After a short introductory chapter, a critical summary of previous work is contained in chapter 2, and the need for coincidence methods in dealing with more complex decay schemes is discussed. The contents of these chapters are drawn mainly from original papers although use has been made of previous reviews. In chapter 3 an account is given of a search for possible low-energy quanta emitted in coincidence with beta-particles in the decay of tritium. This work formed the final part of a more extensive examination of the decay of tritium by Dr. G. M. Insch. The author's part in these coincidence experiments consisted in assisting Dr. Insch with the experimental work and with analysis of the results. Chapter 4 describes how the primary beta-spectrum of RaD was isolated for the first time. The design of this experiment and preparation of the source were due to Dr. Insch; the experiment itself was conducted solely by the author; the analysis of the results was shared equally between Jr. Insch and the author. Further elucidation of the decay scheme of KaD was practicable only by the aid of coincidence techniques. Chapter 5 gives an account of how a single-channel pulse analyser, built by the author during his early research programme, was developed to provide a satisfactory method of recording coincident events. The electronic circuits described here are due to Mr. R. Chiles although several modifications were made by the author. Application of the resulting equipment to the further study of the KaD decay scheme is described in chapter 6. The work described in this and in the succeeding chapters was conducted independently by the author although the method of approach was influenced by frequent discussions with Dr. S. C. Curran. The use of solid radioactive sources, as in the experiments with KaD, leads to some uncertainty regarding the effect of back-scattering of electrons from the source support, and data on back-scattering generally available were inconsistent. The author therefore initiated independent experiments upon this general problem. The results of these experiments, described in chapter 7, are in fairly good agreement with those obtained by earlier workers using a source of beta-particles placed outside a Geiger counter, but show marked disagreement with those which made use of a source inside a Geiger counter. Chapter 8 describes a series of experiments aimed at explaining this disagreement between the two types of Geiger counter measurement. This thesis is not presented in strict chronological order. Due to the duration of the experiments on back-scattering, these were to some extent conducted in parallel with the coincidence examination of the KaD decay scheme
