740 SCIENCE AND HYPOTHESIS 



done by the electro-dynamical actions is zero. In other words, there 

 is an electro-dynamical potential of the two circuits proportional to 

 the product of their intensities, and depending on the form and rela- 

 tive positions of the circuits; the work done by the electro-dynamical 

 actions is equal to the change of this potential. 



(2) The action of a closed solenoid is zero. 



(3) The action of a circuit C on another voltaic circuit C' depends 

 only on the " magnetic field " developed by the circuit C. At each 

 point in space we can, in fact, define in magnitude and direction a 

 certain force called "magnetic force," which enjoys the following 

 properties : 



(a) The force exercised by C on a magnetic pole is applied to that 

 pole, and is equal to the magnetic force multiplied by the magnetic 

 .mass of the pole. 



(&) A very short magnetic needle tends to take the direction of the 

 magnetic force, and the couple to which it tends to reduce is propor- 

 tional to the product of the magnetic force, the magnetic moment 

 of the needle, and the sine of the dip of the needle. 



(c) If the circuit C' is displaced, the amount of the work done by 

 the electro-dynamic action of C on C' will be equal to the increment of 

 " flow of magnetic force " which passes through the circuit. 



2. Action of a Closed Current on a Portion of Current. Ampere 

 being unable to produce the open current properly so called, had only 

 one way of studying the action of a closed current on a portion of 

 current. This was by operating on a circuit C composed of two parts, 

 one movable and the other fixed. The movable part was, for instance, 

 a movable wire aft, the ends a and ft of which could slide along a 

 fixed wire. In one of the positions of the movable wire the end a 

 rested on the point A, and the end ft on the point B of the fixed 

 wire. The current ran from a to ft i.e., from A to B along the 

 movable wire, and then from B to A along the fixed wire. This cur- 

 rent was therefore closed. 



In the second position, the movable wire having slipped, the points 

 a and ft were respectively at A' and B' on the fixed wire. The current 

 ran from a to ft i.e., from A' to B' on the movable wire, and re- 

 turned from B' to B, and then from B to A, and then from A to A' 

 all on the fixed wire. This current was also closed. If a similar 

 circuit be exposed to the action of a closed current C, the movable 

 part will be displaced just as if it were acted on by a force. Ampere 

 admits that the force, apparently acting on the movable part A B, 

 representing the action of C on the portion aft of the current, re- 

 mains the same whether an open current runs through aft, stopping at 

 a and ft, or whether a closed current runs first to ft, and then returns 

 to a through the fixed portion of the circuit. This hypothesis seemed 

 natural enough, and Ampere innocently assumed it; nevertheless the 



