Tin-; c;ykorcoi'k. 57 



The gyroscopic force, as has been shown, always acts at 

 right angles to the plane in which the axis is moving, chang- 

 ing in direction as the plane of motion of the axis changes^^ 

 and neither tending to increase nor decrease the velocity of 

 motion of the axis, but only to deviate it in direction. 



The amount of the gyroscopic force is greater the greater 

 the centrifugal force of the particles. Since the centrifugal 

 force of a body varies directly as the square of its velocity 

 and inversely as the radius, obviously the gyroscopic force 

 increases as the velocity of rotation of the wheel increases 

 and also as the motion of the axis is more rapid. Again, for 

 the same amount of material in the revolving plane and the 

 same angular velocity of rotation it follows that the gyro- 

 scopic force will be greater the further the mass of the wheel 

 is disposed from the centre. Likewise is the gyroscopic force 

 greater as the rotating mass is greater, as, other things being 

 equal, more particles or systems of particles join together to 

 produce this force. 



What has been found regarding the gyroscopic force may 

 be summarized as follows : 



I. The gyroscopic force always acts at right angles to the 

 plane of motion of the axis, neither accelerating nor retarding 

 it and only tending to change its direction. The gyroscopic 

 force is of the nature of a couple, and can only be balanced 

 by an equal couple. 



II. The gyroscopic force is greater, other things being 

 ecjual, as the velocity of motion of the axis is greater, as the 

 velocity of rotation of the wheel is greater, as the mass of the 

 wheel is greater and as this mass is more distantly situated as 

 regards the centre of the wheel. 



Having now traced out the cause and nature of the gyro- 

 scopic force, let us see what part this force plays in the action 

 of the gyroscope. Iti order to investigate the matter properly 

 it is necessary to first treat of the motion of the theoretically 

 perfect instrument and then afterwards to ascertain the effect 

 of friction and other causes in modifvinu" this motion. 



