1. Description of a method ("method of the trochoid") of concentrating and focussing weak electron beams so that they form strong sharp lines on a photographic plate. 2. Displacement of the beam thus formed by an additional field, enabling the observer to recognize the sign of the charge and to estimate the charge-to-mass ratio of the particles, with an accuracy thus far brought up to 15 percent. 3. Absorption, in thin films of platinum and a large number of other elements, of the positive and negative electrons proceeding from a source composed of a radioactive substance emitting strong gamma-rays and enclosed in lead; it is shown that the absorption follows an exponential law over a wide range of thicknesses, and the value of the mass absorption-coefficient is obtained from observations on the imprint made upon a photographic plate behind the absorber. 4. When in the foregoing experiments the thickness of the absorber is increased beyond about 500 mg/${\mathrm{cm}}^2$, it becomes evident that the imprint on the plate is partly due to something else than the transmitted electrons. This "something else" is considered to be radiation; with negative electrons it consists entirely of secondary x-rays, with positive electrons there is an additional component ascribed to the merging of positive with negative electrons and their conversion into photons. 5. The absorption-coefficient of these photons implies that their energy is about 0.5 MEV, and the intensity of the radiation implies that there are about two of them per positive electron—two results which agree well with Dirac's theory. 6. Positive electrons have also been observed in conditions where it seems that they proceed directly from radioactive substances.

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