4 1
5 1 . 5 7
57. 7^
5^.38
55.0"3
5 6.16
57.?"
5 c« . 4 1
5 9 . = 7
M'. h?
61 . 7?
67.81
6 -3 . H ''
1 .c"
7 . 9 8
4 . 4 6
5 . o 3
7.^0
8.84
10.29
] 1 7 7
1 ° . 1 5
V*. c ''
1 r- . o ^
r7 . ? P
1 8 . 7 7
20. 1^
21.53
??.«o
74. ~c-
?6.6'_
76.04
;> P . T»
79.60
30.91
32.7?
3 ? . 5 7
Q 4 . P 1
"6.09
-37. ?6
33.63
39.89
41.14
4 7 . -3 R
4-5.61
44.8"
46.05
47.76
4 8.46
49.6 5
50.3?
5 2. . n !
6 -- . 1 P
54. -V*
55.4 °
5 6 . 6 3
57."' 7
5*. on
60.0?
M.I?
6?.74
63.^4
64.4 ''
-1 ?
-------
ITR-9a
Addendum to Intralaboratory Technical Report
A Table for Determining the True Time
Representing an Observed Count Rate
by
B. W. Hoffman and S. B. Van Camerik
Radiochemical Laboratories Program
The accompanying table is an abbreviated form of the table presented
with ITR-9.
As indicated in the section, "Use of the Tables", in the previous report,
if one holds R, the ratio of count time to half-life, constant, then a
true value of the time correction may be obtained by multiplying the
time correction value at unit half-life by an appropriate factor to obtain
i
the value at the actual half-life.
Example:
If one has,
Count Time = 4. 00 min.
Half-Life = 4. 00 min.
R = 1.00
Locate T on the table for R = 1. 00. Then multiply this number by 4. 00
to obtain the correction. In this case we have,
T = 0.47122, and Half-Life = 4.00 min.
so,
(4.00) x (0.4712Z) = 1.88488 minutes.
Thus if the count had been started at 1400 hours, the true time for the
observed activity would be,
1400 hours +1.88 min. = 1401.88 hours.
-------
DECAY CORRECTION TABLE FOR DECAY DURING COUNTING
H = COUNT TIME/HALF LIFE
T = TIME CORRECTION FACTOR
R
.05,
. 10
. 15
. 20
.25
. 30
. 35
.40
.45
.50
. 55-~
.60
.65
. 70
. 75
.80
. 85
.'90
.95
1.00
1.05
1. 10
1. 15
1.20
1. 25
.02492
.04970
.07434
.09883
.12319
. 14739
. 17145
.19537
.21915
.24278
.26626
.2396].'
.31281
.33587
.35878
.38155
.40418
.42667'
.44902
.47122
.49329
.51521
.r.3699
.55864
.580 .1 4
1 .30
1 .35
1 .40
1.45
1.50
1.55
1.60
1.65
1.70
1. 75
1 .80
1.85
1.90
1 .95
2.00
2.05
2. 10
-I i ti
------- |