The work to be here considered is a continuation of a previous investigation by Prof. Laby and the present author, in which the existence of fluctuations in the ionisation due to γ-rays from radium was demonstrated. In the present paper the quantitative measurement of this fluctuation is described, and its relation to the theory of γ-rays investigated. At the present time two theories exist for the explanation of the Röntgen and γ-rays (the two radiations exhibit so many properties in common that they are regarded as phenomena differing only in degree), viz., the pulse and entity theories. According to the former, the rays are conceived as propagated from the source, with a continuous wave front, while the latter theory includes the corpuscular form of Bragg, the pulse in a tube of force, or bundle, theory of Sir J. J. Thomson, and the quantum form postulated by Planck and Stark. In any of these last theories the disturbance has a discontinuous wave front and is propagated from the source along a straight line.