The idea of a flux tube comes from the flow of a fluid between stream lines. Here are some links which trace the concept back through time.
1879 Hydrodynamics - Lamb
1873 A Treatise on Electricity and Magnetism - Maxwell
1855 On Faraday's Lines of Force - Maxwell
1852 On the Physical Character of Lines of Magnetic Force - Faraday
Faraday even makes the analogy of lines of force with rays of light! An earlier attempt to arrive at the concept might have been,
1771-81 The Electrical Researches of Henry Cavendish (Maxwell 1879)
Cavendish's canals are remarkably similar to flux tubes. Cavendish studied the electric force in fluids and came close to arriving at the field concept. The idea of an electrical "fluid" is difficult to differentiate from that of electricity. It may have been an early form of an aether theory.
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