58 Louis Schwendler — On the General [No. 2, 



If we substitute the value of r from the balance equation in the expres- 

 sion for P, we get 



Eq 



-V a 



4 a + 2 L + b 



which has an absolute maximum with respect to a only, namely 



Substituting this value of a in the last expression for P we get : 



4 ^/ 2 L + b 



Whence it follows that P becomes largest for b = o, otherwise b re- 

 mains indeterminate ; q on the other hand should be made as large as 

 possible. 



T 



If we now put v = — and develope its value from the balance equa- 

 tion, we get 



r 1 / b 



v = = — / 



q 2VH + 5 



The solution of the 1st problem of the differential method, when the 

 line is perfect in insulation, is therefore 



h = d ■= 

 f = b = iv + p 

 Lb 



1 I 



2V J 



2I + J 



The absolute value of b is left indeterminate,* and we only know that 

 the smaller it can be made the better. 



But to fulfil this best condition f= b = w + fi = represents a 

 physical impossibility, since neither /3, the internal resistance of constant 

 galvanic cells, can be made zero, not even approximately, nor b, which must 

 have convolutions in order to act magnetically. 



The larger f= b = w + /3 becomes, for practical reasons, the more 

 the differential method, even under the best quantitative arrangements as 

 given above, will become inefficient as compared with the double balance. 



* Practically, however, it may be said, that b is given ; for generally j8, the inter- 

 nal resistance of the signalling battery is determined by the nature and number of 

 galvanic cells required for duplex working. "We must only remember that b should be 

 made somewhat larger than /3, in order to have an adjustable resistance w in the battery 

 branch, which may be used for compensating any variation of the battery resistance' 

 that the equation /= b = w + /3 may be permanently fulfilled. 



