Potential, tension forces (Spannkraft) and living force in mechanics and electricity

Helmholtz, in Über die Erhaltung der Kraft (1847), treated free material points that attract or repel with forces depending only on distance. For them, he wrote, the loss of tension force always equals the gain of living force, and the reverse. The sum of the two is therefore constant. He called this the principle of the conservation of force¹. He extended the argument to electricity. Following Gauss's usage for magnetism, he named the quantity for two electric elements their potential. The gain in living force over any movement equals the excess of potential at the end of the path over that at the start².

Later biologists borrowed the term for energy in general. Driesch (1908) argued that a medium holding high potentials, such as sunlight and warmth, does not by itself make becoming possible. He held that differences are needed between potentials of coupled energies that can be transformed into one another³. Leduc (1911) described potential energy as slumbering, locked up in a body. A small outside stimulus could release it, and the stimulus bore no quantitative relation to the amount released⁴. Bayliss (1915), citing Ostwald, noted that chemical potential cannot be raised directly by the fall of potential in just any other reaction⁵.

By the 1920s potential also meant a measured voltage in living tissue. Lillie (1923) reported that Macdonald first showed the demarcation potential of nerve varies with the salt concentration of the adjoining solution. The variation resembled that between a metal electrode and its solution⁶. Child (1924) linked the electric potential differences along physiological gradients to differences in metabolic rate or oxidation along the gradient. He called this probable but added that metabolism was not the only possible source of such differences⁷.

Recent reviews use potential mainly for the voltage across the cell membrane. Urrego and colleagues (2014) describe an early finding that holding the potential of Chinese hamster ovary cells at a fixed hyperpolarized value stopped DNA synthesis, which resumed on release⁸. Abdul Kadir and colleagues (2018) recall that the resting potential was long treated as a cocked gun for firing action potentials in excitable cells. Their title points to roles beyond that⁹.