210 



DEEP BOREHOLE SURVEYS AND PROBLEMS 



an angle <t) with the earth's axis, this is then the smallest 

 of all possible angles between a horizontal line and the 

 earth's axis. For a horizontal line of any azimuth Awe 

 get the corresponding angle of inclination a, from Napier's 

 laws. Thus 



cos a = cos </) cos A (13) 



Angle a is greater than 4> because its cosine is smaller. 

 In Fig. 146 point I^ rotates, owing to the earth's rotation 

 in time t, to position 11^. The gravity direction lines in 



I^ and 11^ do not now make an angle of coo = I5t as at 

 the equator, but a smaller angle co^ which can be computed 

 from 



sin 



. Wo 

 sm -^ cos cj) 



(14) 



Thus for small intervals of time we may write 15t cos 0. 

 The directing force of the gyroscope thus decreases with 

 latitude, it being only a half in 60 deg., a quarter in 75 

 deg., and a tenth at 85 deg. latitude, of the force at the 

 equator. It is nil at the pole where all great circles are 

 meridians. On the gyroscope axis swinging into the merid- 

 ian plane from the east, the east end of the axis is somewhat 



