This is true if the circuit _C_ is closed and if the system _S_ contains only closed currents. This would no longer be true, if one accepts the theory of Ampère, if there were open currents. So that not only induction will no longer be the variation of the flow of magnetic force, in any of the usual senses of the word, but it can not be represented by the variation of anything whatever. II. THEORY OF HELMHOLTZ.--I have dwelt upon the consequences of Ampère's theory, and of his method of explaining open currents. It is difficult to overlook the paradoxical and artificial character of the propositions to which we are thus led. One can not help thinking 'that can not be so.' We understand therefore why Helmholtz was led to seek something else. Helmholtz rejects Ampère's fundamental hypothesis, to wit, that the mutual action of two elements of current reduces to a force along their join. He assumes that an element of current is not subjected to a single force, but to a force and a couple. It is just this which gave rise to the celebrated polemic between Bertrand and Helmholtz. Helmholtz replaces Ampère's hypothesis by the following: two elements always admit of an electrodynamic potential depending solely on their position and orientation; and the work of the forces that they exercise, one on the other, is equal to the variation of this potential. Thus Helmholtz can no more do without hypothesis than Ampère; but at least he does not make one without explicitly announcing it. In the case of closed currents, which are alone accessible to experiment, the two theories agree. In all other cases they differ. In the first place, contrary to what Ampère supposed, the force which seems to act on the movable portion of a closed current is not the same as would act upon this movable portion if it were isolated and constituted an open current. Let us return to the circuit _C'_, of which we spoke above, and which was formed of a movable wire [alpha][beta] sliding on a fixed wire. In the only experiment that can be made, the movable portion [alpha][beta] is not isolated, but is part of a closed circuit. When it passes from _AB_ to _A'B'_, the total electrodynamic potential varies for two reasons: 1º It undergoes a first increase because the potential of _A'B'_ with respect to the circuit _C_ is not the same as that of _AB_; 2º It takes a second increment because it must be increased by the potentials of the elements _AA'_, _BB'_ with respect to _C_. It is this _double_ increment which represents the work of the force to which the portion _AB_ seems subjected. If, on the contrary, [alpha][beta] were isolated, the potential would undergo only the first increase, and this first increment alone would measure the work of the force which acts on _AB_.