Table 22. Further Values of P

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 26-28.-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 26-28) 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 10-sdynecm'g-2

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-'

Ice-point (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 air-free 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