NATUKE 743 



to Ampere it would not be true if the systems contained open cur- 

 rents. It is sufficient to remark, for instance, that if a magnetic pole 

 is placed at A and an element at B, the direction of the element being 

 in AB produced, this element, which will exercise no action on the pole, 

 will exercise an action either on a magnetic needle placed at A, or on 

 an element of current at A. 



5. Induction. We know that the discovery of electro-dynamical 

 induction followed not long after the immortal work of Ampere. As 

 long as it is only a question of closed currents there is no difficulty, 

 and Helmholtz has even remarked that the principle of the conserva- 

 tion of energy is sufficient for us to deduce the laws of induction from 

 the electro-dynamical laws of Ampere. But on the condition, as 

 Bertrand has shown, that we make a certain number of hypothe- 

 ses. 



The same principle again enables this deduction to be made in the 

 case of open currents, although the result cannot be tested by experi- 

 ment, since such currents cannot be produced. 



If we wish to compare this method of analysis with Ampere's 

 theorem on open currents, we get results which are calculated to 

 surprise us. In the first place, induction cannot be deduced from 

 the variation of the magnetic field by the well-known formula of 

 scientists and practical men; in fact, as I have said, properly speaking, 

 there is no magnetic field. But further, if a circuit C is subjected to 

 the induction of a variable voltaic system S, and if this system S be 

 displaced and deformed in any way whatever, so that the intensity of 

 the currents of this system varies according to any law whatever, 

 then so long as after these variations the system eventually returns to 

 its initial position, it seems natural to suppose that the mean electro- 

 motive force induced in the current C is zero. This is true if the 

 circuit C is closed, and if the system S only contains closed currents. 

 It is no longer true if we accept the theory of Ampere, since there 

 would be open currents. So that not only will induction no longer 

 be the variation of the flow of magnetic force in any of the usual 

 senses of the word, but it cannot be represented by the variation of 

 that force whatever it may be. 



II. Ilelmlioliz's Theory. I have dwelt upon the consequences of 

 Ampere's theory and on his method of explaining the action of open 

 currents. It is difficult to disregard the paradoxical and artificial 

 character of the propositions to which we are thus led. We feel bound 

 to think " it cannot be so." We may imagine then that Helmholtz 

 has been led to look for something else. He rejects the fundamental 

 hypothesis of Ampere namely, that the mutual action of two ele- 

 ments of current reduces to a force along their join. He admits that 

 an element of current is not acted upon by a single force but by a 

 force and a couple, and this is what gave rise to the celebrated polemic 



