721 Motions in the so-called Bohnenberger 1 s Machine. 



the direction R^) ; and if (second main combination) a pre- 

 cession (in the direction RJ be artificially produced, there 

 always results a nutation (in the direction R y J . 



In accordance with the law of equality of action and 

 reaction, a direct acceleration, for example, of precession (by 

 the rotation of an axis parallel to the ?/-axis) calls forth a 

 nutation (about an axis parallel to the ?/-axis) opposed to that 

 which itself originally caused the precession — a relation which 

 under certain conditions is very well illustrated by the Fessel- 

 Pliicker apparatus, although the construction of this latter 

 was not, properly speaking, undertaken for the purpose of 

 demonstrating this most complicated phenomenon. If the 

 rotating disk be arranged w r ith its axis at the end of a long- 

 arm, sufficiently flexible to vibrate readily, and if the apparatus 

 be vibrated (e. g. by attaching it to an electromagnetically 

 driven diaphragm) , then the vibrations take place in succession 

 in every possible direction about the arm so long as the disk 

 is at rest. But if the disk be at the same time rotating, so 

 that there occurs, according to the adjustments, a more or less 

 rapid precession (first main combination) , then the vibrations 

 of the axis appear — to use a frequently criticised (and justly 

 so) phrase of the optician — polarized, elliptically at first, until 

 the horizontal component presently becomes reduced to zero, 

 and only plane-polarized vibrations take place in the vertical 

 plane : these denote an alternating nutation which becomes 

 associated with the precession. 



If the rotating disk forms part of a larger rotating system, 

 with whose axis of rotation the axis of rotation z of the disk 

 makes an angle a. > 0, the disk tends, by becoming inclined to 

 an instantaneous diameter wdiich crosses at right angles the 

 axis of rotation of the rotating system, to bring its own axis 

 of rotation z into parallelism with the axis of rotation of 

 the system, so that, as is evident again from the diagram, 

 both rotations get the same direction. This gives rise to a 

 directive force, inherent f. i. to any rotating body at the 

 earth's surface : Fixing the x- or the ?/-axis of a Bohnen- 

 berger's machine, viz. causing it to follow the earth's rotation, 

 Foucault* saw the axis of rotation z of the disk turning 

 about the remaining y- or #-axis and setting itself as near as 

 possible — with widest possible angle a — parallel to the axis 

 of rotation of the earth. 



Rotterdam, Feb. 13, 1905. 



* " Sur les phenomenes d'orientation des corps tournants entraines par 

 im axe fixe a la surface de la Terre." Paris, 1852. 



