Mr. E. H. M. Bosanquet on Practical Electricity. 255 



Let E be the tension of one cell at rest, 



x the current in the principal cells, 



y the current in the side cells, 



e the change of tension per cell per ampere, 



m the number of the principal cells, 



n the number of the side cells. 

 Then, 



Tension of armature-terminals, or of principal cells 

 =m(E + e#); 



Tension of magnet -terminals, or of side cells 

 =n(E+ey). 



Then, if E, be the resistance of the magnets, sin*ce the diffe- 

 rence of these tensions drives current y through R, 



7?? 



(E + eaO-w(E + ey) = Ky; 



(m — n) E + mex = (we + ~K)y ; 

 dx _ ne + R 

 dy me 



Put n = m—d, where d is the difference between the principal 

 cells and side cells; then 



dx n R-ed 

 j- = 1-1 j 



dy me 



which is > 1 if B, > ed. 

 In the case above given, 



6 =-05, R=-74, d=3; 

 whence ■=- = 2 nearly, and the change of the current through 



the principal cells is twice that in the magnet circuit. 



Of course it is the change in the magnet-current that alters 

 the excitation, and gives rise to instability; so the more we 

 throw the change off the magnet-current, the more stable the 

 arrangement will be. 



The behaviour of the balance as ascertained by experiment 

 corresponds with this theory. The magnet-current alters 

 more slowly than the other. 



To deduce the magnitude of the balancing current in any 

 particular case, put y — x in the equation 



m(E + eas)_ — «(E + ey) = ~Ry; 



(m — n)E+ \(m— n)e— Rj-«=0. 



