the so-called Bohnenberger's Machine, 723 



since the various elements are rigidly connected together, 

 it is only possible for the entire disk to rotate about the .r-axis, 



whereby a rotation of the axis originally along z takes place 

 in the y—z* plane, here to be regarded as the limiting case of a 

 conical surface whose apex is at the centre of the disk, while 

 its generating line glides along a loxodromic or logarithmic 

 spiral along the direction B^y on the concentric spherical 

 surface. (2) Similarly, an independent torque acting in the 

 direction E x imparts to each element of the rotating disk as 

 it crosses the ?/-axis a tendency to move along the direction 

 of a resultant R X2 , which with respect to the solidly built up 

 disk now means a tendency towards rotation about the y- axis, 

 so that the axis of rotation (originally along z) becomes dis- 

 placed in the x-z plane, and in the general case follows the 

 direction B yx of a spiral on the spherical surface. 



Each eccentrically situated point of the rotating disk itself 

 obviously describes, during a very brief interval of time, ;i 

 geodetic line on the corresponding spherical surface, so that 

 during such an interval the resultant, the hypothenuse of 

 a spherical right-angled triangle, is given by cos R yz = 

 cos lv y cos K-, and cos R z - = cos K x cos R z respectively. 



These relations hold for every position of the coordinate 

 system in -pace. 



With the stationary :-axis along the horizontal, the first 

 main combination gives the phenomenon of precession, the 

 second that of nutation. Now, as is immediately evident from 

 the diagram, both phenonema mutually influence each other : if 

 (first main combination) a nutation (in the direction R y ) be 

 artificially produced, there necessarily follows a precession (in 



