203 WlDCOifSIN ACADEMY SCIENCES, ARTS, AND LETTERS. 



potential V, then these quantities will satisfy the following con- 

 ditions: 



dH dG ^ dF dll ^ dG dF ^ 



dy dz ' dz dx ' dx drj 



But if F^ G, H, be taken to represent the components of the 



vector-potential, they will satisfy the conditions 



dH dG ^ dF dll ^ . dG _^ ^^ p 



dy dz ^ dz dx ' dx dy ' 



where a, b, c, are the components of the magnetic induction. 

 In words, tlie line integral of the vector-nMential round a closed 

 curve representing any circuit, is numerically equal to the surface- 

 integral of the magnetic induction over a surface, bounded by the 

 curve representing the circuit. 



We have also, if a. b, c, represent components of magnetic force, 

 and M, V, w, components of electric current, 



. ^ dc do 



dy dz 



. .. da, dc r^ 



iD^'V = -, J- G. 



dz dx 



, 4, dh dSi 



dx dy 



as the equations of electric currents: or, in words, the line-integral 

 of magnetic force round a closed curve is numerically equal to the 

 current through the closed curve multiplied by 4m*. 



The values of F, G, II, are also given by the following equations 



where m is the quantity Icnown as the specific inductive capacity of 

 a medium, or \i% permeahilitij to m-ngnetic lines of force. 



*The letter <n is put for 3.1416. 



