178 W. E. Ayrton— Quantitative Method [No. 2, 



Select two other earths which are neither in metallic connection 

 with each other nor with the telegraph earth to be tested. Two 

 iron telegraph posts near the office answer the purpose very well, 

 only care must be taken that there is perfect metallic contact be- 

 tween the leading wire and the iron post in each case. In the dry 

 season it would be advisable to pour water over the three " earths" 

 used. Measure the resistance between each set of " earths,' * 

 and in this way obtain three independent equations containing the 

 three resistances of the three " earths," and the known resistances 

 of the three leading wires going respectively from each " earth" to 

 the testing arrangement. For instance calling x the resistance 

 of the " earth" to be measured, that is, the resistance between the 

 copper plate or iron wire (or whatever the " earth" consists of) and 

 the ground, and a the known resistance of the wire leading from this 

 " earth" to the testing arrangement, y and z the resistances of 

 the other two earths, and /5 and y the resistances of their leading 

 wires we have — 



y + z + P + y-=*2 

 z -f x + r + a == r 3 



From these three equations, eliminating y and z, we obtain 

 r, - r 2 -f r 3 



X = 2 a ® 



And the question would be completely solved, if earth circuits 

 did actually behave as simple metallic circuits. This is, however, not 

 the case. For in the first place an " earth" long used for telegra- 

 phic purposes frequently acquires a highly polarized state, giving 

 rise to a current. Secondly if the " earths" used are not of the 

 same material, for instance one an iron post and the other a copper 

 plate, they will form a galvanic element with the ground giving 

 rise to a current. Thirdly a real earth current may exist from ter- 

 restrial causes, and lastly the testing current itself polarizes the 

 " earths." Consequently the measurement of the same set of 

 earths taken successively with positive and negative currents will 

 not agree, and they will differ from each other much, if the 

 current, due to the " earths," is large in comparison with the test- 

 ing current itself. It, therefore, becomes necessary to devise some 

 method by which trustworthy tests may be made, and to see how 



