I. Present Status of the Problem of Absorption and Scattering of X Rays by Elements of Small Atomic Weight.---The mass scattering and mass absorption coefficients are defined, and a brief summary is given of the results of previous absorption and scattering measurements in the regions of wave-lengths on the short wave-length side of the K radiation of the absorbing substance, in so far as they relate to the present investigation. The current views in regard to the mechanism of absorption and scattering, and some of the theoretical work which has been advanced to account for these phenomena, has been outlined with regard to their bearing on the work reported in this paper.II. Absorption and Scattering of Homogeneous X Rays by Water, Lithium, Carbon, Nitrogen, Oxygen, Aluminium, and Iron at various Wave-lengths within the Region Bounded by 0.13 and 1.05 \AA{}. U.---(1) The total absorption coefficient of homogeneous X rays obtained by passing the X rays from a Coolidge tube through a Bragg X ray spectrometer was measured for the above-named materials at various wave-lengths in the range indicated. The total mass absorption coefficient was found to be proportional to the cube of the wave-length of the X rays over certain regions, but for all the substances where the investigation was complete over the whole range mentioned, the constant of proportionality was different for different ranges of wave-length. (2) Hydrogen is apparently an exception to the above statement, for its total mass absorption coefficient appears to be proportional to the nine halves power of the wave-length of the X rays. (3) The constant which multiplies the cube of the wave-length to give the true mass absorption coefficient is found to be approximately proportional to the cube of the atomic number of the absorbing element, except for lithium, and this indicates that Moseley's law will not be found to hold for this latter element. (4) The true mass absorption coefficient for iron is apparently not proportional to the cube of the wave-length for waves between 0.70 and 1.05 \AA{}. U. No explanation is suggested for this. (5) The true mass absorption coefficient for the elements, with the exception of iron, for wave-lengths less than 0.20 \AA{}. U. are smaller than is to be expected from theory if the electron has a diameter of the order of ${10}^{\ensuremath{-}13}$ cm. Compton's modification of the expressions for these absorption coefficients accounts for these experimental results if we assign to the electron a diameter of 0.75 to 0.85 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ cm. (6) The lack of this decrease in the coefficients for iron is attributed to a shrinkage in the diameter of the electrons in the atoms on account of the closer packing of the electrons in this element. (7) The mass scattering coefficient of all the substances used is less than that given by Thomson's theory, but no explanation has been found. (8) The mass scattering coefficient for hydrogen is approximately twice that for the other elements, and this is interpreted as further evidence that hydrogen has twice the number of scattering electrons per unit mass as the other elements. (9) The mass scattering coefficient for iron apparently increases for wave-lengths longer than 0.70 \AA{}. U. It is suggested as an explanation of this fact that the distance between the scattering electrons in the iron atom is of the order of magnitude of 0.70 \AA{}. U.III. Projects for Further Absorption and Scattering Measurements.---(1) The scattering of X rays should be measured as a function of the angle of scattering. (2) The absorption and scattering of hydrogen should be measured directly.