310 ANNUAL REPORT SMITHSONIAN INSTITUTION, 196 



axis of circular symmetry and mounted in gimbals, or carried by some 

 other means, that allow it to have rotational freedom about directions 

 at right angles to its spin axis. The action of such a gyroscope (a 

 name applied by Foucault to devices with the features just described) 

 depends on Newton's law of motion, wliich states that a particle of 

 mass acted on by a force has a rate of change of its velocity vector in 

 the direction of the applied force. The magnitude of this rate of 

 change is directly proportional to the magnitude of the force and is 

 inversely proportional to the moving mass. Any space in which 

 Newton's law of motion applies is by definition an inertial space. 

 The possibility of inertial navigation depends on the fact that matter 

 used for equipment parts responds to applied forces by motions with 

 respect to an inertial space that is essentially identical with the space 

 determined by the fixed stars. 



In a moving, rigid body, such as a gyroscopic rotor, interactions 

 among individual particles combine to give the rotor an angular mo- 

 mentum that is equal to the product of the moment of inertia about 

 the spin axis and the angular velocity of spin. The consequence of 

 Newton's law of motion as far as it pertains to a gyroscopic rotor is 

 that a torque applied to the rotor about any axis at right angles to 

 the spin axis causes the spin axis to rotate toward alinement with the 

 torque axis. The angular velocity associated with this rotation, which 

 is called precession, is proportional to tlie magnitude of the applied 

 torque and is inversely proportional to the magnitude of the rotor 

 angular momentmn. 



When the torque applied to a gyroscopic rotor is zero, the angular 

 velocity of precession is zero, and the spin axis perfectly holds its 

 existing orientation with respect to inertial space. For the purposes 

 of navigation, the important fact is that the space in which a torque- 

 free gyroscopic rotor holds its spin axis in a fixed direction is identical 

 with the celestial space associated with the fixed stars. This means 

 that a geometrical reference member controlled by two or three gyro- 

 scopic rotors designed for substantially torque-free operation will hold 

 its orientation almost perfectly with respect to celestial space. Thus, 

 a mechanical member inside a navigation system can supply all the 

 necessary geometrical-reference information, without the need for 

 external radiation contacts of any kind. 



In addition to this feature, wliich supplies the essential need of self- 

 contained navigation equipment, gj-roscopic inertial members are more 

 convenient for reference purposes than celestial space, which must be 

 used through the medium of a few nonsystematically located fixed 

 stars. This convenience stems from the fact that torque-free gyro- 

 scopic rotors do not tend to move toward any preferred direction, but 

 hold any orientation they may have when applied torques are reduced 



