JQ2 TABLE 40 (continued) 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



Thus the statement that the absolute cm unit of resistance is one cm • sec." 1 involves the 

 assumption not only of unit permeability, but also of dimensionless permeability. In a 

 number of the equations given in Table 43 the two sides of the equation do not check 

 dimensionally unless one assumes 11 and e to be dimensionless. It follows from this that 

 the name of the unit stated in the table applies strictly only to one side of such an 

 equation. In such cases the unit applies to the left side of the equation, since this is the 

 quantity being evaluated. The right side gives merely the most direct derivation of the 

 numerical magnitude, in terms of quantities already evaluated. Since this ambiguity does 

 not affect the numerical magnitude, it is inconsequential in the present discussion. As 

 examples of this situation we cite the fine structure constant a, which is dimensionless. 

 To satisfy this condition one should write a = 2ire 2 /e hc where e is numerically unity, 

 and represents merely the dimesions of e. The ratio of the Bohr magneton Mi to the 

 Bohr unit of angular momentum (1i/2tt) is strictly fioHc/m), where Mo is numerically 

 unity, and represents merely the dimensions of permeability. 



The mole is a (variable) unit of mass, equal to the molecular weight in grams. The 

 gram equivalent is a similar (variable) unit of mass, equal to the atomic or molecular 

 weight in grams, divided by the valence. 



The various quantities appearing on page 103 of this table and in Table 42 have been 

 discussed. No general explanation will be given of the meaning or use of the quantities 

 appearing in Table 43 ; any adequate explanation would constitute a textbook of modern 

 physics and physical chemistry. For the more specialized constants, no explanation is 

 needed by investigators working with such constants, and it is to such persons that the 

 data will be most useful. 



In conclusion, attention should be directed merely to two constants for which the 

 formula used here differs from that normally given. It is customary to use for the 

 speed of the electron in the normal orbit of hydrogen, as given by Bohr's original theory, 

 a value which refers to the nucleus considered as the center of coordinates. This is called 

 Vo(= ac) in Table 43. It would seem more logical to give the speed referred to the 

 center of mass, the quantity denoted Vo in Table 43. There is a similar discrepancy in the 

 case of the radius of this orbit. The electron, according to Bohr, moves about the center 

 of mass in a circle of radius a»', as it is denoted in Table 43. This is not the same as the 

 constant separation of the nucleus and electron, which is here denoted a . In the literature 

 these two quantities, a , and a</, are sometimes confused. The expressions for Vo, Vo, a , and 

 ad given in Table 43 include also the factor (1 — a 2 ) 1 / 2 , arising from the variation of 

 mass with speed. 



Birge. Probable values of e, h, elm and a Phys. Rev. 40, 228, 1932. 



e, (4.7688 ± 0.0040) X io" 10 cs units 

 h, (6.5443 — 0.0091 )X io" 27 erg • sec. 

 elm, (1.7611 ± 0.0009) X io 7 cm units • g" 1 



l/a, I37-307 ± O.O48 



Smithsonian Tables 





