191;i] on Gyrostats and Gyrostatic Action 641 



real })eriod of vihnitiuii about the vertical ; in the other the period 

 is mathematically unreal, and the gyrostat axis moves farther away 

 from che vertical. No better illustration of the two cases of the 

 equation can be found. 



The behaviour of the tray gyrostat is exemplified also in the 

 gyrostatic compass. A heavy and rapidly rotating flywheel is mounted 

 so that its axis is maintained horizontally by means of an elastic sup- 

 port. Under these conditions the equilibrium position of the flywheel 

 under the horizontal component of the turning velocity of the earth 

 (which corresponds to the turning of the tray) is arranged to be that 

 in which the axis of rotation points due north and south. If time 

 permitted, I should be glad to make an experiment with, a carefully 

 balanced motor-gyrostat, which w'ould not only show the turning of 

 the earth under the gyrostat, but enable the rate of turning to be 

 measured. 



I would now direct your attention to this motor-gyrostat, which 

 forms the bob of an ordinary compound pendulum (Fig. 10). The 

 tube carrying the gyrostat is attached, by means of a universal joint, 

 to the apex of a triangular stand, made of telescope tubing. The 

 gyrostat is attached to the lower end of its supporting tube, by 

 means of a special cap provided with spring contact pieces, to allow 

 the current to be led into the motor, and the flywheel is free to 

 rotate about an axis coincident with the rod. Screwed to t\\e lower 

 side of the gyrostat is a pen, which presses lightly on a card placed 

 below. 



We have now the pendulum rod in the vertical position. I draw 

 the pendulum to one side and let go, when you see that it vibrates to 

 and fro, and the pen traces out a straight line on the paper. The 

 flywheel has as yet no spin. I start the flyw^heel revolving, draw 

 the pendulum to one side, and let go, either from rest, or with a 

 certain amount of sidelong motion, when you observe that the pen 

 describes a flower-shaped path (Fig. 11). The path is shown for 

 different amounts of sidelong motion. The peculiar appearance of 

 these curves is due to the rapid falling off of amplitude produced by 

 friction. 



When the flywheel is revolving there are, in general, two couples 

 acting on the pendulum, one due to gravity, the other due to gyro- 

 static action. At an instant at which the axis of the gyrostat is 

 vertical the former couple is zero, and the latter one is a maximum, 

 for at that instant the angular velocity with which the axis of the 

 gyrostat is changing direction is greatest. When the pendulum is 

 at one extremity of its swing the former couple is a maximum, and 

 the latter one is zero. At that instant the deflection of the bob from 

 the vertical is a maximum, and it is at rest, or is moving sideways, 

 according to the mode of starting, except in so far as the initial 

 conditions have been interfered with by friction. By this relation 

 of the couples the form of the path can be explained. 



