«,() FELL SYSTEM TEC! IMC. IE Jorh'X.IE 



normal stale (the state of energy —47?/;) are so far out in the iillra- 

 violet region of the si)ectrum tliat no one lias \el succeeded in delect- 

 ing them. 



We will now take account of the fact thai the numerical values 

 of the constant R calculated for hydrogen (equation l(i) and for ionized 

 hehuni (ec|uatit)n 2o) are not quite the same; they are in fact propor- 

 tional to /u, ihe quanlily wiiich determines the motion of the nucleus, 

 and which \aries from one atom lo anoliuT. In ]).iriicular 



R„, K!,=M!Ir ////=(l+w .1///) {\+IU Miie) (26) 



in which the symbols tii, Mn, .1///, denote the masses respectively 

 of the electron, the hydrogen nucleus and the helium nucleus, which 

 stand to one another as .000542; 1.000:3.908. Consequently the 

 right-hand member of equation (2a) is equal to 1.000403, and the 

 ratio of the freciuencies of corrcspnnding lines in the spectra of ionized 

 helium and of h>'drogen is 



A Rii, ./?// caicuialed = 4.0011)12 (27) 



The values of Rn, and Rn deduci'd from frcquenr\- measuren'.ents yit4d 

 the ratio 



\ R,i, /?// ol)ser\c(l = 4.0(1 l(i2 12 (28) 



The \er\-exactl\-kiiown oliserwd \aluc lies well within liie margin 

 of uncertainly <if the calculated \alue. The calculated \alue of the 

 ratio de|)ends on otherwise-made measurements of the mutual ratios 

 of ihe three masses (those of the electron, the hydrogen nucleus, the 

 lulium nucleus). These otherwise-made measurements are not of 

 the grade of precision claimed for the measurements of 4 Ru, Rii by 

 the obser\ations on the spectra. Hence if we combine the observed 

 value of the ratio ARhc, Rn with (for instance) the ratio ^1///, Mn 

 derived from density-measurements upon the two gases, we can 

 calculate a value for the ratio .1/// 'm ostensibK' much more precise 

 than ihe amount ascerlained li\' dui'cl measuri'nienl. This \.ilue i^ 



Mil w = lS47. (2!!) 



l.et me stale briefly what the numerical agreement between the 

 "calculated" and "observed" values of 4Rii, • Rii specifies. 1 1 is a 

 test of this set of assumptions; the hydrogen atom and the ionized 

 helium atom may each be represented by a single electron and a 

 nucleus of charge -j-r in one case and +2c in the other; each stationary 



