154 Mr. A. Gray on the Determination of the 
same meaning as before ; we get by equating moments of 
forces, w 
I=-^(tan6\+tan0 2 ) (8) 
(7) The third method is one which has been frequently used 
in the Physical Laboratory of the University of Glasgow, and 
consists in exploring the magnetic field by means of the in- 
duced current in a wire moved quickly across the lines of 
force over a definite area in the field. The wire is in circuit 
with a reflecting "ballistic" galvanometer — that is, a galva- 
nometer the system of needles of which has so great a moment, 
of inertia that the whole induced current due to the motion of 
the wire has passed through the coil before the needle has been 
sensibly deflected. The deflection thus obtained is noted, and 
compared with the deflection obtained when, with the same 
circuit, a portion of the conductor is made to sweep across the 
lines of force over a definite area of a uniform field of known 
intensity, such as that of the earth or its horizontal or vertical 
component. 
In performing the experiments, it is necessary to take pre- 
cautions to prevent any action except that between the definite 
area of the field selected and the wire cutting its lines of 
force. For this purpose the conducting-wire, which is covered 
with insulating material, is bent so as to form three sides of a 
rectangle, one of which is of the length of the portion of field 
to be swept over. This side is placed along one side of the 
space over which it is about to be moved so that the connecting- 
wires lie along the ends of the space ; and the open rectangle 
is then moved in the direction of its two sides until the oppo- 
site side of the space is reached. The connecting-wires thus 
do not cut the lines of force, and the induced current is wholly 
due to the closed end of the rectangle. 
Instead of a single wire cutting the lines of force, a coil of 
proper dimensions (for many purposes conveniently of rectan- 
gular shape), the mean area of which is exactly known, mav 
be suspended in the field with its plane parallel to the lines of 
force, and turned quickly round through a measured angle of 
convenient amount not exceeding 90°; or it may be suspended 
with its plane at right angles to the lines of force and turned 
through an angle of 180°. If n be the number of turns. A 
their mean area, and I the mean intensity of the field over the 
area swept over in each case, then, in the first case, if 6 be the 
angle turned through, the area swept over is nk sin 6, and the 
number of lines cut is nlA sin 6 ; in the second, the area is 
2»A, and the number of lines cut is 2nIA. 
In order that with the feeble intensity of the earth's field a 
sufficiently great deflection for comparison may be obtained, 
