C. B. WARRING. 139 



the diagram, a b will revolve around the supporting 

 point, and in the same direction as the wheel itself. 



The explanation is this : The friction of the axle of 

 the gyroscope on the side toward b tends to make the 

 bar move in the direction of the arrow, m, while the 

 friction on the opposite side tends to send it back- 

 ward. These are equal, but their influence is not equal 

 because the moment of the first, i. e., its product by 

 its distance from the fixed point, p, is greater than that 

 of the second. Hence, since the stronger prevails, the 

 bar goes in the first direction, that of the arrow m. The 

 difference in the effect of these moments increases as 

 the distance from the centre grows less ; therefore the 

 rotation around p grows more rapid as d is moved to 

 points nearer to the centre. 



If, instead of being vertical, the gyroscope is put in 

 tube No. 2, the same result follows, but with less speed 

 of revolution of the horizontal bar. The effect continues 

 to diminish if the inclination is increased, until the axis 

 is horizontal, and then it becomes nothing. 



In every case the result is the same as would be pro- 

 duced by a force varying according to the position of the 

 axis, applied perpendicularly to the bar, in the plane of 

 its motion, and pushing it around the supporting point 

 in the same direction as that in which the wheel revolves. 



It makes no difference whether we have an upright, 

 separate supj)ort, as in fig. 21, or whether the bar is bent 

 down so that the tip rests on the table (on a plate of 

 glass), as in fig. 22. In this case, too, the difference in 

 the moments of the frictional forces on the two sides of 

 the axle will act as a gentle pressure applied at d, caus- 

 ing the gyroscope to accelerate its gyration : — remember 

 that this last is always in the direction in which the 

 lower side of the wheel goes. 



But, by our first gyroscopic law, accelerating the gyra- 



123 



