524 Ruijal Society. 



plane which contains the two axes of impressed rotation, a case exactly 

 analogous to the preceding. The beam ascends and descends in like 

 manner, after rotation has spontaneously taken place round the ver- 

 tical axis in consequence of the equilibrium being disturbed, when- 

 ever this rotation is any how accelerated or retarded ; the disc ro- 

 tating from right to left and its weight predominating, the rotation 

 round the vertical axis is from left to right ; accelerating the latter 

 motion will cause the disc to descend, and retarding it will occa- 

 sion it to ascend. 



As the centre of gravity of the beam is below its point of suspen- 

 sion, even when equipoised it is in perfect equilibrium only when it 

 is horizontal, consequently, if it be elevated above or depressed be- 

 low this position it will endeavour to resume it, tending to produce 

 in the two cases rotations in opposite directions round a horizontal 

 axis ; the rotation of the disc combined with this tendency gives 

 rise, as in the other cases I have mentioned, to a continued rotation 

 round the vertical axis. If the disc rotate from right to left, and 

 the end of the beam carrying it be elevated above the horizontal 

 position, the rotation round the vertical axis will be from right to 

 left ; if, on the contrary, the same end of the lieam be depressed 

 below the horizontal position, that rotation will be from left to right. 



In all the experiments above mentioned the axis of the ro- 

 tating disc has remained in the prolongation of the beam, but, by 

 means of an internal ring moveable round a line perpendicular 

 thereto, this axis may be placed at any inclination and at any azi- 

 muth with respect to it. Very obvious considerations show that the 

 inclination of this axis should produce no difference in the character 

 of the effects but merely in their intensitj', since in any inclined po- 

 sition of the disc its rotation is resolvable into two others, one per- 

 pendicular to the beam, and the other, which is incapable of pro- 

 ducing any effect, in a plane containing it. When the axis of the 

 rotating disc is vertical and at right angles to the beam, no rotation 

 on the vertical axis ought to take place in any case ; but, contrary to 

 this expectation, although the beam be horizontal and in perfect 

 equilibrium, a motion round the vertical axis results, M'hich is in 

 opposite directions according as one or the other end of the axis of 

 the disc is uppermost. It is, however, easy to see that this rotation 

 is not owing to the same cause which gives rise to the phaenomena 

 hitherto considered, for whether it be accelerated or retarded no 

 change is produced in the horizontal position of the beam ; it is, in 

 fact, occasioned by the friction of the pivots of rotation dragging 

 the beam into a corresponding motion. Attention to this extraneous 

 cause of rotation will explain numerous anomalies whicii present 

 themselves in many of the instruments contrived to exemplify the 

 phaenomena of combined rotary motions. It is one of the advantages 

 of Fessel's apparatus that the phaenomena may be exhibited in their 

 more important phases without being affected by this source of error. 



We may form a clearer conception of these phaenomena by first 

 considering some simpler facts which do not appear to me to have 

 been hitherto sufficiently attended to. For this purpose let the 



