718 



Professor Andrew Gray 



[April 29, 



axis of rotation here again remains nearly horizontal, but turns slowly 

 round in a horizontal plane as before. 



The explanation in general terms is this. The weight gives a 

 couple tending to turn the gyrostat about a horizontal axis at right 

 angles to that of rotation. This coujDle in any 

 short interval of time produces moment of momen- 

 tum about the axis specified, the amount of which 

 is the moment of the couple multiplied by the time, 

 and may be represented in direction and magnitude 

 by the line B. This must be compounded with 

 the moment of momentum A already existing 

 about the axis of rotation, and gives for the resultant 

 moment of momentum the line O C, which is the 

 direction of the axis of rotation after the lapse of the 

 short interval of time. The axis of rotation thus 

 turns slowly round in the horizontal plane, and the 

 more slowly the more rapidly the fly-wheel rotates. 

 The gyrostat in fact must have this precessional 

 motion, as it is sometimes called, in order that the 

 moment of momentum of the gyrostat about a ver- 

 tical axis may remain zero. That it must remain 

 zero follows from the fact that there is no couple 

 in a horizontal plane acting on the gyrostat. 



Thus any couple tending to change the 

 direction of the axis in any plane produces a 

 turning in a perpendicular plane. For ex- 

 ample, if a horizontal couple, tliat is about a 

 vertical axis, were applied to the axis of the 

 gyrostat in the last figure it would turn about a horizontal axis, that 

 is, would tilt over. 



Again, consider a massive fly-wheel mounted on board ship on a 

 horizontal axis in the direction across the ship. The rolling of the 

 ship changes the direction of the axis, and produces a couple applied 

 by the fly-wheel to the bearings, and an equal and opposite couple 

 applied by the bearings to the fly-wheel. I'his couple is in the plane 

 of the deck, and is reversed with the direction of rolling, and has its 

 greatest value when the rate of turning of the ship is greatest. Thus 

 the force on one bearing is towards the bow of the ship, the force on 

 the other towards the stern, during a roll from one side to the other ; 

 and these forces are reversed daring the roll back again. This is the 

 gyrostatic couple exerted on its bearings by the armature of a dynamo 

 on shipboard. 



In the same way when a gyrostat is embedded in a medium and the 

 medium is moving so as to change the direction of the axis of rota- 

 tion, a couple acting on the medium in a plane at right angles to the 

 plane of the direction of motion is brought into play. To fix the 

 ideas, think of a row of small embedded gyrostats along this table, with 

 their axes in the direction of the row, and their fly-wheels all rotating 



Fig. 14. 



