94] 



EXPERIMENTAL REALIZATION. 



293 



If now c = d, as in the case of the top, both these expressions 



become equal to plus or minus unity, so that both ellipses become 



circles. The motion of the top 



making small oscillations about 



the vertical is accordingly to be 



described by saying that its apex 



describes epicycloids (epitrochoids) 



or hypocycloids (hypotrochoids) 



upon the horizontal plane. It is 



to be noticed that according as 



we take the signs in 149) the 



relative sense of the rotations in 



the two circular motions will be 



alike or different. By considering 



which way the top tends to fall 



we may decide whether the cusps 



are turned inwards or outwards, 



and it will be found that if the 



center of mass is above the point 



of support the cusps or loops 



are turned inwards, and the curves 



are epicycloids, while if it is 



below the cusps or loops are 



turned outwards and the curves Mg 102 



are hypocycloids. 



An instrument to show these properties of the motion has been 

 constructed by the author, and is shown in Fig. 102. A heavy 



Fig. 103 a. 



Fig. 103 b. 



symmetrical disc hangs by a universal joint (Hooke's or Cardan's 

 suspension) from a shaft which is rotated by an electric motor. 



