58 C. M. BROOM ALL : 



The theoretical gyroscope we are to consider is one that 

 runs with constant wheel velocity, unaffected by friction of 

 any kind, and whose axis is subjected to an applied couple. 

 It will be assumed supported by the pivot at some point of the 

 axis, the weight of the wheel and the reaction of the pivot 

 constituting the couple, and the apparatus being free to fall if 

 unrestrained. A special case arises when the wheel is mounted 

 in gimbals ( which is equivalent to supporting it at the middle 

 of the axis), but in this case a weight must be applied to one 

 end of the axis, which weight, in conjunction with the reac- 

 tion of the support, supplies the couple. 



Consider now the first method of mounting, which is the 

 general case. Suppose the wheel to be in rapid rotation and 

 one end of the axis to be supported on the pivot. Let the 

 instrument be suddenly released. The free end of the axis 

 will of course begin to fall. The moment it starts to fall, 

 however, the gyroscopic force or couple, begins to act, devel- 

 oping a couple at right angles to the plane of its fall, that is, 

 horizontally. The end of- the axis at the pivot being fixed in 

 position the effect of the gyroscopic couple is to act on the 

 free end of the axis so as to deviate it from the vertical fall, 

 carrying with it the whole mass of the wheel. The path of 

 the free end of the axis is now inclined so that the gyroscopic 

 force, always in a plane at right angles to the plane of the 

 motion, is now directed slightly upward as well as horizon- 

 tally. The fall of the free end of the axis is now still further 

 deviated from the vertical and at the same time its downward 

 fall is somewhat checked by the vertical component of the 

 gyroscopic force or couple. This deviating force continues 

 until finally the axis is moving horizontally and the downward 

 motion has been entirely checked. The gyroscopic force or 

 couple is now directed upward and reacting on the pivot as 

 before begins to deviate the free end of the axis upward. As 

 the path of the axis begins to curve upward the gyroscopic 

 force is directed upward and backward, raising the wheel and 

 at the same time destrovingr some of its horizontal velocitv. 



