Theory of the angular distribution of electrons scattered by a positive nucleus of limited field.—(1) Simple theory. It is shown that if a random distribution of electrons moving on parallel lines with a common velocity, corresponding to $V$ volts, is projected into a central field of force given by $\frac{E}{r^2}$ for values of $r<\mathrm{}\rho$, and by zero for $r>\mathrm{}\rho$, the intensity of scattering in a direction making an angle $\Psi$ with the incident beam will be proportional to ${\left[\frac{(2\mathrm{}\mu -1)}{\left[{(2\mathrm{}\mu -1)}^2\right(1+cos\Psi )+(1-cos\Psi \left)\right]}\right]}^2$, where $\mu =\frac{V_{\rho }}{E}$, provided the variation in mass of the electron with speed is disregarded. (2) Allowing for variation of mass of the electrons with speed so that the trajectories of the electrons through the limited field conform to the orbits calculated by C. G. Darwin, the distribution patterns will depart considerably from those calculated on the simple theory, particularly for small values of $V$. Semi-graphical methods are developed for constructing the distribution curves when $V$, $\rho$, and $E$ are given. (3) Taking into account the mutual energy of electron and nucleus according to the view suggested recently by H. A. Wilson, the actual scattering patterns may be expected to conform closely to those calculated on the simple theory.

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