the poles of the magnet used and the speed of rotation of the cylinder. The cylinder is of mild steel, and has diameter and length each 10 inches (25'4 cms.). It is shown in section in fig. 1. In order to find the average value of the intensity of induction over elements of the cross-section of the cylinder, holes ^ inch (0'635 cm.) diameter are drilled as shown in a plane containing the axis of the cylinder. By threading insulated copper wires through these holes certain areas were surrounded and the ends of the coils brought out through a hole in the gunmetal shaft to a terminal board fixed thereto. The areas in fig. 1, numbered 1, 2, 3, I, II, III, have in each case been sur- rounded by exploring coils, each coil consisting of nineteen complete turns. Another coil is wound entirely round the cylinder in the same plane of section and numbered 4. A D'Arsonval galvanometer and resistance box were included in each circuit, and twin wires were used in each case to reach from the terminal board to the galvan- ometers.
The magnet consists of two slabs of soft iron each 40 \ inches (103 cms.) long, 19 inches (48'3 cms.) broad, and 8^ inches (21'6 cms.) thick, joined together by a yoke at one end, giving a distance of 8 inches (20*3 cms.) between the opposing broad sides of the slabs. The cylinder rotates in gunmetal bearings bolted to the poles of the magnet, which are tapered so as to concentrate a powerful magnetic field upon the cylinder if necessary. The bore of the pole-pieces is 10|- inches (25-7 cms.) diameter. The arc embraced by each pole-piece is 170, and the length of the pole-piece next to the cylinder is 10 inches. The cylinder is turned by means of a worm and worm wheel. The worm wheel has 90 teeth, and the worm a single thread, so that one revolution of the worm shaft per second corresponds to a periodic time of 90 seconds for the cylinder. The wheel on the worm shaft is turned by hand, while by aid of a clock beating seconds and a scale fixed under the wheel the speed is controlled. For the highest speed the ratio of the gearing was increased four-fold. The operator at the wheel counted seconds aloud, thus enabling the epoch of the simultaneous observations at the galvanometers to be determined. The electromotive forces so obtained have been plotted in terms of the time on squared paper, and by integration the average value of the induction density with respect to any coil has been found. The area taken for each coil is that defined by the centre line of the drilled holes. The areas of coils Nos. 1, 2, 3 are each taken to be 25-8 sq. cms. The areas of coils I, II, III are taken to be 49'2, 51 -6, 51-6 sq. cms. respectively, and the area of No. 4 coil is taken to be 645 sq. cms. Throughout the paper the curves of electromotive force are numbered to agree with the coils from which they have been obtained.
Before dealing with the results obtained, it may be stated that
