Remarks on the Scattering of X-Rays by Gases and Crystals

§ §1 and 2: Woo's most recent formulas for the separation of the diffusely scattered radiation from polyatomic gases and simple crystals into coherent and incoherent radiation are discussed. It is shown that Woo's formulas for the total scattered radiation reduces to the author's respective classical formulas when $\alpha (=\frac{h}{\mathrm{mc}\lambda })$ is made zero. This removes the objection made by the author in a previous note. It is shown that the incoherent scattered radiation depends upon the root mean square of the $E\text{'}\mathrm{s}$ while the coherent radiation depends upon the arithmetic mean of the $E\text{'}\mathrm{s}$, thus giving a mathematical distinction between the incoherent and coherent radiation even in the classical theory. §3: Evidence is presented in favor of the true atom form factor $f$ of an atom in a crystal (sylvine) being a function of the temperature of the crystal. The average electron distribution about the center of an atom in a crystal must be a function of the violence of the thermal agitation of the atom. At 0°K the electron distribution in an atom of sylvine is more diffuse than in an atom of argon. As the temperature rises above 0°K the electron distribution becomes less diffuse and finally becomes like that of argon at about room temperature. §4: It is shown that the $S_g={(S+\frac{F^2}{Z})}_c$ relation can be replaced by a relation between experimental quantities alone—otherwise, an empirical relation. §5: A digression on the philosophy of physics in which it is noted that the empirical relation of §4 contains no vestige of the Thomson or any other theory of x-rays. This supports the view that physical laws express relations between pointer readings. §6: The classical theory for the diffuse scattering of x-rays by a crystal consisting of atoms of several kinds is worked out and a formula obtained. By the use of Woo's method, the formulas for the coherent and incoherent radiation are also obtained. The restrictions upon these formulas are discussed.