43$ CURRENTS AND MAGNETIC SHELLS. 



The action is therefore inversely as the square of the distance 

 of the pole from the element; it is applied to the element, and 

 is perpendicular to the plane passing through the element and 

 the pole. 



Fig. 103. 



459. RECIPROCAL ACTION OF Two ELEMENTS OF A CURRENT. 

 We have seen (347) that the action of two shells may be expressed 

 as a function of the two contours. The action of the two currents 

 may then be considered as the resultant of the actions exerted 

 between the elements of the current which constitute it. 



This elementary action d 2 (f> is not determinate, but if we assume 

 that it takes place along the right line which joins the two elements, 

 it is expressed by 



Jr tofc' 



If 6 and & are the angles of the two elements with the right line 

 joining them, and e the angle which the two elements make with 

 each other, we have 



(10) d*ip = + cos - - cos cosO' I dsds'. 



The formulae (9) and (10) represent the elementary laws dis- 

 covered by Ampere. 



The method adopted by Ampere to arrive at this result was 

 entirely different ; it will form the object of the following chapter. 



460. ELECTROMAGNETIC INTENSITY OF A CURRENT. We have 

 hitherto defined the intensity of the current by the quantity of elec- 

 tricity which passes through a section of the circuit in every unit 

 of time. The strength thus defined is called the electrostatic intensity; 

 it may be determined by measurements of capacities and potentials, 

 or by electrochemical phenomena. The electromagnetic intensity 

 introduced above (450) is defined by the condition of being ex- 



