45 



disc is in motion the usual effect of gravity disappears, and there is 

 substituted for it a continued rotation round a vertical axis, that is, 

 round an axis perpendicular to the plane which contains the axes of 

 the two original rotations. 



A similar composition of forces takes place when the disc is caused 

 to rotate while the equilibrium of the beam is maintained, by im- 

 pressing on the beam a rotation round the vertical axis. When the 

 disc rotates from right to left, the slightest pressure tending to pro- 

 duce rotation round the vertical axis in the same direction, causes 

 the end of the beam carrying the disc to ascend, and a pressure in 

 the opposite direction causes it to descend, that is, the beam is con- 

 strained to move round a horizontal axis perpendicular to the vertical 

 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 beam 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 



