150 AN EMPIRICAL STUDY OF GYRATING BODIES. 



friction as does a point, while, if inclined, the friction is 

 only the same as for a truncated cone. 



A sharp point on a hard and smooth surface will 

 gyrate, but will not really " sleep." The least disturb- 

 ance will throw it out of the vertical, and once out it 

 will not go back. 



From all that we have done, we may draw these gen- 

 eralizations : 



(1.) For a top to become upright it is necessary that 

 the point of contact with the supporting plane should 

 not be in the axis of rotation. 



(2.) The tendency to become upright is proportional 

 to the distance this point is from the axis. 



We have all noticed how some tops run about the floor 

 when spinning, and, doubtless, have wondered why they 

 behave in this manner. 



To show the reason, we take a top ending in a truncated 

 cone measuring, for example, one-eighth of an inch 

 across the lower surface. It revolves on its axis — any 

 good top does — some thirty or more times a second. If 

 the axis is inclined, the weight comes on the edge of 

 this small surface, but as that revolves, say, thirty times 

 in a second, it tends to roll along twelve or thirteen 

 inches in that time. If the " point" is larger, of course 

 the top will roll along faster, and vice versa. 



Sometimes it is desirable to change the obliquity with- 

 out much disturbing the top. Suppose fig. 29 is such 

 a top, and that it is revolving as indicated by the small 

 arrows. The gy rational, or precessional, movement 

 will be from the observer. Now with a small light stick 

 — a lead pencil is excellent — strike the axle near its up- 

 per end a smart, horizontal blow, taking care to strike 

 squarely and firmly. If the blow is struck from behind, 

 the top will rise towards a vertical, and a succession of 

 blows will put it in that position. But, if the blow is 

 delivered in front, the obliquity will increase. 



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