ON THE MOTION OF GYROSCOPES.* 

 Alexander S. Chessin. 



The gyroscopes used to demonstrate the interesting phe- 

 nomena connected with rapid rotary motion are, in many cases, 

 80 constructed that the subsidiary parts of the apparatus are 

 apt to greatly influence the character of the motion. Yet, 

 these subsidiary parts are never taken into account in mathe- 

 matical investigations because of the difficulties involved. I 

 have in mind, especially, the gyroscope of FoucauU and the 

 polytrope of Sire. In the theory of these instruments, it has 

 been customary to neglect the mass of the subsidiary parts of 

 the apparatus. It is the purpose of this paper to show how 

 the character of the motion of a gyroscope maybe determined 

 without neglecting the mass of any part of the whole appar- 

 ratus. 



Sire's polytrope was invented to demonstrate the influence 

 of the earth's rotation on spinning tops. It is, in principle, 

 a Foucault gyroscope mounted on a metallic circle which rep- 

 resents a meridian of the earth and may be revolved about a 

 diameter, thus producing an effect similar to that of the 

 earth's rotation on the top. The polytrope of Sire, as dem- 

 onstrating such effects, has a certain advantage over Fou- 

 cault' s instrument, because the metallic circle may be revolved 

 with any velocity we please while, of course, experiments 

 with a Foucault gyroscope are necessarily restricted by the 

 actual angular velocity of the earth's rotation. 



This is not the place to describe either of the above men- 

 tioned apparatus. A schematic figure will suffice to under- 

 stand the derivation of our formulas. 



♦ Presented and read by title before The Academy of Science of St. Louis, 

 April 21, 1902. 



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