132 AN EMPIRICAL STUDY OF GYRATING BODIES. 



because the weight being removed there is no longer any- 

 downward movement). 



Hence, by onr first law, the gyroscope rises ; but 

 making it rise is the same in effect as pulling it upward 

 by the string ; and that, in accordance with our third 

 law, sends it backwards and so stops the gyration. 



But this is not all. Sending the gyroscope backward 

 makes it fall (by our second law) ; and falling makes it 

 go forward (fourth law) ; and going forward makes 

 it rise (first law) ; and rising makes it go backward 

 (third law). Thus we get a complete circle with no 

 loss of energy except from friction. If that and the air 

 were removed, this motion, so far as I now see, would 

 go on forever. 



We have here the curious case of a body whose centre 

 of gravity revolves around a fixed immaterial line, at a 

 sensible distance from it, under the influences of forces 

 wholly within itself. This more nearly resembles the lat- 

 ter case where the actual axis revolves around one of the 

 two stable principal axes. It does not, however, seem to 

 be identical, for in this case both axes pass through the 

 centre of gravity, which, itself remains at rest, while the 

 center of gravity of the wheel revolves around a fixed 

 point. There is apparently no tendency to approach 

 that point, or to leave it. Circular motion without cen- 

 tripetal or centrifugal force ! 



I have called this Conical Rotation, for the axis of 

 the Gyroscope describes the surface of a horizontal cone, 

 whose vertex is at the point of support. 



HIE UNDULATORY MOTION. 



When a gyroscope first starts there is often in un- 

 skilled hands, a brief undulatory movement of the free 

 end. This has attracted considerable attention. General 

 Barnard has devoted to it a large part of his articles in 

 the Amer. Jour. Education. 



116 



