The motion of charged particles in electromagnetic fields has been the subject of many contributions to this series-the first volume, published in 1948, contained chapters on the deflection of beams of charged particles and on particle accelerators by R.G.E. Hutter and M.S. Livingston respectively and later volumes have included chapters by many of the leading scientists in charged particle optics: H. Moss on cathode-ray tubes, P. Grivet on electron lenses, G. Liebmann on numerical methods for field plotting and ray tracing, for example, and, particularly relevant, A.J. Dragt and E. Forest on the Lie algebraic theory of charged-particle optics and electron microscopes. Supplement 7 by myself dealt with quadrupole optics and the three volumes of Supplement 13, edited by A. Septier, with applied charged-particle optics.