742 SCIENCE AND HYPOTHESIS 



current. He concluded that the action of a closed on an open cur- 

 rent, or vice versa, that of an open current on a fixed current, may 

 give rise to continuous rotation. But this conclusion depends on 

 the hypothesis which I have enunciated, and to which, as I said 

 above, Helmholtz declined to subscribe. 



4. Mutual Action of Two Open Currents. As far as the mutual 

 action of two open currents, and in particular that of two elements of 

 current, is concerned, all experiment breaks down. Ampere falls 

 back on hypothesis. He assumes: (1) that the mutual action of two 

 elements reduces to a force acting along their join; (2) that the 

 action, of two closed currents is the resultant of the mutual actions of 

 their different elements, which are the same as if these elements 

 were isolated. 



The remarkable thing is that here again Ampere makes two hypo- 

 theses without being aware of it. However that may be, these two 

 hypotheses, together with the experiments on closed currents, suffice 

 to determine completely the law of mutual action of two elements. 

 But then, most of the simple laws we have met in the case of closed 

 currents are no longer true. In the first place, there is no electro- 

 dynamical potential; nor was there any, as we have seen, in the case 

 of a closed current acting on an open current. Next, there is, pro- 

 perly speaking, no magnetic force; and we have above defined this 

 force in three different ways: (1) By the action on a magnetic pole; 

 (2) by the director couple which orientates the magnetic needle; (3) 

 by the action on an element of current. 



In the case with which we are immediately concerned, not only 

 are these three definitions not in harmony, but each has lost its 

 meaning : 



( 1 ) A magnetic pole is no longer acted on by a unique force applied 

 to that pole. We have seen, in fact, the action of an element of cur- 

 rent on a pole is not applied to the pole but to the element; it may, 

 moreover, be replaced by a force applied to the pole and by a couple. 



(2) The couple which acts on the magnetic needle is no longer a 

 simple director couple, for its moment with respect to the axis of the 

 needle is not zero. It decomposes into a director couple, properly so 

 called, and a supplementary couple which tends to produce the con- 

 tinuous rotation of which we have spoken above. 



(3) Finally, the force acting on an element of a current is not 

 normal to that element. In other words, the unity of the magnetic 

 force has disappeared. 



Let us see in what this unity consists. Two systems which exercise 

 the same action on a magnetic pole will also exercise the same action 

 on an indefinitely small magnetic needle, or on an element of cur- 

 rent placed at the point in space at which the pole is. Well, this is 

 true if the two systems only contain closed currents, and according 



