The techniques of multiple beam interferometry have been fully developed during the last few years by Tolansky (1946) and his co-workers. The theory of the low order multiple beam fringes in transmission has been discussed by Tolansky (1946a), Brossel (1947), and Wilcock (1951), and the corresponding theory in reflection has been developed by Holden (1949). The theoretical discussion in this thesis will therefore be limited to a summary of the conclusions of the above workers, and the influence of these conclusions on the present experimental investigation. Two types of low order multiple beam fringes have been used to study the surface features of diamond, fringes of equal thickness, and fringes of equal chromatic order