Prof. Rijke on some Properties of the Induced Current. 261 

 i the intensity of the current which circulates in MN 



% a i) 3i 



m 



2 1 33 33 33 



*2 3) 33 33 



J 



2 3 33 33 33 



APB 



AM 



MB 



AN 

 NB. 



'4 33 33 33 



We shall have from Ohm's law, 



«!=* +«3, (a) 



i ]= zi 2 + i , (b) 



%=*0 + *4i ( C ) 



and from KirchhofFs principle, 



i r + i 1 r l + i 2 r 2 = e + e v (e) 



i 2 r 2 + i 4 r 4 — i r = 0. ...... (f) 



Eliminating i 2 and z'y, 



i + i—h + h=0, (g) 



«O r O— *B + *l( r I+ r «) saa «lJ ( h ) 



— i r 2 -\-ir + i l (r { +rc i ) = e-\-e v .... (i) 



-*o( r + r 2) + % r 3 + *4 r 4= ( k ) 



Eliminating z 4 from the equations (g) and (k), we get 



— *o( r O + r 2 + ^)— *>4 + *l( r 2 + r 4)= ' • • 0) 



The equations (h), (i), and (!) give by the elimination of i and i i3 



r a r c 



and replacing r 4 by its value -^-^ 



? 'i 



?n = 



e,r 2 



ibfa+rj+rgfa+ra) 



Thus the last member of this equation contains neither e nor r. 

 Let us suppose now that we have at P a voltaic apparatus, at 

 S a spiral or any other apparatus in which an extra current could 

 be induced, and at D a Weber's dynamometer. Tn this case e 

 will represent the electromotive force which operates at P, e x that 

 which is induced in S, and i\ the resistance of the spiral and of 

 the conductors which join its ends to the knots A and M. If 

 we break the primary current at C, for instance, r will represent 

 the resistance of the voltaic apparatus increased by the resistance 

 which the primary current meets in its passage in P and B and 

 P and A, and which is variable, seeing that the resistance of the 

 voltaic arc formed at C is comprised in it. The deflection which 

 the moveable helix of the dynamometer will undergo, provided it 

 is not too large, will be proportional to the quantity 



Jo 



*i»g 



'o( r I+ r *)+ r l( r i+ r 3)-J 



dt } 



