Analysis of Variance of the 1952 Data on the Atomic Constants and a New Adjustment, 1955

The 1952 data used by DuMond and Cohen in an evaluation of the atomic constants are analyzed for the presence of systematic errors by a variance analysis performed by an electronic digital computer. For simplicity the velocity of light is treated as a fixed constant of known value and there remain then eleven linear equations in four unknowns subject to least-squares adjustment. Least-squares adjustments of 219 over-determined subsets of these equations have been made and ${\chi }^2$ has been evaluated for each such subset. An analysis of these data indicates that small systematic errors are most likely to exist in the following input data: (1) The determination of the Faraday by the silver voltameter. (2) The determination of the cyclotron resonance frequency of the proton by the inverse cyclotron method of Bloch and Jeffreys. (3) Certain of the higher voltage determinations of $\frac{h}{e}$ by the continuous x-ray quantum limit. In descending order of magnitude of discrepancy from the remaining data on the constants are the determinations of (a) Felt, Harris, and DuMond made at 24 500 volts, (b) Bearden and Schwarz at 19 600 volts, (c) Bearden and Schwarz and also Bearden, Johnson, and Watts in the region between about 10 kv and about 6 kv. An analysis of the various observations taken by these observers at different voltages reveals a possible systematic trend when discrepancy is plotted against either voltage or window width in volts. Conjectures to account for the effect are discussed.

The modifications called for by this analysis yield a new 1955 adjustment in which ${\chi }^2$ is smaller than it was for the November, 1952 adjustment. The new ${\chi }^2=3.25\mathrm{}$ is satisfactorily close to its expected value, 3. Thanks to the fact that the error measures adopted in the November, 1952 adjustment for the output values were conservatively based on the criterion of external consistency, the changes in the values occasioned as a result of the present analysis are all well within those estimated limits. A welcome effect of this new adjustment is that the adjusted output value of $\frac{{\lambda }_g}{{\lambda }_s}$, the conversion factor from Siegbahn's $x$-units to milliangstroms, now lies much closer to the input value. A new table of constants and conversion factors is presented.