68 



J. G. Barnard on the Gyroscope, 



lias acquired a velocity due to its actual fall a cZ; but this velocity 

 lias been deflected to a horizontal direction. The ascent of the 

 branch h d is precisely the converse of its descent. The acquired 

 horizontal velocity impels the axis horizontally^ while the de- 

 flecting force due to it (now at its maximnm) causes it to com- 



mence ascending. 



As 



the normal 



direction of this force opposes itself more and more to the hori- 

 zontal, while gravity is equally counteracting the vertical, veloc- 

 ity. As the horizontal velo 



med 



ded 



it is 



lift 



cloidal undulation is completed, to be again and again repeated, 

 and the axis of figure, performing undulations too rapid and too 

 minute to be perceived, moves slowly aromid its point of sup- 

 port. 



Eeferring to fig. 3, the equator of the revolving body (a plane 



horizontal plane of xy 

 the position delineated. 



E^ E^, Its intersection with the 



N 



In 



K 



progression 



quator (supposed to 



the bodv) would move 



upwards m the direction of the arrow a, while the node moves- 



from (of the arrow 



Fig. 5. 



Were 



figure below the horizontal plane, (fig. 5) the upward rotation of 

 the point would be from to E^ (as the arrow a), while the pro- 

 gression of the node (in the same direction as before as the arrow 

 o!) would be the reverse, and the motion of the node would be 

 rdroarade — ^yet in both cases the same in space. 



