428 BELL SYSTEM TECHNICAL JOURNAL 



atom in the process of pouring out radiation of the frequency v. The 

 right-hand side is the difference between two terms. One term is 

 the energ>' of the hydrogen atom before it emits the radiation of fre- 

 quency v; the other is the energy of the atom after the emission is 

 concluded. The radiation of frequency v is emitted by reason of a transi- 

 tion between two stationary states of the hydrogen atom; the energies of 

 these states are equal to the terms whereof the frequency v is the difference, 

 each term multiplied by h. The terms of the spectrum formulae are 

 the energy-values of the stationary states of the atom, when trans- 

 lated into the same units by multiplying them by h. When trans- 

 lated into proper units, the terms are energies, and the energies are 

 terms. This is Bohr's great and memorable idea. 



Once this idea is accepted, the known stationary states of the atom 

 increase enormously in number. The paltry one, two, or half-dozen, 

 which are all that Iiave been detected by obser\ing the energy-losses 

 of rebounding electrons, are multiplied into hundreds and thousands. 

 The accuracy with which each energy-value is known is augmented 

 tenfold or a hundredfold, sometimes far more; for spectroscopic 

 measurements are among the most accurate in ph\sics, although the 

 necessity of extrapolating the observed frequencies to arri\e at the 

 series-limit neutralizes some of their precision. 



One point must be kept clearly and always in mind, at the peril of 

 infinite confusion. The energy-values which the spectrum terms supply 

 are not the energy-values of the stationary states measured from 

 the normal state, as might seem natural; they are the energy-values 

 measured from the state of the ionized atom. These being negative, 

 it is the negati\'e term-value which is significant. Equation (6) 

 must ihcrcfore be rewritten in this fashion: 



'-H-J^-H-m^- (^) 



The energies of the successive stationary states of the hydrogen atom 

 are -RJi. -Rli/4, -Rli/9, -Rh/l(i, and so forth, relatively to the 

 energy of the ionized atom as zero. They are not Rh, Rh/4, Rh/9, 

 and so forth, relati\cly to the normal state of the atom as zero. Any- 

 one who entertains this last idea is doomed to trouble. 



The stationary states of the hydrogen atom are shown in Fig. 5, 

 which is constructed like Fig. 1, with the energy-values of the various 

 le\cls measured downwards from the state of the ionized atom, and 

 affixed f)n the right. The distances from the various levels to the 

 zero-line are (iroportional to these energy-values (this feature will 

 henceforth be found too inconvenient to maintain). 



