[1.] The magnetic balance recently described by Professor D. E. Hughes promises to be so convenient and useful an instrument in the laboratory, that the theory of its action and graduation deserves attention. In the actual instrument constructed by Hughes the graduation was empirically determined for a number of values, the remainder being found by interpolation. The instrument consists of a small suspended needle lying in the magnetic meridian provided with a zero-mark placed upon a platform in which a horizontal groove is cut magnetically east and west. In this groove the piece of iron or steel whose magnetism is to be tested is laid, in the “firs position” of Gauss (“end on”), within its magnetising coil, a second coil being added on the other side of the suspended needle compensate the action due to the coil alone. At a certain distance along the platform, and having its centre upon the line of the plat form groove, is set a magnet—called by Hughes the “compensator"—of considerable magnetic moment. The compensator is so pivotte as to be capable of being rotated round a vertical axis through it centre over a scale ; and, according to the original design of tin instrument, the compensator and scale are provided with an arrangement whereby they may be shifted along the platform, so that the can be made to approach nearer to the suspended needle when a more powerful compensation is desired, or removed further away when more delicate magnetic force is to be compensated. In practice the balance was obtained by fixing the central pivot of scale and compensator at a distance of 30 or more centims., and turning the compensator upon its pivot until its magnetic force on the suspended needle, or rather its resolved part in the axial line of the platform, was exactly equal and opposite to that of the piece of iron or steel.