116 Dr. EL Stanley Allen on the Anqular Momentum 



The Relation of Lewis and Adams. 



From their theory of ultimate rational units Lewis and 

 Adams * deduced a relation between Planck's constant, h, 

 and the electric charge, e, of the form 



or 



15A 3 c 3 = 87r 5 (47re) 6 , 



where e is in electrostatic units. 



Using the notation employed in an earlier paper f, in 

 which I discussed certain numerical relations between elec- 

 tronic constants. 



hcq = 27re 2 , 



where q is a pure number and =7*28077 . . X 10 -3 . 



It is worthy of remark that the numerical factor 87r°/15, 

 which occurs under the cube root in the expression above, 

 may be written as 487ra, where 



a==l + 



4+3i+j4+- ••• =1-0823. .=fr 4 B 2 , 



B 2 being the second Bernoulli number = 1/30 J. 



The relation given by Lewis and Adams receives very 

 strong support from the experimental determinations of the 

 constants involved, as has been shown by R. T. Birge § in a 

 paper on the most probable value of Planck's constant. 

 He gives the mean value of 7i as 6*5543 + 0*0025 x 10~ 27 

 erg. sec, assuming e = 4*774 x 10" 10 and c — 2*9986 x 10 10 . 

 The calculated value he gives as 6 - 560x 10" 27 . 



- By combining McLaren's 

 Lewis and Adams we find 



•esult with the relation of 



^-* e =V^(S) x(4,re)! 



or 



in electrostatic units. 

 Hence 



•3 / /8t 5 \ 



N ™ C= V ("i5 ) xl6?r26 0] 



\ire l 



'lire 



<1 



* Phvs. Rev. vol. iii. p. 92 (1914). 



t Proc. Pbys. Soc. vol. xxvii. p. 425 (1915). In Sommerf eld's 

 papers on the fine structure of spectrum lines in the Anncden der Physik 

 for 1916, the constant which I termed q is denoted by ci. 



% Planck's • Pleat Radiation ' (Masius) § 160. 



§ R. T. Birge, Phys. Rev. vol. xiv. p. 361 (1919). 



