The verniers having been read, the cross-arm is rotated so as to deflect the needle _a_ in the opposite direction, and a new setting is taken. Half the difference between the two readings gives the angle through which the needle a has been deflected under the action of the needle _b_. This angle depends on the ratio of the magnetic moment of the needle _b_ to the total force of the earth's field. It also involves, of course, the distance between the needles and the distribution of the magnetism of the needles; but this factor is determined by comparing the value given by the instrument, at a shore station, with that given by an ordinary magnetometer. Hence the above observation gives us a means of obtaining the _ratio_ of the magnetic moment of the needle _b_ to the value of the earth's total force. The needle _b_ is then substituted for _a_, there being now no needle in the clamp attached to the microscope arm, and the difference between the reading now obtained and the dip, together with the weight added to the needle, gives the product of the moment of the needle _b_ into the earth's total force. Hence, from the two observations the value of the earth's total force can be deduced. In an actual observation the deflecting needle would be reversed, as well as the deflected one, while different weights would be used to deflect the needle _b_. For a description of the method of using the Fox circle for observations at sea consult the _Admiralty Manual of Scientific Inquiry_, p. 116, while a description of the most recent form of the circle, known as the Lloyd-Creak pattern, will be found in _Terrestrial Magnetism_, 1901, 6, p. 119. An attachment to the ordinary ship's compass, by means of which satisfactory measurements of the horizontal component have been made on board ship, is described by L. A. Bauer in _Terrestrial Magnetism_, 1906, 11, p. 78. The principle of the method consists in deflecting the compass needle by means of a horizontal magnet supported vertically over the compass card, the axis of the deflecting magnet being always perpendicular to the axis of the magnet attached to the card. The method is not strictly an absolute one, since it presupposes a knowledge of the magnetic moment of the deflecting magnet. In practice it is found that a magnet can be prepared which, when suitably protected from shock, &c., retains its magnetic moment sufficiently constant to enable observations of H to be made comparable in accuracy with that of the other elements obtained by the instruments ordinarily employed at sea. (W. Wn.) FOOTNOTES: [1] _Annals of Electricity_, 1839, 3, p. 288. [2] Humphrey Lloyd, _Proc. Roy. Irish Acad._, 1848, 4, p. 57.