212 DEEP BOREHOLE SURVEYS AND PROBLEMS 



being seldom more than 1 deg.) Below the point of the 

 pendulum is the midhne m, m, of the apparatus, and, 

 owing to the dip, the pendulum deviates a little way a 

 from this line east or west. This amount a is measured 

 and if, say, the deviation is a mm. and the pendulum 20 

 cm. long, then in a length of 2 m. the hole is displaced 2 cm. 

 to the west. If we carry all measurements at 2 m. and add 

 all the deflections a we get the total deviation of the hole 

 toward the west in centimeters. Similarly the north-south 

 pendulum point may give deflections h at the same times 

 and these are also added as above algebraically. Both 

 displacements are plotted on coordinate paper which 

 permits the position of the hole with respect to its origin 

 being easily found. Thus, for example, for a 300-m. depth 

 in a hole, we employ 150 measurements on the north-south 

 and east-west pendulums and add them for the resulting 

 displacement, say west and south. 



Figure 1 (Plate XIII) shows the interior of the apparatus 

 which is protected by a steel casing, for loosening which a 

 nut at the bottom can be drawn out. It is tightened with 

 India-rubber gaskets which will suit pressures of 150 atm. 



The most important part of the device is the gyrocompass 

 hanging under the inclination measurer, the action of which 

 is based on Foucault's law that the earth exerts, on every 

 horizontal rotating shaft, by its revolution, a force which 

 turns the shaft in the north-south direction, so that the 

 turning of the earth is of the same sense as that of the shaft. 



The directing force we have discussed on page 208 to 

 be the product of the moment of inertia of the wheel, its 

 angular velocity, the angular velocity of the earth, the 

 cosine of the geographical latitude and the sine of the angle 

 between the meridian and the wheel axis.^ 



If the suspension is free enough this directing force lets 

 the axis of the wheel swing into the north-south line, for 

 then the sine of the angle is nil, but in order to attain suffi- 

 cient force the velocity of the wheel must be great. 



1 Martienssen, O., Die Theorie des Kreiselkompasses, Ztschr. f. 

 Instrumentenkunde, 1913. 



