The thesis opens with an account of the five-dimensional relativity theory of Klein and Kaluza and its development by Flint as a five-dimensional matrix geometry. This leads to a fundamental equation which contains the Dirac equation for the electron as a special case. The introduction of the nuclear field in a manner analogous to that of the electromagnetic field in four-dimensional relativity theory leads to an equation representing the behaviour of a fundamental particle in the nuclear field. Comparison of this equation with the Dirac equation applicable to such a particle shows the presence of extra terms giving rise to an additional amount of energy which is considered to be due to the interaction of the particle with the field. By analogy with Maxwell's electromagnetic theory the nuclear field equations are obtained for the various types of field and compared with those of other authors. The interaction energy is calculated in each case and agrees with the accepted forms.An interesting result emerges when the total energy of the system (that is, field and particle) is considered, suggesting a possible escape from the difficulty of the infinities arising in the calculation of the interaction energy. Finally, the case of the electron is considered in thelight of the nuclear field theory.