Two cases of calculation of mechanical forces in electric circuits

A formula is derived for the mechanical force in a circle of round wire, due to its own current. A formula, F = I
²
logh a
1
/a
2
, is also derived for the longitudinal force exerted on a round conductor, due to its own current, where it changes its diameter. Where there is a constriction in a liquid conductor, this force acts in both directions away from the constriction, thus tending to accentuate it. It may be that this has more to do with the rupturing of a liquid conductor by heavy current, than the better known forces acting in a radial direction, which have been usually referred to under the name “pinch effect.”