Chap. 10] ELECTRICAL METHODS 645 



the milliammeter to the two external electrodes and through the com- 

 mutator in such a manner that the direction of the current through the 

 ground is reversed periodically while it is passing in the same direction 

 through the milliammeter. The potential difference set up between the 

 internal pair of potential electrodes is likewise of an alternating nature 

 but is "rectified" by the double commutator, so that D.C. potentials are 

 read on the potentiometer. The ratio of voltage and current, multiplied 

 by a spacing factor, gives the resistivity 



V 

 p = 27ra.y . (10-11) 



The derivation of this formula is given on pages 709-710. If R is substi- 

 tuted for V/I, the formula takes the form R = p/27ra, which is seen to be the 

 resistivity of a hemisphere with the radius a (length of current path = a, 

 surface = 2Tra) (see Fig. 10-11). On this relation is based the thumb rule 

 that the depth penetration of the Gish-Rooney arrangement is equal to 

 the electrode separation. 



The "Megger" differs from the Gish-Rooney arrangement in that a 

 direct reading ohmmeter (cross-coil instrument, giving the ratio of V/I) 

 is substituted for the ammeter and potentiometer and that power is sup- 

 plied by a hand-cranked generator instead of by batteries (see Fig. 10-60). 



4. Low-frequency A.C. methods. These methods are well suited for 

 laboratory measurements because low-frequency A.C. is readily available, 

 no commutation device is required, and disadvantages of continuous D.C. 

 are avoided. For high-resistance specimens 110 volt A.C. may be used 

 directly. For lower resistances it should be stepped down by a lamp bank, 

 a carbon resistor, or a transformer. As an indicating instrument, a D.C. 

 current meter of high sensitivity together with a copper oxide rectifier, 

 a vibration galvanometer, or any other oscillographic instrument of high 

 current sensitivity, will be satisfactory. A Wheatstone bridge circuit or 

 the substitution method are applicable (see Fig. 10-12). 



Ground resistivity may be determined directly with a Wheatstone 

 bridge, using two electrodes only. If their radius is a, if I is the distance 

 between their centers, and R is the resistance measured on the bridge, the 



op 



resistivity p = -— tt^^- I^ the distance is a multiple of the 



1 ^_ 0.8a 0.85 



electrode radius so that a — l/n the resistivity is 



2R 



p = 



n CL8 _ 0.85 

 1'^ nl ~T 



