80 TABLE 53.— RADIATION CONSTANTS 



Velocity of light c = 2.99776 X 10 10 cm sec" 1 



Planck's constant h = 6.6242 X 10" 27 erg sec 



Boltzmann's constant k = 1.3805 X 10" 16 erg deg" 1 



Stefan-Boltzmann constant * o- = 5.673 X 10 s erg cm" 2 deg -4 sec" 1 



Wien's displacement law A = Aci\~ s F(\T) 



The principal corollaries are: X m T = b 



AT= bi 



The first corollary is sometimes given as the Wien's displacement law, and b as the 

 displacement constant. 



Wien displacement constant b = 0.2897 cm deg 



First radiation constant t 



All lengths in cm, d X = 1 cm Ci = 3.740 X 10~ B erg sec" 1 cm 2 



Area cm 2 , X in m, d\ = 0.01/t Ci — 3.740 Xl0 B erg sec" 1 cm 2 



Second radiation constant c 2 = 1.4380 cm deg 



The unit of energy chosen for the above values is the erg. Any other unit of energy (or 

 power) may be used if the proper conversion factor is used (Table 7). 



Values of c 2 used at different times. — This second radiation constant has been de- 

 termined many times in the last 40 years. Shown below are the values used at different 

 times. [A new determination of the value of c 2 by G. A. W. Rutgers (Physica, vol. 15, 

 p. 985, 1949) gives two values: 14325. ± 20 and 14310. ± 20 m deg.] 



National Bureau Nela 



Date of Standards Park 



1911 14500m °K 14500m °K 



1915 — 14460 



1917 14350 14350 



1922 14320 1 14350 



1925 14320 § 14320 



1936 14320 II 14320 



1944 14320 14320 



1949 14380 — 



* For 2ir solid angle. t For the general case, Ci may be written in the following symbolic form: 



(wavelength unit) 5 x power unit 



<*i = numeric ; ; — : ; — — 



area x wavelength interval x solid angle 



This form shows that the value of the numeric depends upon the several units used — in this case 5. 

 If /, is the normal intensity, i.e., per unit solid angle perpendicular to the surface, ir/ x gives the 



radiation per 2ir solid angle. The energy radiated within a unit solid angle around the normal, is 0.92 J . 

 The above values are for a plane blackbody; for a spherical blackbody the radiation for 2tt solid angle 

 equals 27r/ . 



For calculations the use of the radiation constants a and c 2 as given follows directly and causes but 

 little trouble. The numeric for c 2 must be expressed in the unit of wavelength times the absolute tempera- 

 ture. If the wavelength is expressed in u the numeric becomes 14380. 



When Planck's equation is used for calculations, it may be written as follows for blackbody of area A: 

 J x d\ = C4c,X-s/ [exp (c 2 /\T) — 1])<A 



where d\ is the wavelength interval for which the radiation is to be calculated. The first value of fi 

 given in the table is for all dimensions in centimeters — a condition almost never met in practice. The 

 second value is for the wavelength expressed in microns and d\ = 0.01/t. 



If this second value of c 2 be used in calculation with Planck's equation and summed step by step, 

 the results will be the total energy per second, per 2tt solid angle, per unit area for the wavelength 

 interval covered, X expressed in ti. 



t I. G. Priest, in January 1922, used c 2 = 14350 in his work on color temperature. § J. F. Skog- 



land, in 1929, used c 2 = 14330 in his tables of spectral energy distribution of a blackbody. || D. B. 



Judd, in 1933, used c 2 ~ 14350 in his calculations related to the I.C.I, standard observer. 



SMITHSONIAN PHYSICAL TABLES 



