GYROSCOPIC COMPASS METHODS OF SURVEYING 207 



Figure 144 shows a plan and elevation of a rotating disc 

 I with a force acting partially on its axis; also its imagined 

 neighboring position II into which the disc is for the time 

 being inclined. (For clarity the drawing is much exag- 

 gerated.) In the plan the narrow ellipse I gives the original 

 position and II the inclined position of the disc. The direc- 

 tion of the disc in plane I in the plan is shown by the hori- 

 zontal diameter AB oi the ellipse. Any mass particle m 

 of the rotating disc I will remain in this position in conse- 

 quence of its inertia, even if the disc inclines a little due 



Elevoi+ion 



Plan 



Fig. 144. — Precession. 



to a lateral torque. This direction of persistence must 

 thus also be present when the particle m rotates in the 

 inclined plane II. If the particle is now compelled to 

 rotate in plane II it still has the tendency to remain in the 

 direction of plane I. The tangents to plane II give the new, 

 those to I the old, directions of movement. These direc- 

 tions are only equal in C and D, also in E and F; in all other 

 points they differ. Let the divergence of corresponding 

 tangents be indicated by 5 and the angle between planes I 

 and II by A and further let the angular rotation of the 

 particle proceeding from D be co, then we get the relation 



sm H = sm ^ sm co 



(12) 



