66 C. M . liKooMAl.l. : 



more or less downward, and the wheel will therefore tend to 

 slowly fall. Owing to the slowness of the orbital motion this 

 action is small compared with that due to the slowing down 

 of the wheel, and cannot interfere with the production of the 

 non-nutating motion just described. 



Another curious action due to friction must be considered. 

 As a matter of experiment it is found that if the end of the 

 axis of the gyroscope be raised above the support and then 

 released it will, under certain circumstances, begin to rise. 

 This difference between theory and practice is due to the fact 

 that the apparatus consists of two parts — the first, the wheel, 

 rotating with friction inside the second, the supporting ring, 

 which does not rotate with it. The friction of the axle tends 

 to produce in the mounting a rotation similar to that of the 

 wheel. The mounting, however, is only free to rotate around 

 a vertical axis, as for instance, if the plane of the wheel were 

 horizontal and it were standing with the end of its axis on the 

 pivot. This ideal position is the only one in which the wheel 

 and its frame could rotate together. In all other positions 

 this force tending to produce rotation of the mounting can be 

 decomposed into two couples, respectively about vertical and 

 horizontal axes, the first acting with full effect, while the 

 latter is destroyed at the point of support. If the axis of the 

 wheel is horizontal, the couple about the vertical axis also 

 disappears. If the end of the axis is above the horizontal, 

 this couple about the vertical axis acts in the same direction 

 as the orbital motion. If the axis is below the horizontal, 

 the couple acts in the reverse direction. The result therefore 

 is the same as if an extraneous horizontal force (constantly 

 increasing with the angle from the horizontal ) were applied 

 to the free end of the axis, acting in the one case with 

 the orbital motion and in the other against it. The effect will 

 therefore be to cause the end of the axis U) rise, if above the 

 horizontal, and to fall, if below the ho-izontal. The effect 

 just described rapidlx- becomes unimportant as the fotational 

 velocity of the wheirl decreases. 



