liotatory Motion, the Gyroscope, tjc. 137 



wheel than in the sphere, the mass of the former being so much less ; 

 but the position of the resultant axis depends directly on the angular 

 velocities, not on the forces producing them. Let the action of the 

 weight, during a very short interval of time, be supposed the same as 

 that of an impulse which would have the effect of making the line c c, 

 in the plan, fig. 5, the position of the resultant axis of rotation. At the 

 instant the change of axis takes place, the wheel lies obliquely to the 

 line c c, but each point in the wheel immediately endeavours (if I may 

 use the expression) to rotate in a plane at right angles to this line C c, 

 and the horizontal components of the centrifugal forces due to the rota- 

 tion consequently act in directions parallel to the arrows E, fig. 5. An 

 inspection of the figure will show that the two halves of these centrifu- 

 gal forces are directed onQfrom each side of the axis c c, and that they 

 are so circumstanced as to tend to produce rotation, in consequence of 

 the planes of their directions not coinciding. The centrifugal forces 

 (their vertical components being balanced, as a little consideration will 

 show) thus give rise to a resultant couple of forces, which tend to turn 

 the wheel round about a vertical line, so as to bring the spindle a a 

 towards c c ; and this tendency will cease (in the case in which the 

 second force is an impulse) on the spindle a a coinciding with c c, when 

 the centrifugal forces will be balanced, and no longer inclined to the 

 wheel. In the case of the perfect sphere, no unbalanced centrifugal 

 forces arise to move the original axis into a new position ; but the sphere 

 turns about a new set or line of its component particles as an axis, and 

 the pole of the original axis descends or moves in the direction of the 

 force changing the direction of rotation.* But to return to the gyro- 

 scope and the diagi-am, fig. 5 — a weight is attached to one end of the 

 spindle A a, and the movement caused by the centrifugal force, being 

 entirely in a horizontal direction, cannot directly cause the weight to 

 move horizontally, though it might combine with the downward motion 

 the weight would otherwise have, to give it an intermediate direction — 



* Even wilh tlie Rohnenberger gyroscope the centrifugal resultant is not in all cases 

 sufficient to carry the weiglit round horizontally. If a very slow rotation is imparted to 

 the wheel, the weight will describe vertical curves, provided tlie instrument turns very 

 freely on its pivots. With this form of instrument, however, there is in all cases a cen- 

 trifugal resultant of tlie land descril)ed, and this resultant causes any curves that may 

 appear at starting to be gradually reduced to a liori/.ontal line, as will be explained far- 

 ther on. In the case of the spliere, on the other hand, there is no such centrifugal resul- 

 tant under any circuinstances ; and if the rotation remains uniform, tlie weight will 

 continue to describe equal vertical curves, if not influenced by the supporting mechanism. 

 To simplify the explanation, it is at first assumed that the rotatory velocity of the 

 Iwdy is such, that the centrifugal resultant arising is sufficient to carry the spindle round 

 horizontally. 



Vol. IV. -No. I. t 



