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



where G stands for the resistance of one of the coils of the 

 galvanometer. 



By formuhe (II) (III) or (IV) the resistances respectively be- 

 tween each set of earths can be correctly calculated, and these 

 values being substituted for r, r 2 and r 6 in formula (I), we can find 

 x the required resistance of the earth. 



When a Wheatstone's bridge or differential galvanometer are 

 not available the required resistance of the " earth" may be ob- 

 tained in the following way by comparative deflections. For 

 simplicity two leading wires only need be used, one just long 

 enough to reach to the most distant " earth" of the three, and the 

 other just long enough to reach the next distant. 



Make the five following observations of deflections with the 

 galvanometer, the same battery being used in all cases, and each 

 test made with positive and negative currents and the mean taken. 



I. When the galvanometer alone is in circuit : deflection = a°. 



II. When the two leading wires, and the galvanometer are in 

 circuit : deflection = b°. 



III. When the Telegraph earth, one of the new earths, the two 

 leading wires, and the galvanometer are in circuit : deflection = c°. 



IY. When the Telegraph earth, the other new earth, the two 

 leading wires and the galvanometer are in circuit : deflection — d°. 



V. When the two new earths, the two leading wires, and the 

 galvanometer are in circuit : deflection = e°. 



Then if the deflections are small, so that they are proportional 

 to the currents, we have 



_Gr + E /a a a a V 



"~~2 \c d ~b ~" e/ 



where x is the required resistance of the "earth" G- and F 

 ths known resistances of the galvanometer and battery respectively. 

 If the deflections be large and the galvanometer used by a sine 

 or tangent galvanometer, then the sines or tangents respectively of 

 the deflections must be substituted in the above formula instead of 

 the simple deflections themselves. 



* (See Appendix IV, p. 183). 



