GYROSCOPIC COMPASS METHODS OF SURVEYING 205 



taken mainly by the firm of Siemens and Halske. Owing 

 to insufficient technical assistance and faulty knowledge 

 these experiments were more or less abortive. 



A gyroscope^ consists of a heavy wheel mounted on bear- 

 ings free to spin about different axes, usually symmetrical 

 axes perpendicular to the equatorial plane (Fig. 143). 

 When the conditions of dynamical symmetry are not obeyed 

 we get bad static balance, as when 



a. The center of mass of the gyroscope does not lie 

 on the spinning axis; as in the case of an eccentrically 

 mounted disc. 



b. The principal moment of inertia is not coincident 

 with the spinning axis, a torque being thrown on the bear- 

 ings; as when we get oblique but central mounting. 



c. The moments of inertia about all axes through 

 are not normal to the axis of spin; as when we have an 

 elliptical centrally mounted disc. 



These are corrected mainly by distribution of small 

 masses on the disc. When all the axes xx, yy and zz are 

 as in Wheatstone's gyroscope shown in Fig. 143, it is said 

 to be ''free," and if any one is locked it is said to be ''con- 

 strained." This latter feature sets up certain phenomena 

 applied in borehole surveys. 



Degrees of Freedom. — The spin of the disc about zz 

 is known as the first degree of freedom, the rotation of the 

 disc about yy axis the second and that about the xx axis 

 the third degree of freedom. When the disc spins about 

 zz there is an instantaneous angular movement of the axis zz 

 known as "precession." It can be noted if a heavy 

 cycle wheel is held vertically in front of the body with 

 the left hand by means of an axle and spun clockwise 

 with the right. The bearing pressure on the left palm 

 tends to vanish and the wheel under the influence of the 

 spin and gravitation rotates anticlockwise about the experi- 

 menter's body. The free gyroscope tends to keep the axis 



^ Glazebkook, Sir R., "Dictionary of Applied Physics," Vol. 1, p. 421. 

 Ross, J. F. S., " Introduction to the Principles of Mechanics," Cape, 1923. 

 Haussmann, K., "Der Kreiselkompass in Dienste des Bergbau," 1914. 



