366 M. L. Schwendler on the Galvanometer Resistance 



In this equation only g is taken as variable ; and the question 

 now is, what must be the value of g in order to raise Y to its 

 maximum. 



This will be the case when g— ^-, or, by substituting the 

 values of W and V, 



9- 



f(b + c)(a + d)+ab(c + d) + cd(a + b) 



(c + d){a + b)+j\a + b + c + d) ' 



by dividing both numerator and denominator by ac } we obtain 

 an equation better suited to our purpose, 





(i) 



This equation (1) establishes a general dependence between 

 the resistance of the galvanometer and that of the other five 

 branches, including the battery branch when the magnetic 

 moment of the galvanometer-coil is a maximum. The above 

 equation having been developed without reference to a balance, 

 we must obtain the known law of simple circuit if we put 



a=c—co . 



Fig. 1 is then changed into fig. 2, and equation (1) gives us 



g=f+b + d, 



Fie. 2. 



^ I i I ■ I 



which is the law for simple circuit, proving the general applica- 

 bility of this equation. 



