The work described in this Thesis was carried out at the Imperial College of Science and Technology under the direction of Professor G.P. Thomson. It has already appeared in two papers in the Philosophical Magazine, one in November 1935 and the other in November 1936. Part A is concerned mainly with the Investigation of the theory of the diffraction of electrons by a single crystal cleavage face. In connection with this I should like to express my gratitude to Mr. J.W. Harding for the help which he has given in frequent discussions upon the theoretical aspect. Part B is in the nature of a summary of observations made during an examination carried out with the primary object of discovering the best mode of preparation of evaporated metal films for searchlight mirrors. In view of the considerable amount of work at present being conducted in connection -with the preparation and properties of evaporated metal films, it was felt that any Information about the actual crystal structure of such films might be of help and should be published. I wish to thank Sir Robert Robertson and Professor W.T. Gordon for their kindness in lending the diamonds. Finally, I wish to express my gratitude to Professor G.P. Thomson, who suggested the main problem dealt with in Part A, for his helpful advice and kindly Interest throughout the work.