is somewhat interesting theo- 
in the 
Intensities of Powerful Magnetic Fields. 145 
below for each, the details of the experimental arrangements, 
and the results I am alone responsible 
(a) The first method, which 
retically, is one which was use 
determination of the magnetic field-in- 
tensities in the space in which the 
signal-coil is suspended in some of Sir 
William Thomson's Siphon Recorders 
made with permanent magnets. In it 
advantage is taken of the signal-coil, 
which consists of a rectangular coil a 
little more than 5 centim. long and 
2 centim. broad, made of thin wire and 
supported by a silk thread above, so 
as to hang in a vertical plane round 
a rectangular core of iron, which 
nearly fills, but nowhere touches, the 
coil. To the lower end of the coil two 
silk threads are attached, as shown in 
the diagram, and are stretched against 
a bridge B by two weights resting on 
the inclined plane W. This bifilar 
arrangement gives a directive force, 
tending to bring the plane of the coil 
into parallelism with that of the bifilar 
threads ; so that when the coil is dis- 
turbed from that position, which is one 
of stable equilibrium, and then left to 
itself, it will, if the circuit be not 
closed, vibrate about the position of 
equilibrium with a determinate period 
of oscillation, with slowly diminishing 
range, until at last it comes to rest. 
But if the circuit be closed through a high resistance, the 
coil will come more rapidly to rest; and if we gradually 
diminish this resistance, deflecting the coil through the same 
angle and _ noting its subsidence at each diminution, we 
shall find it come more and more quickly to rest, until a 
resistance is obtained with which in circuit it just returns to 
the position of equilibrium without passing that position. 
When this resistance has been determined, the strength of the 
field can be calculated. 
Let be the deflection of the coil from the position of equi- 
librium at time t, and T its period of oscillation when the 
circuit is not closed. We have then, neglecting the resist- 
ance of the air and other disturbances, for the equation of 
motion, d 2 d 47 _ 2 
dt*+TT =° (1) 
