44 ELEMENTARY ACTIONS. 



CHAPTER II. 

 ELEMENTARY ACTIONS. 



462. AMPERE'S METHOD. The course we have followed is, so 

 to say, the inverse of that which led Ampere to the law of ele- 

 mentary actions. The importance of the subject, and the interest 

 which Ampere's experiments and reasonings present, will justify the 

 fresh statement of the question which we shall make, based on the 

 ideas of this illustrious philosopher. 



Ampere considered the actions exerted by currents, on magnets 

 or on currents, as the resultant of the actions of each of the elements 

 of length, into which the current may be decomposed, and he endea- 

 voured to deduce from experiment the law of these elementary 

 actions. 



If we inquire to what extent an elementary law thus defined is 

 directly accessible to experiment, it will be seen that in strictness it 

 is possible to study the action of a single pole on a current element 

 by working with a solenoidal magnet so long that the action of the 

 other pole may be neglected, and with a portion of the current as 

 small as we like, which is made movable ; this, however, is not the 

 case when we consider the action of a current element on a pole, or 

 the interaction of two current elements. Only the entire circuit 

 of the current, or in all cases a closed current, can be made to act 

 on a movable current element as on a pole. 



The investigation of a mathematical law, in the way in which 

 Ampere views the problem, corresponds then at least in the second 

 case to a purely mathematical conception ; but the method is none 

 the less legitimate so long as we merely propose to determine the 

 resultant action of the whole circuit, the elementary law being then 

 restricted only by the condition that the integral relative to a closed 

 circuit gives a result which agrees with experiment. But it is clear, 

 also, that the problem thus stated is not completely determinate, and 

 that there may be several elementary laws which satisfy this funda- 

 mental condition. 



