POTENTIAL OF A LAMELLAR MAGNET. 321 



The two formulae (15) and (16) may be simplified if we observe 

 that the integral I d& is equal to zero for external points, and to 



-47T for internal points. 

 We get then 



(15)' 

 (16)' 

 Denoting by 12 a function defined by the ratio 



(17) 



we might put the potential in the form 



(15)" V. = fl + 4T($-$ )- 



(16)" V, = fi. 



336. It is easy to show that, notwithstanding the difference in 

 form of the expressions for V e and V\, the potential varies in a 

 continuous manner when the surface of the magnet is traversed. 

 For consider two infinitely near points M. e and M i? one without and 

 the other within the surface S. In passing from M e to M^ the 

 function fi diminishes by 



Hence, on both sides of the surface, we have 

 (18) fl t = fi i + 4 ,r(*-* ). 



The magnetic potentials at M e and M^ are 



the two values are therefore equal. 



Y 





