6 UNIVERSITY OF COLORADO STUDIES 



It is easily proved that under these conditions the total number 

 of lines of magnetic force passing outward 

 through a closed surface cannot vary with 

 the time (Fig. 1). The e. m. f. around 

 the closed line 1, equals the rate of decrease 

 of tlie lines of magnetic force through the 

 surfaces S^ and Sg from left to right. 

 The rate of decrease in the number of ^^^- ^• 



lines is the same for S^ as for Sg, and equals the rate of increase in 

 the number of lines through S^ from right to left — i. e., outward from 

 the space enclosed by S^ and S^. Hence, considering S^ and Sg as a 

 single closed surface, the rate of decrease in the number of lines 

 passing outward through it equals the rate of its increase; or the 

 total number of lines of magnetic force passing outward from any 

 closed surface does not vary. 



Apply the above to a small closed surface fixed in space sur- 

 rounding one and only one of the elementary magnets. The number 

 of lines of force outward through the surface cannot vary, even if 

 the magnet should move completely out of the enclosure. Hence 

 there must be as many lines of force running toward the magnet as 

 away from it. 



The question now arises: If we adopt the electronic theory of 

 the conduction of electricity, can we generalize the second law so as 

 to hold for material bodies, even in case the change is due to motion 

 of the electrons? It is immediately evident that we cannot do so 

 without special hypotheses, for if we surround an electron the charge 

 of which is e, by a small closed surface, the number of lines of 

 electric force through the surface outward is 4 tt e, and if the 

 electron moves out of the enclosure the number changes to zero. 



We may, however, generalize the second law as follows: The 

 magneto-motive force around any closed curve equals the rate of in- 

 crease of the number of lines of electric force running through any 

 surface bounded by the curve, provided we take account of that in- 

 increase only which is due to the cutting of lines of force across the 

 closed curve. 



