The apparatus and techniques of transmission electron microscopy and diffraction have much in common. Both require a high vacuum, a source of electrons with high velocity, and electromagnetic lenses for focusing the electron beam. In both cases, specimens are usually thin films or dispersions of thin particles supported on a thin substrate. For many years, however, the two disciplines progressed independently. and attracted entirely different groups of scientists. Although it is often stated that the possibility of an electron microscope with high resolution was suggested by de Broglie's (1924) hypothesis of the wave nature of electrons, reviews of the early history of the electron microscope by Mulvey (1962) and Freundlich (1963) clearly indicate that the wave properties of electrons were not seriously considered during development, from 1928, of the first instrument of this type built by Knoll and Ruska (1932a). The concept of an electron microscope arose from attempts to construct an improved cathode-ray oscilloscope, and at the time it was believed that there were no theoretical restrictions to the ultimate resolution. Later in 1932, however, Knoll and Ruska (1932b) made the remarkably accurate prediction of 2·2 Å as the resolution limit for 75 keV electrons. As the resolving power of production microscopes has improved, consideration of the wave nature of electrons has become increasingly important for interpretation of micrographs, especially from crystalline specimens such as minerals.