of the floating wire, to pass into the other trough through the floating bridge, and so to return along the second trough, the floating bridge moves along the troughs so as to lengthen the part of the mercury traversed by the current.
Professor Tait has simplified the electrical conditions of this experiment by substituting for the wire a floating siphon of glass filled with mercury, so that the current flows in mercury throughout its course.
Fig. 40.
This experiment is sometimes adduced to prove that two elements of a current in the same straight line repel one another, and thus to shew that Ampère's formula, which indicates such a repulsion of collinear elements, is more correct than that of Grassmann, which gives no action between two elements in the same straight line; Art. 526.
But it is manifest that since the formulae both of Ampère and of Grassmann give the same results for closed circuits, and since we have in the experiment only a closed circuit, no result of the experiment can favour one more than the other of these theories.
In fact, both formulae lead to the very same value of the repulsion as that already given, in which it appears that , the distance between the parallel conductors is an important element.
When the length of the conductors is not very great compared with their distance apart, the form of the value of becomes somewhat more complicated.
688.] As the distance between the conductors is diminished, the value of diminishes. The limit to this diminution is when the wires are in contact, or when . In this case
