§ 1. In 1880 Stringham proved that in space of four dimensions there exist six and no more regular rectilinear figures, whose boundaries are regular polyhedra. The same result was arrived at independently by Hoppe in the following year. In 1883 Schlegel gave an extensive investigation of the same problem, and constructed projection-models of the six regular figures, which were exhibited at the Magdeburg meeting of the Society of German Naturalists in 1884. This series of models was published by the firm L. Brill of Darmstadt and is obtainable from their successors, Martin Schilling in Leipzig.

In January 1913 I communicated a paper on the changes of resistance of nickel when subjected to a combination of longitudinal and transverse magnetic fields (1). The following paper contains an account of exactly similar experiments with iron and steel.

Each steel or iron strip formed the core of an anchor-ring coil which was double-wound, with two exactly equal coils of copper wires. When the current was passed through the two contiguous coils in series in the same direction the metal cores were magnetized longitudinally. When the current was passed in opposite directions through the two coils there was no magnetization produced in the cores, but the heating effect was the same as in the first case. At the beginning of each experiment the current was applied in the latter or unmagnetizing arrangement, and was sustained for a sufficient time to permit the temperature to become practically constant. With reversal of the current in the one half of the enveloping coil a longitudinally magnetizing force was established within the region occupied by the iron or steel core. By means of a succession of reversals and rereversals the core could be subjected to a cyclical variation of magnetizing force, while the temperature remained practically constant.