1871.] of Testing a Telegraph Earth. 179 



from the tests the real resistances of the " earths" may be arrived 

 at. 



Before and after each set of tests note the whole, or a definite 

 portion, of the current caused by the two earths under measure- 

 ment, by simply joining the two earths together through a galva- 

 nometer and observing the deflection. If this deflection is practi- 

 cally the same before and after the two tests with reverse currents, 

 the " earths" have not altered their electrical condition while being 

 tested, and the two values obtained may be used for further calcu- 

 lation. In order to keep the electrical condition of the ''earths" 

 constant, by preventing them becoming polarised by the testing 

 current, it is necessary to measure with only momentary currents. 



The formula which gives the actual value of the resistance of a 

 pair of earths from the two values obtained by testing with posi" 

 tive and negative currents depends, of course, on the kind of testing 

 arrangement employed. For a Wheatstone's balance the formula is 



BF(A + B)(W'+AV")+B 9 (A(W' + W ff ) + 2W / W / ] 



r = AB (W +~ W") +~2 AF(A + B) + 2 A 2 ~B (II) * 



where A and B represent the branch resistances in the bridge, 

 A the resistance opposite to r the resistance to be measured, 

 F the resistance of the testing battery, and W and W" the 

 resistances unplugged respectively in the comparison coil to obtain 

 balance when testing with reverse currents. Putting A equal to 

 B, or testing with equal branches we have 



- ( 2 F + A ) (W / + W) + 2W / W ff 



1 " W ; + W" + 2(2~F + A) ( } 



If W ' and W" are very nearly equal, or small compared with A 

 and F we have 



W' + W" , 

 r = — t 



If the instrument used be a differential galvanometer in which 

 the two coils have equal resistance, but opposite magnetic momem- 

 tum, then 



_ (2 F + G) (W ' + W " ) + 2 W / W" 

 r W' + W"~+2(2F + G) * UV)I 



* (See Appendix I, p. 181). f (See Appendix II, p. 182). 



% (See Appendix III, p. 183). 



