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



To make /3 therefore as small as possible, a sensitive construction of the 

 differential instrument becomes requisite ; further cells of high e. m. f. and 

 low constant resistance are best adapted for forming the signalling battery. 

 In order to get the widest limits in the variation of w it is clear that that fi 

 should be selected which is calculated from the maximum number of cells 

 required to produce the signals with sufficient force. The greatest number 

 of cells is obviously required when the line is at its lowest insulation, in 

 India during the monsoon. 



The value v = — is what has been termed the mechanical arrangement 

 9. 

 of the differential instrument.* 



If h = w -f- /? has been determined by fixing (3, then v has its smallest 

 value for L largest, which is the case when the line is perfect in insulation ; 

 when the coil a must be closest to the magnetic pole acted upon, and the 

 coil b furthest away from it. 



The highest value of v we obtain by substituting the lowest L, i. e. 

 when the line is at its lowest insulation ; when the coil b must be nearest to 

 the magnetic point acted upon, and the coil a furthest away from it. 



Hence the two limits of v being fixed by the known limits between 

 which L varies, the extent of movement of the two coils is also fixed, and 

 consequently, if q is chosen arbitrarily, the construction of the differential 

 instrument is determined. But even q is not quite arbitrary, since we know 

 the form, dimensions and resistance of the coils, which, for instance, in Sie- 

 mens' polarized relays on any given line, have to produce the magnetism in 

 single circuit to get the signals with engineering safety. 



The solution of the 1st problem of the differential method is therefore : 



1. Balance in each station must be obtained by a 

 movement of the two acting coils or their armatures, 

 either singly or better simultaneously in the same di- 

 rection, and not by an alteration of the resistances in the 

 branches. 



2. If this mode of adjusting balance be adopted, then the solution is : 



d = h = o 



f = b = W + /3 

 L , b 



a =2 + 4- 



= r = 1 j b 

 V q 2V2L+b 



It will now be clear that the given solution fulfils the following essen- 

 tial conditions : 



* J. A. S. B., Vol. XLI, Pt. II, p. 148. 

 Phil. Mag., Vol. XLIV, p. 166. 



