ON THE INDUCTION-COIL. 201 



a=ù=ei/(l— e 2 ), 



— (7-0(è'-S-'> 



becoming in the limiting case of the sphère (e=0), 



and at the other extrême of elongatiou assuming the fo-rm 



„The force actually operative upon the iron is found by subtracting 

 iV"3f from that externally imposed, so that 



S ? = S ? '-N%; 



and if frorn experiments on very elougated ellipsoids (N=0) we know 

 the relation between J£) and 3, then the above équation gives us the 

 relation between Jjï)' and 3 f° r an y proposée! ellipsoid of moderate elon- 

 gatiou. If we suppose that Jf> is plotted as a f miction of 2f> wc have 

 only to add in the ordinates.iV 3? proper to a straight line, in order to 

 obtain the appropriate curve for Jf)'." 



The work expended in magnetizing the iron is per unit of volume 



/«•: i-Vj 2 , 



if Ave reckon from the condition of zéro magnetization. The first part 

 is practically wasted ; the second, which in most cases of open magnetic 

 circuits is imich the larger, is completely recovered when the iron is 

 demagnetized. 



If it appear paradoxical that the large intégral electromotive force 

 which would accompany the disappearance of high magnetization in a 

 closed iron circuit should be so inefflcient, we must remember that the 

 mechanica! value of electromotive force dépends upon the magnitude 

 of the current which it drives, and that in the présent case the existence 

 of more than a very small current is inconsistent with that drop of 

 magnetization upon which the electromotive force dépends. 



The considérations above explained are of interest in the présent 

 question as affording a limit depending only upon the iron core and 



