C. B. WARRING. 151 



Why is this ? Fix the mind on two points in fig. 29, 

 which, at the instant of striking, are at the ends of a 

 horizontal diameter, calling the one nearest the observer 

 x and the other y. The blow in the rear tends to tilt 

 the instrument in such a manner that x moves away 

 from the "point" of the top. More exactly speaking, 

 it moves for the initial instant parallel to the axis. 

 Motion once imparted continues forever, or till some 

 work is done by the moving body. Therefore x, when 

 in the course of its very rapid rotation, 1 it comes on the 

 under side of the axis, will push that side in the same 

 direction, which means raising the top towards a vertical. 

 The mass, y, at the initial instant goes downward, but 

 being brought on the upper side of the axis by a semi- 

 revolution, its influence aids that of x. 



If this is understood, it will be easy to see why strik- 

 ing the axle in front makes it more oblique, and causes 

 it to gyrate more rapidly, while striking it behind makes 

 it gyrate less rapidly. 



Both cases are merely illustrations of our first and 

 second laws. 



Instead of striking the axle of the top with a stick, 

 it is, in some respects, a better plan to insert a small 



1 Two important remarks occur to me here, which are equally applicable to all gyrating 

 bodies. 



1. " Rapid rotation." All gyrating effects may be produced with slow rotation, provided 

 the action of gravity be neutralized (as in fig. 2), and the tilting force due to gravity be 

 replaced by a more moderate force, the pull of a string, for example. The necessity of very 

 rapid rotation is a mere accident, dependent upon the degree of strength and constancy of 

 the pull. 



2. If when x comes on the upper side it tends to pull the top towards a vertical, why, when 

 it returns to the lower side, does it not pull the top back again ? Simply because it expanded 

 all its energy in lifting. To do anything more there must be a new influx of energy, and 

 this can only come from a renewal of the fall. There is, therefore, a constant gain of energy 

 by the top from the fall, and an expenditure in lifting. As the lateral motion requires no 

 expenditure of energy, it would seem as if those were right who say that, but for friction, 

 the top would stay up forever. 



The explanation given for the gyroscope applies here. The fall during the instant a 

 section is horizontal imparts equal momentum to each end of it, and in the same direction. 

 viz., downward. Consequently, when the plane of the section becomes vertical, there is 

 from this source no upward tendency. Hence a top will fall even in a vacuum and with- 

 out friction. 



135 



