SOME CONTEMPORARY ADVANCES IN niYSICS—X 101 



which in the atom-model is reaHzed when the electron circulates in a 

 rosette, or precessing ellipse, for which w=3 and k = 2. Orbits for 

 which k=n are circles; orbits for which k<n are (precessing) ellipses, 

 and the farther k falls below n the more eccentric (narrower) is the 

 ellipse, although its major axis is independent of k. I have repeated 

 all of these statements about precessing ellipses and their quantum- 

 numbers, because a great part of the speculation about atoms pos- 

 sessed of more than one electron consists of persevering and obstinate 

 attempts to interpret their behavior by as nearly as possible the same 

 ideas. 



It is essential to remember also that all the energy-values of the 

 Stationary States are reckoned from the "State of the Ionized Atom," 

 in which State the energy — i.e., the energy of a system composed of 

 one atom deprived of an electron, and one electron far away — is 

 equated to zero. 



N. Introduction to the Speculations About Atoms 

 WITH More than One Electron 



All atoms, except those of hydrogen and ionized helium, possess 

 more than one electron. There is much evidence of various kinds 

 for this assertion; and certainly the spectra of these other atoms 

 cannot be interpreted as those of the first two have been. Thus we 

 are confronted with the problem of a system composed of a nucleus 

 and more than one electron. The similarities between the spectra of 

 hydrogen and ionized helium, and those of other elements, are im- 

 portant enough to make it desirable to use the same sort of explana- 

 tion. We imagine the various electrons, when there are two or more, 

 each to describe certain permitted orbits, set apart from the multi- 

 tude of other conceivable orbits by peculiar features expressible by a 

 Principle of Quantization. 



Here at the outset we meet with the great hindrance to success 

 in this problem. It is not possible to determine what features are 

 common to permitted orbits, for it is not possible even to trace the 

 permitted orbits. The general problem of tracing the paths of three 

 or more bodies, attracting or repelling one another according to the 

 inverse-square law, remains unsolved. Considering that for cen- 

 turies the related but simpler problem of celestial mechanics has been 

 under continual and powerful attack, the general problem may fairly 

 confidently be regarded as insoluble. There is very little hope of ever 

 dominating it to such an extent, that the spectra of atoms with two 

 or more electrons can be interpreted exactly by Bohr's atom-model, 



