Our Present Dilemma Regarding the Values of the Natural Constants e, m and h. A New Graphical Method of Presentation

Fourteen experiments each of which determines some function of one or more of the constants $e$, $m$ and $h$, are classified, according to the function determined, into nine groups. The latter number is reduced to seven by the elimination of five of the thirteen experiments as unreliable in the light of our present knowledge. Three cardinally good experiments, the directly measured x-ray values of $e$, the many concordant measurements of $\frac{e}{m}$ and the values of $\frac{h}{e}$ from the limit-of the continuous x-ray spectrum are exhibited on a new type of diagram showing separately results of all independent reliable determinations to portray the consistencies graphically. The indubitable nature of the discrepancy is thus made evident and the remaining four experimental values also plotted on the diagram seem to give better support to the first two named cardinal experiments than to the last. The new type of diagram is an isometric projection of a cartesian coordinate system whose axes represent the relative deviations of $e$, $m$ and $h$ from conventionally assumed values. Planes in this space represent the different experimental determinations of functions of $e$, $m$ and $h$ and the discussion brings out the absolute geometric property that five of these planes are "cozonal" (parallel to a common axis). Though there are seven equations it thus appears that to solve for $e$, $m$ and $h$ either the direct $e$, equation or alternately the ${R}_{\ensuremath{\infty}}$ equation is indispensable.The results are briefly recounted of a careful examination both by the author and others of numerous possible experimental and theoretical sources of the discrepancy. Modified diagrams are shown for (a) the assumption that the velocity of propagation of radiation in vacuum suffers a slow decline with increasing frequency (the velocity for 20,000-volt x-rays is assumed to be \textonequarter{} percent lower than the low frequency optical value); (b) the alternative assumption that the Bohr-Rydberg formula must be revised to include a factor ($1\ensuremath{-}\ensuremath{\alpha}$). Both assumptions rectify the diagram as regards the three cardinal experiments but throw the remaining experiments out of line with them. Since the two assumptions named are about equally objectionable both on theoretical grounds and in their results on the diagram they are now rejected as unlikely. The author concludes that in all probability some unsuspected theoretical or experimental flaw in the determination of $\frac{h}{e}$ by the continuous x-ray spectrum method is the source of the discrepancy and emphasizes the need for renewed study of this experiment along with x-ray ionization and excitation potentials over a wider range of voltages with better spectral resolution. The weakness of low voltage measurements of ionization and excitation potentials is pointed out. It is emphasized that when systematic error is as glaringly evident as at present the temptation to obtain compromise or "best" values of the natural constants by least-squares methods should be strongly resisted for it is not inconceivable that the discrepancy may reveal some important error of principle or theory.