208 DEEP BOREHOLE SURVEYS AND PROBLEMS 



For small angles 5 = A sin w. The value of 8 is nil in points 

 D and F, a maximum in A and a minimum in B. 



Corresponding to the divergence of the tangents there 

 appears a force acting at right angles to the disc, which is 

 nil in D and grows to A and from here on again declines to 

 nil at F then back to D in the same manner but taking a 

 course in the contrary direction. 



These lateral components effect a rotation of the spinning 

 disc about the diameter DF or in relation to the original 

 position I about the normal diameter CE; and this turning 

 annuls at every moment the tendency to lateral inclina- 

 tion. This turning motion at right angles to the direc- 

 tion of the applied force is called precession. We shall 

 not go into the lesser motion appearing in the periodic 

 repeated dip and rise of the axis known as nutation. The 

 preceding construction applies very fully to a gyroscope 

 imagined as frictionless. In practice the axis of the 

 gyroscopic disc will, in the course of time, show more and 

 more marked inclination owing to the action of friction. 



As a proof that a force applied to the axis of a rotating 

 gyroscope brings about a lateral movement we have but to 

 consider the common spinning top or child's hoop. 



The Action of the Gyroscopic Compass. — Imagine a 

 gyroscope wheel suspended at the equator so that its axis 

 A^,Ae (Fig. 145) is horizontal and it goes round from west 

 to east. Regarded from west or south the wheel has a 

 clockwise direction of rotation as shown by I in (Fig. 145). 

 Next instant the wheel, owing to the earth's rotation, is in 

 position II (much exaggerated in the drawing). 



Owing to the inertia of the disc the axis AJAJ stays in 

 position II parallel to its former position A^Ae, while the 

 direction line of gravity in II makes an angle of coq ^ 15^ 

 with that in I, owing to the interval t in time between 

 positions I and II and the fact that gravitation acts toward 

 the earth's center. Thus the disc axis is no longer at right 

 angles to the direction of gravity; its east end is too high, 

 so that the force of gravity acts unequally on the axis. 

 On the west end an upward pull is exerted and on the east 



