52 Louis Sch wen dler — On the General [No. 2, 



that the re-adjustment of balance is restricted to a variation of the resis- 

 tances h and d. 



But as p is a function of h and d, to establish balance by altering one 

 of them only, would invariably result in an alteration ofp, and consequently 

 immediate balance would become an impossibility. 



Thus in order to readjust balance, and at the same time to keep p 

 constant,* we must vary h and d simultaneously. 



Now, it can be proved in exactly the same manner for the differential 

 method as it was for the bridge, that in order to make the disturbance 

 of balance for any given variation in the system as small as possible we must 

 make p as large as possible, whence it follows from the form of p that 



f=l + d 

 the " regularity condition" for the differential method. 



But since 



/==■!* + : -j8 

 it follows that to re-establish 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 bran- 

 ches h, d, w and f simultaneously, in such a manner that their variations 

 fulfil the following condition : 



Sf= 8d = 8w = — (2 870 

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

 nevertheless shows again the inferiority of the differential method as com- 

 pared with the double balance, i. e., in order to fulfil immediate balance, the 

 Tcey equation, and the regularity condition 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 one branch 

 only variable (the b branch). 



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

 ing immediate balance for the differential method by the adjustment in one 

 branch, namely, wheny= o, 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= to + /?, it would follow 

 from/= o, that /? must be zero also, which represents a physical impossi- 

 bility inasmuch as the internal resistance of galvanic cells cannot be reduced 



f b + d + f 



keep a, b and /constant and vary h and d, whence we should have : 



5p = (b + d + f) {b + d + f + M) Sh + f 2 M = o 

 an equation, which it is always possible to fulfil for any variations of h and d if taken of 

 opposite signs, although it may be difficult to achieve it practically by a simple motion, 

 such as that of turning a handle. The absolute value of these variations depends of 

 course on the variation of c which disturbs the balance, and in order to have accelerated 

 balance we ought to decrease h and increase d when c increases, and vice versa. 



