634 Professor Andrew Gray [Feb. 14, 



two numbers together, one representing the spin-inertia of the wheel 

 (which is greater the more the mass is placed in the rim), the other 

 the speed of turning. The turning action or " couple " is also got 

 by multiplying the force with which I push by the arm or leverage 

 of the force about the axis. So then we represent these two by Knes 

 drawn at right angles to the two planes, making the lines of lengths 

 to represent the two products. Standing on one side of the plane of 

 the flywheel, you see it turning against the hands of a clock ; stand- 

 ing on one side of the plane of the turning action which I apply, you 

 observe that action tending to turn the body also against the hands 

 of a clock. The two lines representing the two products drawn 

 towards you from the two planes represent also the directions of the 

 turning actions of the couples. For example, the direction of rota- 

 tion of the flywheel being that shown by the curved rod, the line 

 representing the spin-momentum points outwards from the side of 

 the gyrostat to which the rods are attached. I call this the spin-axis. 

 The other line, representing the turning action which I applied, I call 

 the coiiple-axis. 



Now observe that I set the couple-axis so as to point toward your 

 left. I push down the side of the gyrostat nearest me, and you see 

 that the spin-axis turns towards the left. Again, I turn the couple- 

 axis so as to point to your right. When so placed it represents a 

 turning action tending to depress the end of the axle of the flywheel 

 that is nearer you. I apply such an action, and the spin-axis turns 

 towards your right. In both cases the spin-axis turned towards the 

 instantaneous position of the couple-axis. 



Now I set the couple-axis vertical, pointing up. It represents a 

 turning action tending to produce horizontal turning in the counter- 

 clock direction as seen from above. I apply such an action to the 

 fork, when you see that the gyrostat turns the spin -axis towards the 

 upward direction. Finally, I set the couple-axis vertical but point- 

 ing down, as in Fig. 1. It now represents a turning action tending 

 to produce clock-wise rotation as viewed from above, counter-clock 

 rotation as seen from below. I apply the action represented and the 

 gyrostat turns the spin-axis towards the downward direction. 



These experiments may be summed up as follows : — The flywheel 

 is spinning about axis (1). Any attempt to tilt the gyi'ostat about 

 axis (2) produces turning about (3) ; an attempt to tilt it about (3) 

 produces turning about (2). This response of the body seems para- 

 doxical, but in point of fact, and this is the secret of the whole affair, 

 this turning of the body as a whole amounts to the jjroduction of spin- 

 momentum about the couple-axis at exactly the proper rate. It is quite 

 easy to prove this by the consideration, in the most elementary 

 way, of the accelerations of the different particles composing the 

 wheel. 



The turning of the spin-axis towards the couple-axis is called a 

 precessional motion, from a similar motion of the earth which pro- 



