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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



1, 2, 3 . . . by the arcs r^o, 2t 2 u>, ^t 3 oj . . . respectively. 

 From this follows in a striking manner the important result that 

 the relative "inertia path" consists of a circle which will be de- 

 scribed twice in the absolute time of revolution T and in such a way 

 that the direction of the rotation is opposite to that of the rotation 

 of the surface. 



FIG. 1 



Introducing 6 different modifications regarding the form of the 

 elliptical path and the direction in which the body traverses t, 

 we can exhibit clearly in a direct geometrical manner the mutual 

 dependence of the absolute and relative motions and also, for exam- 



Fig. 1, for example, differs from fig. 2 only in the circumstance that 

 the ellipse is traversed in the opposite direction; the relative velocity and 

 circle of inertia are in consequence about 2% times as great as in fig. 1. 



