144 AN EMPIRICAL STUDY OF GYRATING BODIES. 



around with the edge of the wheel in close proximity to 

 the glass, till at last — perhaps after six or seven minutes 

 — it strikes, and then it rushes backward till its remain- 

 ing energy is expended. 



We naturally ask, first, why does it not fall at once? 



The top is, in reality, only a ringless gyroscope, with 

 the end of its axis resting directly on the supporting 

 body. I shall, therefore, attack these problems in the 

 same waj^ that I did those of the gyroscope. 



I take a tee-square, and hold it so that the arms are 

 in a vertical plane, and the other end of the leg rests on 

 the glass plate as in fig. 26, the instrument being inclined 

 at any convenient angle. If it be let fall from the posi- 

 tion indicated by the heavy lines to that indicated by 

 dotted ones the ends A and B will acquire motions each 

 of which can be decomposed into two, a vertical and a 

 horizontal, the former not represented in the diagram, 

 the latter indicated by the arrow m for the mass A, and 

 n for the mass B. 



If at this moment, and before the arms stop, they are 

 instantly reversed — a process which will not affect m and 

 n, since it is at right angles to them — n, coming now on 

 the upper side, will push its end towards the left, while 

 m, for a similar reason, will push its end towards the 

 right. Together they tend to push the top back to its 

 first position. It is our gyroscope over again, and it is 

 unnecessary to go any farther. The same reasoning ap- 

 plies and we get the same result— the instrument seems 

 to defy gravity ; for although it really descends, it is 

 with so slow a movement that it requires several minutes 

 to reach the plane on which it is revolving. 



The total velocity which gravity can produce is indi- 

 cated by the formula obtained for the gyroscope, viz., 

 ^1 s^: where b equals the inclination of the axis to the 

 horizon, and a, the angle between the axis and a line 

 drawn from the "point" to the circle, which, in a top 



128 



