Intensities of Powerful Magnetic Fields. 155 
it is necessary that a relatively large area of the field should 
be swept over by the conductor. One convenient way is to 
mount on trunnions a coil of moderately fine wire of a consi- 
derable number of turns wound round a ring of large radius, 
like the coil of a standard tangent-galvanometer, and arranged 
with stops so that it can be turned quickly round a horizontal 
axis through an exact half-turn, from a position in which its 
plane is exactly at right angles to the dip. This coil, of course, 
always remains in the circuit of the ballistic galvanometer. 
The change in the number of lines of force passing through 
the coil in the same direction relatively to the coil, produced by 
the half-turn, is plainly equal to twice as many times the area 
of the turn of mean area as there are turns in the coil (the 
effective area swept over) multiplied by the intensity of the field. 
A sufficiently large area of the earth's field, for comparison, 
may otherwise be obtained very readily by carrying the wire 
along a rod of wood (say two or three metres long), and sus- 
pending this rod in a horizontal position by the continuations 
of the conductor at its ends from two fixed supports in a hori- 
zontal line at a distance apart equal to the length of the 
rod, and securing the remaining wires in circuit so that they 
may not cause disturbance by their accidental motion. The 
rod will thus be free to swing like a pendulum by the two 
suspending-wires. The pendulum thus made is slowly de- 
flected from the vertical until it rests against stops arranged 
to limit its motion. It is then quickly thrown to the other 
side against similar stops there, and caught. The straight 
conductor thus sweeps over an area of the vertical component 
of the earth's field equal to the product of the length of the 
rod into the horizontal distance between the two positions of 
the conductor at the extremities of its swing. The rod may 
be placed at any azimuth, as the suspending portions of the 
conductor in circuit, moving in vertical planes, can cut only 
the horizontal lines of force : and the induced currents thus 
produced have opposite directions and neutralize one another. 
The calculation of the results is very simple. By the theory 
of the ballistic galvanometer (the same mutatis mutandis as 
that of the ballistic pendulum), if q be the whole quantity of 
electricity which passes through the circuit, and if 6 be the 
angle through which the needle has been deflected, or the 
" throw," we have . . 
where (jl is the moment of inertia of the needle and attach- 
ments, m the magnetic moment of the needle, H the earth's 
horizontal magnetic force, and Gr the constant of the galvano- 
meter. If 6 be small, as it generally has been in these expe- 
m * 
