464 Mr. L. Schwendler on the General Theory 



But, since 



f=w + /3, 



it follows that to reestablish balance by an alteration of the 

 resistances h and d while a, b, /3, and p keep constant, we have 

 to vary all the four branches h, d, w, and/ simultaneously in 

 such a manner that their variations fulfil the following condi- 

 tion, 



Sf=Sd=8w=-{2M), 



which is simple enough to allow of its practical application, but 

 which nevertheless shows again the inferiority of the differential 

 method as compared with the double balance; i. e. } in order to 

 fulfil immediate balance, the key -equation, and the regularity -con- 

 dition for the differential method, we have to make the four 

 branches of the system simultaneously variable, while in the 

 double balance the same effect can be obtained by having only 

 one branch variable (the b branch). 



It is worth while to mention here that there is a special case 

 of obtaining immediate balance for the differential method by the 

 adjustment in one branch, namely when f=0; for then p would 

 be independent of d, and therefore balance could be obtained by 

 varying d without altering p. 



However, on account of the key-equation f=w+/3 } it would 

 follow from/=0 that (3 must be zero also ; which represents a 

 physical impossibility, inasmuch as the internal resistance of 

 galvanic cells cannot be reduced to zero, not even approximately. 

 Besides, the electromotive force requisite for duplex working being 

 necessarily comparatively large, (3 will always be a quantity which 

 cannot be neglected against the other resistances of the system, 

 even if the single cells were of small resistance. . 



But supposing it were practicable to construct a battery of 

 exceedingly low internal resistance, then, as /= b + d, it would 

 be necessary to make b=0 and d=Q, another physical impossi- 

 bility, as b must consist of convolutions to produce magnetism, 

 and d must be variable to produce balance. 



This solution /= b + d=w + (3 = 0, or even each of these three 

 branches of an only exceedingly small resistance, must therefore 

 be rejected. 



(b) Adjustment of balance by moving the coils or armatures. 



This, it will be clear, is the solution for immediate balance; 

 for such a mode of adjustment would involve no relation between 

 the resistance of the three branches, leaving their determination 

 free for other purposes. In order that the slightest movement 

 of the two coils or their armatures may produce the required 

 balance, it will be best to move both the coils or armatures simul- 

 taneously in the same direction. In fact, to be able to produce 



