Table 22. Further Values of P
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44
TABLE 23.VALUES
OF T H E FACTOR 0.67454=
This factor occurs in the equation ra = 0.6745
observation, and other similar equations.
I2
0
1
2
3
d..s

5
4
1
for the probable error of a single
6
7
8
9
10
20
30
40
0.2248 0.2133
.1547 .1508
.1252 .1231
.lo80 .lo66
0.6745 0.4769 0.3894
.2034 ,1947 ,1871
.1472 .1438 .1406
. E l 1 .1192 ,1174
.I053 .lo41 ,1029
0.3372 0.3016 0.2754 0.2549 0.2385
.1803 .1742 .1686 .1636 .1590
.1377 .1349 .1323 ,1298 .1275
.1157 .1140 .1124 .1109 .lo94
.lo17 .lo05 .W94 .0984 ,0974
50
0.0964 0.0954 0.0944 0.0935 0.0926
.0878 .0871 .0864 ,0857 ,0850
.0812 .0806 .(I800 .0795 .0789
.0759 .0754 ,0749 .0745 ,0740
,0715 .0711 ,0707 .0703 ,0699
0.0918 0.0909 0.0901 0.0893 0.0886
.0843 .0837 ,0830 .0824 .0818
.0784 .0779 .0774 .0769 ,0764
,0736 .0732 .0727 .0723 ,0719
.0696 .0692 .0688 .0685 .0681
00
60
70
80
90
TABLE 24.VALUES
OF T H E F A C T O R 0.6745
This factor occurs in the equation ro = 0.6745
arithmetical mean.
n
1
40
50
60
70
80
90
3
4
___
1) for the probable error of the
5
6
7
a
9
0.4769 0.2754 0.1947
.0587 .0540 .0500
.0314 .0300 .0287
.0214 .0208 .0201
,0163 .0159 .0155
0.1508 0.1231 0.1041 0.0901 0.0795
.0465 0435 .OM9 .0386 .0365
.0275 .0265 .0255 .0245 0237
.0196 .0190 .0185 .0180 .0175
,0152 .0148 .0145 .0142 .0139
0.0136 0.0134 0.0131 0.0128 0.0126
.0113 .0111 .0110 .OlO8 ,0106
.0097 .OW6 .0094 .0093 .0092
.0085 .0084 .0083 .0082 .0081
,0075 .0075 .0074 .0073 ,0072
0.0124 0.0122 0.0119 0.0117 0.0115
,0105 .0103 .0101 .0100 .0098
.0091 .0089 ,0088 .0087 ,0086
,0080 .0079 .0078 ,0077 .0076
.0071 ,0071 .0070 .0069 .0068
00
10
20
30
2
4
0.0711 0.0643
.0346 .0329
.0229 .0221
.0171 .0167
SMITHSONIAN PHYSICAL TABLES
T A B L E 25.LEAST
45
SQUARES
of the factor 0.8453
Part 1.Values
This factor occurs in the approsimate equation
Y
zlvl
for the probable
= 0.8153 ___
d n ( n  1)
error of a single observation.
1
11
2
3
5
4
6
7
8
9
10
20
30
40
0.0891 0.0806
.0434 .0412
.0287 .0277
.0214 .0209
0.5978 0.3451 0.2440
.0736 .0677 ,0627
.0393 .0376 .0360
,0268 .0260 .0252
.0204 .0199 .0194
0.1890 0.1543 0.1304 0.1130 0.0996
.0583 ,0546 .0513 .0483 .0457
,0345 ,0332 ,0319 .0307 .0297
.0245 ,0238 .0232 .0225 .0220
,0190 .0186 .0182 .0178 .0174
50
0.0171 0.0167 0.0164 0.0161 0.0158
.0142 ,0140 .0137 ,0135 .0133
.O 122 .0120 .0118 ,0117 .0115
.0106 .0105 .0104 .0102 .0101
.0094 .0093 .0092 ,0091 .0090
0.0155 0.0152 0.0150 0.0147 0.0145
.0131 ,0129 .0127 .0125 .0123
,0113 ,0112 .0111 .0109 .01M
.0100 .0099 .0098 .0097 .OW6
.0089 .0089 .0088 .0087 .0086
00
60
70
80
90
1
===
ndn 1
This factor occurs in the approximate equation yo = 0.8453 z(v( for the probable
Part 2.Values
of 0.8453
ndgi
error of the arithmetical mean.
1
I1
2
3
4
5
6
1
7
8
9
10
20
30
40
0.0282
.0097
.0052
,0034
0.4227 0.1993 0.1220
0.0243 ,0212 ,0188 .0167
.0090 .0081 ,0078 .0073
,0050 ,0047 .0045 .0043
.0033 .0031 .0030 .0029
0.0845 0.0630 0.0493 0.0399 0.0332
.0151 ,0136 .0124 .0114 .0105
.0369 .0065 .0061 .0058 .0055
.0041 .0040 .0038 .0037 .0035
.0028 .0027 .0027 .0026 .0025
50
0.0024 0.0023 0.0023 0.0022 0.0022
.0018 .0018 .0017 .0017 .0017
,0015 ,0014 ,0014 .0014 ,0013
.oo12 .oo12 .oo11 0011 .oo11
,0010 ,0010 .0010 .0009 .0009
0.0021 0.0020 0.0020 0.0019 0.0019
.ON6 ,0016 .0016 .0015 .0015
.0013 .0013 .0013 ,0012 .0012
.oo11 .0011 .0010 .oo10 .0010
.0009 ,0009 ,0009 ,0009 .a009
00
60
70
80
90
SMlTHSONlAN PHYSICAL TABLES
46
TABLES 2628.GENERAL
PHYSICAL CONSTANTS
Some of the most important results of physical science are embodied in the
numerical magnitudes of various universal physical constants. The accurate
determination of such constants has engaged the time and labor of many of
the most eminent scientists. Some of these constants can be evaluated by
various methods. The experiments used to study and measure these constants,
in many instances have yielded some function of two or more of the constants
(see Table 26) such as h/e, e/m, F / N , h/m, m N , F ( e / m ) , e " / ( m / h ) , etc.,
rather than the direct value of the constant. Each of the many relations has
been investigated by various experimenters at various times, and each investigation normally produces a result more or less different from that of any other
investigation. Under such conditions there arises a general and continuous
need for a searching examination of the most probable value of each important
constant. This makes necessary some comparison and analysis of all these experimental data to arrive at the most probable value. An important factor in
such work is that there are but few of the constants that do not require for
their evaluation a knowledge of certain other constants. These relations are so
extensive that most of the physical constants can be calculated from the value
of five or six of the selected principal constants and certain ratios.
Many such critical reviews of these natural constants and conversion factors
have appeared in the last 30 to 40 years. The data and discussion given here
for the constants and their probable errors are the values arrived at by three
physicists, R. T. Birge,17 J. W. DuMond, and J. A. Bearden, and their associates, who have made some very careful reviews and critical studies of the published experimental data on these general physical constants and have published
several papers giving what they consider as the most probable value. Reference
should be made to their original papers for details.
Birge says in his 1941 paper that as a result of such critical work the situation in respect to these constants has vastly improved over values of about 10
years ago, and again one can say that such studies have resulted in more work
and thus a more accurate set of constants.
In 1941 Birge published a very extended list of physical constants and
gave calculated values of many other physical constants that depend upon the
fundamental constants. Because of the extent of this list, and also because so
many of the relations among these constants are given therein, this 1941 list
is given here. Almost all these constants in this table (Table 26) are accurate
within the limits given.
DuMond and Cohen18 prepared a table of some of these constants for the
Atomic Energy Commission. A part of this appeared in the July 1953 issue
of the Review of Modern Physics. Table 27 gives their values of a number
of these physical constants.
Bearden and Watts in 1950 made a study of values of a number of physical constants, using some new values in their calculations. They are continuing
this work and are now lSboffering some new and more accurate values. Table
28 contains their 1950 values (corrected for their newer values) and newer
calculated values of some additional constants.
A comparison of the final values of these fundamental physical constants
arrived at by these physicists shows in a real manner the accuracy that may
now be claimed. A number of the principal radiation constants were taken
from these tables (Tables 2628) and are given in Table 53. These values
have been used for the calculations in the tables in this book since they were
available when the work was started and since the newer values would make no
practical changes.
1' Phys. Rev. Suppl., vol. 1, p. 1, 1929; Rev. Mod. Phys., vol. 13, p. 233, 1941 ; Amer.
Journ. Phys., vol. 13, . 63, 1945.
1sPhys. Rev., vol.
p. 457, 1940; Rev. Mod. Phys., vol. 20, p. 82, 1948.
'*'Bearden, J. A., and Watts, H. M., Phys. Rev., vol. 81, p. 73, 1951.
l a b Bearden, Earle, Minkowski, and Thomsen, private communication from J. A. Bear
38,
den.
SMITHSONIAN PHYSICAL TABLES
47
T A B L E 26.OENERAL
PHYSJCAL CO NS TANTS ACCORDING T O BIRGE *
P a r t 1.Principal
constants and ratios
Velocity of light.. . ...............c = (2.99776 t O.OOO04) x 10" cm sec'
Gravitation constant ............. . G = (6.670 fO.005) X 10sdynecm'g2
Liter (= 1000 ml). . ............... I = 1000.028 3 0.002 cm'
Volume of ideal gas (O"C, A,) . . . .V o= (22.4146 f.0.0006) X 105 cms atm' mole"
V', = 22.4140 0.0006 I atm' mole'
..V,, = (22.4157 t 0.0006) X 10' cmaatm'mole'
Volume of ideal gas (O'C, As).
Va5= 22.4151 f0.0006 1 atm' mole'
Atomic weights (see Part 2).
Standard atmosphere ........... .A0 = 1.013246 2 0.000004) X 108 dyne cm'
45" atmosphere . . . . . . . . . . . . . . . .A,s
. = (1.013195 f.0.000004) x 10'dyne cm'
Icepoint (absolute scale). ...... ..To = 273.16 2 0.01"K
Joule equivalent .................Jls = 4.1855 2 0.0004 abs joule/calla
Toule eauivalent (electrical). .... .J',3 = 4.1847 2 0.0003 int joule/calls
Faraday constant
(1) Chemical scale ...........F = 96501.2 t 10 int coul/g equiv.
= 96487.7 f 1.0 abs coulla eauiv.
= 9648.772 1.0 abs emu/g equiv.
F' = Fc = (2.89247 2 0.00030) X 1O"abs esu/g equiv.
(2) Physical scale ...........F = 96514." f 10 abs coul/g equiv.
= 9651.4, k 1.0 abs emu/g equiv.
F' = Fc = (2.89326 f.0.00030) X lo" abs esu/g equiv.
Avogadro number (chemical scale). N o = (6.0228s t 0.001 1) X 1 p molecules/mole
Electronic charge .................e = F / N o = (1.602033 f0.00034) X lo" abs emu
e' = ec = (4.80251 2 0.0010) X lo'' abs esu
Specific electronic charge. ......e / m = (1.7592 0.0005) X lo7abs emu/g
e'/m = ec = (5.2766 f.0.0015) x 10" abs esu/g
(see Part 4)
Planck's constant .................h
*
P a r t 2.Atomic
weights
Physical scale (0'"= 16.0000)
iH' = 2.01473 t O.oooO1p
1H' = 1.00813 f0.00001~
iH = 1.00827s 2 O.OoOO17
(from H'/H2 abundance = 6900 k 100)
,He4 = 4.00389 C 0.00007
,C'" = 13.00761 % 0.00015
,C" = 12.00386 2 0.0004
C = 12.01465 zk 0.00023
(from C"/C" abundance = 92 f.2)
7N" = 15.0049 f 0.0002
,N1' = 14.00753 2 0.00005
N = 14.01121 f.0.00009s
(from N1'/Nm abundance = 270 f 6)
,O" = 16.0000
= 17.0045
80"
= 18.0049
0 = 16.004357 t 0.00008a
[from abundance Ole : 0" : 0" == (506 5z 10) : 1 : (0.204 2 0.008) I
Chemical scale (0 = 16.0000)
Ratio physical to chemical scale :
r = (16.004357 2 0.000086)/ 16 = 1.00272 4 0 . 0 0 0 ~ 5
H1 1.00785, 3 O.OOOOIs (from physical scale)
H2= 2.0141& f.0.00002, (from physical scale)
H = l.008002 2 O.OO0Ol8 (from physical scale)
He' = 4.00280 2 0.00007 (from physical scale)
C = 12.01139 f 0.00024 (from physical scale)
N = 14.00740 2 0.00012 (from physical scale)
N = 14.0086 rt 0.0007 (direct observation)
Na = 22.994 t 0.003
CI = 35.457 f0.001
Ca
40.080 2 0.005
Ag = 107.880 f 0.002
I = 126.915 t 0.004
.Unless otherwise specified, all quantities in this table that involve the mol or the gram equivalent
are on the chemical scale of atomic weights.
(contiwed)
SMITHSONIAN PHYSICAL TABLES
48
T A B L E PB.GENERAL
Part 3.Additional
P H Y S I C A L CONSTANTS ACCORDING T O BlRGE
(continued)
quantities evaluated or used in connection with Part 1
..........
Ratio of esu to emu (direct).
c' = (2.99711 f 0.0001) X l(Yo cm'/' set"/' ohm'/*
= (2.9978, 2 O.OOOlo) X 10" cm/sec
Ratio of esu to emu (indirect). ...... .c' = c = (2.99776 f0.0004) X 10'' cm/ser
Average density of earth.. ............6 = 5.517 f0.004 p/cm'
Maximum density of water. ....am(H20) = 0.999S2 2 0.000002 g/cm'
Acceleration of gravity (standard). ... .go = 980.665 cm/sec'
Acceleration of gravity (45"). ........ g =
~ 980.616 cm/sec?
Density of oxygen gas (OOC, A ) .... .L1= 1.42897 f0.0003 g/liter
Limiting density of oxygen gas (OOC, A K )
L t i m = 1.427609 2 0.000037 g/liter
Factor converting oxygen (O'C, All)
to ideal gas.. ..................1  a = l.OOO953s2 0.000009,
Specific gravity of H g (O'C, Ao) referred to airfree water at maximum
density ..........................
.po = 13.59542 f 0.00005
Density of Hg (0°C. A ) .............DO= 13.59504f 0.00005, g/cm8
Electrochemical equivalents (chemical
scale) :
Silver (apparent) .............EA, = (1.11800 t0.00012) x 10'g/int coul
(corrected) .............E A , = (1.11807 2 0.00012) x
g/abs coul
Iodine (apparent) ..............E I = (1.315026 fO.oooO25) x lo*g/int coul
(corrected) ..............E I = (1.31535 f0.00014) x lo* g/abs coul
Effective calcite grating space ( W C )
d"a = 3.02904 X lo' cm
Siegbahn system
True calcite grating space (20°C). .. . # Z O = 3.029512 X 10.' cm
Siegbahn system
True calcite grating space (20°C). . . .dm = (3.0356742 0.00018) X 10'cm
cgs system
Ratio of grating and Siegbahn scales of
wavelengths ...................X I / L = 1.002034 f0.000060
Density of calcite (20°C). ............. p = 2.71029 U0.00003 g/cm*
Structural constant of calcite (20°C). . = 1.09594 2 0.00001
Molecular weight of calcite (chemical
      . naos
 .M = inn.091.f
scale) ...........................
Rydberg constant for hydrogen (HI). .RH = 109677.5812f 0.007, cm' (LA. scale)
Rydberg constant for deuterium (H') . .RD= 109707.419af0.0076 cm' (I.A. scale)
Rydberg constant for helium.. ......R I I ,= 109722.263 C 0.012 cm' (I.A. scale)
Rydberg constant for infinite mass. ...R, = 109737,303& 0.017 cm' (LA. scale\
or f 0.05 cm' (cgs system)
.*
SMITHSONIAN PHYSICAL TABLES