Rotatory Motion, the Gyroscope, ^c. 139 



cessional motion actually increases as the rotatory velocity diminishes, 

 because the ratio between this velocity and that which the weight tends 

 to impart becomes more favourable to the latter. Of course, as the 

 horizontal precessional motion increases, the friction and consequent 

 retardation increase also, and the weight descends with gradually 

 increasing rapidity. 



It may perhaps be thought that having shown that the weight is 

 sustained, my explanation is now complete, as far as regards the case 

 under consideration. Not so — for I have still to show what becomes 

 of the pressure of the weight. I have made out its removal, as it were, 

 from one spot, but I have not shown where it is to be looked for. We 

 cannot annihilate the weight, nor do we do so by removing it from a 

 particular situation. In the case we are considering, the weight cannot 

 really produce motion, for it does not descend, but retains its potential 

 energy unimpaired. I have already shown that with the horizontal 

 precessional motion there is a pressure tending to turn the spindle 

 A A upwards. Eeferring to fig. 6, let a force (or, more correctly, a couple) 

 act on the lever A G, tending to turn it about the centre r, so as to press 

 the end A up against the obstacle w — one-half the pressure acting on 

 each side the centre F. It will be obvious that a pressure equal to 

 that pressing up against the obstacle w reacts downwards upon the 

 centre F. Now, in the gyroscope, the weight applied to the spindle 

 end acts as an obstacle to the upward pressure, which does not exceed 

 it in amount, and there is obviously, in consequence, a reactionary down- 

 ward pressure upon the point of support of the instrument, precisely 

 equal in amount to the weight. We have thus at last ferreted out the 

 whole of the effects involved in the phenomena (except, indeed, those 

 due to friction and the resistance of the air). The weight tending to 

 turn down the spindle of the rotating wheel occasions a horizontal angu- 

 lar or precessional motion, through which it is itself sustained, its down- 

 ward pressure being, as it were, transferred to the point of support of 

 the wheel. Simple as this last deduction may seem, and notwithstand- 

 ing the facility with which it is derived from what precedes it, it is a 

 very important element in the explanation. It is in fact the keystone 

 of the theory, which without it would fall to pieces. The upward pres- 

 sure which supports the weight cannot exist without a reactionary 

 downward pressure on some point of resistance. If the theory were 

 complete without this element, it would prove too much ; for it is quite 

 applicable to the case of an unsupported disc rotating about a horizontal 

 axis ; and were it applied to that case it would seem to prove that gra- 

 vity ought to make it travel horizontally, instead of falling vertically. 

 In reality, however, wc jjass to this case from that of the gyi'oscnpc, by 



