The above is only a simple illustrative example of the possible complexity in the physical determination of ionization potentials. The interpretation of four successive critical potentials for hydrogen has been discussed by Franck, Knipping and Krüger,[16] while eight have been detected by Horton and Davies[17] for the same element. Similarly Smyth[18] discusses four critical voltages for nitrogen. No explicit attempt has yet been made to use these facts for the interpretation of astrophysical data, but they may account for the unexplained absence of some neutral elements from the cooler stars. The absence is generally to be attributed, as will be shown in Chapter V, to the non-occurrence of suitable lines in the part of the spectrum usually examined. But [Pg 20] it is possible that the persistence of the molecule has a definite significance in the case of nitrogen, where the ionization potential is as high as 16.9 volts. Figure 4 Relation between ionization potential and position in the periodic system. Ordinates are ionization potentials in volts, on the equal but shifted scales indicated alternately on left and right margins. Abscissae are columns of the periodic table. Physical determinations of ionization potential are indicated by open circles; dots give spectroscopic determinations, and crosses denote astrophysical estimates. Conjectural portions of the curve are indicated by broken lines, and atoms of unknown ionization potential are enclosed in parentheses. The increasing completeness of the table of ionization potentials suggests a re-examination of the relation recently traced by the writer[19] between ionization potential and atomic number. The original diagram, in which columns of the periodic table are treated as abscissae, and the ordinates are ionization potentials on equal but shifted scales, so that analogous elements fall one below another, is here reproduced, with the addition of data more recently obtained. [Pg 21] The Displacement Rule of Kossell and Sommerfeld leads us to expect a pronounced similarity between the line drawn in the diagram from the point representing one element to that representing the next, and the corresponding line for the ionized atoms of the same elements, the latter being shifted one place to the left for each electron removed. The points for once and twice ionized atoms are inserted into the diagram on this principle, and the parallelism is found to exist. The regularities of the diagram and their possible significance (such, for example, as the pairing of the valency electrons, the second being harder to remove than the first) were discussed in the original paper. All the more recent data appear to confirm the conclusion there set forth, that the relation between ionization potential and atomic number is very closely the same in each period. DURATION OF ATOMIC STATES