C. B. WARRING. 149 



proach us. It is in this way that the vis viva of the top 

 is expended in accelerating its gyration, and this accel- 

 eration makes it rise. 



To see the reason why, let us suppose our top (fig. 30) 

 is turning on its axis in the direction of the arrows, and 

 is gyrating with all the speed gravity can give it. In 

 some way, push c towards you, i. e., accelerate the gyra- 

 tion ; b will, in consequence, get an extra (if we may use 

 the term) motion to the right, and a to the left. In a 

 fraction of a second, a will be at a', and b at b', each push- 

 ing in the same direction as before. But pushing a' to 

 the left and b' to the right means tilting the top towards 

 a vertical. It is as if a string tied at a' had been pulled 

 horizontally to the left, and one at b', horizontally to the 

 right. Such pulling, it is easy to see, would tend to 

 make the axis vertical. In fact this is only another in- 

 stance of the working of our "first law" of gyrating 

 bodies. 



THE SLEEPING OF THE TOP. 



If a top, having for a "point'"' either a truncated 

 cone, or some form resembling a hemisphere, is set go- 

 ing with its axis inclined, it will rise to a vertical, and 

 remain so quiet that, in common parlance, it is said " to 

 sleep." If disturbed, it quickly returns to its upright 

 position, and resumes its sleep. Every one has seen 

 this, and wondered why the top should do so. 



Disturbing an upright top, means tilting it, and that 

 causes it to rest on one edge of its "point ;" and when 

 this happens, it strives, as was shown when answering 

 the last question, to rise to a vertical. Every disturb- 

 ance, therefore, results in a force sending it back to an 

 upright position ; — and there is no counteracting force ; 

 therefore, it stays there, or " sleeps." 



A hemispherical "point" is best for this purpose, 

 because, when erect, it meets, if running upon a glass 

 plate, or other hard and smooth surface, almost as little 



133 



