This thesis descrihes the author's work on elastic and inelastic interactions of positive K mesons with protons at 10 GeV/c. The experiment which is a collaboration between the Universities of Birmingham, Glasgow and Oxford, was undertaken to continue the study of the high mass spectrum and to test the predictions of various phenomenological models. The exposures were taken in the CERK 2-metre liquid hydrogen bubble chamber using a radio-frequency separated beam from the 28 GeV proton synchrotron at CERN, Geneva. In chapter one there is a summary of the experimental data of relevance to the author's work and of the theoretical interpretation of these results. It is shown that further experimental studies of the elastic scattering reaction and of the high mass K* spectrum would be useful. An outline of the techniques of beam handling and of the film analysis system is given in chapter two. Chapter three discusses the estimation of the cross sections for the reactions with two charged secondary tracks with and without a detected neutral decay, the proton contamination and the selection of events for a physics analysis. In chapter four, the elastic scattering events are analysed and the results are found to be consistent with those obtained at other energies. This suggests that the claims of some theorists that the earlier data was incorrectly normalised are Tinjustified. The predictions of various phenomenological models are compared in chapter five with the data from reactions with three bodies in the final state. It was concluded that the double Regge and modified Chan, Loskiewicz and Allison (C.L.A.) models are very weak and completely fail to predict the resonance production features of the data. Although the adaptation of the modified C.L.A. model suggested by Plahte and Roberts predicts the correct masses for the resonances, it gives the wrong decay distributions for the N*(1236) in the reaction K+p-K0p+. The generalised Veneziano model was found to give good fits to the reaction however for the reaction which is probably dominated by the exchange of a Pomeranchuk trajectory, the predictions of the model are not in agreement with the data. Although the modifications to this model, suggested by Kajantie et al. to include the exchange of a Pomeranchuk trajectory, improve these fits, they are not entirely satisfactory. In chapter six the high mass K* spectrum is investigated. This suggests that, from the reactions studied, the dominant L meson decay mode is and that the decay via lower mass K* resonances is weak. Further evidence for the existence of K*s at 2240 and 2640 MeV is found to be weak. The data from an experiment in which the bubble chamber was used as a missing mass spectrometer, suggest the possible existence of a K* at 2.8 GeV of width 35 MeV.