6o C. M. BROOM ALL : 



axis. Obviously therefore at every level on the two arcs the 

 velocity is the same. Again, the deviating force being a 

 function of the velocity of the axis, it follows that at points 

 on the same level on the two arcs the deviating force is like- 

 wise the same. The velocity and deviating force being the 

 two factors which determine the curvature of the path at a 

 given instant, we see that the two arcs are described under 

 such a law that they have always the same radius of curva- 

 ture at points on the same level. Hence the curves must be 

 similar and equal. 



The greater the velocity of rotation of the wheel, the 

 greater is the gyroscopic force and hence the arcs described by 

 the end of the axis are smaller and more frequent. The result 

 is the average orbital velocity is less because the fall now 

 being less the maximum horizontal velocity at the bottom of 

 each loop is less, and hence the average horizontal velocity is 

 likewise less since the curves are in all cases similar. On the 

 other hand, if the weight of the mountings of the wheel is 

 increased or the weight of -the wheel itself increased in such a 

 way as not to compensate for the increase of weight by an 

 increased gyroscopic force, the orbital velocity will be greater. 

 This will result from the fact that it will take the gyroscopic 

 force longer to deviate the fall of the mass into horizontal 

 motion and longer to reconvert the horizontal motion into 

 potential energy at the same level again. The loops will 

 hence be longer, the fall greater and the average resulting 

 orbital velocity greater. The nutations will be more nearly 

 perceptible, if not indeed visible. 



The direction of the orbital motion depends of -course upon 

 the direction of rotation of the wheel. In order that the 

 apparatus shall not fall, the deviating force must be such as 

 to act upward when the axis is moving horizontally. If in 

 Figure i we assume that we are looking down upon the top of 

 the gyroscope in operation it is obvious that the gyroscopic 

 couple acts in such direction as to make the apparatus self- 

 supporting when the end a of the axis rests upon the pivot. 



