652 
Proceedings of the Boyal Society 
required length as determined by a screw gauge. To enable the 
circles of equal radius are scratched on each glass disc, and the adjust- 
ment is made by looking from above downwards upon both discs from 
holes in the top of the balance case; The ends of the wires pro- 
ceeding from the fixed coils dip into mercury pools formed in the 
base board of the balance, which also serve for making connections 
with the battery and the vertical rods which convey the current 
into the suspended coils. The connections are so arranged that the 
current circulates in opposite directions in each fixed and corre- 
sponding suspended coil. In this way repulsion is always produced, 
no matter how the current enters and leaves the entire circuit. The 
repulsion is measured by the number of grammes required to restore 
the balance to exact equilibrium. 
From the above description it will be obvious that any motion of 
the beam in the act of weighing causes only a very slight motion of 
the platinum wires which dip into the fluid contained in the cups. 
In this way the resistance due to the viscosity of the fluid is very 
small, even in the case of mercury, and much smaller when dilute 
acid is used. In point of fact, the diminution of sensibility due to 
this cause is less than in the case of determining the specific gravities 
of solids by weighing in water in the ordinary way. With mercury 
it is quite easy to weigh accurately to a milligramme. 
The repulsion between each pair of coils can be calculated from 
the formula given by Neuman for the action between two current 
elements. 
Let a = radius of each coil. 
x = the distance between their planes. 
0 = the angle between the directions of an element ds of 
Then, if M denote the potential energy due to the mutual action of 
the two circuits when each carries unit current, we have 
respective pairs of coils to be placed concentric with each other, 
the one circuit, and in element ds' of the other. 
r = the distance between these elements. 
r 
