On The Relation between the K Series and the L Series of X-Rays

Synopsis.---The object has been to measure both the emission and the absorption wave-lengths in the K and L-series characteristic of a chemical element (tungsten), using the same X-ray spectrometer throughout, to see if general relations among them could be found. Graphs have been drawn representing the ionization currents as functions of the crystal table angle. The peaks in these graphs corresponding to the lines ${\ensuremath{\alpha}}_{1}$ (strong) and ${\ensuremath{\alpha}}_{2}$ (medium) appear completely separated from each other, although the difference between their wave-lengths amounts to only 2.2 per cent. There is also faint evidence of a third (very weak) line, ${\ensuremath{\alpha}}_{3}$.A sharp drop in the absorption graph occurs near the $\ensuremath{\gamma}$ line in the K-series corresponding to the K-critical absorption wave-length, and three sharp drops (a strong, a medium and a weak one occur near the L-series, indicating three critical absorption wave-length in that series. The critical absorption frequencies calculated from these graphs are, for the K-series: $\ensuremath{\nu}=\mathrm{I}.680\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}$; and for the L-series, ${\ensuremath{\nu}}_{1}=.2438\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}(\mathrm{strong})$, ${\ensuremath{\nu}}_{2}=.2773\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}(\mathrm{medium})$, ${\ensuremath{\nu}}_{3}=.2917\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}(\mathrm{weak})$. The frequencies calculated from the peaks representing the emission lines are ${\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{1}}=\mathrm{I}.437\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{12}(\mathrm{strong})$, ${\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{2}}=\mathrm{I}.405\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}(\mathrm{medium})$ ${\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{3}}=\mathrm{I}.39\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{19}(?)(\mathrm{weak})$. The precision of measurement is such that the probable error amounts to less than 1/5 per cent.It appears from these data that to within 1/5 per cent. $\ensuremath{\nu}\ensuremath{-}{\ensuremath{\nu}}_{1}={\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{1}}(\mathrm{strong})$, $\ensuremath{\nu}\ensuremath{-}{\ensuremath{\nu}}_{2}={\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{2}}(\mathrm{medium})$ and $\ensuremath{\nu}\ensuremath{-}{\ensuremath{\nu}}_{3}={\ensuremath{\nu}}_{{\ensuremath{\alpha}}_{3}}(\mathrm{weak})$; in other words each $K$ $\ensuremath{\alpha}$ emission line frequency equals the difference between the $K$ critical absorption frequency and one of the $L$ critical absorption frequencies to within the limits of experimental error. If this law, that an emission frequency equals the difference between two critical absorption frequencies applies to all emission lines we must assume critical absorption frequencies in the M series, etc. Two critical absorption frequencies lying between $\ensuremath{\nu}=4\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{17}$ and $\ensuremath{\nu}=5\ifmmode\times\else\texttimes\fi{}{\mathrm{I}0}^{17}$ taken together with those mentioned above will explain the presence of the $\ensuremath{\beta}$ line in the K-series and six of the emission lines in the L series, etc.