146 AN EMPIRICAL STUDY OF GYKATING BODIES. 

 TOPS WHOSE "POINTS'' ARE NOT POINTS. 



Few tops have fine and true points, accurately centered. 

 The great majority end either in truncated cones, or in 

 forms more or less nearly hemispherical. For the pur- 

 pose of studying the laws of such tops, a truncated cone 

 is to be preferred since in that case the size of the ; ' point ' ' 

 does not vary, while in spherical forms the "point," i. e., 

 the amount of surface that comes in contact with the 

 supporting plane, varies with the inclination of the axis. 



If we set one of the former going, we shall find, in ad- 

 dition to most of the peculiarities which have been dis- 

 cussed, certain others which stand in need of explanation. 

 For example, we shall see it start off in a circle of larger 

 or smaller radius, and after a series of movements in 

 gradually narrowing spirals, shall see it by degrees be- 

 coming more and more nearly perpendicular to the floor, 

 till the axis becomes vertical. Then it will stand for a 

 long time "sleeping," as the children call it, until at 

 last it begins to incline to one side, and, in a moment 

 more, falls to the floor. 



Before attempting to answer the questions that arise, 

 it is best to study experimentally the movements of the 

 top. 



It is commonly believed that the top revolves in a 

 circle, more or less perfect, around the projection of its 

 centre of gravity. Fig. 28 is drawn to show this. It 

 represents the top as leaning towards the circle des- 

 cribed by its point, and whose centre is directly under 

 the centre of gravity. This is General Barnard's idea, 

 ;is set forth both by a diagram and in the text on page 

 536, Am. Jour. Ed. vol. in. He says also that the center 

 of gravity will have no horizontal motion. 1 To deter- 



1 General Barnard says that the centre of gravity will have an up-anddown motion. To 

 this he attributes great importance, and regards it as the cause of the top's staying up. 

 This appears tome to be an error, as was shown when treating the gyroscope. The top, 

 save from accidental disturbance, has no such vibrating movement. This will be shown 

 when we come to nutation. 



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