MAGNETIC SHELLS. 313 



The potential at the point P (Fig. 76) of this element of the 

 shell is expressed by 



cos0 





6 being the angle formed by the perpendicular N drawn externally to 

 the positive surface, with the right line r, which joins the point P to 

 the element ^S. 



Fig. 76. 



The solid angle du, under which the element d is seen from the 

 point P, is given by the equation 



d$ cos = rVw or du> = . 



From this it follows that 



As the factor <> is constant, the potential of the shell at P is 

 expressed by 



(9) V = $a>. 



It is important to define with precision the significance of the 

 solid angle o>. The potential dV is positive or negative according as 

 the point P views the positive or the negative surface of the element 

 d$ of the shell that is to say, according as the angle is acute or 

 obtuse. The angle </<o, considered itself as positive or negative in 



