Intensities of Powerful Magnetic Fields. 153 
If instead of a single weight, W, several weights, Wi, W 2 , 
&c, at distances r l7 r 2 , &c. be used to restore equilibrium, we 
have of course, instead of Wr in this formula, simply the sum 
W 1 r 1 + W 2 r 2 + &c. 
Another modification of this method may be convenient in 
some cases. The field-magnets may be so placed that the 
plane cutting the poles in which the intensity is to be deter- 
mined is vertical, and a rectangle made of the proper dimen- 
sions and hung by a torsion-thread or wire, or by means of a 
bifilar, so that it is in equilibrium in the required position, and 
turns when deflected round a vertical axis bisecting it. The 
ends of the wire forming the rectangle are carried down, in- 
sulated from one another, from the middle of the lower side, 
and bent so that their points are in the vertical line bisecting 
the rectangle, and dip, like the terminals of an Ampere frame, 
into two mercury-cups placed one above the other on supports 
arranged below. Two pendulums are arranged so that their 
points of suspension can be moved along horizontal bars at 
right angles to the equilibrium position of the frame, one in 
the vertical plane through each side of the rectangle. These 
pendulums carry at the ends of light but strong threads equal 
known weights ; and each pulls horizontally on the correspond- 
ing side of the rectangle by means of a thread attached at one 
end to the middle point of the side, at the other to the pen- 
dulum-cord. The pendulums and threads are so arranged that 
the pulls are applied in opposite directions ; and thus when 
the pulls are equal they give a couple tending to turn the 
frame round a vertical axis. Corresponding to each pendulum 
are a pair of horizontal scales, arranged like those shown in 
the second diagram above, by means of which, in the manner 
already described, the tangent of the inclination of the pen- 
dulum to the vertical is at once read off. 
The method of experimenting is similar to that last de- 
scribed. The magnets are excited, and a measured current 
sent round the suspended rectangle, from a battery connected 
with the mercury-cups, in the direction to cause the rectangle 
to turn round in the direction opposite to the motion which 
the pendulums are arranged to produce. The points of sus- 
pension of the pendulums are then moved so as to restore the 
frame to the initial position, and the tangents of the inclina- 
tions of the cords obtained by means of the scales. If the field 
be symmetrical about the axis of suspension of the coil, the 
electromagnetic action of the frame will be a pure couple, and 
the equilibrating forces will form also a couple; but in general 
this will not be exactly the case. Let W be the mass, in 
grammes, of each pendulum-weight, 6 X , 6 2 the inclinations of 
the pendulum-cords to the vertical, and let L, b, 7 have the 
