through Heterogeneous Telegraph Circuits. 215 



battery is less than the receiver resistance, and least in the 

 contrary case. Now if the battery is always in circuit, as in 

 making signals with a reversing key, the effect of any arbitrary 

 signals may be calculated by the same formula, and the maxi- 

 mum working-speed (always provided it be within the reach 

 of the apparatus) will be least when the station nearest the 

 cable receives, if the battery is less than the receiver resistance, 

 and greatest in the contrary case. Generally, the more cen- 

 trally the capacity is situated the greater the retardation. 



The influence of leakage or faults may be readily determined 

 in a similar manner, since the retardation is proportional to 

 the resistance through which the charge in the cable discharges 

 to earth. In all cases the retardation is reduced by a fault, 

 and the more so the nearer the fault is to the centre of capa- 

 city. If a fault be introduced on the long land-line b, the dif- 

 ference of the retardation in opposite directions is the same as 

 before as regards direction, while its percentage amount is in- 

 creased. The influence of the natural leakage of the iand- 

 lines is the same, since nearly all the loss will, under ordinary 

 circumstances, take place on the long land-line. But if a 

 fault be introduced on the short land-line, the percentage dif- 

 ference is reduced instead of being increased, and its direction 

 may even be reversed. 



We have thus found that on any circuit consisting of a cable 

 with land-lines of unequal resistance at its ends, a difference 

 in the retardation in opposite directions is necessarily intro- 

 duced when the battery and receiver have not the same resist- 

 ance. Suppose, in figs. 1 and 2,/=l, <2 = 10, c = 10, 6 = 100, 

 <7 = 10; then the retardation from A to B is to the retardation 

 from B to A as 184 : 265, i. e. 44 per cent, greater from B to 

 A than from A to B ; and the natural leakage of the land- 

 lines increases this difference. But with Wheatstone's trans- 

 mitter the observed difference is greater than can be thus 

 accounted for, and exists even when there is no inequality in 

 resistance of the battery and receiver. This is due to a pecu- 

 liarity in the method of making the signals with that instru- 

 ment, which is at the same time the cause of two other ano- 

 malies, viz.: — reduction of working-speed by leakage, although 

 the retardation is thereby reduced ; and increase of working- 

 speed by the addition of resistance, although the retardation 

 is thereby increased. To understand this, it is necessary to 

 examine the way the sending-end of the line is operated upon. 

 The point k in fig. 1, or h' in fig. 2, is always connected with 

 the positive or negative pole of the battery, or it is insulated. 

 Currents of equal duration follow each other, alternately + 

 and — , separated either by no interval, or by intervals equal 



