C. B. WARRING. 14.1 



like mine, is the axis of the rim. Since cos b grows 

 smaller as b grows larger, it follows that the nearer up- 

 right a top is, the slower its descent and consequent gy- 

 ration. And, vice versa as it comes down, the more 

 rapid the gyration. 



By striking the axle of the top, in manner which I 

 shall explain hereafter, the inclination can be varied as 

 often as we please. In every case the result conforms to 

 our formula, the descent and consequent rate of hori- 

 zontal movement varying as does cos b. ' 



Hence those err, who attribute this increase to the 

 gradual loss of axial velocity from friction. The same 

 results, but in a somewhat less degree, would follow if 

 in some way the rotation of the top on its axis were 

 kept absolutely uniform. 



The cause of the top's horizontal motion is the same 

 that makes the gyroscope move in a similar manner. 

 There is the same process of reversing, and the same 

 pushing to the right and left when the arms are hori- 

 zontal. It is the same story throughout. 



Why, when the top reaches the table, does it always 

 go backward ( 



The lower side of the top goes in the same direction 

 that it gyrates. If b and b (fig. 27) represent the direc- 

 tion of the rotation of the disk, d will indicate the 

 direction of the gyration. Now, it is evident that if a 

 wdieel revolving rapidly on its axis, and at the same time 

 moving slowly in the direction of d, be set down on the 

 floor or on the table, the lower side will be stopped by 

 the friction, while the upper half will continue its 

 motion, and consequently send the wheel backward. 

 So with the top. The rim goes very fast, the centre 

 moves in the same direction that the under side does, and 

 when the latter strikes the table, the upper side sends 

 the top backward. 



1 It must be borne in mind that the top for these experiments must have a very line and 

 well-centred point. 



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